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VlkQraw-M Bock Qx 7m 


Hectrical World "^ Engineering' News-Record 
Power V Engineering and Mining Journal-Press 
Chemical and "Metallurgical Engineering 
Electric Railway Journal v Coal Age 
American Machinist "^ Ingenieria Intemacional 
Electrical Merchandising -^ BusTransportation 
Journal of Electricity and Western Industry 
Industrial Engineer 





FELLOW, A. I. E. E., M. AM. 80C. M. E., M. I. E. E., ETC. 

Second Edition 

Entirely Rewritten, Enlarged and Reset 

Tenth Impression 



LONDON: 6 & 8 BOUVERIE ST., E. C. 4 


Copyright, 1909, 1913, by the 
McGraw-Hill Book Company, Inc. 


K»« « ••••''••• 



The writer seeks to keep this book practical and for a reference 
on all matters connected with the operation of transformers and 
static induction apparatus. It is particularly intended for those 
who are operating or constructing plants or transformers and is 
written with the view of assisting engineers out of certain operat- 
ing difficulties which they can readily solve when they are 
short of the right apparatus and need a temporary arrange- 
ment such as using certain changes of phases. 

New schemes of any kind will be appreciated and will add to 
the value of this book. 

William T, Taylor. 
Chaplanca, Peru, South America, 
August, 1913. 

• I 

\ 'i.'» 


Although much has been written on the fundamental principles 
of transformers, little data have been published concerning their 
connection, installation and operation. It was this lack ot 
easily available information and the widespread desire of 
operators and engineers in the field to possess such information, 
that led the author to put in type these notes, which had been 
written up in the course of a number of years of experience in the 

A working knowledge of the fundamental principles of electrical 
engineering is presupposed, and for this reason the treatment 
does not go into the whys and wherefores very deeply, but 
simply states the facts in as few words as possible. To aid in 
understanding quickly the phase relations and relative values of 
the various e.m.fs. and currents involved in a given system, 
vector diagrams are given with all diagrams of circuit connections. 

W. T. Taylor. 
Baramulla, Kashmir, India, 
December, 1908. 





Preface v 


I. Introduction 1 

II. Simple Transformer Manipulations 22 

III. Two-phase Transformer Connections 30 

IV. Three-phase Transformation System 39 

V. Three-phase Transformer Difficulties 84 

VI. Three-phase Two-phase Systems and Transformation .... 97 

VII. Six-phase Transformation and Operation 109 

VIII. Methods of Cooling Transformers 117 

IX. Construction, Installation and Operation of Large Transformers 136 

X. Auto Transformers 170 

XI. Con.stant-current Transformers and Operation 178 

XII. Series Transformers and Their Operation 186 

XIII. Regulators and Compensators 209 

XIV. Transformer Testing in Practice 227 

XV. Transformer Specifications 258 

Appendix 270 

Index .... 273 




Development of Art of Transformer Construction 

The development of the alternating-current transformer dates 
back about 25 years. At that time very little was known re- 
garding design for operation at high voltages, and the engineer 
of the present day can scarcely realize the difficulties encountered 
in the construction of the early transformers. 

The high-voltage transformer made long-distance trans- 
mission work possible, and the increased distances of transmission 
stimulated the design of large transformers. In the early days 
of transformer development as many as 15 to 20 transformer 
secondary windings have been connected in series to facilitate 
the operation of a long-distance transmission system, the maxi- 
mum rating of each transformer being not greater than 10 kw. 
However, a method of constructing large transformers has long 
been devised by which an enormous amount of power may be 
transformed in a single unit. Such designs embody principles 
of insulation for high voltages and various methods for maintain- 
ing a low operating temperature. Ten years ago a 500-kilowatt 
unit was considered to be a large size of transformer. The 
history of ten years' development has shown a most interesting 
process of evolution: it has marked more than a tenfold increase 
in size up to the present day. 

Going back to part of the history of transformer manufacturing 
we find that the first transformer used by Faraday in his historic 
experiments had for their magnetic circuit a closed ring of iron. 
Varley in the year 1856 pointed out the disadvantage of leaving 
the magnetic circuit open, gave it a closed path by bending back 
and overlapping the end of the straight iron wire core. In the 
early days of electric lighting Ferranti modified Varley's method 
by using, instead of iron wires, strips of sheet iron bent back and 
interlaced. The nearest approach to the present day practice 



was to embed link-shaped coils in the recesses of a core built up 
of shaped stampings, afterward completing the magnetic circuit 
either with sheets of laminations or with strips interlaced with 
the ends of the prejecting legs. There is good reason to believe 
that from this construction the "Shell" type transformer of to- 
day received its name. 

00 00 


2 10,000 


S 9.000 


ii 8.000 

t§ 7.000 







at a> 

\ I J 


1 1 

I _^_ 



_ i 1 1 



— =.^^ 


. K.-Volta 


100 3 

90 I 
80 I 

Fig. 1. — Transformer development. 

Not very many years ago it was a question among very 
prominent engineers whether 15,000-volt transformers could be 
made to work. 

Before the time engineers conceived the idea of drying trans- 
former oil, it was not uncommon to see transformers without 
any solid material between coils — the oil space being relied on 
for insulation. At that time the transformer was the only 
limiting feature of transmission. We have only to go back about 
11 years to find the first 50,000- and 60,000-volt transformer 
actually operating (see Fig. 1). At the present time we are 
actually operating transformers at 145,000 volts with as great 
safety and with less liability of break-down than formerly was 



experienced in operating at 15,000 volts, and the actiial voltage 
limit of the transformer is not yet in sight, but on the contrary — 
the transmission line itself is the limiting feature in the voltage 
or the distance of transmission. 

About 16 years ago the first 20,000-volt transformer was made. 
At the present time the commercial manufacture of 175,000-volt 
power transformers is being considered. Fig. 1 represents the 
development of single capacity transformers up to the year 1913. 
Increased voltage means, of course, increased kv-a capacity of 
units, not only as regards the transformers themselves but in 
generators and prime movers. 

Glancing back 25 years we enter upon a time when alternating 
currents were grievously fought in the Law Courts as being a 
current both '^ dangerous and impracticable." 

Just about 20 years ago — the period when three-phase star 
and delta systems of electric distribution were recognized as 
practicable for commercial use — we find universal opposition to 
high voltages (above 1500 volts) and large units (above 500 kw.). 

Going back only 10 years — about the period when 50,000 and 
60,000 volts were recognized as practicable for transmission 
purposes — large commercial units and large commercial electric 
power systems, as recognized to-day, were universally considered 
as impossible, as absolutely unreliable or decidedly dangerous. 

In view of the three above decades, practically accepted 
throughout the entire engineering world, we actually have at the 
present time electric power systems operating as one company 
and one centralized system delivering over 200,000 kw., and 
single units for commercial electric power purposes, as: 
Steam turbines (horizontal type) of 33,000 h.p. 
Steam turbines (vertical type) of 40,000 h.p. 
Water turbines (vertical type) of 20,000 h.p. 
Turbo-generators (horizontal type) of 25,000 kw. 
Turbo-generators (vertical type) of 30,000 k w. 
Generators (vertical type) of 12,500 kw. 
Transformers (shell-type) of 14,000 kw. 
and Transformers (three-phase group of three) of 18,000 kw. 

Fundamental Principles. — The transformer consists primarily 
of three parts: the primary winding, the secondary winding, and 
the iron core. The primary winding is connected in one cir- 
cuit, the secondary in another, and the core forms a magnetic 
circuit which links the two together. 



The principle of the constant-potential transformer is easily 
explained if we neglect the slight effects of resistance drop in 
the windings, leakage of magnetic flux, and the losses. The 
primary winding is connected to a source of e.m.f,, which con- 
nection would constitute a short-circuit were it not for the 
periodic changing in value which permits the flux produced 
by the current to generate a counter e.m.f. which holds the 
current down to a value just sufficient to produce that value of 
flux necessary to generate an e.m.f. in the primary and equal 
and opposite to the impressed e.m.f. This same flux is sur- 
rounded by the turns of the secondary winding, the same e.m.f. 
being generated in each turn of wire whether primary or secondary. 
If El is the impressed e.m.f. 

:e = e.m.f. per turn. 

wherein A^^ is the number of primary turns, 
number of secondary turns. 

Then if A^, is the 

■< — ff — > 


£^2 = -^2^ = secondary e.m.f. 

~ =~ = ratio of transformation. 
A^2 E^ 

When Ni is greater than N2, the transformer is called a " step- 
down transformer" and when A^^ is less than N2 it is called a 
"step-up transformer." 

The reader will understand that a step-up transformer may be 


used as a step-down transformer, or vice versa. The primary is 
the winding upon which the e.m.f. is impressed. 

The primary and secondary windings of a transformer possess 
both resistance and reactance, and the secondary values may be 
reduced to primary terms by multiplying them by the square of 
the ratio of transformation. This applies to the load resistance 
and reactance as well. Thus, consider a circuit containing a 
transformer, a load, etc., as shown in Fig. 2. Obviously, to main- 
tain the core flux a magnetizing current is required, which of 
course must pass through the primary winding. 

(6) is an exact duplicate of the transformer (a). The factors 
R and Xg are respectively the resistance and reactance of the 
primary; R'X's the respective resistance and reactance of the 
secondary winding, and R" and Xg" the load resistance and 
reactance. This representation is about the simplest for treat- 
ment of the transformer circuits. 

Points in the Selection of Transformers — The electrical char- 
acteristics of a transformer are mostly dependent upon the 
quality, arrangement and proportion of the iron and copper that 
enter into its construction. The losses are of two kinds: the 
copper loss, due to the current through the coils; and the iron 
loss, caused by the reversing of the magnetic flux in the core. 
These losses appear as heat, and suitable means must be provided 
for the disposal of this heat. 

In selecting a transformer for a given service, it is advisable 
to consider first: 

(a) The ratio of iron and copper loss, which should be such 
that the total cost of the losses is a minimum. 

(b) The cost of the transformer for a given service and the cost 
of its total losses should be a minimum. 

The cost of a transformer for a given service depends on the 
amount which must be paid for the losses during the life of the 
transformer and on the first cost of the transformer itself. In 
considering the losses and price paid for a transformer together, 
the losses may be conveniently represented as a capital cost by 
dividing their annual cost by the interest and depreciation factor. 

Safety to life, durability, and economy are essential features of 
this apparatus in its ability to give continuous and uninterrupted 
service. These factors, sometimes in part and sometimes entire, 
are sacrificed to obtain a higher efficiency, especially in high volt- 
age transformers where so much insulation has to be used. This 


is not considered good practice although the higher efficiency 
is obtained, and a transformer designed and built with the 
main object of efficiency at the expense of safety and reliability 
finally brings discredit to its maker. The loss in revenue alone 
due to the failure of a large power transformer would more than 
offset the saving of several years in gaining an additional fraction 
of 1 per cent, in efficiency, not counting the great loss of confi- 
dence and prestige on the part of the customer. The applica- 
tion of knowledge gained by many years of constant and care- 
ful study of all the properties and characteristics of trans- 
formers in actual practice has placed this type of apparatus 
on a plane which we may now call both safe and reliable for opera- 
ing voltages as high as 110,000 volts. Looking back over the 
development of the transformer we do not pass very many years 
before we enter the time when large units of moderately high 
voltage (20,000 volts) were considered by manufacturers a tedious 
if not altogether a dangerous undertaking, in fact quite as danger- 
ous as designing and building a unit in these days to give an out- 
put of 20,000 kw. at 200,000 volts. 

Cooling. — A well-designed transformer should not only main- 
tain a low average temperature but the temperature should be uni- 
form throughout all of its parts. The only effective way of insur- 
ing uniform temperature is to provide liberal oil ducts between the 
various parts of the transformer, and these should be so arranged 
in relation to the high and low voltage windings as to give the 
best results without sacrificing other important factors. Ducts 
necessarily use much available space and make a high voltage 
transformer of given efficiency more expensive than if the space 
could be completely filled with copper and iron; in view of the 
reliability and low deterioration of a transformer of this type, 
experience has demonstrated that the extra expense is warranted. 

For various reasons the temperature rise in a transformer is 
limited. The capacity for work increases directly as the volume 
of material, and the radiating surface as the square of the dimen- 
sions; therefore, it is evident that the capacity for work increases 
faster than the radiating surface. 

The amount of heat developed in a transformer depends upon 
its capacity and efficiency. For instance, in a 500-kw. trans- 
former of 98 per cent, efficiency there is a loss at full load of 
about 7.5 kw. ; and since this loss appears as heat, it must be 
disposed of in some way, or the temperature of the transformer 


will rise until it becomes dangerously high. This hea,t may be 
removed in several ways; by ample radiation from the surface of 
the tank or case in which the transformer is operated; by the 
circulation of water through pipes immersed in oil; or by the 
constant removal of the heated oil and its return after being 
cooled off. 

The determination of the temperature may be made by 
thermometer or by the measurement of resistance. High tem- 
perature causes deterioration in the insulation as well as an 
increase in the core loss due to aging. The report of the 
Standardization Committee of the American Institute of Elec- 
trical Engineers specifies that the temperature of electrical 
apparatus must be referred to a standard room temperature of 
25° C, and that a correction of 1/2 per cent, per degree must 
be made for any variation from that temperature, adding if less 
and subtracting if more. 

The temperature rise may be determined by the change of 
resistance, using the temperature coefficient 0.39 per cent, per 
degree from and at zero degrees. 

Whenever water is available and not expensive, water-cooled 
transformers are preferable to air-blast transformers of the large 
and moderate sizes (1,500 to 5,000 kw.), as it permits operation 
at lower temperatures and allows more margin for overloads. 
Where water is not available, there is a choice of two kinds 
of air-cooled transformers: the oil-filled self-cooled type, and 
the air-blast type which is cooled by a forced air circulation 
through the core and coils or by blowing air on the outer case 
of the transformer. This type of transformer is not very reliable 
for voltages above 35,000 volts, principally on account of the 
great thickness of the solid insulation needed and the consequent 
difficulty in radiating heat from the copper. 

A great deal has been written about the fire risks of air-blast 
and oil-filled transformers, but this is a matter that depends as 
much on surrounding conditions and the location of the trans- 
formers as on their construction. The air-blast transformer con- 
tains a small amount of inflammable material as compared with 
the oil-cooled transformer, but this material is much more easily 
ignited. A break-down in an air-blast transformer is usually 
followed by an electric arc that sets fire to the insulation material, 
and the flame soon spreads under the action of the forced circu- 
lation of air; although the fire is of comparatively short duration 


it is quite capable of igniting the building unless everything 
near the transformer is of fireproof construction. The chance 
of an oil-filled transformer catching fire on account of a short- 
circuit in the windings is extremely small, because oil will only 
burn in the presence of oxygen, and, as the transformer is com- 
pletely submerged in oil, no air can get to it. Moreover, the oil 
used in transformers is not easily ignited; it will not burn in open 
air unless its temperature is first raised to about 400° F., and with 
oil at ordinary temperatures, a mass of burning material can be 
extinguished as readily by immersing it in the oil as in water. 
In fact, the chief danger of fire is not that the oil may be ignited 
by any defect or arc within the transformer, but that a fire in the 
building may so heat the oil as to cause it to take fire. The idea 
of placing oil-filled transformers into separate compartments is not 
thought of so seriously as it was some years ago, although it does 
not apply in every case and therefore it is necessary to consider 
carefully when selecting this type of transformer. 

Of the large number of factors in the make-up of a transformer 
only four which the operating manager is particularly anxious 
to know enter into the operating costs, namely: the coris and 
copper losses, temperature, efficiency and regulation. All of 
these costs (since they might be called costs as they include the 
cost of generating such losses and of suppl}'ing the station 
capacity with which they generate them) represent quite a large 
amount of energy during the life of the transformer. 

Losses. — The hysteresis and eddy current losses are generally 
combined under the term of " core loss," this loss occurring in 
all magnetic material which is subject to alternating magnetic 
stresses. The hysteresis loss, as is generally known, may be 
defined as the work done in reversing the magnetism in the 
steel, and it may be considered as due to the molecular friction 
from the reversal of magnetism, this friction manifesting itself 
as heat. The amount of hysteresis in a given steel varies with 
the composition, with the hardness, with the frequency of reversal 
of magnetism, with the maximum induction at which the steel is 
worked, and the temperature. The hysteresis loss varies approxi- 
mately as the 1.6 power of induction, and directly as the fre- 
quency. The eddy current loss varies inversely as the ohmic 
resistance, directly as the square of the induction, and decreases 
as the temperature increases. It is greater in thick laminations 
than in thin (hysteresis being greater in hard steel than in soft 


steels), it is also greater as the insulation between adjacent lamin- 
ations is less. Lowering the frequency of supply will result in 
increased hysteresis and higher temperature in the iron; reducing 
the frequency from say 133 to 125 cycles will entail an increased 
hysteresis of about 4 per cent., and a reduction from 60 to 50 
cycles will raise the hysteresis approximately 10 per cent. 

For equal output there will not exist any change in the 
copper loss, but in the case of large power transformers the in- 
creased temperatures due to excessive iron losses will materially 
decrease the output, and the normal rated secondary current or 
low voltage current will become a virtual overload. 

Iron loss and exciting current in addition to decreased kw. 
capacity of the transformer mean greater coal consumption, 
all these factors being directly opposed to commercial operation, 
and as this iron loss is constant while the transformer is con- 
nected to the system, no matter what the load may be, the total 
yearly loss will represent a great loss in revenue. While the iron 
loss is practically constant at all loads, the copper or P R loss 
varies as the square of the current in both the high and low 
voltage windings. The output is the total useful energy de- 
livered to the primary, and consists of the output energy plus 
the iron loss at the rated voltage and frequency plus the copper 
loss due to the load delivered. This loss is within easy control 
of the designer, as a greater or less cross-section of copper may 
be provided for the desired per cent, regulation. In a transformer 
core of a given volume and area, the number of turns for the 
required iron loss are fixed. To secure the desired copper loss 
advantage is taken of a form of coil wherein the mean length 
per turn is kept as low as possible with the necessary 
cross-section of copper. If the form of coil is rectangular it 
is evident that the mean length per turn of the conductor would 
be increased, provided the same cross-section or area of the 
core is enclosed, so in order to secure the shortest length per mean 
turn consistent with good construction it is necessary to adopt 
the square core in which the corners have been cut off. Also, 
in order that the greatest amount of conductor may be allowed 
for the available space, all wire entering into the low and high 
voltage windings is either square or rectangular in shape, as by 
using this form of conductor the area is increased by about 33 
per cent, over that of ordinary round wire. This method permits 
the copper loss to be reduced, and at the same time allows a 


great part of the total copper loss to take place in the high voltage 
winding. The loss due to magnetic leakage is made negligible by 
virtue of the compact construction and the proper disposition of 
the windings with relation to each other and the core. 

The copper loss generally has a less cost than the iron loss, 
due to the reduction in output charge because of its short dura- 
tion, and also has a slightly less capital cost due to its diversity 

The losses due to the magnetizing current and heating are 
determined from manufacturers' guarantees or by test as the 
transformer is received from the factory. The exciting cur- 
rent of a transformer is made up of two components; one being 
the energy component in phase with the e.m.f. which represents 
the power necessary to supply the iron loss, the other component 
being in quadrature with the e.m.f. which is generally known as 
the magnetizing current and is "wattless" with the exception of 
a small P R loss. The magnetizing current has very little in- 
fluence on the value of the total current in a transformer when 
it is operating at full load, but as the load decreases the effect 
of magnetizing current becomes more prominent until at no load 
it is most noticeable. The greater the exciting current, the 
greater is the total current at the peak of the load, and hence the 
greater must be the generating station equipment and transmis- 
sion lines to take care of the peak. 

Regulation. — It is often said that regulation reduces the voltage 
upon the load and therefore causes a direct loss in revenue by re- 
ducing the energy sold. If, however, the mean voltage with trans- 
former regulation is maintained at the same value as the constant 
voltage without regulation, the energy delivered to the customer 
will be the same in both cases, hence there will be no direct loss of 
revenue. As the regulation of transformers is affected at high 
power factor mostly by resistance and at low power factor mostly 
by reactance, both should be kept as low as possible. With 
non-inductive load the regulation is nearly equal to the ohmic 
drop, the inductance having but little effect. With an inductive 
load the inductance comes into effect, and the effect of resistance 
is lessened; depending on the power factor of the load. In 
general, the core type transformer has not so good regulation as 
the shell type transformer; the reason for this is that in the shell 
type transformer there is a better opportunity for interlacing the 


Core Material. — Several grades of steel are manufactured for 
transformers. Certain peculiar ingredients are added to the 
pure iron in such proportions and in such a manner that the 
resultant metal is, actually speaking, neither iron nor steel, and 
for the want of a better name it is termed by the trade an " alloy 
steel." The effect of various substances, such as silicon, phos- 
phorus, sulphur, etc., has long been a matter of common knowl- 
edge among those familiar with the metallurgy of steel, but the 
electro-magnetic properties of some of the late "alloy steels" 
have been known a comparatively short time. Some steels are 
very springy and resist bending, but ordinary steels are compara- 
tively soft and yielding, and easily crease when bent. During 
the past few years a great deal of time has been spent in experi- 
mental work to determine the best shape of core and the propor- 
tioning of the various elements of a transformer to give the high- 
est efficiency with minimum cost. 

If a transformer had a perfect magnetic iron circuit no losses 
would occur due to imperfect iron, etc. Losses do occur and in- 
crease with the aging of the iron. The cost of this iron loss will 
include the cost of generating such loss and of supplying the sta- 
tion capacity with which to generate it, and it also includes the 
cost of transmitting the energy consumed by the loss from the 
generating station to the transformer. The revenue affected by 
imperfect iron of a low grade put into the transformers operating 
at the end of a long-distance transmission line .may be divided 
up as follows: 

Cost of iron losses in the transformers. 

Cost of this energy passing over the transmission line, affecting 
both efficiency and regulation for the same amount of copper. 

Extra cost at the generating station in generators, transformers, 
etc., to take care of this energy. 

Cost of magnetizing current in the transformers. 

Cost of this additional current passing over the transmission 

Extra cost at thie generating station in generators, trans- 
formers, etc., to take care of this extra current. 

Insulation. — While the quality, arrangement and proportion of 
the iron and copper are essentials in transformer design, the proper 
selection, treatment and arrangement of the insulating material 
require even greater skill and wider knowledge than does the 
proportioning of copper and iron. A transformer will not 


operate without sufficient insulation, and the less space occupied 
by this insulation the more efficient will it be, with a given 
amount of iron and copper. 

At the present time the use of solid compounds for impregna- 
tion of the winding of transformers is almost universally adopted. 
The use of this compound marks a great improvement in the mod- 
ern transformer because it helps to make the coils mechanically 
stronger by cementing together the turns and the insulation 
between turns and layers in the windings. 

All high-voltage transformers and practically all transformers 
of any voltage, are dried and impregnated by the vacuum process 
which is now considered to be the most reliable insulating 
material and method of insulating. For this purpose both 
asphalts and resins are the materials available. They can be 
liquified by heat and forced into the coil in that condition, and 
on cooling they harden, forming a solid mass (coil and material) 
which is, if well done, free from porosity and volatile solvents. 
The compound fills the porous covering of the wire-conductors, 
and all other spaces in the coils no matter how small, thus increas- 
ing the dielectric strength and preventing moisture from soaking 
into the coils. Before applying this process, the coils are thor- 
oughly dried either in a separate oven or in the impregnating 
tank. They are then placed in the impregnating tank and 
heat is applied until the coils reach a temperature at which the 
impregnating compound is thoroughly fluid. The air in the 
tank is then exhausted by a vacuum pump. After the vacuum 
has exhausted the last traces of moisture from the coils, hot 
compound from another tank is drawn into the impregnating 
tank until the coils are thoroughly covered, this condition being 
maintained until the coils are impregnated. The pressure gen- 
erally used is 60 to 80 lb. per square inch. The time required 
under vacuum and pressure can only be determined by trial but 
usually from three to six hours' vacuum will dry any ordinary 
high-voltage coil not unduly moist. 

At the present time the fluid point of some impregnating com- 
pounds is about 95° C, but it is possible that the development 
of synthetic gums will soon reach a stage which will permit 
an actual operating temperature of 130° C, 

The National Board of Fire Underwriters specify that the 
insulation of nominal 2000-volt transformers when heated shall 
withstand continuously for one minute a difference of potential 


of 10,000 volts (alternating) between primary and secondary 
coils and the core and a no-load run of double voltage for 30 

All transformers should be subjected to insulation tests between 
the primary and secondary, and the secondary and core. A 
transformer may have sufficient strength to resist the strain to 
which it is constantly subjected, and yet due to an imperfection 
in the insulation may break down when subjected to a slight over- 
voltage such as may be caused by the opening of a high-power 
circuit. The application of a high-potential test to the insulation 
will break down an inferior insulation, or a weak spot or part of 
the structure in the insulation. The duration of the test may 
vary somewhat with the magnitude of the voltage applied to the 
transformer. If the test be a severe one, it should not be long 
continued, for while the insulation may readily withstand the 
application of a voltage five or even six times the normal strain, 
yet continued application of the voltage may injure the insulation 
and permanently reduce its strength. 


In the design of successful transformers, the following equa- 
tions are found reliable: 

Let N = Total number of turns of wire in series. 

= Total magnetic flux. 

A = Section of magnetic circuit in square inches. 

/ = Frequency in cycles in seconds. 

B = Lines of force per square inch. 

E = Mean effective e.m.f. 

4.44= J_. = V2X;r 

4 4^ f6 N 
then ^ = i:^i^^-A d) 

Equation (1) is based on the assumption of a sine wave of 
e.m.f., and is much used in the design of transformers. 

If the volts, frequency, and number of turns are known, then 
we have 

._ gxio« ,„. 


If the volts, frequency, cross-section of core, and density are 
known, we have: 

4.44X/XB"XA '^ 

Magnetic densities of transformers vary considerably with 
the different frequencies and different designs. 

Current densities employed in transformers vary from 1000 
to 2000 circular mils per ampere. 

Efliciency. — The efficiency of a transformer at any load is ex- 
pressed as: 

Efficiency = — ^ ^ , ^, — — — ^j — (4) 

output + core loss -f- copper loss ^ 

In the case of ordinary transformers with no appreciable 
magnetic leakage, the core loss is practically the same from no- 
load to full load. The only tests required, therefore, in order to 
obtain the efficiencies of such transformers at all loads, with 
great accuracy, are a single measurement by wattmeter of the 
watts lost in the core, with the secondary on open circuit; and 
measurements of the primary and secondary winding resistances, 
from which the P R watts are calculated for each particular load. 
The core loss, which is made up of the hysteresis loss and eddy- 
current loss, remains practically constant in a constant-potential 
transformer at all loads. In the case of constant-current trans- 
formers and others having considerable magnetic leakage when 
loaded, this leakage often causes considerable loss in eddy cur- 
rents in the iron, in the copper, and in the casing or other sur- 
rounding metallic objects. It should be borne in mind that the 
efficiency will also depend on the frequency and the wave-form 
and that the iron core may age; that is to say, the hysteresis co- 
efficient may increase after the transformer has been in use 
some time. Generally speaking, the efficiency of a transformer 
depends upon the losses which occur therein, and is understood 
to be the ratio of its net output to its gross power input, the 
output being measured with non-inductive load. 

All -day Efficiency. — The point of most importance in a 
transformer is economy in operation, which depends not only 
upon the total losses, but more particularly upon the iron or 
core loss. For example, taking two transformers with iden- 
tical total losses, the one showing the lower iron loss is to be 
preferred, because of the greater all-day efficiency obtained, and 


the resulting increase in economy in operation. This loss 
represents the energy consumed in applying to the iron the 
necessary alternating magnetic flux, and is a function of the 
quality of the iron and the flux density at which it is worked, or 
in other words, the number of magnetic lines of force flowing 
through it. 

The all-day efficiency mentioned above is the ratio of the 
total energy used by the customer, to the total energy input 
of the transformer during twenty-four hours. The usual 
conditions of present practice will be met, if based on five hours 
at full load and nineteen hours at no load; therefore, "all-day" 
efficiency can be obtained from the following equation: 

All-day efficiency = 

Full loadx 5 

Core lossX24 -|-/ i2 X5 -hFull loadx 5 ^^ 

The importance to the economical operation of a central 
station of testing for core loss every transformer received, 
cannot be overestimated. The variation in core loss of two 
transformers of identical design may be considered, as depending, 
not only upon the constituents of the steel used, but also upon 
the method of treatment. 

It has been found in practice, that transformers having ini- 
tially low iron losses, after being placed in service, would show 
most decided increase under normal conditions. This increase 
is due to the "aging" of the iron. The aging of iron de- 
pends on the kind of material used, and on the annealing 
treatment to which it has been subjected. It has been shown 
that when steel is annealed so as to have a low loss, and then sub- 
jected to a temperature of from 85°C. to 100° C, the loss usually 
increases, in some cases this increase being as much as 300 to 
400 per cent. 

By some manufacturers of transformers it is claimed that the 
steel used in their cores is non-aging, or that it has been artifi- 
cially aged by some process. However, it should be remembered 
that an absolutely non-aging steel is not as yet a commercial 
possibility. Within very short periods the iron losses some- 
times increase, and under very high temperature conditions the 
laminations will become tempered or hardened, whereby the 
permeability is greatly reduced; therefore, the iron losses increase 
with the length of time the transformer is in operation. 


The other factor affecting the efficiency of a transformer is 
the copper loss. It occurs only when the transformer is loaded, 
and while it may be considerable at full load it decreases very 
rapidly as the load falls off. As the transformer is seldom oper- 
ated at full load, and in many cases supplies only a partial load 
for a few hours each day, the actual watt-hours of copper loss is 
far below the actual watt-hours of iron loss. However, for 
equal full-load efficiencies, the transformer having equal copper 
and iron losses is cheaper to manufacture than one in which the 
iron loss is reduced, even though the copper loss is correspond- 
ingly increased. 

Regulation. — The ability of a distribution transformer to de- 
liver current at a practically constant voltage regardless of the 
load upon it, is a very highly important feature. By the use 
of conductors of large cross-section and by the proper inter- 
lacing of primary and secondary coils, extremely close regula- 
tion may be obtained with loads of various power-factors, thus 
tending to lengthen the life of lamps and to improve the quality 
of the light. 

In well-designed transformers, low core loss and good regula- 
tion are in direct opposition to one another yet both are desired 
in the highest degree. The regulation of a transformer is under- 
stood to be the ratio of the rise of secondary terminal voltage from 
full load to no-load, at constant primary impressed terminal vol- 
tage, to the secondary terminal voltage. In addition to the vastly 
improved service, it is possible to adopt the efficient low-consump- 
tion lamp, when the transformers in use maintain their second- 
ary voltage at a practically constant value when the load goes on 
or off. While so few central stations are able to keep their 
voltage constant within 2 per cent, it may be concluded that at 
present the point of best practical regulation on transformers 
from about 5 kw. up, lies between the values of 1.75 per cent, 
to 2.00 per cent. 

Regulation is a function of the ohmic drop and the magnetic 
leakage. To keep the iron loss within necessary limits and at 
the same time secure good regulation is an interesting problem. 
We may reduce the resistance of the windings by using fewer 
turns of wire, but with fewer turns the iron is compelled to work 
at a higher flux density, and consequently with an increased loss. 
If we adopt a larger cross-section to reduce the flux density 
we need a greater length of wire for a given number of turns which 


thus gives an increase in resistance. The remaining expedient 
only is to use a larger cross-section of copper, while keeping 
down the flux density by employing a sufficient number of turns, 
to secure the low resistance necessary for good regulation. For 
ordinary practice the regulation of a transformer for non-in- 
ductive loads may be calculated as follows: 

% regulation = % copper loss — (% reactance drop)^ 



For inductive loads the regulation may be calculated by the 
following equation: 
Per cent, regulation = 

per cent, reactance drop per cent, resistance drop . 

SiiT^ ^ Cosl' ^^ 

wherein is the angle of phase displacement between the cur- 
rent and the e. m. f. 

Regulation on inductive loads is becoming more important as 
the number of systems operating with a mixed load (lamps and 
motors) is constantly increasing. Many transformers while 
giving fair regulation on non-inductive loads, give extremely 
poor regulation on inductive loads. 


In studying the performance of transformers it is simple and 
convenient to use graphical methods. The graphical method 
of representing quantities varying in accordance with the sine 
law has been found to be one of the simplest for making clear 
the vector relations of the various waves to one another. 

The principle of this method is shown in Fig. 3, where the 
length of the line o e represents the magnitude of the quantity 
involved, and the angle e o x = d represents its phase position 
either in time or space. 

In an alternating-current circuit the relation between the 
most important quantities may be represented by the method 
above mentioned. When such diagrams are used to represent 
voltages or currents, the length of the lines represents the scale 
values of the quantities, while the angles between the lines 
represent the angle of phase difference between the various 
quantities. The diagrams are constructed from data available 



in each case. The diagram below represents a circuit containing 
resistance and inductive reactance. Since the / R drop is 
always in phase with the current and the counter e.m.f. of 


Fig. 3. — Vector diagram. 

self-inductance in time-quadrature with the current which 
produces the m.m.f., these two magnitudes will be represented 
by two lines, o e^ and o e^, at right angles to each other; their 

Fig. 4. — Assumed vector diagram of a transformer, assuming an inductive 


sum being represented by o e^^ representing the resultant value 
of these two e.m.fs., and is, therefore, equal and opposite to the 
e.m.f., which must be impressed on the circuit to produce the 



current, /, against the counter e.m.f. of self-inductance, 2Tt fL I, 
and the counter e.m.f. of resistance, / R. Therefore, by the 
properties of the angles, 

e^=(I R), + (27tfLiy (8) 

The angle of lag of the current behind the e.m.f. is shown as 
the angle between the lines representing the resistance e.m.f. and 
that representing the resultant of the resistance and the reactance 
e.m.f. Since the resistance component of the impressed e.m.f. 
is in phase with the current and differs 180 degrees in phase 
from the resistance e.m.f., its position will be that shown by the 
line Ci, and the angle between that line and o e^ is the angle of 

The tangent of the angle, d, is equal to 

o e. 

e^ = 27t f L I and o e^ = I R, 
27zfLl 2nfL 

or tan = '- 

I R 



Denoting 1 = 1. 

(27tfL=Xs = (oL. =jxs) (10) 

Like the e.m.f., the current values can be split into two compo- 
nents, one in phase and one in quadrature with the e.m.f., the 
same results being obtained in both cases. 

Impedance is the apparent resistance in ohms of the trans- 
former circuit, and is that quantity which, when multiplied with 
the total current will give the impressed volts, or / Z = E 

Denoting Z as R+j x; where / is an imaginary quantity 

V-L, or Z = R+\/-l L 



In measuring the energy in an alternating current circuit it is 
not sufficient to multiply ^ by / as in the case of direct current, 
because a varying rate of phase between the voltage and cur- 
rent has to be taken into account. This phase angle can be 
determined by a voltmeter, an ammeter and a wattmeter, 
and is expressed as 



where P is the actual power in watts consumed by the load; 



E I the apparent watts, or P R as it is sometimes called, and Cos (f> 
the angle of phase displacement. 

It is very evident that when the resistance is large compared 

with the reactance, the angle of time-lag is practically zero. 
(See Fig. 174.) If the reactance is very large compared with 
the resistance, the angle of lag will be almost 90 time-degrees; 
in other words, the current is in quadrature with the e.m.f. 








Fig. 6. 


x + 

A problem which can always be solved by the use of trans- 
formers, is the convertion of one polyphase system into another. 
Since in the original system there must be at least two compo- 



nents of e.m.f, which are displaced in time-phase, by vary- 
ing the values of these components a resultant of any desired 
phase.can be obtained. In phase-splitting devices using inductive 
or condensive reactance, an e.m.f. in quadrature with the im- 
pressed e.m.f. is obtained from the reactive drop of the current 
through an inductive winding, or a condenser, and the necessary 

P L 

energy is stored as magnetic energy, — ^— , in the core of the 

E^ C 

winding, or as electrostatic energy, ^ , in the dielectric of the 

condenser; but such devices are of little practical use. 


There are a number of different ways of applying transformers 
to power and general distribution work, some of which are: 

Single-phase (one, two, three or more wire). 

Two-phase (three, four, five or more wire) . 

Three-phase delta (grounded or ungrounded) . 

Three-phase star (grounded or ungrounded). 

Three-phase Tee (grounded or ungrounded). 

Three-phase open-delta. 

Three-phase star to star-delta or vice versa. 

Three-phase star and delta or vice versa. 

Three-phase to two-phase or vice versa. 

Three-phase to two-phase-three-phase or vice versa. 

Three-phase to six-phase, or vice versa. 

Two-phase to six-phase, or vice versa. 

Three-phase to single-phase. 

Two-phase to single-phase. 

The principal two precautions which must be observed in 
connecting two transformers, are that the terminals have the 
same polarity at a given instant, and the transformers have 
practically identical characteristics. As regards the latter con- 
dition, suppose a transformer with a 2 per cent, regulation is con- 
nected in parallel with one which has 3 per cent, regulation; at no 
load the transformers will give exactly the same e.m.f . at the term- 
inals of the secondary, but at full load one will have a secondary 
e.m.f. of, say, 100 volts, while the other has an e.m.f. of 99 volts. 
The result is that the transformer giving only 99 volts will be 
subject to a back e.m.f. of one volt, which in turn will disturb 
the phase relations and lower the power-factor, efficiency and 
combined capacity; in which case it is much better to operate 
the secondaries of the two transformers separately. In order to 
determine the polarity of two transformers proceed with the 
parallel connection as if everything were all right, but connect 
the terminals together through two small strips of fuse wire, then 
close the primary switch. If the fuse blows, the connections 



must be reversed; if it does not, then the connections may be 
made permanent. 

The primary and secondary windings of transformers may be 
connected to meet practically any requirement. Fig. 6 repre- 
sents the ordinary method of connecting a single-phase trans- 
former to a single-phase circuit. Referring to the graphical 
representation in Fig. 6 it is shown that E p and O E s (the 
primary and secondary e.m.fs.) represent two lines of constant 
length, rotating at a uniform rate about as a center. The 
direction of the secondary is not strictly 180 electrical degrees 
out of time phase with the primary, but for convenience and 
elementary purposes it is commonly represented as such. The 
dotted line is vertical to X, so that as the points E por E s move 







FiG. 7. — Straight connection of 
two ordinary single-phase trans- 

nm (W) 

* 50- 



Fig. 8. — Single-phase trans^ 
former with primary and sec- 
ondary coils both in series. 

in the circle, they occupy variable distances from 0. As they 
travel from X through Y , it is evident that they have positive 
and negative values, and that these values vary from zero to a 
definite maximum. They pass through a complete cycle of 
changes from positive to negative and back to positive, corre- 
sponding to a complete revolution, both the e.m.fs varying as 
the sine of the angle = E p A. 

Since the changes of voltages in the primary and secondary 
windings of a transformer go through their maximum and mini- 
mum values at the same time, the result of connecting the two 
windings in series is to produce a voltage which is either the sum 
or the difference of the voltages of the windings, according to the 
mode of joining them. If the windings of a step-up transformer 
are joined in series so that their resultant voltage is the sum of the 
voltages of the two windings, the source of supply may be con- 


nected to the terminals of the composite winding, instead of at 
the terminals of what was originally the primary. If this is done, 
the windings of the transformer may be reduced until the total 
voltage of the two windings equals the voltage of the original 
primary winding. 

Fig. 7 shows the way in which two ordinary single-phase trans- 
formers are connected. 

Fig. 8 shows one transformer which has two secondary coils 
connected in series. If this transformer be of the core type and 
the two coils arranged on different limbs of the core, it will be 
advisable to have the fuse in the middle wire considerably smaller 
than the fuses on the two outside wires. The reason for this is, 
that should one of the fuses on the outside circuits blow, say, for 
instance the fuse on leg A, the secondary circuit through this 
half-section will be open-circuited, and the primary coil corre- 
sponding to this section will have a greater impedance than the 
other half of the coil, the inductance of which will be neutralized 
by the load on the other half of the secondary coil. The result will 
be that the counter e.m.f. of the primary section. A, will be 
greater than that of section C, because the two sections are in 
series with each other, and the current must be the same in both 
coils; therefore, the difference of potential between the primary 
terminals, yl, will be greater than that between the primary termi- 
nals of C, consequently the secondary voltage of C will be greatly 

Manufacturers avoid the above mentioned disadvantage by 
dividing each secondary coil into two sections, and connecting a 
section of one leg in series with a section of the coil on the other 
leg of the core, so that the current in either pair of the secondary 
windings will be the same in coils about both legs of the core. 

Transformers are made for three-wire service having the wind- 
ings so distributed that the voltage on the two sides will not differ 
more than the regulation drop of the transformer, even with one- 
half the rated capacity of the transformers all on one side; with 
ordinary distribution of load the voltage will be practically equal 
on the two sides. 

Fig. 9 shows a single-phase transformer with two coils on the 
primary, and two coils on the secondary. The primaries are 
shown connected in parallel across the 1000-volt mains, and the 
secondaries are also connected in parallel. 

To obtain a higher secondary voltage the coils may be con- 


iiected as shown in Fig. 10. In this case the primary coils are con- 
nected in parallel, and the secondary coils connected in series. 
The difference of potential across the two leads, with the primaries 
connected in parallel and the secondaries connected in series will 
be 200 volts, or 100 volts per coil. 



- — 1000^ *— 1000 







^00 >| - 1 00- 


FlG. 9. 

Fig. 10. 


-^-500 >h 500-> 




Fig. 11. 

Fig. 9. — Transformer with primary and secondary windings both in 

Fig. 10. — Transformer with primary windings connected in parallel and 
secondary windings in series. 

Fig. 11. — Transformer with primary windings connected in series and 
secondary windings in parallel. 

Note — ^For convenience all ratios of transformation will be understood to 
represent ten to one (10 to 1). 

If we invert the arrangement shown in Fig. 10 by connect- 
ing the primary coils in series, and connecting the secondary 
coils in parallel, we shall obtain a secondary voltage of 50, as 
represented in Fig. 11. 

In Figs 12-12* and 13 are represented a right and wrong way of 



connecting transformers in scries or parallel, just as the case 
may be. The connections shown in Fig. 12 represent the right 
way of connecting two transformers in parallel, or in series, the 
solid lines showing the series connection and the dotted lines the 
parallel connection. 




^lOO-H i-lOO-^ 

L ^ 


fvwA Lvwvv 








FiG. 12. — The right way of connecting single-phase 
transformers in parallel. 

Fig. 13.— The wrong 
way of connecting sin- 
gle-phase transformers 
in parallel. 

The connections shown in Fig. 13 are liable to happen when 
the transformers are first received from the factory. Through 
carelessness, the leads are often brought out in such a manner as 
to short-circuit the two coils if connected as shown. In this 
case the sudden rush of current in the primary windings would 
burn out the transformer if not protected by a fuse. 


' cm 

cm rw] 

-lOOH -100-^ 



FiG. 14. 

—Three-wire secondary 

Fig. 15.— Three 1000- volt 
transformers connected in 
series to a 3000-volt circuit. 

The three-wire arrangement shown in Fig. 14 differs in every 
respect from the three-wire system represented in Figs. 8 and 10. 
The two outside wires receive current from the single-phase 
transformer, and the center, or neutral, wire is taken care of by 
a balancing transformer connected up at or near the center of 


distribution. The balancing transformer need only be of very 
small size, as it is needed merely to take care of the variation of 
load between the two outside wires. 

It is sometimes desirable to use a much higher voltage than 
that for which the transformers at hand have been designed, and 
to attain this, the secondary wires of two or more transformers 
may be connected in parallel, while the primary wires may be 
connected in series with the source of supply. 

This manner of connecting transformers is shown in Fig. 15. 
It, however, involves a high-voltage strain inside the separate 
transformers, between the high- and low-tension windings, and 
is therefore used only in special cases of necessity. 




* 900 > 


Fig. 16. Fig. 17. 

Fig. 16. — Connection between primary and secondary windings, which 
gives 1100 volts across the secondary distribution wires. Boosting 

Fig. 17. — Connection between primary and secondary windings from 
which we obtain 900 volts. Lowering transformer. 


While it is possible to insulate for very high voltages, the 
difficulties of insulation increase very rapidly as the voltage is 
raised, increasing approximately as the square of the voltage. 

Consider the case of a single-phase transformer as shown in 
Fig. 7. There is evidently a maximum strain of 1000 volts from 
one high-tension line wire to the other, and a strain of 500 volts 
from one line wire to ground, if the circuits are thoroughly 
insulated and symmetrical. The strain between high-tension 
and low-tension windings is equal to the high-tension voltage, 
plus or minus the low-tension voltage, depending on the arrange- 
ment and connection of the coils. With the arrangement 
shown in Fig. 16, it is quite possible to obtain 1100 volts between 



the wire, B, and ground, and the first indication of any such 
trouble is likely to be established by a fire, or some person coming 
in contact with a lamp socket, or other part of the secondary 
circuit that is not sufficiently insulated. 

Should a ground exist, or in other words, a short-circuit 
between the high-tension and low-tension windings, it will, in 
general, blow fuses, thus cutting the transformer out of service; 
or the voltage will be lowered to such an extent as to call atten- 
tion to the trouble, but the secondary windings must be 

To avoid this danger to life, the grounding of secondaries of 
distribution transformers is now advocated by all responsible 





A__ AAA 

50 >t< 60->| 





100^ H-lOo 


FiG. 18. 

Fig. 19. 

electric light and power companies in America. Differences of 
opinion have arisen as to general details both as regards the scope 
of grounding and the methods to be employed, but there is never- 
theless a decided and uniform expression that the low voltage 
secondaries of distribution transformers should be permanently 
and effectively grounded. 

The National Electrical Code provides for the grounding of 
alternating-current secondaries for voltages up to 250 volts. 
This voltage was decided upon after extensive investigation and 

The principal argument for this grounding is the protection of 
life. A fault may develop in the transformer itself, between the 
primary and secondary wires which are usually strung one set 
above the other (high voltage always above the low voltage 
conductors), or a foreign circuit conductor such as an electrified 
series arc or incandescent lighting line conductor may come into 
metallic contact with a secondary line wire leading from trans- 


former. Both the secondary line conductors and secondary 
transformer windings are liable to several forms of faults and 
danger due to a high voltage. 

Some of the accidents recorded and due to such causes, are the 
handling of portable incandescent lamps and switching on lights 


500 >U SCO 

-500^ <— 500- 
7VW\A_. ^jlAMA/J 





(* ^ (*^ 


FiG. 20. 

Fig. 21. 


*— 600- 


located in rooms with tile, cement or stone floors, by means of 
the switches attached to lamp sockets. 

Fig. 17 represents an arrangement of primary and secondary 
circuits that may accidentally be made. These conditions imme- 
diately establish a potential difference of 900 volts. A great 
number of other single-phase transformer combinations may be 
used, some of which are shown in Figs. 18, 19, 20, 21, and 22. 

If we take a transformer with a ratio . 

of 10 to 1, say 500 and 50 turns respec- 
tively, and join the two windings in 
series, we find the number of turns re- 
quired is only a total of 500 if the volt- 
age is applied to the ends of the whole 
winding since the ratio of primary to 
secondary turns still remains 10 to 1, 
and with the same magnetic induction 
in the core, the primary counter e.m.f. 
and the secondary e.m.f. will both re- 
main exactly as before; the ratio of pri- 
mary and secondary currents remains also the same as before 
but is not produced in quite the same manner since the primary 
current will flow into the secondary and take the place of part 
of the current which would have been induced in the first case 
where the windings are separated. 

■<-50-»J K 50*< 


FiG. 22. 


So far as transformers are concerned in two-phase distribution, 
each circuit may be treated independently of the other as shown 
in Fig. 23, which is connected as though each primary and second- 
ary phase were only a straight, single-phase system. One 
transformer is connected to one primary phase to supply one 
secondary phase, independent of the other phase, and the other 
transformer is connected to the other primary phase, supplying 
the other secondary phase. 

In the two-phase system the two e.m.fs, and currents are 
90 time-degrees or one-fourth of a cycle apart. The results 
which may be obtained from various connections of the windings 
of single-phase transformers, definitely related to one another 
in point of time, may be readily determined by diagrams. 

The vector diagram in which e.m.fs. and currents are repre- 
sented in magnitude and phase by the length and direction of 
straight lines, is a common method for dealing with alternating- 
current phenomena. To secure a definite physical conception 
of such diagrams, it is useful to consider the lines representing 
the various e.m.fs. and currents, as also representing the windings 
which are drawn, to have angular positions corresponding 
to angles between the lines; the windings are also considered to 
have turns proportional in number to the length of the corre- 
sponding lines and to be connected in the order in which the lines 
in the diagrams are connected. 

The method of connecting two transformers to a four-wire, 
two-phase system is shown in Fig. 24. Both phases, as will be 
seen, are independent in that they are transformed in separate 

A method of connection commonly used to obtain economy 
in copper is that shown in Fig. 24 where the primaries of the 
transformers are connected independently to the two phases, and 
the secondaries, are changed into a three-wire system, the center, 
or neutral wire being about one-half larger than each of the two 
outside wires. 



When two transformers having the same ratio are connected in 
parallel with a common load, the total secondary current is 
divided between them very nearly in inverse proportion to their 
impedances. This inverse impedance is usually expressed as 



Z R +\/_i Lw 

Consider, for instance, a 5 kv-a transformer with an impedance 
of 2.9 per cent, and a 4 kv-a transformer having an impedance of 
2.3 per cent. The admittances will be 


a n 

x + 

6' Ep. h .y 

Fig. 23. — Two-phase four-wire arrangement. 

5 4 

;r-^= 1.72 ohms and^^= 1.74 ohms 

The division of a total load of 9 kv-a on these when connected 
directly in parallel is 


for the 5 kv-a -7^.'^'' =4.57 kv-a or 91.5 per cent, rated load. 


for the 4 kv-a ' ^r. =4.53 kv-a or 113 per cent, rated load. 

the value 3.46 is the total sum of admittances or 1.74 + 1.72 = 
3.46 ohms. 

Lighting transformers are generally not mounted closely to- 
gether when parallel operation is required, but are usually on a 
secondary net-work. In such cases where the drop due to the 
resistance of wiring or load between the two transformers is 


considerable, any difference such as ordinarily exists between 
different designs and different sizes would usually be automatically 
compensated for, so that the transformers would each take their 
proper proportion of load. 

Assume these same two transformers are connected in parallel 
at a distance of about 500 ft. apart. Assume also that the center 
of load is 200 ft. from the 5 kv-a transformer and that the second- 
ary wiring consists of a No. wire. Neglecting altogether the 
reactance which will be small, as wires will doubtless be fairly 
close together, the drop due to resistance from the 4 kv-a trans- 
former to the center of load will be 1.94 per cent., and from the 
5 kv-a transformer about 1.62 per cent. Adding these resistances 
to the resistance component of the impedance of the two trans- 
formers, the impedance of the 5 kv-a transformer will be in- 
creased to 4.15 per cent, and the 4 kv-a transformer 4.01 per 
cent. The division of the total load will be 

1 2x9 

for the 5 kv-a -^^o— = 4.92 kv-a or 98.5 per cent, rated load. 

and ^ ' ^ 

1 0X9 
for the 4 kv-a „ ^ =4.08 kv-a or 102 per cent, rated load. 

the value 2.2 being the sum of the admittances 1.2 + 1.0 = 2.2. 

So long as the two transformers are not connected in parallel 
it makes no difference which secondary wire of any one of the 
two transformers is connected to a given secondary wire. For 
example: It is just as well to connect the two outside wires, a 
and b, together, as it is to connect a' and b' as shown in Fig. 24. 
However, it makes no difference which two secondary wires are 
joined together, so long as the other wires of each transformer are 
connected to the outside wires of the secondary system. The 
two circuits being 90 time-degrees apart, the voltage between 
a and b is '\/2 = 1.141 times that between any one of the outside 
wires and the neutral, or common return wire. The current in 
c is \/2 = 1.141 times that in any one of the outside wires. 

Fig. 25 shows another method of connecting transformers, 
where the common return is used on both primary and secondary. 
With this method, there is an unbalancing of both sides of the 
system on an induction-motor load, even if all the motors on 
the system should be of two-phase design. The unbalancing is 
due to the e.m.f. of self-induction in one side of the system being 


in phase with the effective e.m.f. in the other side, thus affecting 
the current in both circuits. 

Various combinations of the two methods shown in Figs. 16 
and 18 can be made by connecting the primaries and secondaries 








-loo— > 


Fig. 24. — Two-phase four-wire primary with three-wire secondary. 

as auto-transformers similar to the single-phase connections 
just mentioned. 

The four ordinary methods of connecting transformers are 
represented by vectors in Fig. 26, a, b, c and d, showing relative 
values of e.m.fs. and currents. 







FiG. 25. — Two-phase three-wire primary with three-wire secondary. 
Eah = 2e Eah = 2e 

Ea'h' = 2e Eaa' = \/2e 


Ea'a = \/2e 

70 = ^/21 

Eab = 2e 

Eaa' = 2\/2e 
la and h = i 
766' = V2* 



Let E = impressed volts per phase for A, B and D. 

E . 
e = - impressed voltage per phase for A, B and D. 

e =E impressed voltage per phase for C. 
I =i = current per phase for A and B. 
Ic = current times \/2 per phase for D. 
la', lb, la, Ih' = \/2 times the current per phase for C. 

U) J, 

. ^ 






(G) (D) 

Fig. 26. — Two-phase three-, four- and five-wire systems. 

Another arrangement is to connect the middles of the two 
transformer secondaries, as shown in Fig. 27. This method gives 
two main circuits, a c and df, and four side circuits, ad,dc, cf, and 
fa. The voltage of the two main circuits, between d and /is 100, 
and between a and c is 100. But the voltage across any one of 
the side circuits is one-half times that in any one of the main 
circuits, times the square root of two, or 50X\/2 = 70 volts. 

Another method shown in Fig. 28, commonly called the five- 
wire system, is accomplished by connecting the secondaries at 
the middle, similar to the arrangement in Fig. 27, and bringing 
out an extra wire from the center of each transformer. 

The difference of potential between a and e will be 100X\/2 = 


141 volts, that across b d will be 50X\/2 = 70 volts, and that 
across any one of the main circuits will be 100 volts. 

Another very interesting two-phase transformation may be 
obtained from two single-phase transformers by simply con- 
necting the two secondary windings together at points a little to 
one side of the center of each transformer (see Fig. 29) . There 

Fig. 27. — Two-phase star or four-phase connection. 

are to be obtained 75X'\/2 = 106 volts between a and /; 
\/7o^ 4- 25^ = 79 volts between a and d, and c and/; 25X\/2 = 35 
volts between d and c, and 100 volts across each of the secondary 

Fig. 28. — Two-phase five-wire secondary distribution. 

It is possible by a combination of two single-phase transformer 
connections, to change any polyphase system into any other 
polyphase system, or to a single-phase system. 

The transformation from a two-phase to a single-phase system 



is effected by proportioning the windings; or one transformer 
may be wound for a ratio of transformation of 1000 to 50; the 


j-j. The secondary of this 

transformer is connected to the middle of the secondary wind- 
ing of the first. 

other a ratio of 1000 to 86.6. or 


-1000 — H 

uKlfMMJ liMiKmJ 


-1000 H 



H> <-35-> <r25 




Fig. 29. — Two-phase multi-wire distribution. 

In Fig. 30, a c represents the secondary potential from a to c in 
one transformer. At the angle of 90 degrees to a c the line, c d, 
represents in direction and magnitude the voltage between c and 
h of the other transformer. Across the terminals, a c, ch, and 
a h, it follows that three e.m.fs. will exist, each differing in 



-1000 — > 


<-50-* i * c ' h -ee.e-^ 


FiG. 30. — Two-phase to single-phase distribution. 

direction and value. The e.m.f. across a & is the resultant of 
that in a c and c 6 or 100 volts. 

A complete list of two-phase, three- and four-wire transformer 
connections is shown in Fig. 31 and a list of two-phase parallel 
combinations is shown in Fig. 32. These might or might not 
represent a certain change in the transformer leads. They are, 


however, only intended to represent those connections and com- 
binations which can be made with the leads symmetrically located 
on the outside of the transformers. 

For grounding two-phase systems several methods are em- 
ployed, the best being those given in Fig. 33. 

(A) represents a two-phase four-wire system, the two single- 
phases being independently operated, consequently two inde- 
pendent grounds are necessary. 



































pq f^'^ 





■«v5" — 1 



FiG. 31. — Complete list of two-phase transformer connections. 


(B) also represents a two-phase four-wire system to be used 
for three-phase and two-phase at the same time. This is similar 
to the " Taylor" system excepting that two units instead of three 
are employed. The maximum voltage to ground is a'— x, 
or i!;x 0.866. 

(C) likewise represents a two-phase four-wire system with 
"T" three-phase primary. In this case the maximum voltage 


strain to ground is E^/ - of voltage between terminals 

(D) represents a two-phase three-wire system. The maximum 
strain to ground in this case is full voltage of any phase. 



{E) represents a " V " two unit system. The maximum voltage 
strain to ground is E 0.866, or the same as (B) . 

{F) represents the two-phase interconnected four- or five-wire 



A I B 









a 6 a 6 

r'^^ c^^!^ V~^^ C2X^ 

nr^ 1 "^^ 


r ^ , ^ 

A^ A^ ^^ AA AA 
a b a b 


WvaaI Iwv^ Uaaa 



/^s/\ AA^^^^AA 


Fig. 32. — Two-phase parallel combinations. 

system. The maximum voltage strain to ground is 50 per cent, 
of any phase voltage and the voltage across any two-phase 
terminals is 70.7 per cent, of full-phase voltage. 



General Principles. — In considering the question of three-phase 
transformation we have to deal with three alternating e.m.fs. and 
currents differing in phase by 120 degrees, as shown in Fig. 34. 

One e.m.f. is represented by the line, A B, another by the 
line, B C, and the third by the line, C A. These three e.m.fs. 


\ 1 /'"^^ 2 


Fig. 33. — Methods of grounding two-phase systems. 

and currents may be carried to three independent circuits 
requiring six wires, or a neutral wire, or common return wire may 
be used, where the three ends are joined together at x. The 
e.m.f. phase relations are represented diagrammatically by the 
lines, ax, b x, and c x; also, A B, B C, and C A. The arrows 
only indicate the positive directions in the mains and through 




the windings; this direction is chosen arbitrarily, therefore, it 
must be remembered that these arrows represent not the actual 
direction of the e.m.fs. or currents at any given instant, but 
merely the directions of the positive e.m.fs. or currents i.e., the 
positive direction through the circuit. Thus, in Fig. 32a the 
e.m.fs. or currents are considered positive when directed from 
the common junction x toward the ends, ah c. 

In passing through the windings from a to h, which is the direc- 
tion in which an e.m.f. must be generated to give an e.m.f. acting 
upon a receiving circuit from main a to main h, the winding, a, 

Fig. 34. — Graphic representation of three-phase currents and e.m.fs. 

is passed through in a positive direction, and the winding, 6, is 
passed through in a negative direction; similarly the e.m.f. from 
b to c, and the e.m.f. from main c to a. The e.m.f. between a and 
b is 30 degrees behind a in time-phase, and its effective value is 


2 E cos 30° = ^3 E; 

where E is the value of each of the e.m.fs. a b, and c. 

With this connection the e.m.f. between any two leads, ab,b c, 
or a c, is equal to the e.m.f. in each winding, a x,b x,ov ex multi- 
plied by the square root of three. 

For current relations we see in Fig. 34 that a positive current 
in winding 1 produces a positive current in main A, and that a 
negative current in winding 2 produces a positive current in 
main A ; therefore, the instantaneous value of the current in main 


A is I1 — I2, where I^ is the current in winding 1, and 1 2 is the 
current in winding 2. Similarly, the instantaneous value of the 
current in main B is /j — ^3, and in main C, it is I^ — I^. The 
mean effective current in main A is 30 degrees behind 7^ in phase; 
and its effective value is the square root of three times the current 
in any of the different phases; so that with this connection the 
current in each main is the square root of three times the current 
in each winding. 

When the three receiving circuits ah c are equal in resistance 
and reactance, the three currents are equal; and each lags behind 
its e.m.f., ah,h c, and a c, by the same amount, and all are 120 
time-degrees apart. The arrangement shown in Fig. 34, by the 
lines, a, h, and c, is called the "Y" or star connection of 
transformers. Each of these windings has one end connected to 
a neutral point, x; the three remaining ends, ah c, commonly 
called the receiving ends, are connected to the mains. The e.m.f. 
between the ends, or terminals of each receiving circuit is equal 
to \/3 E, where E is the e.m.f. between ax, h x, and c x. The 
current in each receiving circuit is equal to the current in the 
mains, ah c. 

The resistance per phase cannot be measured directly between 
terminals, since there are two windings, or phases in series. 
Assuming that all the phases are alike, the resistance per phase 
ir, one-half the resistance between terminals. Should the resist- 
ances of the phases be equal, the resistance of any phase may be 
measured as follows: 

The resistance between terminals a 6 is : 

Resistance of a h = R^ + Ri. 
The resistance between terminals 6 c is: 

Resistance of b c — R^-^-R^. 
The resistance between terminals a c is: 

Resistance of a C — R3+R2. 
Therefore : 

_, Res. a b — Res. b c-|-Res. a c 
R3= 2 ' 

_, Res. 6 c — Res. a c -j- Res. o 6 ,, ^. 

^i 2 ' (15) 

^r, Res. a c — Res. a 6 -|-Res. b c 
R, 2 ■' 


The method of connecting three-phase circuits shown in Fig. 34, 
where the windings, 1, 2 and 3, are connected in series a,t A, B 
and C, is called the delta connection. In this connection the 
e.m.f. on the receiving circuit is the same as that on the mains; 
and the current on each receiving circuit is equal to \/3 times 
that in any winding, or \/3I, where / is the current in 1,2, or 3- 

Assuming that all phases are alike, the resistance per phase is 


equal to the ratio of 3 to 2 times ^ the resistance between A and 

B. In a delta connection there are two circuits between A and C, 
one through phase 1, and the other through phases 2 and 3 in 
series. From the law of divided circuits we have the joint 
resistance to two or more circuits in parallel is the reciprocal of 
the sum of the reciprocals of the resistances of the several branches. 

Hence, -^ is the resistance per phase R being the resistance of 

one winding with two others in parallel. The ohmic drop from 
terminal to terminal with current / in the line, is 

Ohmic drop = 2/X-R. (16) 

To transform three-phase alternating current a number of 
different ways are employed. Several of the arrangements are: 

1. Three single-phase transformers connected in star or in 

2. Two single-phase transformers connected in open-delta or 
in tee. 

3. One three-phase transformer connected in star or in delta. 
With three single-phase transformers the magnetic fluxes in 

the three transformers differ in phase by 120 time-degrees. 

With two single-phase transformers the magnetic fluxes in 
them differ in time-phase by 120 degrees or by 90 degrees accord- 
ing to the connection employed. 

With the three-phase transformer there are three magnetic 
fluxes differing in time-phase by 120 degrees. 

The single-phase transformer weighs about 25 per cent, less 
than three separate transformers having the same total rating; 
its losses at full load are also about 25 per cent. less. 

Two separate transformers, V-connected, weigh about the same 
as three single-phase transformers for the same power transmitted ; 
the losses are also equal. 


A three-phase transformer weighs about 16.5 per cent, less than 
three separate transformers; its losses are also about 16.5 per 
cent. less. 

It is considered that for transformation of three-phase power 
the three-phase transformer is to be preferred to any other com- 
bination method. 

In America it is customary to group together single-phase 
transformers for use on polyphase circuits, while in Europe the 
polyphase transformer is almost exclusively employed. How- 
ever, a change is being made and more single-phase transformers 
are being employed in Europe than formerly. The relative 
merits of three-phase transformers and groups of three single- 


Fig. 35 

-Graphic representation of three-phase e.m.fs. 

phase transformers, in the transmission and distribution of 
power, form a question that is capable of being discussed from 
various standpoints. 

A popular argument in favor of the three-phase transformer is 
the greater compactness of the transformer unit; and the favorite 
argument against the three-phase transformer is that if it becomes 
disabled all three sides of the system must be put out of service 
by disconnecting the apparatus for repair; whereas if a similar 
accident occurs to any one of three single-phase transformers in 
a delta-connected group, the removal of the defective trans- 
former only affects one side of the system, and two-thirds of the 
total transformer capacity would go on working. The relative 
merits of the three-phase transformer and the combination of 



three single-phase transformers that may be employed for obtain- 
ing the same service are frequently discussed on the basis of the 
decrease in cost of the several types of transformers with increase 
in rating; and on such basis it has been shown that the three- 
phase transformer is the cheaper, while the other combinations 
are more expensive on account of requiring an equal or greater 
aggregate rating in smaller transformers. It should, how- 
ever, be borne in mind that a three-phase transformer is not, 
generally speaking, so efficient as a single-phase transformer 
designed along the same lines and wound for the same total 

Fig. 36. — Vector sum of effective e.m.fs. 

It is shown very clearly in Fig. 35 that a connection across the 
terminals, B C, x E, and x D, will receive a voltage which is the 
resultant of two e.m.fs. differing in time-phase by 120 degrees; 
or the result from adding the e.m.fs. of E^ and E^ at 60 degrees, 
which is equivalent to E^ \/3. 

It is shown in Fig. 36, where one phase of a star-connected 
group of transformers is reversed, the resultant e.m.f., x' y' 
and X y, is equivalent to the component e.m.fs., x c', x a' 
and X b, X a; consequently the resultant of all three e.m.fs. is 
zero. This is in accordance with Kirchhoff's law which states 
that where an alternating-current circuit branches, the effective 
current in the main circuit is the geometric, or vector sum of the 
effective currents in the separate branches. The modifications 
of the fundamental laws appertaining to this are discussed in 
many books treating alternating currents in theory, and the 
summary given here is for the purpose of comparison. However, 


it is noted in Fig. 36 that the phase relations between o' and b', 
b' and c', a and c and b and c have been changed from 120 degrees 
to 60 degrees by reversing phases b' and c. The pressure between 
a and b and o' and c' is £' \/S, showing their phase relations to be 

For example, in Fig. 36, considering only secondary coils of 
three single-phase transformers that are supposed to be connected 
in star, but as a matter of fact connected as shown, let us assume 
that E is equal to 100 volts: 

(a) What will be the voltage between terminals of Ea, E/, 
and Ea, Eb, and Ee phases? 

(b) What will be the voltage between terminals a' and c', and 
a and 6? 

(c) What will be the voltage across a' y' and y' c\ also a y 
and y 6? 

(a) The voltage acting on any of these windings is equal to 
E v/3 

100X\/3 = 173.2 volts. 

The voltage acting on Ea , Eb', etc., is 

Ea ;^ X 173.2=0.577 X 173.2= 100 volts. 


(b) The voltage between terminals a' and c', or a and b, is equal 
to \/3 times the voltage acting on Ea- etc., or 

E\/3= 100 X 173.2= 173.2 volts. 

(c) It is evident that the two e.m.fs., a' x' and c' x' , are 
equivalent to their resultant, y' x' , which is equal and opposite to 
b' x' ; the dotted lines, a' y' and y' c', are equal to Ea , Eb' , etc., at 
120 degrees apart; in other words, 


E = a" y',eic.,= -X173.2 

= 0.577X173.2 = 100 volts. 

In Fig. 37 in shown a diagram of three-phase currents in which 
X, y, z are equal and 120 degrees apart, the currents in the leads, 
o, 6, c, are 120 degrees apart and each equal to \/3 times the cur- 
rent in each of the three circuits X, Y and Z. 



The current in each lead is shown made up of two equal compo- 
nents which are 60 degrees apart. 

As an example showing the use of Fig. 35, assume a circuit, of 
three single-phase transformers delta-connected. What will be the 


Fig. 37. — Geometric sum of three-phase currents. 

Fig. 38. — Geometric sum of e.m.fs. at any instant equal to zero. 

current through X-phase winding if the current in h lead is 500 

Since one component, X, has in the lead the same sign as it has 


in its own transformer winding, and the other component, Y, has 
in the lead the opposite sign to that which it has in its own trans- 
former winding, X, is represented in lead by the same vector as in 
its own transformer winding; while the other component, F, is 
represented in the lead by a vector 180 degrees from that which 

represents it in its own circuit, therefore, X =~^ 500. 


The instantaneous values of the currents in any one wire of a 
three-phase system are equal and opposite to the algebraic sum 
of the currents in the other two sides. Therefore, the algebraic 
sum of e.m.fs. or currents at any instant is equal to zero. This 
fact is shown in Fig. 38, the geometric sum of the three lines, 
A, B,C, being equal to zero at any instant. 

Single-phase transformers may be connected to a three-phase 
system in any of the following methods: 

Delta-star group with a delta-star. 

Star-star group with a star-star. 

Delta-delta group with a delta-delta. 

Star-delta group with a star-delta. 

Delta-star group with a star-delta. 

Delta-delta group with a star-star. 

It must, however, be remembered that it is impossible to 
connect the following combinations, because the displacement of 
phases which occurs, when an attempt is made to connect the 
secondaries, will result in a partial short-circuit. 

Delta-star with a star-star. 

Delta-delta with a star-delta. 

Delta-star with a delta-delta. 

Star-delta with a star-star. 

As is well known there are four ways in which three single- 
phase transformers may be connected between primary and 
secondary three-phase circuits. The arrangements may be 
described as the delta-delta, star-star, star-delta, and delta-star. 

In winding transformers for high voltage the star connection 
has the advantage of reducing the voltage on an individual unit, 
thus permitting a reduction in the number of turns and an 
increase in the size of the conductors, making the coils easier to 
wind and easier to insulate. The delta-delta connection never- 
theless has a probable advantage over the star-delta arrangement, 
in that if one transformer of a group of three should become 
disabled, the two remaining ones will continue to deliver three- 



phase currents with a capacity equal to approximately two- 
thirds of the original output of the group. Fig. 39 shows a delta- 
delta arrangement. The e.m.f. between the mains is the same 
as that in any one transformer measured between terminals. The 
current in the line is \/3 times that in any one transformer 

Each transformer must be w^ound for the full-line voltage and 
for 57.7 per cent, line current. The greater number of turns in 
the winding, together with the insulation between turns, neces- 
sitate a larger and more expensive coil than the star connection. 

For another reason the delta-delta connection may be preferable 

Fig. 39. — Delta-delta connection of transformers. 

to the star, inasmuch as the arrangement is not affected even 

though one transformer may be entirely disconnected, in which 

case it is practically assumed that the two remaining transformers 

have exactly a carrying capacity of 85 per cent, of ^ = 0.567. 

In a delta connected group of transformers the current in each 

phase winding is -y=' I being the line current, and if a phase 

displacement exists, the total power for the three phases will be 
V3X^X/XCos^. (17) 

Assume the voltage between any two mains of a three-phase 
system to be 1000 volts; the current in the mains, 100 amperes, 
and the angle of time-lag, 45 degrees. What will be the e.m.f. 
acting on each phase, the current in each phase, and the output? 

The e.m.f. on each phase of a delta-connected group of trans- 
formers is the same as that across the terminals of any one trans- 


former. The line current is \/3 times that in each transformer 
winding, or a/3X 57.7 = 100 amperes, therefore the current in 

each phase is 100 X -y^ = 57.7 amperes. The output being a/3 E I- 

Cos d = 

1. 732 X 1, 000 X 100 X.7 1 = 123 kw. approx. 

In the star-star arrangement each transformer has one terminal 
connected to a common junction, or neutral point; the three 
remaining ends are connected to the three-phase mains. 

The number of turns in a transformer winding for star connec- 
tion is 57.7 per cent, of that required for delta connection and the 



h — 677 ^ H 577 — ^ 












Fig. 40. — Star-star connection of transformers. 

cross-section of the conductors must be correspondingly greater 
for the same output. The star connection requires the use of 
three transformers, and if anything goes wrong with one of them, 
the whole group might become disabled. 

The arrangement shown in Fig. 40 is known as the "star" or 
"Y" system, and is especially convenient and economical in 
distributing systems, in that a fourth wire may be led from the 
neutral point of the three secondaries. 

The voltage between the neutral point and any one of the 

outside wires is — ^ of he voltage between the outside wires, 



1000 X-7- = 1,000X0.577 = 577 volts. 

The current in each phase of a star-connected group of trans- 
formers is the same as that in the mains. 

Fig. 41 shows a star-star connection in which one of the 




secondary windings is reversed. It may be noted that the phase 
relations of phase c have changed the relations of a c and b c from 
120 degrees to 60 degrees by the reversal of one transformer 

connection. The resultant e.m.fs., ac and be, are each — ^ = 


-1000 — > 


< 1000- 


Fig. 41. — Star-star connection of transformers, one-phase reversed. 

57.7, but in reality should be 1 00 volts — the voltage between a and b 
is 57.7 X\/3 = 100. In star-connecting three single-phase trans- 
formers it is quite possible to have one of the transformers 
reversed as shown. 















Fig. 42. — Star-delta connections of transformers. 

In the star-delta arrangement shown in Fig. 42 the ratio of 

transformation is — ;^' or 0.577 times the ratio of secondary to 

primary turns, and the e.m.f. acting on each secondary circuit is 

the same as that between the mains. 


For example, let us assume that 1000 volts are impressed on 
the primary mains. The voltage between any two secondary 
mains is the same as that generated in each transformer, namely, 

57.7 volts, or 100 X —y^ =57.7 volts. 


Fig. 43. — Delta-star four-wire connection of transformers. 

Fig. 41 shows a delta-star connection using three single-phase 
transformers. From the neutral point of the secondary star 
connection, a wire may be brought out, serving a purpose similar 
to that of the neutral wire in the three-wire Edison system, it 







FiG. 44. — Open-delta or "V" connection of transformers. 

being without current when the load is balanced. The ratio of 
transformation for the delta-star arrangement is \/3, or 1.732 
times the ratio of secondary to primary turns. 

The advantage of this secondary connection lies in the fact 



that each transformer need be wound for only 57.7 per cent., of 
the voltage on the mains. 

In the arrangement, commonly called "V" or "open-delta" 
the voltage across the open ends of two transformers is the 
resultant of the voltages of the other two phases; see Fig. 44. 
This method requires about 16 per cent, more transformer capac- 
ity than any of the previous three-phase transformations shown, 
assuming the saijie efficiency of transformation, heating, and 
total power transformed. 







< ^100- 



Fig. 45. — " V " connection of transformers with secondary windings 
connected in opposite directions. 

In comparing the kv-a capacity of two single-phase trans- 
formers connected in open delta, with three similar transformers 
connected in delta, the kv-a capacity is approximately 1 -^ ^^ = 
58 per cent. This is due to the fact that for the delta connection 
the current and voltage of each transformer are in phase with 
each other, while for the open-delta connection the current and 
voltage of each transformer are 30 degrees out of phase with 
each other. 

With the open-delta method a slight unbalancing may exist, 
due to the different impedances in the middle main and the two 
outside mains, the impedance in the middle main being the 
algebraic sum of the impedances in the two outside mains. 

The open-delta arrangement, (where the primary is connected 
like that shown in Fig. 45) is in every respect equivalent to the 
open-delta connection represented in Fig. 42. The primaries are 
connected in a reverse direction, or 180 degrees apart in phase 
with the secondary. 


The vector diagram shows the changed phase relations of 
primary to secondary. By connecting two single-phase trans- 
formers in the opposite direction, that is to say, connecting the 
secondary like that of the primary, and the primary like that of 
the secondary, we obtain the same transformation characteristics. 

Like that of the open-delta arrangement the tee method 
requires only two single-phase transformers. 

As regards the cost of equipment and the e^ciency in opera- 
tion the tee arrangement is equal to either the open-delta, the 
star or the delta methods. 

The tee arrangement is represented in Fig. 46. The end of one 
transformer is connected to the middle of the other. 

1000 > 

< 1000 












X 86.6 



Fig. 46. — Tee or "T" connection of transformers. 

The number of turns on a 6 is ^ ■ =1.16 times the number of 


turns on x c. Its ability to maintain balanced phase relations is 

no better than the open-delta arrangement, and in no case is 

it preferable to either the star or delta methods of connecting 

three single-phase transformers. 

It is worthy of note that the transformer which has one end 

tapped to the middle of the other transformer need not be designed 

for exactly ^^^ = 86.6 per cent, of the voltage; the normal volt- 

age of one can be 90 per cent, of the other, without producing det- 
rimental results. 

Another three-phase combination is shown in Fig. 47. In this 
case it is assumed that the three single-phase transformers 
were originally connected in star at oA, oB and oC as shown by 
dotted line in the vector diagram. 



To change the transformation to the combined system of the 
star-delta, the end of winding oB is connected with the point o' 
of the phase oA, and the end of the phase oC with the point 
o"of the phase oB so that the vector oB becomes o'E' and oC 
becomes o"C'. The length of the three vectors is proportional 
to the number of coils per phase, all coils having the same num- 

mum Kwwwl rmtm 


iX\ ca 




Fig. 4". — Delta connection with 50 per cent, of winding reversed to obtain 
another phase relation for maximum voltage. 

ber of turns. The end o of phase oA is connected to the point 
of the phase o"C\ 

Going over the list of common three-phase connections we find 
there are only four delta-delta systems in common use, these being 
shown in Fig. 48. 

Q kit] Uj 

Q-O n 

Fig. 48. — Common delta connections. 

These, and a combination of them may be so arranged as to 
give not less than sixteen different changes; all these changes 
being given in Fig. 49. 

Taking away one transformer of each of the above combina- 
tions we find open-delta connections like those given in Fig. 50. 

On carefully looking over the eighteen different delta-delta 
combinations given in the above figures, it will be noted that the 
first ten represent changes of one or two of the transformers while 


the remaining eight have all their secondaries connected in a 
direction opposite to their respective primary windings. 

There are also four common star-star connections in general use, 
these being shown in Fig. 51. 

Like the delta-delta, these four star-star connections can be 
arranged to give sixteen different combinations as will be seen 
from Fig. 52. 

Continuing further through the series of three-phase connec- 
tions we come to delta-star or star-delta combinations. The 
star-delta and delta-star in common use are given in Fig. 53. 

iL ijj iij £b=ur4i lAIAj uAi'u LninJ crtru 

m f=^ f^ w^ ""f^ w" 


aJyi cyp^ ^^^#t^ ^Yh^ ^\^ ^Y^ \ ^ 

^^YJY^ Cld~VP n.^iH C Y?T^ 

Fig. 49. — Uncommon delta connections. 

The uncommon systems of star-delta transformer connections 
are shown in Fig. 54. These may be changed about to delta- 
star as desired, thus making twice the number. It must be re- 
membered, however, that none of them can be changed about 
from one set of combinations to another. 


It is customary for all transformer manufacturers to arrange 
transformer windings so that left- and right-hand primary and 
secondary leads are located the same for all classes and types. It 
is not, however, customary for operating companies and others 
to do so after a transformer has been pulled to pieces. The major- 
ity seems to follow manufacturer's prints and wiring diagrams of 
transformer connections coming from the factory, all of which 
are assumed to have the same relative direction of primary and 


secondary windings, thus permitting similarly located leads leav- 
ing the transformer tank to be connected together for parallel 
operation if desired without the necessity of finding the polarity. 
Large and moderate-sized high-voltage transformers are rarely 
used for single-phase service. They may be of single or three- 
phase design but they are used almost exclusively on three-phase 
systems, and connected in star or delta or a combination of the 

^ W U-b b^ d-\j LrSj 

rvp rvi rv^ ^T^ ^Vt^ P^ 

Fig. 50. — Uncommon open-delta connections. 

two methods. Single-phase units in large and medium and small 
sizes (6000 to 0.5 kv-a) are very common. They afford a better 
opportunity for different polarities than three-phase units, which 
are also made in large and medium and small sizes (14,000 to 
1.0 kv-a). 

The delta and star methods of connections generally referred 
to as " conventional " are understood to have all the primary 
and secondary windings wound in opposite directions around 

uJ u kJ u uJ uJ Urrzi b::^ Lj I — i I — i 
cri_rn_r| p p p n rj n |n_pi_p 

Fig. 51. — Common star connections. 

the core. This conventional method is not always followed as 
problems arise in every-day practice showing that it is not always 
carried out. 

Three single-phase transformers or one three-phase trans- 
former may have their windings arranged in the following manner: 

(1) The three primary and secondary windings wound in the 
same direction — positive direction. 

(2) The three primary and secondary windings wound in the 
same direction — negative direction. 


(3) The three primary windings wound in opposite direction 
to the secondary windings — positive direction. 

(4) The three primary windings wound in opposite direction 
to the secondary windings — negative direction. 

(5) One primary winding of the group of three may be wound 
opposite to the remaining two primaries and the three 
secondaries — positive direction. 

J d u u u u u J u uuii L u u cHx-J 
n r| p n q n p rj n "^^-p-n H pi ^ fhR-P 

Lrbrb LrhnJ L b u Lrd-J J f J u u u L 
(rjJrL_r^ n rj n p_p_p n p p r\-p-n n r| n 

LrrhJ JUL J L J Uxra 

r^ p p r^-p_o p rj p n p n 

Fig. 52. — Uncommon star connections. 

(6) One primary winding of the group of three may be wound 
opposite to any of the remaining two primaries and the 
three secondaries — negative direction. 

(7) Two primary windings of the group of three may be 
wound opposite to the one remaining primary and three 
secondary windings — positive direction. 

WwJ k/wJ Vf*i W^ WmI IwmJ UwJ Ivwl Iwyj Ivwl kwj M*\ 

ry^"^ (:^i_iq_r| ^^i-^ ^ n n n 

Fig. 53. — Ck)mmon star-delta connections. 

(8) Two primary windings of the group of three may be 
wound opposite to the one remaining primary and the 
three secondary windings — negative direction. 

(9) One unit may have its primary and secondary windings 
different to the two remaining units, as: 

(a) The unit on the left — positive direction. 

(6) The center unit — positive direction. 

(c) The unit on the right — positive direction. 



(10) One unit may have its primary but not the secondary 
windings different to the remaining two units, as (9) 
but in the negative direction. 

(11) Two units may have their primary and secondary wind- 
ings different to the remaining unit, as: 

(a) The left and center units — positive direction. 

(b) The right and center units — positive direction. 

(c) The left and right units — positive direction. 

(12) Two units may have their primary but not secondary 
windings different to the one remaining unit, as (11) 
but in the negative direction. 

U^ U/w Iv\aI 

rp PL_n 

U/sJ U/vJ Iv>>a| 

U/s/J U^ l\/\A 


U/M U/vJ IwAl 

Iwj IwJ L/j Lj L/J u/J 


iJj uJ iL \it--LLr-\h uil uj lij U-rHljriwJ 


nnn n p n 

, I I I, 


UvvrhJ^*lvvg ' Uv/J ' LvUrh — I 
1^^ i*^^ i'^'*^ f*^ 1*^^ ('^^ 

Fig. 54. — Uncommon star-delta connections. 

Transformers of the same rating and of the same make are as a 
rule assumed to have the same polarity, impedance and ratio of 
transformation. In all cases where transformers are not of the 
same make it is advisable that the secondary connections be 
subjected to polarity tests before connecting them in delta or 
star. The mistakes which can be made, are: 

(1) One or more reverse windings. 

(2) Internal leads crossed. 

(3) Where transformers are located some distance apart, 


A J, c 

^ B (^ ^ B q ^ B 

UwV^rJ Lnaa/J IvnaaI UaaaJ U>na^ Ua/vsI bvvAAl [aaAaI 'naa^ l^AA'^l U»'Vv>J bs/\AN 

rojrn-^ r p r^ pp rv^^^g^ r p r^ pp 

a " c 

I Aa a 

Fig. 55. — Three-phase polarity combinations. 

A B 

V/^/^A '\f\^-y\ ^AA/<J 


l/V^ 2 

/\/^ r^^ 




B A ^ 

UiVnaI UaatJ JwvvI |aa/vJ ^Ka^ 




l/N/^ 2 >^^^^ 3 


a b 

1 ,8 


WV\I Uaa/N V\A/\I l\A/vJ U^/wi Ka/v/nJ |a/V/N/sI 


l^^xx 2 xwv 3 




2 >wv 3 

f^"^ ^/^V^ ^l'^'^ 


2% 3 


Fig. 56. — ^Phase relations and rotation. 



and where connections are made at some distance, 
the leads may become crossed. 
The reversal of two leads of either the primary or secondary 
will reverse the polarity, this being (so far as the external connec- 
tions are concerned) the same as reversing one winding. 

Reversing the line leads of a star-star, delta-delta, star-delta 
or delta-star will not reverse the polarity since the transformer 
leads themselves must be changed in order to make the change 
in polarity. This should be particularly noted when parallel 


Time-Phase Angle Primary Windings' Secondary Windings 

Fig. 57. — Complete cycle of polarity changes. 

operation is desired, for, though the phase relations of two trans- 
former groups may be the same parallel operation might be impos- 
sible (see Fig. 55) . 

The effect of a reversal of one or two primary windings is not 
the same for the four systems of star and delta, but is : 

For Star-star: The reversal of one or two primary windings 
will not produce a short-circuit, but will produce a difference in 
phase relations and voltages. The maximum voltage will not 
be greater than the line voltage (see Fig. 58). 

For Delta-delta: The reversal of one or two primary windings 
will immediately produce a short-circuit when the secondary 


delta is closed. The maximum voltage difference will be 2E 
or double-line voltage (see Figs. 59 and 60). 

For Star-delta: The reversal of one or two primary windings 
will immediately produce a short-circuit when the secondary 
delta is closed. The maximum voltage difference at that point 
which closes the delta will be 2E or double-line voltage. 


a- A 




a- A 


Fig. 58. — Three-phase polarity difficulties. 

For Delta-star: The reversal of one or two primary windings 
will not produce a short-circuit on the secondary side when the 
star is made. The maximum voltage difference will be E or 
line voltage, but voltages and phase relations will be unequal. 

The thick, black lines shown in Figs. 55, 56, 57, 58, 59 and 60 
represent secondary windings. 

Fig. 57 gives all the possible star and delta polarity combina- 
tions, or, sixteen as already explained. 





JvvA/V-i-A/WV — LAA^AJ 




^ a 



^ (a) 

e ,*, — e > 



kvvAl ^v^^N l^/vv^| 6 




i? Vi__: 

arr ' 

-2E H 

Z AC K'SA,^ UaaaI IvvvJ/ 


Fig. 59. — Three-phase polarity difficulties. 


Fig. 58 shows the effects of a reversed winding or transformer. 
Unlike the delta-delta or star-delta no short-circuit exists when 
secondary connections are completed. 

Fig. 59 (a) and (6) shows wrong and right method of connecting 
the delta secondary when one winding is reversed. Across Cx 
of (a) double-line voltage is obtained thus making the delta 
secondary impossible and only operative when connected as 

Connection „ 

q g Reversed . 




Fig. 60. — Three-phase polarity diflSculties with two transformers reversed. 

shown at (b) . Both (a) and (b) have their primary and secondary 
windings wound in opposite directions, as also (h) and (i). 

Fig. 60 (a) and (b) also show a correct and incorrect way of 
connecting the windings in delta when two transformers of a 
group of three are reversed. As before, double voltage or 2E is 
the maximum difference in voltage which can exist. Both (a) 
and (6) and (/), (g) and (h) are assumed to have their primary and 


secondary windings of the same polarity. The primaries and 
secondaries of (c) and (d) are assumed to have opposite polarity. 

Fig. 57 may also have parallel operating polarity combinations 
represented as a complete cycle of changes. 

From the above it is evident that from the four systems of 
delta-delta, delta-star, star-star and star-delta, we obtain 48 
different combinations. 

Delta - Delta 6 a 6 a c a c I c a a c c 


V / \ V acccbbbaabcbab 

a c a c 

Delta -star c b b a a c a b c 

V Vv.'^>-' < >" O' '-< >' "-< 


star - star 
a b 

c b b b a a a c c b c b 

c a c 


IX\ a c a c b c b a b a a c b b a 

c c b 

Star - Delta 

c b a c b a a b c a b 

^ > c<] >» „< E>. ,<] [>» „<] [>c ,<3 

a a b b c c c c b b « 


After we have gotten through with these various combinations 
our next difficulty is in knowing just which one combination can 
be operated in parallel with another. With the primary and 
secondary windings arranged as is usual in practice, not less than 
eight different parallel combinations may be made (although 
sixteen are possible) these being given in Fig. 61. Other inter- 
esting series of parallel combinations are given in Figs. 62, 63, 
64 and 65. 

The problem of paralleling systems, no matter whether they 
be generating or transforming, resolve themselves into such 
factors as equal frequency, equal voltages which must be in time- 
phase, etc. The manufacturer is responsible for a fair part of 
the troubles of operating engineers from the apparatus point of 


view, but the engineer himself shoulders the major portion of 
responsibility so far as the operating life of the apparatus is 
concerned whether the apparatus be operated singly or in multi- 
ple. The manufacturer can, and endeavors, to design apparatus 

J U U U u U UU 


U ul U LniAj 

ryyi rvjYi Q_q-q g q n ^Y^ ^^\^V^ 

lAIAj uUAj c?iira uAJAj Lrb-ta lAm 
^"^ LI ^'^ III ^"^ 

(g) ih) 

Fig. 61. — Three-phase parallel combinations in common practice. 

and deliver same to the customer such that identical polarity, 
equal capacity and equal voltages are obtained and satisfactory 
parallel operation made possible. However, one particular 
manufacturer cannot be held responsible for the methods, etc., 

J d J L Lj L lAIAj iF^4s dxhJ Lrtrb 

' la') (b'y (o'J 

uAirU crtte lAIAu cbt-ra lii LniAj iL lii lL 

1 ' (d') ' ' re'/ ' r/'; 

u u u Lrhm J J J L L u 

Fig. 62. — Common three-phase parallel combinations. 

of another manufacturer who may design the same size and class 
of apparatus which differs in ratio of high-voltage to low-voltage 
turns, in impedance and also in its polarity. 

The fault and responsibility, generally speaking, rests with the 



engineers themselves. Large and moderate size transformers 
are most always operated in parallel and consequently when order- 
ing other transformers for the purpose of parallel operation, and 
when the order is from a different maker, certain specifications 
should be covered if the delta circulating currents are to be 
avoided and the apparatus is to be satisfactorily operated in 

In the parallel operation of delta and star systems, two main 
factors must be kept in mind after due consideration has been 
given to the design of the apparatus to be placed in parallel. 
These are: 

cj-w-ft U u*U u J u u u u Lrd-Q J U ul 
c:i_pi_r| p n p rypgL-n rp i^ <p c^/rua c::bfdtt-j:3 

•^^.w m^^^Tff r^_,.ftn 

tru pu iL [T^T3 

Fig. 63. — Uncommon three-phase parallel combinations. 

(a) No condition is possible whereby apparatus connected in 
delta on both the high-voltage and low- voltage sides can be made 
to parallel with another piece of apparatus connected either in 
delta on the high-voltage side and star on the low-voltage side or 
in star on the high-voltage side and delta on the low-voltage side. 
However, a condition is possible whereby apparatus connected 
in delta on the high-voltage side and star on the low-voltage side 
can be made to parallel with several combinations of another piece 
of apparatus connected in star on the high-voltage side and delta 
on the low-voltage side. 

(b) Some combinations of one group of apparatus or one poly- 
phase unit connected exactly the same cannot be made to operate 
in parallel, as, for instance, a delta-star may have a combination 
that will not parallel with another polyphase unit or group of 
apparatus connected delta-star. 


As already stated, to secure perfect parallel operation the two 
sets of apparatus should have exactly the same ratio of trans- 
formation, the same IR drop and the same impedance drop. 
Too little notice appears to be taken by operating engineers of 
the right size and type, identical characteristics, and the ability 
of transformers to share equal loads when operated in parallel. 

Even though these conditions are obtained it will not follow 
that parallel operation is secured nor possible. For instance, 
assuming conditions are such that the characteristics of two sets 
of apparatus are identical and that they have exactly the same 

LrbnJ nhJ-b] zM:ki cWn LtnJ cJ-d-t 

(a'") ' '(6"r ' ' '(c'")" ' 

Lrl=nJ J U L Lrfcr-J J J L 

Fig. 64. — Uncommon three-phase parallel combinations. 

ratio of high- voltage to low-voltage turns, the same IR drop and 
the same impedance drop, it will not follow that by using iden- 
tical connections at the case of the apparatus, that a star-star can 
be operated in parallel with another star-star or delta-delta. 

If the designs of two polyphase units are such that satisfactory 
operation may be carried out, the next step for the operator is 
to ascertain their phase relations; that is to say, see if their phase 
relations between the high voltage and low voltage are identical, 
for, apparatus coming from the factory may or may not have 
the same polarity. If two three-phase transformer groups 
have in themselves or between them a difference in polarity 
(positive in one and negative in another) it will be impossible to 
operate them in parallel when arranging their external connec- 
tions symmetrically. 

For the satisfactory parallel operation of three-phase systems 
it is necessary first to ascertain that : 


(a) Each single-phase unit or each phase of the polyphase unit 
has the same ratio of transformation, the same IR drop and the 
same impedance drop. 

(h) The phase relation is the same (see Fig. 56). 

(c) The polarity is the same (see Fig. 55) . 

With a slight difference in ratio, unbalanced secondary voltages 
or a circulating current will result. 

With a difference in impedence the total efficiency may become 
badly affected, though not so pronounced as that which would 
exist if each unit or phase was tied directly together and after- 
ward connected in star or delta. 

^.^ y^wW Tfu'Tf 

u L L) LrtTiJ CraFtq cdkL-u uraLfcq fd kitKj 
M (e"") ^ \j"")\\ I 

J L u Lnd-u u L L LttttJ 

' \g"") ih""\ 

Fig. 65. — Uncommon three-phase parallel combinations. 

Phase rotations sometimes offers complications where mixed 
systems of delta and star are employed. To reverse phase rota- 
tion two lines (not transformer terminal leads) must be reversed. 

Polarity complications are even worse and sometimes pre- 
sent much difficulty. To reverse the polarity two transformer 
leads (not line leads) must be reversed (see Figs. 58, 59 and 60). 

Ordinary parallel operation and ordinary connections for 
parallel operation are quite simple. Complications set in when 
two or more groups of different system connections have to be 
operated in parallel. On some of our present day large and cen- 
tralized systems, it happens that certain "make-shift" parallel 
combinations must be made with the available apparatus, 
perhaps in the stations themselves or on some part of the general 
distribution system. Usually the chief operating engineer has 
a list of available transformers at each station and center which 


facilitate their adoption when urgently needed. On the occur- 
rence of a breakdown in any station or center he will issue an 
order to make up a temporary substitute of transformer or trans- 
formers as the requirement calls for. This may mean a simple 
change and use of ordinary connections, or it may mean a sub- 
stitute of one or more transformers of odd voltages or kw. capac- 
ity or both. In fact it may mean, in order to deliver the 
amount of energy necessary and continue operation, that he 
will have to resort to connecting certain transformers in series 
and others in multiple series, etc. It may also mean that such 
unusual parallel combinations as those shown in Figs. 66 and 
66a will have to be made. 

A number of delta-star and delta-delta parallel combinations 
similar to above might be made but great care must be taken to 
phase out the secondary windings of each group before tying 
them together, for, as in well known, a straight delta-star cannot 


Fig. 66. — Unusual parallel combinations. 

be tied in with a delta-delta and vice versa, nor a star-star with 
a delta-star although in a somewhat modified form this has been 
done in Fig. 66. With these and similar "make-shift" combina- 
tions of odd voltages and capacities engineers encounter from 
time to time on our larger systems, the essential points to remem- 
ber are the difference in phase position and rotation and also the 
different impedences of the various transformers differing very 
much in sizes. The two former difficulties show themselves 
immediately parallel operation is tried but the latter only 
demonstrates itself by excessive heating or a bum-out and con- 
sequently is a serious point and one very often neglected by 
operating engineers in their rush to get the system in regular 
working order. 



When refering to parallel operation it is oftentimes stated that 
two or more three-phase groups or two or more three-phase 
transformers may be connected in parallel on the low- or high- 
voltage side and yet it may not be possible to connect them 
together on the other side. This condition does not constitute 
parallel operation of transformers. Parallel operation of trans- 
formers is always understood to mean that before a condition 
of parallel operation can exist both the primaries and the sec- 
ondaries respectively must be tied together, neither the one 
nor the other alone constituting parallel operation. 


In the connection of power transformers for transmission sys- 
tems there is a choice between four main combinations for three- 
phase and three-phase two-phase systems, namely, delta and 
star, see Fig. 67. 


Fig. 67. — The two common systems. 

Where x = y V3, or 100 per cent. 

and y = x^/x or nearly 57.7 per cent, of full voltage between 

lines in case of the star connection; 


100.0^V^3 = 57.7 per cent. 

The delta connection, where x = 100 per cent., the voltage is 
that shown between lines; or 577.7 X\/3 = 100 per cent, 
and three-phase to two-phase; namely, two-transformer "T" 
and three-transformer "T", see Fig. 68. 

y = —- =86.6 per cent, of the voltage between trans- 
former terminals a' , V and c. 


X =t/— y-100 per cent., or full voltage between trans- 
^ former terminals a\ h' and c. 

z = Full terminal voltage a', h' and c, corresponding 

to a ratio of 1.0 to 1.15 of ahc values. 








Fig. 68. — The uncommon systems. 

Star vs. Delta. — It is shown in Fig. 69 that should one of the 
three single-phase transformers be cut out of star, or one of the 
leads joined to the neutral point be disconnected, there will exist 
only one voltage instead of three, across the three different phases. 

This disadvantage is detrimental to three-phase working of 
the star arrangement, inasmuch as two equal and normal phase 



> < 







Fig. 69. — Result of one transformer of a star-connected primary and 
secondary group being cut out of circuit. 

voltages of the three-phase system are disabled, leaving one 
phase voltage which may be distorted to some degree, depending 
on conditions. 

On the other hand, should one phase, or one transformer of a 
delta-connected group be disconnected from the remaining two, 
as shown in Fig. 70, there will exist the same voltage between the 



three different phases, and practically the same operating con- 

The result obtained by cutting out of delta one transformer, is 
simply the introduction of open delta, which has a rating of a 
little over one-half the total capacity; or more correctly, the 
rating of transformer capacity is 

85 per cent. X 0.6666 = 0.5665 

of three transformers of the same size connected in delta. 

In the past it has frequently been urged against the use of 
three-phase transformers with interlinked magnetic circuits that 
if one or more windings become disabled by grounding, short- 

A B C 

^1000 . 






^rW ) f MF | p RHTj 





— -100 — 

Fig. 70. — Result of a delta-connected group of transformers with one 
transformer disconnected. 

circuiting, or through any other defect, it is impossible to operate 
to any degree of satisfaction from the two undamaged windings 
of the other phases, as would be the case if a single-phase trans- 
former were used in each phase of the polyphase system. 

All that is necessary is to short-circuit the primary and second- 
ary windings of the damaged transformer upon itself, as shown 
in Fig. 71. The windings thus short-circuited will choke down 
the flux passed through the portion of the core surrounded by 
them, without producing in any portion of the winding a current 
greater than a small fraction of the current which normally 
exists at full load. 

With one phase short-circuited on itself as mentioned above, 
the two remaining phases may be reconnected in open delta in 


tee or in star-delta for transforming from three-phase to three- 
phase; or the windings may be connected in series or parallel 
for single-phase transformation. This method of getting over a 
trouble is only applicable where transformers are of the shell type. 

The relative advantages of the delta-delta and delta-star 
systems are still, and will always be disputed and wide open for 
discussion. They possess the following advantages and dis- 
advantages, respectively: 

Delta-delta (non-grounded). When one phase is cut out the 
remaining two phases can be made to deliver approximately 58 

Fig. 71. — Result of operating a delta-connected transformer with one 
winding disabled and short-circuited on itself. 

per cent, of the full load rating of transformer (in the case of a 
three-phase shell type) or three single-phase transformers. 

Delta-star (neutral grounded). Advantage of reducing the 
cost of high voltage line insulators for equal line voltage, which 
is a very large item when dealing with long-distance lines; their 
size need only be approximately 58 per cent, of that used on a 
line using the delta system. 

It is also possible, under certain conditions, to operate and 
deliver three-phase currents when one phase or one line conductor 
is on the ground. 

The disadvantages are: 

Delta-delta (non-grounded). Larger transformer or trans- 
formers and larger line insulators for the same line voltage. 

Delta-star (neutral grounded). Not always in a position to 
operate when one phase or one line conductor is cut out. 

Table I gives a comparison of the four common three-phase 




Star-delta to 

Star-star to 

to any 

Delta-star to 

Cheapest cost. . . . 
Best operated .... 
Least potential 









Cheapest Cost. — This represents the lowest price for transform- 
ers and system (complete) of equal kw. capacity and terminal 
line voltage. 

Best Operated. — All the star connections are assumed to have 
their neutral points grounded, and the generators in each case 
star-connected and grounded. Each case is figured to have 
either one line on the ground or one transformer or one phase 
disabled by a burnt-out unit or other fault. 

Least Potential Strain. — This represents the worst voltage 
strain that can be placed on the line and receiving station trans- 
formers, no matter what changes of phase relation might occur 
as the result of open connections, short-circuits or any combina- 
tion of these. 

It is quite evident that the delta-star to star-delta system is 
the best all round system to have. It will also be noted that 
this system takes a second place of importance in the " best 
operated" list, for the reason that a ground on one line short- 
circuits that phase whereas with the delta-delta to delta-delta 
(assuming all other phases thoroughly insulated which is almost 
a practical impossibility on high voltage systems) the system is 
not interrupted. Although a doubtful question it is placed in 
its favor, but beyond this weak point the delta-star to star-delta 
is equally as good and reliable as the delta-delta to delta-delta 
and about equally able to operate and furnish three-phase cur- 
rents with only two transformers. The right order of importance 
giving the best system is: 

First. Delta-star to star-delta. 

Second. Delta-delta to delta-delta. 

Third. Star-delta to any combination. 

Fourth. Star-star to any combination. 


Depending on the voltage and size of transformers the relative 
cost will vary, but the advantages given are about correct for 
almost all high-voltage systems. The same thing applies in the 
case of the best system for operation, but for general cases Table 
I list will be found to be close. In fact, if such questions as the 
third harmonics and the resulting flow of unbalanced currents 
in the closed delta-delta to delta-delta be considered, there is 
still something better in favor of the delta-star to star-delta 

An advantage somewhat in doubt is, that only one high- 
voltage terminal of a delta-star to star-delta system is subjected 
to the full incoming high-voltage surges, whereas the delta-delta 
system has always two or double the number of high-voltage 
transformer terminals connected to the transmission line, and, 
of course, almost double the chance of trouble due to high- 
voltage surges. Impulses coming in over a line will enter the 
high-voltage windings of transformers from both ends, and 
even though the effect be in some degree divided if, say, two lines 
are disturbed, it will not have the same total factor of safety as 
would the delta-star to star-delta system, which has the uninter- 
rupted facility of dividing the impulse between two transformer 
windings. The same impulse will also divide its effect between 
two or three transformer windings of a delta-delta system but 
not with the same effect because of the connections. 

In case one line terminal is disturbed by an incoming surge 
only one transformer winding of a delta-star to star-delta 
system is effected. The disturbance will, of course, be greater 
than that affecting a delta-delta system, but the difference will 
not generally be great enough to cause a break-down on one 
system and not on the other; in fact two transformer windings 
of a delta-delta system may, in the majority of cases, be injured 
to one of the delta-star to star-delta systems. 

Another very important advantage, particularly so where 
very high voltages are employed, not in favor of either the delta- 
delta or star-delta (delta on the high-voltage side) is that each 
transformer of a group of three has its winding terminals exposed 
to every line surge and consequently double the possibility of 
trouble that can occur on delta-star to star-delta systems (star 
on the high-voltage line side); also, the coils of a delta-delta or 
star-delta (delta on the high-voltage side) have a greater number 
of turns of smaller cross-section for a given kw. capacity and 


consequently are more liable to mechanical failure than a delta- 
star connected system (star on the high-voltage side). 

A further disadvantage of the high-voltage delta is that if it is 
thought necessary to ground the delta as a safeguard for high- 
voltage stresses, it will require a group of transformers with inter- 
connected phases or a star-delta connection; therefore additional 
apparatus is required whereas the delta-star system can be 
grounded direct without any additional expense. 

As regards some of the advantages of switching, the delta-star 
has a further advantage over the delta-delta. The delta-star 
(star on the high-voltage side or low-voltage side) can give claim 
to an advantage by its simple, effective and cheap arrangement 
of switches in all stations where it is found necessary to use air- 
break disconnecting or single-pole switches of any kind installed 
on each high- and low-voltage lead. Only two such switches 
instead of four per transformer are needed, the remaining two 
leads being solidly connected to a neutral bus-bar grounded 
direct or through a resistance as thought desirable. Its advan- 
tage in this respect is important on very high-voltage systems 
where stations are cramped for space; as an illustration of this 
take one three-phase group and we find : 

Twelve switches are required for a delta-delta group of three 

single-phase transformers. 
Nine switches are required for a delta-star group of three 

single-phase transformers. 
Six switches are required for a star-star group of three 
single-phase transformers. 
In this it is also well to remember that a spare single-phase trans- 
former arranged to replace any of the three single-phase trans- 
formers of the group, will require the same number of switches, or 
twelve, nine and six respectively. All the switching referred 
to here only holds good when the neutral point of the star is 

There exist a large variety of system connections quite different 
from the common ones mentioned above. For instance, it is 
not unusual now to see in one station a group of three single- 
phase transformers operating in parallel with two single-phase 
transformers, the two groups being connected in delta and open- 
delta respectively. It is well known that the open-delta system 
does not claim to possess any merits over any of the common sys- 
tems above mentioned, but it is oftentimes necessary to fall back 


on this system as a stand-by or in an emergency and from this 
point of view it becomes very useful. Now, in certain cases of 
station wiring layout, particularly in those stations operating 
above 50,000 volts, it might be only possible to use the delta 
connection for parallel operation after considerable loss of time 
rearranging the wiring. The wiring layout of a station, however, 
might be such with respect to the location of transformers that 
with a disabled unit of a group of three connected in delta-delta 
it would not be possible to connect the two remaining transform- 
ers in parallel and in open-delta with a group of three others 

A :b 

a b c 


A" B' 

Ua/^ Ivwl vvv" Iwv Iwv lw\^ Ivvvv V^/^^ 

. . (1) (2) (3) 

a' b' c' 

a b c 

j^c ^.' p> 

Fig. 72. — Correct method of connecting the transformers. 

located some distance away. Suppose for example that the 
station bus-bar wiring in the high- and low-tension bus-bar 
compartments is arranged to meet any delta and open-delta 
combination and that two groups of delta and one group of open 
delta-connected transformers have already been operating in 
parallel and suddenly one of the delta groups develops a burn-out 
on one transformer leaving two good units for further operation. 
The first question to be asked is — what is the best thing to do? 
Or, what is the best combination to make to be in a position to 
take care of the biggest amount of energy put upon the whole 
of the remaining transformers? If it is kept in mind that it is 
impossible to get any more than 80 per cent, of the normal output 
per unit when an open-delta group is operating in parallel with 
a delta group of transformers, it will be an easy matter to know 
just how to proceed. Just wha.^ can be done and what ought 
to be done are given in Fig. 72 and Fig, 73. Supposing groups 



No. 1 and No. 2 have been operating in closed delta and open- 
delta respectively and group No. 3 has j ust had a burn-out of one 
unit (see Fig. 72), it is quite evident that by connecting the three 
groups as shown more energy can be delivered than is possible 
with those connections shown in Fig. 73. In fact, it is possible 
to deliver more energy from six of the transformers shown in 
Fig. 72 than from the seven transformers with the connections 
given in Fig. 73. 


A' B' C 

A" B" C 

tvN/v4 U/VSaI IvvN/nI l/VwJ I'vA/vJ bsA/V^ WS'^S^ In/n/vJ 

a b c 

a' b' c' 

a" b" c" 

b \ b' l~ 

iS) ^c" 



Fig. 73. — Wrong method of connecting open-delta transformers in parallel. 

Single-phase vs. Three-phase Transformers. — As the art of 
transformer design and manufacture improves, the three-phase 
transformer is sure to be as extensively used as the single-phase 
transformer, especially so for high voltages; its only disadvantage 
being in the case of failure and interruption of service for repairs, 
but this will be offset by other important features since break- 
downs will be of very rare occurrence. 

From the standpoint of the operating engineer (neglecting the 
losses in the transformer) the single-phase transformer is at the 
present time preferable where only one group is installed and the 
expense of a spare unit would not be warranted as in the delta- 
delta system. If one of the three transformers should become 
damaged it can be cut out with a minimum amount of trouble 
and the other two can be operated at normal temperature on 
open-delta at approximately 58 per cent, of the total capacity of 
the three. With a three-phase transformer a damaged phase 
would cause considerable inconvenience for the reason that the 
whole transformer would have to be disconnected from the 



system before repairs of any kind could be made, which, in the 
case of a shell-type transformer, could probably be operated 
depending on the amount of damage, as it is not always possible 
to tell the exact extent of break-down before a thorough examina- 
tion is made. 

In the absence of any approved apparatus that can be relied 
on to take care of high-voltage line disturbances such as we 
have on some of our long-distance transmission lines, the whole 
burden being thrown on the insulation of this important link 
of a power undertaking, the three-phase transformer appears 
to be handicapped. Its break-down as mentioned above 
would entirely interrupt the service until a spare transformer is 
installed or the faulty one temporarily arranged with its faulty- 
short-circuited winding in the case of the shell-type. The en- 
gineer who has the responsibility of operating large power 
systems has not yet taken very favorably to the three-phase 
transformer for this very reason, his main object being reliability 
of service and not the first cost or saving of floor space. 

It has for many years been appreciated by American and 
European engineers that apart from the decrease in manufactur- 
ing cost with increase in size of units, the three-phase unit has 
the advantage of requiring less material and is more efficient 
than any other single-phase combination of transformers of the 
same kw. capacity. The relative difference in the losses and 
weights being: 

Three single-phase transformers weigh about 17 per cent, more 
than one three-phase. 

Three single-phase transformers have about 17 per cent, more 
losses than one three-phase. 

Used in open delta, two single-phase transformers weigh about 
the same as three single-phase transformers. 

Two single-phase transformers have about the same losses as 
three single-phase transformers. 

Used in tee, two single-phase transformers have a sum total 
weight of about 5 per cent, less than three single-phase 

Two single-phase transformers have the sum total weight of 
about 5 per cent, less than two single-phase transformers 
connected in open-delta. 

Two single-phase transformers have about 5 per cent, less 
losses than three single-phase transformers. 


Two single-phase transformers have about 5 per cent, less losses 
than two single-phase transformers connected in open-delta, 

Where a large number of transformers are installed in one 
building, say three groups or above, it is unquestionably a great 
saving over any combination of single-phase transformers, and 
the possibility of using two sets out of the three or three sets out 
of the four, and so on, offsets to a large extent the important 
drawback reliability, and places the three-phase transformer on 
almost an equal footing in this respect as the three single-phase 
transformer combination. The building is thereby reduced a 
considerable amount (also compartment insulator bushings and 
busbar high and low voltage insulators), besides simplifying the 
wiring layout in the stations. 

To fulfil the requirements of a three-phase transformer using 
a combination of single-phase transformers, it is necessary to use: 

Basis. — One three-phase transformer of 100 per cent. kw. 

Delta Connected. — Three of 33.3 per cent, each, or a total 100 
per cent. kw. capacity. 

Star Connected. — Three of 33.3 per cent, each, or a total 100 
per cent. kw. capacity. 

Open-delta Connected. — Two of 57.7 per cent, each, or total 
115.5 per cent. kw. capacity. (For three units, 173 per cent, 
kw. capacity is required.)* 

"Scott": "T" (Two-Transformer Connection).— One of 57.7 
per cent. kw. capacity, and one of 50 per cent, kw., or total 107.8 
per cent. kw. capacity. (For three units, 165.6 per cent. kw. ; 
capacity is required.)* 

"Taylor": "T" {Three-Transformer Connection).— Three of 
maximum 50 per cent, each, or total 150 per cent. kw. capacity. 

From this it is evident that the three best combinations are 
delta, star, and the three-transformer "T" connections. With 
the delta and "T" (three-transformer) systems a spare trans- 
former is not warranted, and in case of a break-down of a unit, 
the minimum amount of time is lost in cutting it out of service. 
With the open-delta and "T" (two-transformer) systems, the loss 
of any unit stops the system from operating three-phase current. 
A further advantage of the three-transformer methods — delta, 
star, and "T "-three transformer — is, a spare unit costs less than 
one for either the open-delta or the "T"-two-transformer methods. 

* Not always in service, hence a disadvantage. 



In Fig. 74 several methods are shown for grounding three- 
phase systems. For (A) and (B) there is a choice between the 
ground shown, or the ground at x. For (A) the ground as shown 

Fig. 74. — Method of grounding three-phase systems. 

represents a maximum difference of potential between ground 

and line terminal of —t~ E, and — y^ E for the ground at x. 

For {B), the maximum voltage stress from line terminal to 
ground is full-line voltage, but with a ground made at x the 



maximum voltage stress is only approximately 87 per cent, of 
full voltage between terminals. 

The delta-star system shown at (c) of Fig. 74 is the most 
uncommon of any of the systems given. Like (A'), three single- 
phase windings are required before grounding can be made 
possible. The maximum voltage strain from any line terminal 
to ground is E' + (0.57 E), or assuming E = 100, and E' = 100, we 
have 100 + (0.57 X 100) = 157 volts maximum strain from neutral 
ground to star-line terminal. 

The diagrams of (A'), (B') and (C) of Fig. 74 represent the 
two well-known systems and their three methods of grounding. 
The two best methods for grounding are (A') and (B'). The 
method (C) is used only where auxiliary apparatus cannot be 
had for grounding through the star connection. 

The delta and star systems shown at (B") and (C") represent 
systems grounded as shown at (A') and (B') but with one high- 
voltage terminal grounded. For (A") the system is insulated 
with the exception of ground at high-voltage line terminal. 
Both B" and C" show the effects of grounding either the low 
voltage or high voltage or both. Where both neutral points 
are grounded, the high-voltage stresses on the low-voltage 
windings when an accidental ground occurs on the high-voltage 
side is reduced to a minimum, but is of maximum value on sys- 
tems operating without grounded neutrals. 

Three-phase to Single-phase Transformation. — An interesting 
three-phase to single-phase arrangement is given in Fig. 75. 
For this service three single-phase transformers or their equiva- 
lent (somewhat special in their construction) are required, the 
magnetizing current being much stronger than that used in the 
ordinary static transformer in order that the iron may be super- 
saturated. This modification will result not only in satisfactory 
transformation of voltage and current, but transformation of 
the frequency as well. 

With three transformers connected as shown in Fig. 75, the 
secondary windings would under ordinary conditions show no 
e.m.f. across A-C; but if the iron is saturated the secondary 
becomes so transformed that an e.m.f. is obtained having 3f or 
three times the frequency of the primary. 

The advantage of this arrangement is felt where arc and incan- 
descent lighting is required and where the frequency is 15-25. 
The constant extension of electric traction on railways operating 


at these frequencies has resulted in the use of polyphase lamps and 
the triple frequency transformer arrangement. Single-phase 
railways are much more general than three-phase, and, therefore, 
it is really more important to be able to increase the frequency 
of single-phase than of three-phase current. 

Also, in general, three-phase high voltages and energy are 
transmitted long distances to electric traction plants at a fre- 




Frimary A' 

■^E^-A *— ^"-^ -" — E^ 

^v^Sv^ Uv^^/sl ^^^v^ ^ 

p^ p^ p^ "-^M\ y 


Fig. 75. — Method of transforming from three-phase to single-phase and 
changing the frequency. 

quency of 60 cycles. It is therefore important from several view- 
points to be able to transmit electric energy at, say, 60-?- 3 = 20 
cycles and single-phase; thus reducing the voltage drop due to 
the higher frequency, and reducing cost of line construction, 
insulators and its maintenance in general. 



Most of the troubles which occur on transmission systems are 
put down to line surges, resonance, or some unknown phenom- 
enon on lines, and as a matter of fact most of the troubles 
might be in the transformers themselves, which may be damaged 
and their phase relations twisted so as to produce, in some in- 
stances, many times the normal voltage. 

The most disastrous troubles that can happen to a three-phase 
system are those of complex grounds and short-circuits. Witli 
a grounded neutral star system, a ground on any one phase is a 
short-circuit of the transformers, and the entire group becomes 
disabled until changes are made. 

^ <-4000 


< 4000- 






-600CO > 

-60000^ ^60000-^ 

< 60000 

Fig. 76. — One transformer short-circuited and cut out of delta. 

The voltage between windings and the core is limited to 57.7 
per cent, of that of the line, and the insulation between the 
windings and the core is likewise reduced in proportion. The 
voltage between mains and the ground is 57.7 per cent, of the 
line voltage, with a star connection, but the neutral point may 
move so as to increase the voltage with an ungrounded system. 
If one circuit is grounded, the voltage between the other two 
circuits and the ground is increased, and may be as great as the 



full line e.m.f. Such unbalancing would cause unequal heating 
of the transformers and if a four-wire three-phase system of 
distribution were employed, would prove disastrous to the regu- 
lation of the voltage. 

With a star-delta system as shown in Fig. 76, where a trans- 
former is short-circuited and cut out of delta on the secondary, 
it is possible to obtain V 3 times the potential of any one of the 
transformers. In Fig. 7Q A B C represents the vector triangle 
of e.m.fs. on the primary with full line voltage or 4000 volts, 
impressed on the transformers, which under normal conditions 
should be 

4000 X— 7= = 2300 volts. 

The phase relations are changed to 60 degrees, converting 
the original star arrangement to an open delta; one phase is 

Fig. 77. — Primary e.m.fs. and phase relations. 

reversed, the resultant e.m.f.being the same as that across any 
two phases. See also vector diagram. Fig. 77. 

As each transformer is only designed for 2300 volts the e.m.f. 
across the secondary windings should be 34,600 volts, but in this 
case the voltages are 34,600 times V 3 or 60,000 volts. 

The secondary vector e.m.fs. are graphically represented to the 
right of Fig. 76. In order to bring the resultant vector secondary 
e.m.f., a and c, in its proper position the components must be 
drawn parallel with the primaries. 

One secondary winding is short-circuited and cut out of delta 
leaving an open-delta connection reversed in direction, its phase 
relations being changed from 60 to 120 degrees: increasing the 
voltage between a and c to 

34,600X1732X1732=103,557 volts. 
or\/3X\/3X34,600= 103,577 volts. 


This is a very important point to bear in mind, especially 
when generators are tied directly to the system without fuses or 
any protecting devices. 

The voltages impressed on the primary windings of Fig. 7G 
and 77 are: 

Aand B = 4000 volts, 
5 and C = 4000 volts, 
A and C = 4000 volts. 
E.m.fs. between the primary neutral and any line, are: 
A &nd A' = 4000 volts, 

which should be 6000X0.577 = 2300 volts; 
B and S' = volts, 

which should be 2300 volts; 

C and C = 4000 volts, 

which should be 4000X0.577 = 2300 volts. 
The e.m.fs. between the secondary lines, are: 
a and 6 = 60,000 volts, 

which should be 60,000X0.577 = 34,600 volts; 
& andc = 103,577 volts, 

which should be 103,577^2.99 = 34,600 volts; 
a and c = 60,000 volts, 

which should be 60,000X0.577 = 34,600 volts. 
The increases in e.m.f. across the secondary lines, are: 
a and c = 173 per cent, above normal, 
b and c = 300 per cent, above normal, 
a and & = 173 per cent, above normal. 
It is also found that where the neutral points of the primary 
and secondary windings are grounded, the opening of one or two 
of the three line circuits will cause currents to flow through the 
ground. A partial ground on a line circuit will partially short- 
circuit one transformer and cause current to flow through the 
ground and the neutral. 

The actual strain between high-tension and low-tension wind- 
ings is equal to the high-tension voltage plus or minus the low- 
tension voltage, depending upon the arrangement and connection 
of the coils; but as the low-tension voltage is usually a small per- 
centage of that of the high-tension, it is customary to assume 
that the strain between windings is equal to that of the high- 
tension voltage alone. 

If the neutral points of the high-tension and low-tension 
windings are grounded, the iron core being also grounded, then 



as long as the circuits are balanced the voltage strains will be the 
same as with the windings ungrounded, and balanced; but in 
case of a ground on either high-tension or low-tension line, or in 
case of a connection between high-tension and low-tension wind- 
ings, a portion of the windings will be short-circuited. 

Assuming that all lines and transformers are in good shape, 
that is to say, clear from grounds and short-circuits, it is possible 
to obtain any of the following results shown in Figs. 78, 79, 80 and 
81, by connecting the receiving ends of transmission lines to a 
wrong phase terminal receiving three-phase current from another 
source of supply, or by switching together groups of two or more 
transformers of the wrong phase relations. 

Fig. 78. — Re.sultant e.m.fs., and phase relations of improper delta-delta 
and star-star connected group of transformers. 

Fig. 78 represents the result of a delta-delta and star-star 
combination thrown together at 120 degrees apart, both trans- 
mission lines receiving three-phase currents of the same potential, 
phase relations, and frequency. 

The resultant voltage obtained in attempting to parallel two 
groups of three transformers star connected is \/^ times the 
e.m.f. between any two line wires, or 

Star = (57.7 X 1.732 = 100) X (1.732) = 173.2 volts. 

The combination shown in Fig. 79 represents four groups 
(three single-phase transformers in each group) connected to one 
set of busbars. Each group receives three-phase current from 
independent source of supply and is so tied in on the primary 
and secondary busbars as to involve a partial short-circuit. 

In common practice this combination is more often likely to 
happen on large distributing systems where all transformers in 



groups are tied together on primaries and secondaries. As wih 
be noticed, any attempt to connect such a system with all pri- 
mary windings and all secondary windings of each group in 
parallel will produce a short-circuit. 

Fig. 79. — Representation of a complete combination of delta-delta and 
delta-star transformer group connections. 

Figs. 80 A and B. — Graphic illustration of e.m.fs. and phase displacement 
of two delta-delta to delta-star connected groups of transformers. 

With a delta-star presupposed parallel operation it is impos- 
sible to change the magnetic field to correct the phase displacement 


which occurs, though it is possible in the case of generators which 
are necessary for permitting the 30 degrees electrical displace- 
ment to be corrected by a mechanical twisting of the phases with 
respect to their magnetic fields; but with transformers it is 

The phase displacements show a star connection introduced in 
which the relative e.m.f. positions are changed by an angle 30 
degrees. If, for example, we assume the line potential to be 
60,000 volts, and we attempt to connect the groups as shown in 
diagram, the result will be voltages as high as 116,000. 

Fig. 81. — E.m.fs. and phase relation of a delta-delta to delta-star connected 
group of transformers. 

The resultant e.m.fs. established by this experiment, are shown 
separately in Figs. 80 and 81. They are correctly: 

B" to B = 84,840 volts, which should be = 

B'' to C =116,000 volts, which should be =60,000 
A" to C =116,000 volts, which should be =60,000 
A'' to B =116,000 volts, which should be =60,000 
A' toB = 84,840 volts, which should be =60,000 
A' to C = 31,000 volts, which should be =60,000 
C to B =116,000 volts, which should be =60,000 
C to B =116,000 volts, which should be =60,000 
C to C = 84,840 volts, which should be =60,000 
B'" to B = 31,000 volts, which should be = 

B"' to ^ = 31,000 volts, which should be =60,000 
A'" to A = 31,000 volts, which should be = 

A"' to B = 84,840 volts, which should be =60,000 
A fact not very well recognized, is the impossibility of parallel- 
ing certain primary and secondary three-phase systems. The 
following combinations can be operated in parallel: 



Delta-star group with a delta-star. 
Star-star group with a star-star. 
Delta-delta group with a delta-delta. 
Star-delta group with a star-delta. 
Delta-star group with a star-delta. 
Star-star group with a delta-delta. 

Fig. 82. — ^Practical representation of a delta-delta to delta-star connected 
group of transformers. 

These delta-star combinations necessitate changing trans- 
former ratios of primary and secondary turns, as: 
Delta-star is a constant of VS =1.733 to 1. 

Star-delta is a constant of — ;= =0.577 to 1. 


consequently, special ratios of secondary to primary turns are 
needed in delta-star or star-delta transformers, in order to pro- 
duce standard transformation ratios. 

As already explained, displacement, of phase relations occur 
on the secondary side of transformers when two or more groups 
are connected delta-delta and a delta-star; the delta-delta having 
a straight ratio and the delta-star a ratio of 1 to 0.577; or any 
of the following combinations: 

Delta-star ratio —= to 1^ and star-star with ratio 1 to 1, or 

any ratio. 

. 1 
Delta-delta, ratio 1 to 1, with a star-star ratio ~;Eto 1, or any 




Star-delta, ratio 1 to —-^, and star-star with ratio 1 to 1, or 


any ratio. 

The phase relations occupy a relative shifting position of 30 
degrees on one group of transformers to that of the other. A 
more practical representation of the secondary voltages and 
phase relations of a delta-delta and delta-star is shown in Fig. 82. 

In order to tie in a large number of local existing plants con- 
sisting of gas, steam and water-driven generators, etc., with two- 
and three-phase distributing systems, special care and thought 
are required in laying out the right scheme of connections. One 
sometimes meets with a two-phase three- and four-wire distri- 
bution and several other kinds of systems of odd voltages and 
frequencies which must be tied in on the main high-voltage trans- 
mission system through transformers (and probably frequency 
changes), all of which requires special knowledge on the part of 
those whose duty it is to operate them. 

Consolidated systems of this kind generally have to contend 
with parallel operation of local power plants, this sometimes 
being done directly from the high voltage side or line side of the 
power transformers for voltages as high as 60,000 volts, by the 
application, of potential transformers. Only a small number 
use this method of synchronizing their auxiliary stations and it 
is not considered good practice. 

Before parallel operation of any kind is done it is always 
advantageous to know all about the connections and voltages of 
the different transformer groups. With the delta and star 
systems it is (as has already been explained) only possible to 
parallel six combinations out of the ten so commonly used. Of 
these six combinations the transformers to be paralleled must 
have equal impedance and equal ratio of resistance to impedance. 
With equal impedance the current in each unit will be in propor- 
tion to their rated capacity in kw.'s, although the sum of the 
currents may be greater than the current in the line; if, on the 
other hand, the impedance of the units is unequal, the current 
in each unit will be inversely proportional to its impedance; that 
is to say, if one unit has 1 per cent, impedance and the other 2 
per cent, impedance, the first unit will take twice as large a per 
cent, of its rated capacity as the second unit — the sum of the 
currents in the two units may be or may not be equal to the line 
current. With equal ratios of resistance to reactance the current 



in each unit will be in phase with the current in the line, also the 
sum of the currents will be the same as the line current. With 
unequal ratios of resistance to reactance the current in each unit 
will not be in phase with the current in the line, therefore the 
sum of the currents will be greater than the line current. If, 
however, the impedance of the units is the same, both will 
carry the same per cent, of full-load current; and if, in addition, 
the ratio of resistance to reactance is the same in both cases, the 
current in the two units will be in phase with each other, and 
their numerical sum will equal the load current, thus there will 
exist perfect parallel operation. 



l^'V^V. ^>N^^ j^S.^^ f^ ^"^^ 

& \o c\ \a a\ b c\ a 6 

Fig. 83. 

Whatever scheme of transformers is decided on for a given 
system it will always be advisable to keep to that scheme if 
possible; this is particularly applicable on some of the larger 
systems of 100 megawatts and over where networks of high- 
voltage transmission lines and sub-stations are numerous. 

Quite a number of systems have distance sub-stations with 
only two groups of transformers, both groups being operated in 
parallel at all times. Assuming the transformers to be con- 
nected in delta-delta and one transformer of one of the groups 
becomes damaged, it might mean, if the load is great, that at 
least one of the other group must be cut out. If the load is not 
greater than 80 per cent, of their total rating it will be possible 
under ordinary circumstances to operate the closed delta group 
with the open-delta as shown in Fig. 83. 

It is not generally known that there are sixteen different con- 
nections on one transformer star-connected group, and that these 
connections can be changed about to obtain several parallel 
combinations, such as those shown in Fig. 84 giving the time- 
phase of 0, 30, 60, and 90 degrees (electrical). 


Primary Conaection of 


Secondary Connection of 

In Phase 


60 degrees out of 

bt-- — 



30 degrees out of 


90 degrees out of 

Fig. 84. 




Not including the straight star or delta connection with a 
time-phase angle equal to zero, we find that there are no less than 
three different groups such that transformers belonging to the 
same group can be connected in parallel, while if of different 
groups, no parallel connection is possible without a special 
rearrangement of the internal connections of the transformers. 

Fig. 85. — High-voltage line grounded, producing maximum strain on low 
voltage windings. (Neutrals non-grounded.) 

The troubles usually experienced with high-voltage trans- 
formers can be classified as: 

(a) Puncturing of the insulation between adjacent turns due 
to surges, etc. 

(6) Shifting of coils duo to switching on and off very heavy 

(c) Terminals puncture (transformer insulator bushing and 
other leads), due to either (a) or (b) or both. 

There are a large number of causes for transformer break- 
downs, some of them being : 

(1) Insufficient insulation between layers and turns. 


(2) Insufficient insulation on the end-turns. 

(3) Electromagnetic stresses too great. 

(4) Electrostatic capacity of certain parts too high. 

(5) Condenser effect between coils, and between windings and 
ground too high. 

(6) Improper drying out after construction. 

(7) For want of a choke coil or reactance in series. 

(8) Concentrated condensers in parallel with transformer 




^vA^N^ Un^'V^V/^ t'-N/S^.^ 



-Ey — ^^e- 

—E^A^JJ, \ 1 

Fig. 86. — Showing the effect of grounding the low-voltage neutral. 

(9) Two or more of the above in connection with concentrated 

(10) Internal short-circuits. 

(11) Conditions of switching, surges, arcing grounds, lightning, 

(12) Improper treatment of the oil. 

(13) Oil not suited to the transformer. 

(14) Thickening of oil and clogging of cooling medium stopped. 

(15) Leaking water-coils, or, circulation of cooling medium 

(16) Breathing action (prevalent in damp localities). 


(17) Improperly installed protective apparatus. 

(18) High winds which bring live conductors in oscillation. 

(19) Defective governors or prime-movers. 

(20) Variation in speed of generators. 

(21) Variation in generator voltage. 

(22) Roasting by constant over-load. 

(23) Puncturing of transformer terminals. 

(24) When transformers are connected to generating stations 
and systems and bus-bars having a total kw. capacity many 
times greater. 

Figs. 85, 86, and 87 show other causes for break-downs in high- 
voltage transformers. Three different conditions of operation 
are given; one for an insulated delta-delta system showing the 
effects of a grounded live conductor, one for a delta-delta system 
with the neutral point of low-voltage windings grounded, and the 
other for a delta-delta system with both high- and low-voltage 
windings grounded. The approximate maximum potential 
strains are shown by the vector relations. These serve to show 
other greater difficulties which receiving-station transformers 
are subjected to in addition to those usually impressed on the 
transformers at the generating stations. 



With two or three single-phase transformers it is possible to 
have three-phase primaries with two-phase secondaries, or vice 
versa. For long-distance transmission of electric power the 
three-phase system is universally adopted because it requires 
less copper for the line than either the single-phase or the two- 


Uy^(\ri l/N/vvJ U./>^saI 

i^'iddc kiac 




Fig. 87. — This shows the effect of grounding both the high- and low- 
voltage neutrals, resulting in minimum voltage strain. 

phase systems to transmit a given amount of power with a given 
line loss, and with a given line voltage. The two-phase system 
offers certain advantages over the three-phase system when 
applied to local distribution of electric power. 

In Fig. 88 is shown the well known three-phase three-wire to 
7 97 



two-phase four-wire transformation. Two transformers are all 
that is necessary in this arrangement, one of which has a 10 to 

1 ratio and the other a 10 to 0.866. or 10 to^. 

Fig. 88. — The three-phase two-phase connection* (Scott system). 

One wire, 6, of the 10 to 0.866-ratio transformer is connected 
to the middle point of the 10 to 1 ratio transformer, the ends of 
which are connected to two of the three-phase mains, a c; d, the 


-1732 — >< — ^1732 




!!!4 ^'H 




Fig. 89. — Three-phase to two-phase star-connected transformers. 

end of the other transformer is connected to the remaining wire 
of the three-phase mains. 

It is customary to employ standard transformers for the three- 
phase two-phase transformation, the main transformer having a 
ratio of 10 to 1, and the other transformer a ratio of 9 to 1. 

* Patent No. 521051, June 5th, 1894. 



Hy a conibination of two transformers it is possible to change 
one polyphase system into any other polyphase system. 

The transformation from a three-phase to a two-phase system 
may be effected by proportioning the windings, as shown in 
Fig. 89. The three transformers are wound with a ratio of 
transformation of 10 to 1. The secondaries of two of the trans- 
formers have two taps each, giving 57.7 per cent, and full voltage, 
so that they serve as one phase of the two-phase transformation. 
The primary windings are connected in star. 

The secondary windings are also connected in star. In Fig. 
89, & 6' represents the secondary voltage from b to b' in one trans- 




TnnjTnn nnnnnri rsr\jw 








FiG. 90. 

former. At an angle of 90 degrees to 6 6' the line, a a', represents 
in direction and magnitude the voltage, a to a', which is the 
resultant of the two remaining transformer e.m.fs., giving 577. 
per cent, of the full voltage, 57.7 X\/3 = 100. From the prop- 
erties of the angles it follows that, at the terminals, a a' and b b' , 
two equal voltages will exist, each differing from the other by 
90 degrees, and giving rise to a two-phase current. 

Still another method of getting two-phase from three-phase, 
or vice versa, consists in cutting one phase, say (Fig. 90) the 
middle transformer of the delta-connected group, in half, and 
arranging one-half to the left at 6' c, and the other half to the 
right at 6" a. 

The resultant of a b' and &' b is one side, or one phase of the two- 
phase transformation. 

The resultant of a b" and b"c, is the other phase of the two- 
phase transformation. 



It is evident as shown in Fig. 90 that the two-phase relation 
is a trifle over 90 degrees; since the angle, 6 b" x and b b' x, is 

60 degrees, and the sine of 60 degrees is equal to 


0.866. the 


tangent of the angles, b c x and b ax, are likewise -^^=0.866. 

Therefore, the angle, ab c, must equal 90 degrees nearly. 

The angle, b c a, whose tangent is 0.866 is an angle of 40.67 

degrees; therefore, 

(6 ca; = 40.67) + (& a a; = 40.67)+ (a 6 c = 98.66) =40.67 + 40.67 + 

98.66 = 180 degrees, nearly. 

The approximate voltage obtained between c 6 and fe a is 133 


Fig. 91. — Three-phase to three-phase two-phase* (Steimnetz system). 

With two or more transformers it is possible to transform from 
three-phase to two distinct phase currents of three-phase and 
two-phase systems. In the arrangement shown in Fig. 91 only 
two transformers are used. The two primary windings are con- 
nected to the three-phase mains. One transformer is wound 
with a ratio of transformation of 10 to 1. The other with a 
ratio of 0.866 to 1. The primary and secondary windings of this 
transformer are connected to the middle of the primary and 
secondary windings, respectively, of the first. 

a b represents the secondary voltage from a to 6 in one trans- 
former. At right angles to a 6 the line, x c', represents in direc- 
tion and quantity, the voltage, x to c', of the second transformer. 

* Patent No. 809996, January 16th, 1906. 


At the terminals, ab c, three equal voltages will exist, each 
differing from the other by 60 degrees, and giving rise to a three- 
phase current. 






\' n u 


<— hco— J 





FiG. 92. — Three-phase "T" to two-phase four-wire. 

It also follows that, at the terminals a b and x c', two equal 
voltages will exist, each differing from the other by 90 degrees, 
and giving rise to a two-phase current. As will be noted, the 











Fig. 93. — Three-phase open delta to three-phase two-phase (Taylor system). 

voltages obtained in the three-phase side are equal to those 
between any phase of the two-phase system. 

The arrangement in general is similar to that of the ordinary 
"V" or open-delta system. 



Another combination somewhat similar to the above is shown 
in Fig. 93. The primary windings of the two transformers are 
connected in open-delta. The secondary windings are connected 
in such a manner as to give two distinct phase currents; one 
kind differing in phase by 90 degrees, and the other by 120 
degrees. From one secondary winding two special taps of 50 
per cent, and 86.6 per cent, are brought out to complete the 
circuits of three-phase and two-phase secondary. By this 
method of connection it is possible to obtain two-phase currents 
from A A' and B B' , also three-phase currents from x A' , A' B, 
and B x, the two-phase e.m.fs. will be 86.6 per cent, of those of 
the three phase. 

The method shown in Fig. 94 is a device patented by the writer, 

Fig. 94. — Three-phase delta to three-phase two-phase* (Taylor system). 

and employed to operate both two-phase and three-phase electric 
translating devices, on one four- wire system of distribution; and 
to operate independent systems in parallel circuit on said four- 
wire system. 

Three single-phase transformers are used. The primary wind- 
ings are shown connected in delta, and the secondary windings 
also connected in delta. A distribution line, 7, tapped at the 
middle of the secondary winding, 2a; a distribution line, 8, tapped 

\/3 • . 

at -— - per cent, of the length from one end of the wmdmg, 3a; a 

distribution line, 9, tapped on the connection between the end 

windings, 2a and 3a; a distribution line, 10, tapped at -—- per 

* Patent No. 869595, October 29th, 1907. 



cent, of the length from the end of windhig la, and translating 
means connected on said distribution lines both for two- and 
three-phase on. 

At la, 2a and 3a are the secondary windings of said trans- 
formers. The secondary winding, la, is tapped at D, which is 
about 86.6 per cent, of its length, by the line, 10; which serves also 
as a leg for both the two- and three-phase circuits. 

The secondary winding, 2a, is tapped at its central point A, by 
a line, 7 ; forming one leg of the two-phase circuit. The secondary 
winding, 3a, is tapped at approximately 86.6 per cent, of its 
length from one end, at about the point, B, by a line, 8, to serve 


\ 1 , I i ^ ft^ 

Fig. 95. — Three-phase to two-phase, giving 86 per cent, standard trans- 
former taps. 

as one leg of both the three- and two-phase circuits. C represents 
the point of a tap taken from the junction of two secondary 
windings which are shown connected in the series circuit, 
which serves as another leg for both two- and three-phase 

The arrangement accomplishes the operating of non-synchro- 
nous apparatus of two-phase and three-phase design without 
the aid of transformers or split-phase devices. The operation 
consists in generating three-phase alternating currents in the 



lines, 4, 5 and 6, transforming the same into three-phase cur- 
rents in the legs, 8, 9 and 10, and into two-phase currents in 
the legs, 7, 8, 9 and 10; and in operating translating devices 


< E > « E > 

^^A/wJ IAAW\ 



< e' > 

Fig. 96. 

at G and H in parallel with the two- and three-phase current 
circuits. The two-phase windings used on the motors must be 







-1000 — > 


Fig. 97. 

independent as the interconnected type of winding would not 
operate on this system, 

A three-phase single-phase transformation is shown in Fig. 98. 



The objection to this connection is the distorted effect of the 
relative voltages and phase relations of the three-phase when a 
single-phase load is put on one of the phases. To obviate this to 
some extent it would be necessary to give the three-phase voltage 
a slight distortion. The unbalanced voltages and phase relation 
when a single-phase load is applied is shown by the vector in Fig. 
98, it having the effect of twisting the phase relation when a load 
is applied between b-c from a symmetrical point as shown at the 
point a'. 


-1000 — >- 

< 1000 — ^ 

Vv/VwJ \AA/v/W 

/S^V^ /S^>s.^ 




FiG. 98. — Three-phase to 







fToooD"! nmm 



FiG. 99. — Another three-phase single-phase secondary operation. 

It is possible to take currents from a three-phase system 
and transform them into a single-phase current (see Fig. 99). 
All that is necessary is to arrange two transformers so that 
their connections are identical with the ordinary two-phase to 
three-phase transformation, the only difference being in the 



secondary, which has the two windings connected in series for 
supplying a single-phase circuit. 

In the ordinary three-phase to two-phase transformation, the 
two components in each half of the winding differ in phase by 90 




" Steinmetz ' 




Fig. 100. 

Two-phase transformer windings. 
Transformer windings. — 

Resultant two-phase voltages. 
Resultant three-phase voltages. 

degrees. However, when the secondary circuits are connected 
in series, these two component currents are of one phase. 

The maj ority of three-phase two-phase transformer connections 
employed are for temporary or special purposes. This is particu- 

FiG. 101. — Combination of systems given in Fig. 100. 

larly so when only two transformers are used. The systems used 
in Europe and America are shown in Fig. 100, in the form of 
vectors. In comparing these various systems by means of the 
Vectors given, it is very interesting to note how near they are to 



being one and the same thing. The relations are about the same 
but the transformers in each case are connected quite dififerently. 
The combinations are shown in Fig. 101. In (^1) the Meyer 
and Steinmetz are combined into one; in (B) the Arnold and 
Steinmetz are combined, and in (C) the Scott and Taylor systems 
are shown combined into one. All of the systems given here 
serve to show their likeness and are interesting to all those who 
might be in need of emergency substitutes. 


Figs. 102 and 103. — Other three-phase two-phase methods using standard 


Besides these systems given in Figs. 100 and 101 there are 
other connections of less value but nevertheless important in 
that they might be found useful in some particular instant of 
break-down of existing apparatus, or for temporary purposes. 
These are shown in Figs. 102 and 103, where (a) is composed of 
two single-phase transformers of 10 to 1 and 9 to 1 ratio 
respectively, or of two 10 to 1 ratio transformers, one of the 
transformers being tapped at the 9 to 1 ratio point and connected 
to the 50 per cent, point of the other transformers. (6) is the ordi- 
nary delta connection with the two halves of one winding or 
one single-phase unit reversed, (c) is the ordinary delta system 
with taps taken off as shown, (d) is the ordinary star with one 
transformer secondary winding cut into three equal parts, (e) 
is a "distributed" star, 1-1 a, 2-2a and 3-3a representing three 


single-phase transformers with winding cut into two equal parts 
and connected as shown. (/) is a star connection with one trans- 
former winding reversed, (g) is an ordinary open-delta connec- 
tion. With the exception of (a) and (g) which consist of two 
single-phase transformers, all the others are three-phase two- 
phase combinations using three single-phase transformers. 

By the use of transformers other than standard ratios and 
design, the three-phase two-phase transformer combinations 
shown in Fig. 104 can be made. 



In transforming from three-phase to six-phase there are four 
different ways of connecting the secondaries of the transformers: 
namely, diametrical — ^with or without the fixed neutral point; 
double star; double delta; and double tee. In the first three cases 
the primaries may be connected either star or delta, according to 
the voltage that each winding will stand, or to obtain a required 

Fig. 104. — Three-phase to two-phase using special transformer tops. 

secondary voltage. In the last case, the primary windings are 
connected in tee. 

For the diametrical connection three single-phase transformers 
may be used with one central tap from each transformer second- 
ary winding, or there may be six secondary coils. For the 
double-star or double-delta connection two independent second- 
ary coils are required for each transformer; the second set are all 




reversed, then connected in a similar manner to the first set. 
Hence, the phase displacement is shifted 180 degrees. 

For the double-tee connection two single-phase transformers 
are required, one of which has a 10 to 1 ratio and the other a 10 

to 0.866, or 10 to ^ ratio. 

There are two secondary coils giving 10 to 1 ratios, and two 
giving 10 to 0.866 ratios. 

In six-phase circuits there are coils with phase displacements 
of 60 degrees; each coil must move through 180 electrical degrees 
from the position where the current begins in one direction, before 

Fig. 105. — Six-phase diametrical e.m.fs. and phase relation. 

the current begins to reverse. Hence, for the double star, 
diametrical, double delta and double-tee connections if the ends 
of the transformer coils are reversed, the phase displacement of 
the e.m.f. is in effect shifted 180 electrical degrees. 

Take, for instance, the e.m.fs., a a', hh' and c c' , as graphically 
explained in Figs. 106 and 107, for a diametrical connection they 
are equal io 2 a x, 2 h x, 2 c x, etc. 

For double-star connection: 

a ¥, h' c, c a, etc., is V 3 times x a, x h' , x c, etc. 

For double-delta connection: 

xa, x b', X c, etc., is —7- =0.577 per cent, of a h' , h" c, c a, etc. 
For double-tee connection: 


a b', ¥ c, c a, etc., is 13.3 per cent, more than a' y, or a z. 

The general statement of relationship between e.m.fs. in Fig. 
106 may demonstrate that if the value of a a', etc., is represented 
by the diameter of a circle, the values of a' h, etc., are repre- 



l^\[ *-^^ 

^^^ ^1^ f 

\ ^V. ^'**S^ 

.^^ .^^ / 

\ ^s^^ X. 

,/y^ J 


i\ — . * / 1/ 


\^s^ / 

\ ^^^ 

\ ^Sw/ 

"^^^ ^ 

\ /^\^ 

^^\ / 

\ / ^^ 

^^ \ / 

2 A y 

<^ / 

^^^. / ^ 

V- \y^ 

^^^^^/ ^ 


* / 

___——_ — ^__ — 


Fig. 106. — Six-phase e.m.fs. graphically represented. 

sented by a 120-degree chord, and the values of a 6, etc., are 
represented by a 60-degree chord of the same circle. 

If the voltage between, a 6, etc., is not required, only three 
secondary coils are needed; but if this voltage should be required, 

| < 1 000—^ <= 1000 — »■ < — looo — ^ 







Fig. 107. — Six-phase diametrical connection. 

then six secondary coils are needed, or three coils with a center 
tap like that shown in Fig. 107. The diametrical connection of 
transformer secondaries as represented in Fig. 107 is the most 
commonly used of any three-phase to six-phase transformations. 
One secondary coil on each step-down transformer is all that is 



necessary; whereas the double-star, double-delta, and double-tee 
connections require two secondary coils, and therefore four 
secondary wires for each transformer. 

The two secondary wires from each transformer are connected 
to the armature winding of a rotary converter at points 180 degrees 
apart — such as shown at a a' , b h' , c c' ; therefore, arrangements 
for the diametrical connection are much simpler than any of the 

A part of the three-coil secondary diametrical connection may 
be used for induction-motor service to start the rotary converter. 




Fig. 108. — Six-phase diametrical connection with five-point switch used in 
connection with motor for starting synchronous converters. 

and when sufficient speed is obtained the motor may be cut out 
of service. The arrangement is shown in Fig. 108. By means of 
this connection, which is made through the introduction of a 
five-pole switch, a three-phase e.m.f. may be obtained, giving a 
value equal to half the e.m.f. of each secondary winding times 
V 3. That is to say, if half the e.m.f. of each secondary winding 
is equal to 50 volts, then assuming the switch to be closed, we 
obtain 50X\/3=86.6 volts. 

Similar ends of the three windings are connected to three points 
on one side of the five-pole switch. The three wires on the other 


side of the switch are led off to the three-phase motor service. The 
two remaining points of the switch receive three wires from the 
neutral points of the three secondary windings. Connections are 
so made that when the switch is closed a star-connection is 

With the double-star arrangement of secondary windings, 
shown in Fig. 109, a rotary converter may be connected to a given 
three of the six secondary coils, or one rotary may be connected 
to the six secondary coils. The disadvantage of star connection 
is that in case one transformer is burned out, it is not possible to 
continue running. 

—1000 — -*p-- 1000 — -^ — ^1000 — > 

Fig. 109. — Six-phase double-star connection. 

An arrangement for six-phase transformation is shown in Fig. 
1 10, which differs from that of Fig. 109 in that the middle point of 
each transformer winding is tied together to form a neutral point 
for the double star combination. 

It is common practice to connect the neutral wire of the three- 
wire, direct-current system to the neutral point of the star 

It may be seen that the similar ends of the two coils of the same 
transformer or similar ends of any two coils bearing the same 
relation to a certain primary coil are at any instant of the same 

The double-delta secondary arrangement should preferably be 
connected delta on the primary, as it permits the system to be 
operated with only two transformers, in case one should be cut 
out of circuit. 




One set of the three secondary coils is connected in delta in the 
ordinary way, but the leads from the second set are reversed and 
then connected in a similar manner. 

It can be seen from Fig. Ill that two distinct delta connections 
are made, and in case it is desired to connect the six leads, ab c- 
a' h' c' , to a six-phase rotary converter it is necessary that each 
be connected to the proper rings. 

The double-tee connection requires only two transformers, and 
so far'as concerns the cost of the equipment and the efficiency in 

-1000 — > 

-1000 — > 

-1000 — > 


n^ nyn nnn n)Fi cw\ nJFi 

<-50-H ■^-M 

— • 'V 

-50 VJ- 
-100 — 



-100 — 

-50 >S^ 




-50 vF- 

FiG. 110. — Six-phase double-star with one neutral point for the six secondary 


operation two tee-connected transformers are preferable to the 
delta or star connections. This connection can be used to trans- 
form two-phase to six-phase, and from three-phase to six-phase. 

It is worthy of note that the transformer with the 86.6 per cent, 
winding need not necessarily be designed for exactly 86.6 per 
cent, of the e.m.f. of the other transformer; the normal voltage 
of one can be 90 per cent, of the other, without producing detri- 
mental results. 

Fig. 112 represents the tee-connection for transforming from 
three-phase to six-phase e.m.fs. 

With reference to its ability to transform six-phase e.m.fs. and 
maintain balanced phase relations, the tee-connection is much 
better than either the delta or star connections. 

Another interesting method of ti'ansforming from three-phase 
or two-phase to six-phase is shown in Fig. 113. The two trans- 


formers bear the ratio of 10 to 1 and 10 to 0.866, as explained in 
the previous example. For a two-phase primary supply, A A' 
is tapped on one phase, and B B' is tapped on the other; the line, 
X, being cut loose. For a three-phase primary supply the lines. 



a^ -^6' 


MJtflQflflfla.J LflJKlfiflfifl.O.QQJ LfififiaAflAflflA. 

UaiL n , r vQQOn 



-100— >f*— 50 — >K-100- 




— 86t6 
Fig. Ill . — Six-phase double-delta combination. 

A, A' , and B, are connected to the three-phase mains. The 
secondary connections in both cases remain the same. 

If a neutral wire is required as in the case of the three-wire, 
direct-current system, it may be taken from the point, y. For 













"■ I * 




.6^ "^100^ 












* Fig. 112, — Six-phase tee connections. 

running a blower motor, or to furnish current for running the 
rotary converter up to synchronous speed by an induction motor 
mounted on the same shaft, any one of the two secondary tee- 



connections may be used. The three-phase e.m.f. obtained 
would have a value equal to the full secondary voltage used for the 
rotary converter. 

a' B' 





-This wire for 

I — \mEm 





3 'n 

Neutral wire 

.j^ Three-phase 
V Motor 

Fig. 113.— Six-phase from three-phase or two-phase. 




Fig. 114.— General group of six-phase transformer combinations. 

Fig. 114 shows all the six-phase transformer combinations in 
use at the present time. 



Small transformers do not require special cooling devices since 
they have large radiating surface compared with their losses. 
Large transformers will not keep cool by natural radiation; some 
special cooling devices must be provided. 

The various cooling methods are: 

Self-cooling dry transformers. 

Self-cooling oil-filled transformers. 

Transformers cooled by forced current of air. 

Transformers cooled by forced current of water. 

Transformers cooled by forced current of oil. 

Transformers cooled by some combination of above means. 

Self-cooling Dry Transformer. — ^Transformers of this kind are 
usually of small output, and do not require any special means of 
cooling, the natural radiation being depended upon for cooling. 

Self-cooling Oil Transformers. — ^This arrangement is employed 
for at least 60 per cent, of transformers in use, the core and coils 
being immersed in oil. The two advantages gained by immersing 
these transformers in oil, are: Insulation punctures can in many 
cases be immediately repaired by the inflow of oil, and the 
temperature is reduced by ojfifering means of escape for the heat. 

Many manufacturers depend upon the high insulating qualities 
of the oil itself, and, therefore, introduce less insulating material 
such as cambric and mica, etc. On the other hand if oil is punc- 
tured it will close in again, unless the puncture be the result of a 
short-circuit in the transformer, in which case an explosion is 
liable to occur, or a fire started. In this way electric plants have 
been destroyed. 

For the purpose of obtaining the necessary radiating surface, 
tanks of the large self-cooled transformers of many manufacturers 
are made of thin corrugated steel or cast iron. The thin cor- 
rugated steel metal tanks are not sufficiently strong to be safely 
handled in transportation with the transformers in them. A 
slight blow is sufficient to cause the oil to leak at the soldered 



seams between the different sheets of thin steel, or at the joints 
between the sides. The cast-iron case is unquestionably the 
best, and the most suitable for oil transformers; the great strength 
and stability of cast-iron cases insure the safe transportation of 
the transformer. 

In the design of oil-insulated transformers, interior ventilation 
is provided by oil passages or ventilating ducts, between the 
coils, and in the iron. These secure an even distribution of heat 
and a uniformity of temperature throughout the transformer, 
results which can be secured only by a free internal circulation 
of oil. 

Without good oil circulation, transformers of large size may 
reach an internal temperature greatly in excess of that of the 
external surface in contact with the oil, and in poorly designed 
transformers this may lead to the speedy destruction of the insu- 
lation of the coils. 

The number and size of the oil passages, or ventilating ducts 
are planned to keep all parts of the transformer about evenly 
cooled. Such ducts necessarily use much available space and 
make a transformer of a given efficiency more expensive than if the 
space could be completely filled with copper or iron. Experience 
with oil-insulated transformers of large size and high voltage has 
shown that oil increases the life of the insulation, in addition to 
acting as a cooling medium, and adds materially to the capability 
of the transformer to resist lightning discharges, in other words 
such a transformer is safer than a dry transformer. 

The amount of heat developed in a transformer depends upon 
its load and its efficiency. In a 500-kw. transformer of 98.5 per 
cent, efficiency there is a loss at full load of 7.0 kw. Since this 
loss appears as heat, it must be disposed of in some way or the 
temperature will rise until it becomes dangerously high. 

The self-cooled oil-insulated transformer is now made in sizes 
up to 3000 kv-a capacity and represents one of the best advances 
in the manufacture of transformers. This new design is a very 
important development of the art of transformer manufacture. 
This type will be more in demand than the air-cooled type (air- 
blast) where water is or is not available, is expensive or not suffi- 
cient. It requires a minimum amount of attention and no 
auxiliary apparatus or equipment. The great problem to be 
solved in this type was that of providing sufficient surface to 
radiate the heat generated and keep the temperature rise within 


certain limits. The total amount of surface broken up into 
corrugations depends on its efficiency which may be defined as 
the watts radiated per square inch of surface, as well as on the 
amount of heat to be radiated. A plain surface is found to be 
the most efficient as both the air and oil come into close contact 
with it, but as it is broken up into corrugations, the efficiency is 
decreased slightly. The most modern self-cooled type is pro- 
vided with auxiliary pipes or radiators whereby the actual surface 
of the tank can be greatly increased and at the same time the 
radiating efficiency of the surface kept very high. The method 
of cooling consists essentially of fitting the outside of a plain 
cast-iron or plain boiler-plate tank with a number of vertically 
arranged tubes, the upper ends of which enter the tank near the 
top and the lower ends near the bottom. 

An idea of the limitations in this direction can be best obtained 
by making a rough comparison of two transformers of widely 
different kv-a capacities. 

Assume for a small transformer 100 kv-a capacity, and for a 
large transformer one of 4000 kv-a capacity. Now, if the same 
densities obtain in both copper and iron, namely, if the larger 
transformer has losses proportional to the increase in output, the 
losses will be increased 4000-^100 = 40 times, while the area or 
surface of radiation would only be increased about one-fourth 
as much as the losses. From this method of comparison it is 
seen that in order to keep the heating within proper limits it is 
necessary considerably to increase the size of the transformer, 
resulting in a cost very much greater than that of a transformer 
having auxiliary means of cooling. For this reason self-cooled 
oil-insulated transformers are not generally manufactured in 
sizes above 2000 kv-a. For sizes up to about 500 kv-a, the tank 
is single corrugated and above this size compound corrugations 
are used to obtain the necessary radiating surface. 

Hot air tends to flow upward, so that, in providing for 
station ventilation, it is essential that the inlet of the cool air 
should be low down and the outlet somewhere near the roof, 
the inflow and outflow of air being well distributed about the 

Self-cooled oil-insulated transformers of large size should be 
given good ventilation or else the life of the transformer will be 
shortened. The first indication of increased temperature will be 
darkening of the oil and a slight deposit on the inside surfaces 


of the transformer. Once this deposit begins to form the tend- 
ency is quickened because of the decreased efficiency of heat dissi- 
pation from the transformer. 

In this type of transformer the only remedy where the oil has 
thickened to a considerable extent and a deposit accumulated, is 
to thoroughly clean the transformer by scraping off the deposit 
and washing it out with oil under high pressure. 

Transformers Cooled by Forced Current of Air. — ^This type of 
transformer is commonly called the "air blast," and may be 
wound for any desired voltage not exceeding 40,000. 

Air-blast transformers are cooled by a blast of air furnished 
by a blower. The blower may deliver air directly into a 
chamber over which the transformer is located, or if it is 
more convenient, the blower may be located at a distance 
from the transformer, feeding into a conduit which leads to 
the air chamber. The blower is usually direct connected to an 
induction motor, though it may be driven by other means. One 
blower generally supplies a number of transformers in the same 
station, and the transformers are usually spaced above an air 
chamber, in which a pressure is maintained slightly above that 
of the surrounding air. The air for cooling the iron passes from 
the lower housing selected to suit the transformer capacity. When 
the efficiency of an air-blast transformer is known, an approximate 
estimate of the amount of air required can be made by allowing 
150 cu. ft. of air per minute for each kilowatt lost. For the most 
satisfactory operation, the velocity of the air in the chamber 
should be as low as possible, and should never exceed 500 ft. per 
minute. That is, the cross-section of the chamber in square feet 
should at least be equal to the number representing the total 
volume of air required per minute by the transformer, divided 
by 500. The power required to drive the blower for furnishing 
air to the transformers is so small as to be practically negligible, 
amounting in most cases to only a fraction of 1 per cent, of the 
capacity of the transformers. 

The three-phase, air-blast shell-type transformer, when delta 
connected, has the same advantage as three single-phase trans- 
formers of the same total rating that is, by disconnecting and 
short-circuiting both windings of a defective phase, the trans- 
former can be operated temporarily at two-thirds, or thereabout, 
of the total capacity from the two remaining windings. 

Coming under this heading of transformers cooled by forced 


current of air, there exist two methods, viz., oil-insulated trans- 
formers cooled by means of an air-blast on the outside of the tank, 
and those in which the air is forced directly between the coils, 
and through ducts in the laminations. 

The forced air-cooled transformer may be of the shell type or 
core type, but preferably of the former for large or moderate sizes. 

The question of air-blast against oil-cooled transformers has 
been settled in practice long ago in favor of the oil-cooled type. 
Some of the chief advantages claimed are the additional safety 
due to the presence of the oil round the windings, and the exclu- 
sion of a forced current of air and consequently exclusion of dirt 
and dust from all parts of the windings. 

Three-phase transformers require larger air chambers than 
single-phase transformers of the same total capacity. The tem- 
perature of the out-going air compared with the temperature of 
the in-going air is the best indication whether sufficient air is 
passing through the transformers, but in general, and on the basis 
of 25° C, the best results are obtained when the temperature of 
the incoming air is not greater than this value. Depending on 
the temperature of the surrounding air or entering air, the out- 
going air will leave the transformer greater or smaller as the 
case may be. Also, depending on the design, the difference 
in temperature of the supply of air and the air leaving the trans- 
former will vary between 12° and 20° C. 

The insulation of air-blast transformers must be impervious 
to moisture, and must have superior strength and durability. 
It must also permit the ready discharge of the heat generated 
in the windings, as otherwise the transformer temperature may 
reach a value high enough to endanger the life of the insulation. 
In building such a moisture-proof insulation, the coils are dried 
at a temperature above the boiling point of water, by a vacuum 
process which thoroughly removes all moisture. After a treat- 
ment with a special insulating material, they are placed in drying 
ovens, where the insulating coating becomes hard and strong. 
Then the coils are taped with an overlapped covering of linen and 
again treated and dried, there being several repetitions of the 
process, depending on the voltage of the transformer. The 
insulating materials are so uniformly applied and the varnish so 
carefully compounded that the completed insulation on the coils 
is able to withstand potentials two or three times greater than 
the same thickness of the best insulating oil. 


Transformers Cooled by Forced Current of Water. — This type 
of transformer is usually called " oil-insulated, water-cooled." 

Inside the cast-iron tank and extending below the surface of the 
oil, are coils usually of seamless brass tubing through which the 
cooling water circulates. These coils are furnished with valves 
for regulating the flow of water, and the proper adjustment 
having once been made, the transformer will run indefinitely 
with practically no attention. Another method of cooling is by 
drawing off the oil, cooling it, and pumping it back, the operation 
being continuous. In the design of oil-insulated, water-cooled 
transformers, interior ventilation is provided by oil passages 
between the coils, and in the iron. These secure an even distri- 
bution of heat and a uniformity of temperature throughout the 
transformer. Without good oil circulation, transformers of 
large size may reach an internal temperature greatly in excess 
of that of the external surface in contact with the oil. As a 
means of securing the best regulation, oil insulation is of immense 
advantage inasmuch as it permits close spacing of the primary 
and secondary windings. It effects great economy of space, and 
its fluidity and freedom from deterioration greatly assist in 
solving the difficult problems of transformer insulation. Its 
good qualities come into play with remarkable advantage in 
building high-potential transformers. 

Water-cooling coils are made of seamless tubing capable of with- 
standing a pressure of from 150 to 250 pounds per square inch. 

Transformers Cooled by a Combination Method. — ^Transformers 
cooled by this method require the service of a pump for circu- 
lating the oil. The oil is forced upward through spaces left around 
and between the coils, overflows at the top, and passes down over 
the outside of the iron laminations. With such a scheme trans- 
formers can be built of much larger capacities than the largest 
existing water-cooled transformers of the ordinary type, without 
such increase in size as to show prohibitive cost and to necessitate 
transportation of the transformers in parts for erection at the 
place of installation. The forced-oil system allows the circulation 
of the oil to be increased to any extent, thereby producing a rapid 
and positive circulation which greatly increases the cooling 
efficiency of the fluid. Moreover, this method of oil circulation 
ensures such uniform and positive cooling that much higher 
indicated temperatures may safely be permitted in transformers 
operating at moderate overloads. 


With ample capacity provided in oil- and water-circulating 
pumps, the transformer can without danger be called upon to 
carry extreme overloads under emergency conditions. Trans- 
formers of the forced-oil type have recently been built for a nor- 
mal capacity of 7500 kilowatts, and are actually capable of carry- 
ing 10,000 kilowatts continuously at a safe temperature. 

Of the very large modern designs of forced-oil type transform- 
ers two methods of cooling are employed. The old method was 
to place the cooling apparatus outside of the tank, and the new 
method is to place the cooling apparatus inside the transformer 
tank, the external in this case not being employed. Not unlike 
the water-cooled type the cooling coil is placed inside of the 
tank except that it reaches much lower down into the tank than 
the water-cooled type. A cylindrical or elliptical metal casing, 
depending on the form of tank, separates this coil from the oil- 
chamber with the exception of one or two openings at the bottom. 
The oil is pumped out at the top and into the space enclosing 
the cooling coil; the static head caused by the resulting difference 
in level greatly increases the natural oil circulation through the 
coils and core. This method of cooling is extremely simple in 
design and is as flexible as any water-cooling system. It is not 
possible as in the older system of cooling to communicate one 
transformer trouble to another due to moisture or a break- 
down of any kind; it is free to be changed about without inter- 
fering with any other transformer in the station, and has several 
advantages in case of fire. On all very large capacitj'' transform- 
ers it is customary to circulate sufficient water (in addition to 
forced-oil circulation) tp dissipate the heat with a rise in tempera- 
ture of the water of about 10° C. If the temperature of the in- 
coming water is 15° C, that of the out-going should be 25° C. 
This usually requires about one-third of a gallon per minute 
per kilowatt loss in the transformers. The rate of flow of the 
cooling oil through the various coils and core is generally about 
25 feet per minute, or somewhere between 15 and 30 feet per 

It is well known that high-voltage large-power transformers 
cannot run continuously, even at no-load, without the cooling 
medium, since the iron loss alone cannot be taken care of by 
natural cooling. A device is now in common use whereby an 
alarm is given to the operator when the water has ceased to flow 
through the cooling coils and also when the temperature has risen 



above a certain given value in the transformer. This outfit is 
shown in Fig. 115 and consists of a water relay or balance which 
is actuated by a volume of water in such a manner that if the 
water slacks off or ceases to flow, it will light the incandescent 
lamp shown. The bell alarm is so arranged that it will operate 
as soon as the temperature of the transformer, as indicated by 
the thermometer, reaches a certain limit. 

In the water-cooled transformer, the heat generated by losses 
is disposed of as above mentioned, and the arrangement is so 



Lo w VoltapJe R elay 

Th ?rmometer 



Water Relay 

Fig. 115. — Water, thermometer, and bell danger indicator for large high- 
voltage power transformers. 

effective that but very little heat is dissipated from the tank and 
consequently no advantage is derived from the use of corrugated 
tanks. There are, however, installations of transformers where 
a satisfactory supply of cooling water is not available at all 
periods, and also cases where the meter rate of cooling water is 
excessive, in which cases a tank with corrugations may be used. 
The usual design of a tank with corrugations provides for approxi- 
mately 70 per cent, of total capacity without cooling water. 
Its cost is, in general, about 10 to 15 per cent, greater than a 
standard boiler-iron tank. This corrugated type has been used 
to advantage in very cold climates where water-freezing diffi- 
culties are common. 

Fig. 116 shows the result of cutting off the water supply of 
a water-cooled transformer. A five-hour duration has resulted 
in a temperature rise of 35° C. (60 — 25 = 35° C), while a two 
and one-quarter hour duration shows an increase in temperature 
of 17° C. (57-40 = 17° C). 

The cooling coil of this type of transformer is sometimes 


coated on the outside with a deposit from the oil while the inside 
is lined by impurities in the cooling water, 

A good method of cleaning the inside of cooling coils is to pour 
equal parts of hydrochloric acid and commercially pure water 
into the coil. After the solution has been standing for about 
one hour, flush the coils out thoroughly with clean water. 

When deposit has accumulated on the outside of the cooling 
coil, it is necessary to remove it from the tank for cleansing. 
The deposit can be wiped or scraped off. 

Sometimes moisture is condensed at the top of this type 
transformer when located in a damp atmosphere. To avoid 
this, the transformer should be kept warm; that is, the tempera- 
ture of the oil should never go below 10° C. In some cases a form 
of "breather" has been used, which consists of a vessel of chloride 
of calcium, so arranged as to allow the water taken out of the air 
to drain off without mixing with the air that is going in on account 
of the contraction of the transformer oil in cooling. An indica- 
tion of condensation of moisture is the accumulation of rust on 
the underside of the transformer cover at the top. 

On all large high-voltage transformer installations provision 
should be made for continuous sampling and filtration of the 
oil in any transformer without removing the unit from service. 
This is usually done by means of valves at the bottom and top 
of transformer tank and withdrawing the oil and filtering it by 
forcing it, at a 200-lb. pressure, through a series of about twenty- 
five filter sections, each containing five 8-in. by 8-in. filter papers, 
making a total thickness of almost 0.75 in. of paper. The paper 
filters the oil and removes all moisture, returning it to the tank 
dry and clean. The capacity of oil-containing tanks should not 
be less than the oil capacity of any one transformer, but prefer- 
ably slightly greater in capacity than the largest transformer in 
the station. About four hours should be sufficient to filter the 
entire contents of any transformer and on this basis the capacity 
of a filter equipment may be provided for. 


Core-t3rpe (vertical cylindrical coils, turns of the conductor 
being in a horizontal plane). — With this type of winding the 
ends of the coils will be somewhat cooler, owing to the heat 
which passes out at those points. If the temperature of the oil 
adjacent to the top portion of the coils is much higher than at 



the bottom, there will be a tendency to transmit heat downward 
in the coil. The heat transmitted will be small, but the thermal 
resistance is high as compared with the temperature difference 
in this direction. The most important result will be that the 
temperature of the top portion of the coil will be almost as 
much higher than the temperature of adjacent oil as that of the 




H 80 

I 70 





(a) Temperature of high voltage winding by reslatance . 

(6) " " low " " " thermometer. 

i-c) " "high 

(.d) " " oil. 

(^) " " water leaving cooling coil . 

7 8a 
Hours Run 

Fig. 116. 

10 11 18 13 14 

bottom portion is above the oil adjacent to it, assuming, of 
course, that the equivalent thermal resistance from the coil 
to the oil is practically uniform throughout the length of the 
duct. The total average temperature of the coil is therefore 
related not to the surface temperature at the bottom of the 


coil but to a temperature which is average for the entire surface 
and which may be considerably higher than that at the bottom ; 
also, the maximum temperature at the top of the coils may be 
considerably higher than the maximum average surface tem- 
perature, and should be figured from the surface temperature 
near the top of the coil. 

The difficult problem with natural circulation of the oil is: 
correct distribution of temperature through the oil from the 
solid surface of the coils to the surface of the tank, or cooling 
coil. For a given velocity the equivalent thermal resistance 
is constant, the temperature drop from coils to oil being directly 
proportional to the watts per sq. in. discharged from the coils. 
With forced-oil circulation (returning the oil to the ducts at a 
definite temperature) the whole problem of cooling is much 
simplified, the only lacking element being a definite knowledge 
of the relation between the equivalent thermal resistance at 
the surface of the coils and the velocity of the oil. With 
natural circulation the oil flow is caused by the difference in 
temperature between the average temperature of the oil inside 
the duct and that of the outside oil between the level of entrance 
to and exit from the duct. 

The effect of the thickness of the duct upon temperature rise 
will be very different for forced-oil circulation than for natural 
circulation. With forced-oil circulation a thin duct will be better 
than a thick one, since the resulting higher velocity of the oil 
will give lower temperature drop from the surface of the coils 
to the oil. 

With natural circulation of the oil a thick duct will give practi- 
cally the same conditions as to temperature rise as that obtained 
on an external surface, the rise being less than for a thin duct. 

Thinning the duct does not cause as great an increase in tem- 
perature rise as might be expected, up to a certain point, since, 
though the temperature rise of the oil while passing through 
will be greater, this temperature rise tends to produce a higher 
Velocity, and hence to cause a smaller drop from the coils into 
the oil, as well as to reduce the net temperature rise in the oil 

The discharge of heat into the duct from both sides, as compared 
with its discharge from one side only, is an important matter in 
connection with cooling. It is found that with a duct of a given 
thickness, if the heat is discharged into it from both sides, at a 


given density in watts per sq. in,, both the temperature rise of 
the oil while passing through the duct, and the temperature rise 
of the coils above adjacent oil, will be smaller than if the heat is 
discharged into one side of the duct only, at the same density. 
Thus twice the heat is carried away by the duct, with a smaller 
temperature rise. This smaller temperature rise of the oil 
while passing through the duct, though absorbing twice the 
heat, indicates that the velocity of flow is more than double, 
and this accounts for the reduced drop from the coils into the 
oil. The great difference in velocity in the two cases is accounted 
for by the friction on the side of the duct where no heat is dis- 
charged, which is much greater than when heat is being 

Shell type (vertical oil-ducts between flat coils).— With this 
type, in general, the larger insulation is not in the path of heat 
flow, and the insulating covering is thin. The equivalent ther- 
mal resistance is uniformly distributed throughout the length of 
the duct, since the rate of oil flow is the same throughout, but 
this resistance will change with changes in the rate of heat 
discharge because the velocity of the oil will be different. If the 
heat generated in any part of the surface which is opposite, the 
oil would receive heat at a uniform rate throughout its passage 
through the duct, and the difference between the temperature 
of the coil and that of the oil would be the same at the top as at 
the bottom. The temperature at the top part of the coil would 
be as much greater than its temperature at the bottom as the 
temperature of the oil leaving the duct is greater than its tempera- 
ture at entrance. This would result in the passage of a con- 
siderable portion of heat downward through the copper, which 
is a good conductor of heat, the effect being that more heat is 
discharged per sq. in. from the bottom part of the coil than 
from the top. 

The temperature rise of the oil in its passage through the duct 
is more rapid in the bottom portion of the duct than at the top, and 
the temperature drop from the oil is also greater in the bottom 
portion of the duct than at the top. The temperature gradient 
in the copper from the top of the coil to the bottom is thus reduced, 
giving a more uniform temperature, as well as a lower average 
temperature. On the other hand, though the temperature of 
the oil where it leaves the duct would be the same, if its velocity 
were the same, since it absorbs the same total heat, yet its average 


temperature throughout the duct will be greater on account of 
the larger proportion of heat which it receives near the bottom. 
This will result in an increase in the velocity of circulation, which 
tends to reduce both the temperature rise of the oil in the duct 
and the temperature drop from the coil into the oil, both of these 
actions affecting further reduction in the temperature of the 

Disc-shape Coils (horizontal position with horizontal ducts 
between). — These coils may be wound either in single turn 
layers, or with several turns per layer. In the former case 
practically all the heat will be thrown out into the horizontal 
ducts, but in the latter the inner and outer layers will discharge 
best through layer insulation in the inner and outer cylindrical 
surfaces. A large portion of the heat will find an easier passage 
out through the horizontal oil ducts than from layer to layer in 
the coils. The relative amounts passing out through the two 
paths will depend upon the circulation of the oil. If the oil is 
stagnant in the horizontal ducts, it reaches a temperature where 
it ceases to absorb heat. 

It is quite evident that more solid matter of the hydrocarbons 
will deposit at those points of the maximum temperature; that 
is, at those points commonly known as "hot-spots." If 80 per 
cent, of the transformer operates at a temperature of 40° C. and 
the remaining 20 per cent, at 80° C, the transformer is badly 
designed and the weakest part of the insulation is at the point of 
the maximum temperature rise. Therefore, a knowledge of the 
distribution of temperature throughout a transformer, and of 
the various things which effect this distribution, is important 
from the standpoint of all those who operate transformers; 
and, if we are to avoid serious trouble with transformers, trouble 
with oil, and oil depositing which necessitates frequent cleaning 
out of the transformers, it is essential there should be no " hot- 

Standard heating guarantees for self-oil-cooled, air-blast and 
water-cooled transformers are given in the following table. 

The oil-cooled transformer measurements are based on the 
surrounding air temperature of 25° C. normal condition of 
ventilation, and a barometric pressure of 760 mm. of mercury. 

The air-blast transformer measurements are based on an 
ingoing air temperature of 20° C. and a barometric pressure of 
760 mm. of mercury. 





Type of trans- 

Temperature rise in degrees C. 


-,_ , 50 per cent. 
25 per cent, over- , , r « 
, J -. „ , overload for 2 
load tor 2 hours , 




f windings 40 
1 core 55 

f windings 55 
[ core 55 







The water-cooled transformer measurements are based on a 
normal supply of ingoing water at a temperature of 15° C. 

All corrections for variations in the three above types of 
transformers are made by changing the observed rise of tempera- 
ture by 0.5 per cent, for each degree Centigrade temperature 
variation, or for each 5 mm. deviation in barometric pressure. 


As the subjects of treating transformer oil and the properties 
of oil are so broad, and have been treated in a thorough 
manner by other writers, only a few important notes are given 

The most important characteristics of transformer oil which 
interest the operating engineer are summed up in the following 



Quality (A) 

Quality (B) 

Flash temperature 

188° C. 

210° C. 

-10° C. 

100 to 105 

Dark amber 

133° C. 

Burning temperature. 

Freezing temperature 

146° C. 
-16° C. 


Specific gravity at 15.5° C 

Color of oil 

40 to 42 


Similar to water 


Usually oil is received abroad testing less than 30,000 volts 
per 0.2 in., but before it is placed into the transformer it is 
brought up to a test at least 30,000 volts per 0.2 in. for trans- 
formers designed for an operating voltage 9f 44,000 volts and 
under; not less than a 40,000 volt test per 0.2 in. is required for 
transformer oil used in transformer operating above 44,000 

At a temperature somewhat below the fire test or burning 
temperature shown above, the oil begins to give off vapors 
which, as they come from the surface of the oil, may be ignited in 
little flashes or puffs of flame, but the oil itself will not support 
combustion until it has reached the temperature of the fire test 
as shown above. The lowest temperature at which these ignita- 
ble vapors are given off is called the flash point. The differ- 
ence between flash point and burning temperature test varies 
considerably in different oils and the actual location of the points 
themselves varies somewhat according to the method used in 
their determination. A high flash point and a high fire test are 
very desirable in insulating oils in order that the fire risk attend- 
ent on their use may be reduced to a minimum. Viscosity and 
flash point vary together, that is to say, an oil having a high 
flash point, compared with another oil, will probably also be 
high in viscosity. For all transformers that depend entirely 
upon oil for dissipating the heat as in the oil-filled self-cooled type, 
a relatively high flash point is of the utmost importance. 

For oil-filled water-cooled transformers it is customary to use 
another grade of oil than that used in the self-cooled type, the 
oil operating at a lower average temperature, consequently a 
high flash is not of the utmost importance. There are several 
grades of mineral seal oil with flash points varying from 130° C, 
used in water-cooled transformers. 

A very small quantity of water in transformer oil will lower 
its insulation to a marked degree; moisture to the extent of 0.06 
per cent, reduces the dielectric strength of the oil to about 50 per 
cent, of the value when it is free from moisture. The most 
satisfactory method of testing insulating oils for the presence of 
water is to measure the break-down voltage required to force a 
spark through a given gap between two brass balls immersed 
in a sample of the oil. Free oil from moisture should have a 
break-down voltage of at least 25,000 volts between brass 
knobs 0.5 inch in diameter and separated by a 0.15 in. space. 


Often it is desired to determine the insulating qualities of an 
oil when there are no high voltage testing transformer and 
apparatus available for making a test. When this is the case, 
a very good idea of the insulating properties of the oil can be 
obtained by testing for the presence of water with anhydrous 
copper sulphate. To prepare the anhydrous copper sulphate, 
heat some copper sulphate crystals (blue-vitriol) on top of a 
hot stove. The heat will drive out the water of crystallization, 
leaving as a residue a white powder, which is known as anhy- 
drous copper sulphate. 

Fill a test tube with a sample of the oil, add a small quantity 
of the anhydrous copper sulphate, and shake well. If there is 
any moisture present in the oil, it will combine with the anhy- 
drous copper sulphate, forming a distinctly blue solution. This 
test is quite delicate and a very small quantity of moisture can 
be detected by it. If this test does not show the presence of 
water it is quite safe to assume that the insulating properties of 
the oil are fairly high. 

When obtaining a sample of oil for testing, always get the 
sample of oil from the bottom of the tin or barrel, because, as 
water is heavier than oil, the maximum quantity of water will 
always be found at the bottom. To obtain a sample from the 
bottom, use a long glass tube of small diameter, hold the thumb 
tightly over one end and plunge it to the bottom of the barrel. 
Remove the thumb letting the air escape, then press the thumb 
tightly over the end of the tube and withdraw it with the sample 
of oil. 

The real importance of the light oil known to the trade as 
mineral seal oil is that it tends to decrease the deposit thrown 
down on the bottom of the transformer tank, cooling-coils 
and the transformer coils themselves. The (A) class referred to 
here is a dark-colored oil having a specific gravity somewhat 
higher than the mineral oil, its flash and fire points are much 
higher but when subjected to continued heating it throws down 
a deposit tending to clog up the oil ducts of the transformer 
and impede the circulation of the oil. So far as is known this 
deposit is caused entirely by the effect of the heat on the oil. 
It can be removed by filtering through a bed of lime and then a 
sand bed, or preferably by using one of the oil-drying outfits 
now on the market. The (B) class oil is light and practically 
white, and is usually referred to as mineral seal oil; it has rather 


low flash and fire points but does not throw down a deposit 
when subjected to long and continuous heating. The usual life of 
transformer oils depends altogether on the thoroughness with 
which the oil is protected against absorption of moisture, and, 
when heavy oils are used, the temperature at which the trans- 
formei*s are operated, the higher the operating temperature the 
more rapid are thin oils affected. It is the general practice to use 
the mineral seal oil in water-cooled transformers because of its 
tendency to keep down the temperature and also because it is 
practically free from the slimy deposit referred to above. With 
the use of class (A) oil the deposit would, besides accumulating 
and probably clogging the oil-ducts, close in around the cooling- 
coils causing a consequent increase in the temperature of the oil 
and this in turn would decrease the efficiency of the transformer. 
No specific information can be given as to the length of time 
throughout which an oil may be in use continuously; it might 
last five years or it might last only five months, but under 
ordinary service conditions the oil for high-voltage transform- 
ers should be good for at least 18 months. Several good oil 
drying and purifying outfits are now in common use, the prin- 
cipal elements of this modern outfit being an electric oven, a 
pump and strainer, filter-press and blotting paper. The interior 
of the oven is provided with rods for supporting and separating the 
blotting paper to facilitate rapid and thorough drying. A 
thermometer is attached to the oven and a switch is provided 
for regulation of the temperature. For drying and filtering 
oil, five layers of 0.025-in. blotting paper are used between 
sections of the press. The separation of this filtering material 
is of the greatest importance. Special care must be exercised 
in drying the blotting paper, which should be suspended from 
the rods in such a way that air is accessible to both sides of 
each sheet. The blotting paper should be dried at least 24 
hours at a temperature not over 85° C, and then put into a tank 
of dry oil the instant it is removed from the oven and before it is 
cooled, as exposure to normal air for a few minutes is sufficient 
to neutralize the drying. It should not come into contact with 
the hands because of the danger of absorbing perspiration. A 
small quantity of anhydrous calcium chloride placed in the oven 
will take up the moisture in the air and quicken the process. 
A higher temperature than that given above might scorch the 
blotting paper or impair its mechanical strength. As the paper 


is somewhat weakened by saturating with oil, it should be care- 
fully handled after removal from the bath. A tank of suitable 
size for the paper should be filled with dry, clean oil and the paper 
should be submerged in the oil. The paper should be carefully 
suspended in the tank, the bottom edge of the paper being kept 
3 or 4 in. from the bottom. The oil level should be at least 
2 in. above the top of the paper. A strainer is provided to 
prevent anything of appreciable size from entering and in- 
juring the pump. It is easily accessible and should be cleaned 
occasionally. The rating in gallons per minute is usually for 
average conditions in filtering clean heavy oil or dirty light oil. 
The best oil temperature for filtering is between 25 and 75° C. 
In the installation of this outfit the pump should be placed so 
that oil falls by gravity and as fast as the pump will take it. 
With clean oil the pressure and volume will remain nearly con- 
stant, the volume being nearly proportional to the pressure, 
but with dirty oil the pressure will increase very rapidly. With 
dirty oil and paper the volume increases much more slowly 
than the pressure and there is little gained by an increase in 
pressure over 75 pounds per square inch. In general, class (B) 
oil is filtered twice as fast as the class (A) oil, and the greater 
capacity is obtained by frequent renewal of paper, the total 
capacity per day depending largely on the time consumed in the 
operation. In placing paper in the press, care should be taken to 
have the holes in the paper corresponding with those in the plates. 
Oil is admitted at any pressure not over 100 pounds per square 
inch. The pressure will at first be very low, gradually increasing 
as the paper clogs with dirt. It is found that after three re- 
placements of the paper, the dielectric strength of the oil is apt 
,to fall off, and that it is best to discard the full charge of paper 
and begin again. The amount of oil which can be filtered through 
one set of papers depends entirely on the quality and tempera- 
ture, hot oil being filtered with great facility because of its low 
viscosity. By this process oil may be dried to withstand a 
puncture test from 40,000 to 60,000 volts with a standard spark 
gap consisting of two 0.5 in. diameter discs spaced 2/10 in. 
apart. With oil of an average quality as regards moisture and 
foreign matter one treatment will usually remove all sediment 
and bring the puncture voltage to 40,000 volts or more. Oil 
which has been damaged by overheating from continuous over- 
load or bad burn-out may be treated in this purifying outfit, 


and the sediment removed although the oil will still be darker in 
color than it was originally. If the oil is thickened to a slimy 
nature, it will quicken the operation to heat it to 75° C. just 
before running it through the press. 




£ v50 










'"'* — 


Water- Parts In 10,000 by Volume 

Fig. 117. — Curve showing the effects of water in oil. 

The curve Fig. 117 very clearly shows the serious effects of 
water in amounts less than 0.010 per cent. It shows that the 
water present in the oil must not exceed 0.001 per cent, in 
order to obtain a dielectric strength of 40,000 volts in the 
standard test (0.2 in. between 0.5 in. disc). 




There are various types of transformers on the market differ- 
ing so much in design that it is difficult to tell exactly whether 
they are of one or the other design (shell or core type) ; in fact, 
what some manufacturers call a shell transformer others call 
a core-type transformer. However, the design and construc- 
tion of transformers referred to here are strictly of the core 
and shell types respectively, of high-voltage large-capacity 
design, and of American manufacture. 

Transformers are always sent from the factory as completely 
assembled in their tanks as their size and transportation facilities 
in the countries they have to pass through will warrant. When 
they are sent disassembled, which is usually the case if they 
are for very high voltages and large capacity, the tanks are 
usually protected for shipment abroad but left unprotected for 
home shipment; the coils are carefully packed in weatherproof 
boxing, and the core if of the shell type is packed in strong wooden 
boxes of moderate size (in a loose state) , the core of the core type 
being shipped already assembled each leg being packed in one 
box and the end-laminations in separate boxes. Whether the 
transformer is built up at its destination or sent already assembled, 
it should be thoroughly inspected before being permanently 
put into the tank. If the transformer is sent from the factory 
in its tank, which is very seldom done, it should be removed and 
thoroughly inspected and cleaned before giving it a "heat-run." 

Let us deal first with the core-type transformer which consists 
essentially of two or three cores and yokes which when assembled 
form a complete magnetic circuit. These cores and yokes are 
made up of laminated stampings which vary from 0.010 to 0.025 
in. in thickness according to the frequency of the system on 
which they are to be used and the different manufacturers. 
The laminations are insulated from each other by a coat of 
varnish or paper to limit the flow of eddy currents. 

It is shown in Fig. 1 18 that there are three cores of equal cross- 



section joined by a top and bottom yoke of the same cross-section 
as the cores, and that upon each core are placed the low and high 
voltage windings for one phase. The low and high voltage 
windings are connected so that the fluxes in the cores are 120 elec- 
trical degrees apart, making their vector sum equal to zero at any 

The usual designs of core-type transformers made by the best 
manufacturers have a uniform distribution of dielectric flux 
between high and low voltage windings, excepting at the ends of 






Fig. 118. — Three-phase core-type transformer. 

the long cylinders where the dielectric flux will be greater and its 
distribution irregular. 

As already stated, the core-type transformer has its lamina- 
tions shipped already assembled, wrapped in insulating material 
of horn-fiber and bound with strong binding tape which serves as 
a binding to keep the laminations of the assembled sections 
intact. The different sections are assembled on wooden pins of 
the size of the holes in the laminations; first, in one direction, 
and then this end in the opposite direction, alternating spaces 
thus being left for assembling the end laminations. The approxi- 
mate number of laminations per inch required in building up 


tliese laininuted sections may be detoniiiiied from the informa- 
tion that the iron solid, would be about 90 per cent, of the 
height of the built up laminations, 36 and 64 laminations per 
inch being about the number of laminations required for the two 
standard thicknesses, 0.025 and 0.10 in. respectively. The 
required number of laminations are built in an insulating channel 
piece, and on the top of the channel piece and the pile of lamina- 
tions another channel piece is placed, the whole being pressed 
down to dimensions and the channel pieces stuck together with 
shellac under the influence of pressure and heat. The various 
sections are then assembled with wooden pins to hold them 
together, these remaining in the holes permanently, and the 
assembled sections clamped to dimensions and finally wound 
with a layer of strong binding tape of half-lap, which should not 
extend beyond the beginning of the spaces for the end-laminations. 

The core is now built up, the next process being to insert the 
end laminations at the bottom, their number corresponding to 
the spaces left for them, making them so fit into the spaces as to 
form butt-joints. These laminations are assembled while the 
cores or "legs" are resting in an horizontal position. While in 
this position the bottom clamp with its insulation is fastened 
over the end laminations and the whole raised by the help of an- 
other clamp and cross-bars to a vertical position, with open ends 
upward. The clamping bolts are then placed in a loose state, 
reliance being put on the bolts (which hold the bottom clamps 
in position) to keep the cores in a vertical position during the 
assembly of coil-supports and coils. 

The coils, which are of a cylinder form, are raised by means 
of a stout tape and slipped over the cores. All of the coils which 
connect together at the bottom should be connected immedi- 
ately after the coils are in position. Between the cylinder low- 
voltage coils and the high-voltage coils is placed a cylinder 
shaped insulating separator, the separator being held in posi- 
tion by means of spacing strips of wood. All connections be- 
tween outside coils can be conveniently made before the spacing 
strips are inserted between the high and low-voltage windings, 
when the coils may be easily turned to such positions as will 
leave the coil connections as distant as possible from the side of 
the steel tank. The top connections should be made after all 
the coils of the high-voltage winding are in position. A press- 
board insulating piece or casing is finally placed over the whole 


assembly of coils and tied around with tape. The connections 
or taps and the terminal leads are brought out at the top and 
supported in a similar manner to those mentioned in the assembly 
of shell-type transformers. 

The shell-type water-cooled transformers and forced oil-cooled 
transformers are built in larger sizes than the core type trans- 
formers, the former size having been built in 6000 kv-a single- 
phase units and 14,000 kv-a three-phase units. 

The shell-type transformers shown in Fig. 119 consist of three 
single-phase transformers placed in one tank, the laminated 
cores being constructed to form a single structure. The reduc- 
tion of iron for the magnetic circuit amounts to from 10 to 
20 per cent, of that used in three single-phase transformers 
placed side by side. 

In this type it is difficult to insulate the large number of 
edges and sharp corners exposed between adjacent high and low 
voltage windings and between windings and core. At these 
points the dielectric density is very great, and it is much more 
difficult to insulate them than the ends of the cylinder coils of a 
core-type transformer, and much more insulation is required and 
consequently a larger space-factor. In fact, a 60,000 volt — 2000 
kv-a — 25 cycle transformer of the core type will have a space- 
factor of the windings (ratio between the total section of copper 
conductors to the total available winding space) of about 28 per 
cent., whereas, in the shell type of the design shown in Fig. 119 
the space-factor is only about 17 per cent. The result of this 
increased space-factor in the winding of a shell type transformer 
is lower efficiency and worse regulation, and consequently a 
heavier and more expensive transformer for a given capacity and 
efficiency. It is sometimes recommended to use graded insula- 
tion in high-voltage transformers between the high-voltage and 
low-voltage windings or between the windings and core because 
of the unequal distribution of the dielectric flux. In all prop- 
erly designed transformers for high voltages, the only change 
in the grade of insulation is at the ends of the windings, this 
being the only grading considered necessary. 

In assembling the coils of a shell-type transformer, this being 
the first thing to be done in the assembly of this type, care should 
be taken to eliminate dirt and dust, and the coils at all times 
should be kept clean and dry. In unboxing the coils, each one 
should be wiped oflf with a dry cloth and stacked in the right 



order of assembly. The assembly of coils is begun in an hori- 
zontal plane, and stacked one above the other as shown in Fig. 
121, the outer press-board insulation piece being set on two 
wooden-horses, correctly spaced, depending on the size of the 
transformer to be assembled. The first coil, taken from the top 

Fig. 119. — Three-phase shell-type transformer. 

of the stack is placed in position with its inner edges insu- 
lated by means of channel-shaped insulation pieces. Each coil 
before it is placed in the assembly has the same shaped insula- 
tion pieces on its outer edges; insulation separators are arranged 

Fig. 120. — Single-phase transformer iron assembly. 

in symmetrical order for both the low and high-voltage coils 
with wooden filling blocks and channel pieces set at the inside 
top and bottom of coils. The assembly of these coils if of 
large size can easily be lowered into position. 


Tlic iron laminations must be laid with great care, steel being 
used to keep the alignment, on which the laminations butt. 
(See Fig. 120). 

In connecting the coils together, all the soldering is best done 
as the assembly progresses, also all taping of the connections, 
since the short stub connections are only accessible at this stage 
of erection. Before commencing to solder, a cloth should be 
spread over the ends of coils to prevent splashing solder on 
them which might get inside of the coils and ultimately cause a 
burn-out. During the assembly of coils, great care should be 
taken to keep them and the insulation separator in alignment. 
To facilitate this, all the insulation separators are slit at 
their four corners and a long round strip of wood is threaded 
through as the coils are being built up. After the assembly of 
coils and the placing of the outside top insulating piece or collar 
position, the whole is clamped down to dimensions. While the 
end clamps are holding down the coils to dimensions, strong 
cloth tape is wound around the coils, between the two clamps, 
under considerable tension, the ends of tape being finally secured 
by sewing them down, after which the whole is painted with 
a black, insulating air-drying varnish. 

Getting the assembled coils from the horizontal position in which 
they rest to the vertical position necessary for the assembly of 
iron and completion of transformer, requires the greatest care 
especially where transformers are of a larger size than 2000 kv-a. 
This is accomplished by means of blocking the space, inside of 
coils, leaving sufficient space in the center of coil-space for a 
lifting piece. The rope or cable for lifting should be slid over the 
rounded ends of the lifting piece, care being taken that the 
wooden spacer is sufficiently high about the coils to prevent 
striking the sling when swinging to vertical position. 

The bottom end frame or core support is now ready to be 
set into position where it is desired to build up the iron, 
which is arranged in a similar manner. The coils should 
be exactly vertical. Lapping of the laminations should be 
avoided, otherwise difficulty will be experienced in getting 
in all of them. Raw-hide mallets should be used for driving 
the laminations into line; or in case these mallets are not 
available, hard wood pieces pressed against the laminations 
may be hammered. During the building up of the laminations 
they should be pressed down two or three times, depending on 



160 Turns 
188 Turns 
188 Turns 

PI Not Crossed 
P2 Crossed 
P3 Not Crossed 

P4 Crossed 
P5 Not Crossed 
P6 Crossed 

P7 Not Crossed 

P8 Crossed 
P9 Crossed 

PIO Crossed 
Pll Not Crossed 
P12 Crossed 

Not Crossed 

S7 Crossed 

S6 Not Crossed 

S5 Crossed 

S4 Not Crossed 

S3 Crossed 

S2 Not Crossed 

SI Crossed 

Fig. 121.— Assembly of coils for a shell-type transformer. 


the size of transformer being built. For this clamping, the 
top iron frame is usually lowered and forced down with espe- 
cially made clamps or the regular clamping bolts may be used if 
the threading on them is sufficient to lower the clamp to the 
required dimensions; these clamps or bolts may be left in posi- 
tion over night if any difficulty is found in getting in the lamina- 
tions. In the case of transformers without a top piece or frame, 
an especially constructed rigid frame of wood may be used. The 
laminations should be built up to such a height as will permit 
the core-plate to be forced into position under considerable 
driving. It is always a difficult matter to put in all of the lamin- 
ations that come from the factory as special facilities for pres- 
sing are available there. After the laminations have been 
clamped down, the low- and high-voltage leads should be sup- 
])orted and insulated in a right manner; care being taken in 
supporting the leads to see that they are properly spaced, for if 
they are placed too close together a short-circuit might occur. 
At the cast-iron frames, the insulator bushings used for this 
purpose are held by metal supports to the frame, and at the 
point where the leads pass through the bushings, cement is 
used to hold the leads into position. Both the high and low 
voltage winding end-leads connect to the terminal-board which 
is located above the assembled coils and core. In the case of 
oil-cooled and water-cooled transformers all the leads are brought 
out at the top; usually' air-blast transformers have their leads 
terminate at the base or part at the base and part at the top of 
assembled coils. 

In lowering transformers into their tanks, care must be taken 
to get the bottom cross-bar, into which the tie-bolts are screwed 
into the correct position, which requires that the transformers 
should be properly centered in the tank. 

Of the two types of transformers, the core type is the easiest 
one to assemble, and a full description of one particular method 
of assembly of this type might well be said to cover practi- 
cally every manufacture, whereas the shell type varies in many 
ways and is a difficult piece of apparatus to assemble, especially 
in the larger sizes. 

Air-blast transformers are regularly built in capacities up to 
4000 kv-a and for voltages as high as 33,000 volts. The effi- 
ciency of this type of transformer, in good designs and with the 
required amount of air pressure, is sometimes better than the oil- 


filled water-cooled type of the same capacity and voltage. Its 
general design is very much like the ordinary shell-type trans- 
former with the exception of a few modifications in the iron 
assembly where certain air-spaces are left open for the circula- 
tion of air. The air space area in these transformers is consider- 
ably in excess of the actual area required for the pressure of air 
specified for cooling. For this reason dampers are provided to 
regulate the air so that, where a number of transformers are in- 
volved, each transformer will receive its portion. The air always 
enters the transformer at the bottom and divides into sepa- 
rate paths, flowing upward through the coils and ducts con- 
trolled by the dampers at top of the transformer casing, and 
through the core ducts controlled by a damper at the side of 
the casing. 

This type of transformer is always shipped already assembled 
so that in the larger sizes great care is necessary in handling 
them. For shipment abroad the larger sizes would, of course, 
have to be disassembled, but as this is of rare occurrence the 
above holds for practically all sizes. 

These transformers are placed over an air-chamber made of 
brick or concrete the sides being made smooth to minimize fric- 
tion and eddy currents of air. From the blower to the chamber 
should be as free as possible of angles, and where these occur, 
they should be well rounded off. Sufficient space should 
be allowed for the location of the high- and low-voltage 
leads, and necessary repairs and inspection. Three-phase 
transformers have larger air-chambers than single-phase trans- 
formers of the same aggregate capacity. The temperature of 
the out-going air compared with the temperature of the incoming 
air is the best indication whether sufficient air is passing through 
the transformers; if there is not more than 20° C. difference, the 
supply of air will be found sufficient. As transformers are 
generally designed on the basis of 25° C. the best results are 
obtained when the temperature of the in-coming air is not greater 
than this value. 

Installation of Transformers. — ^In the installation of high 
voltage transformers of the self-cooled oil-filled, water-cooled 
oil-filled, forced-oil-cooled oil-filled, and the air-blast types, the 
following points of importance should be born in mind : 

(a) In generating and receiving stations the transformers 
should be so situated that a burn-out of any coil, a boiling over 


of the oil, or burning of the oil in any unit will not interfere with 
the continuity of service. 

(b) In generating and receiving stations the transformers 
should be so located that the high voltage wiring from trans- 
formers to bus-bars is reduced to a minimum. 

(c) The transformer tanks, which are, of course, made of a 
metallic or non-combustible material, should be permantly and 
effectively grounded, preferably to the ground cables to which 
the station lightning arresters are connected. 

(d) Sufficient working space should be allowed around each unit 
to facilitate the making of repairs and for necessary inspection. 

(e) During the entire process of assembly of transformers of 
low or high voltage, the best and most careful workmanship is 
of utmost impoi'tance. 

(f) (This might be considered as the last process in the instal- 
lation of transformers but by no means the least important.) 
Extra special knowledge and care is necessary on the part of all 
those whose duty it is to dry out transformers — ^the difficulty is 
not in drying out the coils, as is usually supposed, but the drying 
of the whole insulaiion surrounding them and the core. No 
matter what the factor of safety the transformer has been built 
for it avails little in the case of carelessness or neglect to dry out 
the transformer properly. 

Before transformers leave the factory they are given a high- 
voltage test, the standard being, to apply twice the rated voltage 
between the high- and low-voltage windings, the latter being 
connected to the iron core. The main object of applying this 
test which induces twice the rated voltage to one of the windings, 
is to determine whether the various portions of the coils are 
properly insulated from each other. It is now believed that 
the greater causes of failure in high- voltage transformers are 
punctures between turns and not between the high and low- 
voltage windings. 

To install properly and place in good working order high-volt- 
age power transformers is quite as important as their design, 
since upon this depends the life of the transformer. All trans- 
formers of high voltage should be thoroughly dried out on 
arriving from the factory, and all transformers which show 
evidence of being unduly moist, or that they have been subjected 
to conditions that would cause them to be unduly moist, should 
be taken special care of in the drying process. 



Testing Cooling Coils — Before high-voltage transformers 
are put into operation they are subject to a "heat-run," 
and in the case of transformers with cooling coils, the coils 
are made subject to a pressure test. These coils must be 
assembled before the heat run can be made. If the coils 
show evidence of rough usage, such as heavy indentations and 
disarrangement of layers, the coils should be given the usual 
tests to determine whether a break has resulted. The method 
for testing for leaks is to fill the cooling coil full of water, 
establish a pressure of 80 to 100 lb. per square inch, disconnect 
the source of pressure, holding the water in the cooling coil by 
means of a valve, and note whether the pressure gauge between 
the valve and the cooling coil maintains the indication through- 
out a period of about one hour. Care should be taken that no 
air is left in the cooling coil in filling it with water. In removing 
the source of pressure it is preferable to disconnect entirely from 
the cooling coil, in order both to make sure that the source of 
pressure is entirely removed and to note whether the lowering 
of the pressure indicated by the gauge connected to cooling coil, 
is due to leakage through the cooling coil valve or to leakage 
through a hole in the cooling coil. If the gauge indicates a 
lowering of pressure in the cooling coil, it should be inspected 
throughout its entire length until the hole is discovered. The 
water will gradually form at the hole and begin to drip. After 
the cooling coil is filled with water, a small air-pump may be 
used for giving the required pressure, in case there is not a satis- 
factory water source for obtaining the pressure. As the test 
is only to determine whether the cooling coil has a leak in it, it 
will in no case be necessary to establish a greater pressure than 
JOO lb. per square inch. Some engineers prefer to submerge 
the cooling coil in a liquid, under an air pressure of 80 to 100 lb. 
per square inch for a period of about one hour, and note the 
bubbles rise to the surface of the liquid. 

Drying-out Transformers. — Several methods exist for drying 
out high-voltage transformers, the best being considered as 

1. Short-circuit either the high or low- voltage winding and 
admit sufficient current to raise the temperature of the windings 
to approximately 80° C. The amount of heat necessary to 
effect this temperature will range between one-third and one- 
fifth of the full-load current, depending on the room temperature 


and design of transformer. Tlic impedance volts necessary to 
give the specified range in current, vary from 0.4 per cent., to 
1.5 per cent, of the rated voltage of the winding to which the 
impedance voltage is applied. In any case, the current ad- 
mitted must be so regulated that the temperature of the wind- 
ings does not exceed the 80° C. limit. 

The temperature of the transformer windings may be deter- 
mined by the increase in resistance, or, if facilities for this method 
are not available, the bulb of a spirit thermometer may be placed 
in direct contact with the low-voltage winding at the top. Low- 
voltage winding is specified for the reason that to place the bulb 
of the thermometer in contact with the high-voltage winding 
may not give the temperature of the coils; the insulating pieces 
set around the coils of the high-voltage winding being built up 
on the copper under the tape to such a height as to prevent the 
thermometer recording the temperature of the copper. The 
bulb of the thermometer should be placed down between the 
low-voltage coils as far as possible. Mercury thermometers 
must never be used for this purpose because of their liability to 
break. The drying process should be carried on while the trans- 
former is out of its tank in order to give as good a circulation of 
air as is possible under the conditions. 

The following table is considered to be within safe limits for 
carrying on the drying process although discretion must be used 
as in the case of an unduly moist transformer and where the kw. 
capacity and voltage enter into consideration. That is to say, 
a transformer coming under the heading of 44,000 to 70,000 
volts, having a kw. capacity of 200 kw. and less, can be taken as 
safe if the heat-run period is only carried on for 60 hours instead 
of 72, or a transformer coming under the heading of 22,000 to 
33,000 volts, having a kw. capacity of 200 kw. or less may be 
considered safe if the heat-run period is carried on for only 
24 hours instead of 48 hours; assuming all transformers in normal 

It is impossible to give anything but an approximate estimate 
of the number of hours necessary to dry out a transformer of a 
given size and voltage. Much will depend on the condition of 
the transformer when it is received from the factory, whether 
in an unduly moist condition or dry. 

(2) This method is to dry the transformer and oil simulta- 
neously under the influence of heat and vacuum, the transformer 




Voltage of system 

Hours of heat-run 

Kilowatt capacity 

22,000 to 33,000 


200 and above 

22,000 to 33,000 


500 to 1000 

22,000 to 33,000 


1000 to 2000 

22,000 to 33,000 


2000 and above 

33,000 to 44,000 


200 to 500 

33,000 to 44,000 


500 to 1000 

33,000 to 44,000 


1000 to 2000 

33,000 to 44,000 


2000 and above 

44,000 to 66,000 


200 to 500 

44,000 to 66,000 


500 to 1000 

44,000 to 66,000 


1000 to 2000 

44,000 to 66,000 


2000 and above 

66,000 to 88,000 


500 to 1000 

66,000 to 88,000 


1000 to 2000 

66,000 to 88,000 


2000 and above 

88,000 to 110,000 


500 to 1000 

88,000 to 110,000 


1000 to 2000 

88,000 to 110,000 


2000 and above 

110,000 to 145,000 


2000 and above 

being dried inside of its tank. The tank is first made vacuum 
tight, this being, in the majority of cases a difficult task to do and 
is only accomplished after considerable time has elapsed with 
the vacuum pump under operation, by closing the holes indicated 
by the whistling noise of the entering air. The leaks are stopped 
by using putty, which should be fairly stiff in order to keep it 
from being drawn into the tank. If the puttying is done a day 
or two before the drying process is begun, thus giving the putty 
a chance to harden, it will be found much easier to obtain the 
required vacuum. 

One of the transformer windings is short-circuited as in method 
(1), although the actual temperature in this case is allowed to 
reach 90° C. instead of 80° C, and the temperature is determined 
by the increase in resistance. The temperature of the oil should 
be maintained at approximately 80° C. during the drying 
process. When starting the heat-run it is found advantageous to 
bring the temperature up quickly, and to do this, full-load 
current might be given until the approximate temperature is 
reached, after which it should be reduced to the specified value. 


In addition to heating by electric current a certain amount of 
heat should be applied under the bottom of the base of the 
transformer. The most satisfactory method of applying heat 
to the base is to use grid resistances supplied with sufficient 
current to maintain the grids at full red heat. The grids should 
be distributed under the base so as to make the heating fairly 
general, and not confined to one portion of the surface. In case 
some other method of heating the base is used, extreme care 
should be taken that the supply of the heat does not become too 
intense, otherwise the oil may be injured. The idea of supply- 
ing heat to the base is to maintain uniform temperature of the 
oil throughout the transformer structure at a uniform tem- 
perature of 80° C. It is found that the temperature of the 
windings reaches 90° C. considerably in advance of the oil's reach- 
ing 80° C; and, for this reason, it is necessary either to disconnect 
the current occasionally or to reduce it to a small percentage of 
full-load current. The base heating should be relied on to 
maintain the oil at a temperature of 80° C. as long as it will, 
which may be almost constantly, provided a sufficient quantity 
of heat is applied. These specified limits of hours referred to 
above are for the actual time the process must be carried on 
after the oil has reached a temperature of 80° C. and after a 
vacuum of 20 in. has been established, and does not refer to the 
time necessary to reach the 80° C. point and 20 in. of vacuum. 

When electric current is not available, steam at a low pressure 
may be used for heating, the steam being admitted through the 
cooling coil. Also, steam may be used for the base heating; in 
which case the entire bottom surface of the base should be sub- 
jected to the heat of the steam. Care should be taken in ad- 
mitting steam through the cooling coils that the temperature of 
the oil does not exceed the Hmit. This method of applying heat 
at the base is not recommended, principally because the steam 
condenses on all parts of the transformer tank. 

(3) This method of drying transformers requires the circulation 
of heated air through the transformer coils and core while it is 
in the tank. The source of heated air should be connected to 
the base valve and the top cover of tank be partly removed. The 
temperature of the air inside of the tank should be maintained 
at approximately 80° C, and the process should be carried on 
under this temperature for a period of three days for units of 
moderate size, the same discretion being used as mentioned in 


methods (1) and (2). The temperature of the heated air as it 
enters the transformer should not exceed 100° C. This method 
of drying transformers is especially adapted to localities where 
no electric current is available. 

The oil may be dried by the vacuum method mentioned in 
(2), or by blowing heated air through it, referred to in the above 
method. Where the vacuum method is used, the tank must be 
filled to within a few inches of the top, so that the cover may be 
kept sufficiently warm to prevent condensation of moisture. In 
case the transformer tank without its transformer is used for this 
purpose, it is sometimes necessary to put temporary bracing 
inside of the tank to prevent collapsing under vacuum; this does 
not refer to the tank of cylinder form. A 12-hour run under 
a temperature of 80° C. with not less than 20 in. of vacuum 
should be quite sufficient to dry transformer oil. All large 
installations are provided with tanks for this purpose, the tanks 
being of the cylinder form. 

The necessary heat for bringing the temperature of the oil up 
to 80° C. may be obtained by placing a steam coil or an electric 
heater in the bottom of the tank. Assuming that the tank in 
which the oil is being dried, will radiate approximately 0.25 
watts per square inch, the amount of electric energy required 
to maintain the oil at the specified temperature may quite 
easily be estimated. The electric heater should be about double 
the size estimated for the purpose of shortening the time neces- 
sary to reach the desired temperature. Whether a steam coil 
or an electric heater is used it must be placed directly on the 
bottom of the tank as it is necessary to maintain the oil 
temperature about uniform throughout. In case steam is 
used, its pressure should not be greater than 10 lb. per square 

The same tank may be used for drying oil by means of forced 
circulation of air. In this case it is necessary to run the piping 
from the valve in the base of transformer up above the oil level, 
and then down to the air pump, the top of the tank having an 
adjustable opening for permitting the air to circulate. The 
oil must be heated to a temperature of approximately 100° C, 
and the process continued until the oil becomes dry as deter- 
mined by test. 

Comparison of Shell and Core -type Transformers. — Trans- 
formers of any type should not be selected at random but only 


after careful investigation of design, reliability and simplicity 
to repair. 

In general the shell type transformer is a difficult piece of 
apparatus to repair in case of a break-down; the difficulty in- 
creases in almost direct proportion with increase in capacity, 
and in the larger sizes it becomes advisable to send for a trans- 
former man from the factory to do repairs. This disadvantage 
has been and is to-day considered the only cause of a large 
number of power companies operating their lines at high volt- 
ages choosing the core-type transformer. 

Experienced transmission engineers never fail to realize the 
severe conditions to which transformers are subjected to in 
practice, and whenever they ask manufacturers for transformers 
to connect to their high-voltage lines, seldom fail to go thoroughly 
into the factor of insulation, which, to them, means continuity 
and uninterrupted service. It is well-known that the insulation 
of a high- voltage transformer is subject to very severe potential 
strains, some of which, are: 

(a) Sudden increase in generator voltage. 

(b) Sudden increase in line voltage from local causes. 

(c) Direct and indirect lightning discharges. 

(d) Ground on one of the lines — depending on the connection. 

(e) Internal or external arcing grounds. 

(f) Line surges, etc. 

Reliable data taken from a number of power companies oper- 
ating long-distance high-voltage transmission lines, show, that 
the shell-type transformer has been more reliable than the 
core type for high-voltage service. 

With such large sizes as there are operating to-day, this class 
of apparatus can very well be considered as one of the most 
important, if not the most important piece of apparatus con- 
nected to a transmission system, and its reliability to satis- 
factorily operate for long periods of time, after it has once been 
put into service, is looked on with much interest and wonder 
from every side. To think, as some do, that once a transformer 
has been put into successful operation it will continue to operate 
indefinitely in a satisfactory manner without any attention is 
a wrong idea. It requires attention, and must be given atten- 
tion or else it will not give good service. 

Late modifications in the grading of insulation on the end 
turns of the core-type transformer has given it a better stand- 


ing, and it is now considered to give better service and can be de- 
pended upon in this regard equally as well as the shell-type 

Some of the most important advantages and disadvantages of 
these two general types might be summed up as follows: 

Advantages in Favor of the Shell-type. — Greater radiating 
surface of coils and core resulting in a lower temperature in all 
parts of transformer. This point has an important bearing on 
the insulation; the life of the transformer depending on the 
strength of the insulation of the hottest part. 

Interlacing of coils resulting in lower reactance voltages, hence 
closer regulation. 

Mechanically stronger and better able to withstand the electro- 
magnetic stresses. As the electro-magnetic stresses are pro- 
portional to the square of the current, a short-circuit of many 
times the normal full-load current will produce abnormal strain 
in the transformer. 

Satisfactory series-parallel operation. This often being neces- 
sary on large transmission systems. 

Advantages in Favor of the Core Type. — ^Easier to repair. 

Disadvantages of the Shell Type. — Difficult to remove a coil. 

Disadvantages of the Core Type. — ^With low-voltage winding 
designed for 22,000 volts and above, the amount of insulation 
next to the core means a larger mean turn of winding; the tem- 
perature and P R loss being increased thereby. 

Radiating surface on the low-voltage winding very poor, 
resulting in higher temperatures. It is a disadvantage if, say, 
90 per cent, of the transformer operates at a temperature of 
50° C. and the remaining 10 per cent, at 80° C. as this point is 
tihe weakest link in the insulation. 

The arrangement of coils (concentric) results in poorer regula- 
tion and higher reactance voltages. 

Less mechanical bracing because of its design and form. 

Not possible to operate a three-phase (delta-delta) trans- 
former in case one winding becomes damaged. 

It is obviously true that equally good results can be obtained 
with either the core-type or shell-type construction, but the de- 
sign of one or the other would depart from the regular standard 
expressed above if equal performances and reliability of opera- 
tion for equal conditions of load, etc., are desired. The differ- 
ence is slight but nevertheless in favor of the shell-type con- 


struction, particularly from the operating point of view, with the 
exception of repairs, should a break-down occur. 

The shell-type transformer is cheaper than the core-type with 
dear copper space (large copper space factor and ordinary iron) . 
And likewise, the core-type transformer is cheaper than the shell- 
type with relatively cheap copper space (low copper space 
factor and alloyed iron). In other words, shell- and core-type 
transformers cost as nearly as possible equal amounts when 
equal volumes of copper and iron spaces are equally expensive. 

Operation of Transformers. — The general idea is that trans- 
formers do not require any care or attention but that they will 
operate quite satisfactorily after having been put in service and no 
further attention is necessary. This is, however, not the way to 
get good results, although in some fortunate cases it might apply 
and has applied. Many losses of large power transformers have 
been recorded resulting from the cessation of the cooling medium, 
all of which could have been saved if proper care had been given to 
them. Hourly temperature reading is the best indication of any- 
thing wrong in this direction. As is well known, high-voltage 
transformers designed to operate with some form of cooling medium 
cannot run continuously, even at no load, without the cooling 
medium, since the iron loss alone cannot be taken care of by 
natural cooling. In case the circulation has been stopped by 
any cause, the transformer may be operated until the coils at the 
top of transformer in the case of an air-blast, or until the oil in 
case of a water-cooled transformer, reaches an actual temper- 
ature of 80° C. This temperature limit under ordinary condi- 
tions will permit the transformer to continue delivering power 
for about three hours; a very close watch must be kept of the 
temperature and the transformer must be taken out of service as 
soon as it reaches this limit. 

The efficiency of a transformer is usually considered to be its 
most important feature by the majority of central station 
engineers and managers operating distribution systems. By 
transmission engineers this factor is not considered to be the 
most important, the most important being the insulation and 
mechanical strength of the transformer, and consequently its 
reliability. The efficiency is no doubt an important feature and 
should not be neglected in the choice of a transformer but it 
cannot be considered as the most important feature of a large 


high-voltage power trunsforiucr. The writer believes the right 
order of importance to be: 

1. Reliability, or ability to supply continuous and uninter- 
rupted service. 

2. Safety, or a condition conforming with safety to life and 

3. Efficiency, or a condition met with after proper allowance 
has been made to conform with 1 and 2. 

Reliability as referred to here means many things both inter- 
nal and external. It might be stated, but not generally, that 
efficiency is the principal point in discussing transformers from 
their operating point of view. Where large high-voltage power 
transformers are concerned, efficiency can be said to take the 
third place of importance, and probably second place where 
low-voltage city distribution transformers are concerned. 

Excepting cases of lightning and roasting of coils due to 
constant overload, the low-voltage transformer (as used for 
city lighting and motor service) is free from harm. Not so with 
the large high-voltage power transformers such as we are using 
at the present day in connection with long-distance transmis- 
sion systems. Causes of failure are numerous; that is to say, 
causes that would and sometimes do bring about burn-outs of 
coils, moving of both coils and iron, and complete failure of a 

Use and Value of Reactance. — A transformer may be absolutely 
reliable electrically but be weak mechanically which might 
bring about its wreck. 

We know the short-circuit stresses are inversely proportional 
to the leakage reactance of the transformer, therefore on large 
systems of large power the use of high reactance or, more 
correctly, high automatic reactance, is required that will vary 
with the current. Several interesting methods are from time 
to time suggested and some of them experimented upon, but, 
to keep the current down to even 15 times normal current on a 
"dead" short-circuit and brace the transformer to take care of 
such a shock and be certain that the transformer is quite strong 
enough to take care of other severe mechanical stresses we 
need more experience. Some of the methods tried and in 
their experimental stage, are : 

(a) Use of reactance, internal or external, or both. 

(6) Use of resistance in the neutral of grounded systems. 


(c) Use of induction generators at the generating stations 
in place of the ordinary synchronous machine. 

(d) Strengthening of the transformers themselves. 
Experience has already demonstrated that due to excessive 

short-circuit current a limiting reactance of some form or other 
must be provided for large power transformers operating on 
systems of large kilowatt capacity, its design being either 
stationary or rotary; that is to say, an inductive reactance or 
an induction generator. With a stationary reactance it is quite 
possible to arrange to have it automatically switched into 
circuit, or switched out of circuit as the case might warrant 
when a short-circuit occurs. This would mean that it is used only 
when required and is always out of circuit under normal operating 

The ability of a modern high-voltage power transformer to 
withstand short-circuits is of far greater importance than 
good regulation. Modern practice does indicate larger reactance 
in both generators and transformers when operating in connec- 
tion with long-distance high-voltage systems, and regulation 
of 6 per cent, or worse is not considered very bad. Where ordinary 
city distribution transformers are used regulation is of another 
order. With our larger systems, larger stations and larger 
transformers, reactance of a certain given value in addition 
to that originally put into the system, station and transformers 
is virtually important and may be necessary if a limit is to be 
provided to check the enormous amount of power that can be 
developed in a short circuit. 

Causes of excessive current and consequent mechanical strains 
are: short-circuits between lines, short-circuits between trans- 
former terminals and leads and bus-bars, and grounds on star- 
connected systems with grounded neutral and other systems 
with grounded neutral. 

In order to arrive at the mechanical stresses occuring in a 
transformer due to a short-circuit it is simply necessary to use 
certain expressions in terms of the terminal voltage, short- 
circuit current, and the distance between primary and secondary 
coils. For example: — Take a 5000-volt, 5000-kw., 25-cycle trans- 
former, full-load current in the primary being 577 amperes and 
measured reactance of the windings, is 2.9 per cent. 

If (as is usually done) the reactance of the windings be given 
in per cent, of the impressed voltage, the short-circuit voltage 


will be equal to the full-load current divided by the percentage 
reactance, or: 

/ 577 

/°= 1^ = 0029 =20,000 amperes (18) 

which represents an amount in excess of 30 times normal full- 
load current. 

If (/) is the force in grams produced between primary and 
secondary windings, and (/) the distance between their magnetic 
centers, the mechanical work done in moving one set of coils 
through the distance (l) against the force (/) would be: 

^=/.^i.X 10^ joules (19) 

At short-circuit very little magnetic flux passes through the 
secondary coils of a transformer, but if the system is sufficiently 
large to maintain constant voltage at the terminals of the 
transformer during a period of short-circuit, full magnetic flux 
passes through the primary coils. Such a condition can never 
exist sufficient to maintain a constant voltage at the terminals 
of transformers located at the end of long-distance transmission 
lines, but for comparatively short distances and on systems of 
practically unlimited power behind the transformers (sufficient 
to roast them) and of close regulation, it is possible to get 
results that will do so much damage as to wreck them entirely. 
Thus a transformer with a 2.9 per cent, reactance would give a 
short-circuit current at constant voltage of 30 times full-load 
current, and one with a reactance of 2.3 per cent, would give 40 
times full-load current, while one with 4 per cent, reactance 
would produce only a short-circuit current of 25 times. This, 
then, certainly demonstrates that more reactance in the trans- 
former circuit for better protection is required, and that the 
reactance should be designed proportional to the current so as 
to be effective. 

The terminal voltage at the transformer during short-circuit 
is taken from the leakage inductance of the transformer, there- 
fore : 

810 E 1° 0.706 E r. , „ 

— ^ g.c.m.= jr-j mch lb, (20) 

is the force exerted on the transformer coils and represents the 
work done in moving the secondary coils until their magnetic 


centers coincide with those of the primary coils (an impossible 
condition) which would cause zero reactance flux to pass between 
primary and secondary coils. 

Now assuming that the transformer in question has three 
primary coils between four secondary coils, and the distance 
between the magnetic centers of the adjacent coils, or half-coils, 
is three inches. The force exerted on such a transformer and 
its respective coils would be something like: 

= 940,000 lb. =426 tons. 

This force is exerted between the six faces of the three primary 
coils and the corresponding faces of the secondary coils, and on 
every coil face is exerted the force of: 

^ 426 ^, , 
-^= -„ =71 tons 
6 6 

If the distance between adjacent coils had been 1.7 inches the 
force exerted on the transformers would have been 1,750,000 lb,, 
and if the distance had been 4.3 inches instead of three inches, 
the force exerted on the transformer would have been under 400 
tons, or about 65 tons for each coil; this is the average force, 
which varies between and 130 tons. 

In the design of such a reactance coil the following formula 
is used : 

4.44 /<i6A^ 
E Jos— 0) 

in which (/) is the frequency, (A^) the number of turns, ((f)) the 
flux enclosed by the conductor. The flux produced by a coil 
without an iron core being: 

9 = ~j^ (21) 

where {N) is the number of turns, {d) the inside diameter, (A) 
a constant which equals 0.28+0.125— (jA and / the current 

in the coil. 

The tendency of leakage flux is not uniform throughout the 
width of the coil of a transformer, but is greater at the center of 

1 (I) is the length and D the mean diameter of the solenoid. 


the coil (if the coil be imbedded in iron). If, then, a short- 
circuit should occur, the coil will have a tendency to buckle, 
and should it not be sufficiently strong to overcome this tendency, 
and its equilibrium be disturbed, the forces of conductor upon 
conductor will not lie in the same plane, and hence are liable to 
break the insulation tape bindings, and heap up on each other 
at the point of most intense density. 

The shell-type transformer coils have the tendency to twist 
at their outer corners, and the vertical portions of the coils to 
form into cable. 

The core-type transformer coils have the tendency to be 
forced upward or downward into the iron core (the heaviest 
current coils being, in most instances, forced out of position). 
If, however, the centers of the primary and secondary are exactly 
coincident the entire force would be exerted in a horizontal 
direction, and there would be no tendency for any of the coils 
to move vertically. Whether the primary or secondary is forced 
up depends upon which coil has its center line above the center 
line of the other. 

It is only recently that the power-limiting capabilities of 
reactance have come to the fore. This has largely been due to 
the marked movement toward consolidation and concentration 
in the central station industry resulting in unified systems of 
gigantic proportions, the loads upon which may fluctuate 
suddenly through a wide range or, still worse, short-circuits on 
such high powered systems may give rise to rushes of current 
the volume of which was hitherto unknown in previous systems. 
In the last few years we have come to larger and larger systems, 
and consequently greater difficulties of operation. The con- 
centration of power for economical reasons in these huge power 
plants, the dependence for vast industrial enterprises and for 
our ever increasing transportation systems, as well as for lighting 
and industrial power from ten, twenty or thrity substations 
distributed over vast areas and supplying large cities, make it 
absolutely essential that they shall l^e protected against disturb- 
ance, and that every possible precaution should be taken, which 
experience or ingenuity can provide, against irregularity in opera- 
tion, because if these huge transformer systems are going to be 
subjected to disturbance and interruption of service other factors 
affecting their regulation and efficiency must be sacrificed to gain 
this end, if need be. 


The advantages of iron and air reactance coils in a power 
station are many, provided the former type is worked at a suf- 
ficiently low magnetic density so that it will not become satur- 
ated at the maximum peak of a short-circuit current, and pro- 
vided the latter type has not too strong an external magnetic 
leakage, and that both types are used only when needed. They 
are effective in protecting transformers against surges, lightning, 
and short-circuits. 

At 11 0,000 volts and over a phenomenon makes itself felt, especi- 
ally in large transformers, which is negligible at lower voltages; 
the distributed capacity of the high-voltage transformer winding. 
At lower voltages, the transformer capacity (c) is negligible, 
and the transformer thus is an inductive apparatus, and as such 
is free from all high-frequency disturbances, such as traveling 
waves, impulses, stationary oscillations, etc. High-frequency 
currents cannot enter the transformer, but produce high voltage 
between the end turns, protection against which is given by the 
high insulation of the end turns of the transformer, and also the 
external or internal choke coil. At very high voltage the 
electrostatic capacity of the transformer becomes appreciable, 
and the high-potential coils of the transformer then represent a 
circuit containing distributed capacity, inductance, resistance 
and conductance. In the high-voltage winding of a transformer 
the inductance is high in value and the capacity low, that is, 
comparatively speaking lower than the respective constants in a 
high-voltage transmission line. The result, in general, is that 
the oscillations are higher in voltage and lower in current, in the 
former. The danger to which a transformer is exposed by high- 
frequency disturbances from the line side, is not limited to the 
end turns only, but damage may be done anywhere inside of the 

A choke coil or reactance between the transmission line and 
transformer might or might not in this case become a source of 
danger. It protects the transformer from certain line disturb- 
ances but does not protect the transformer itself from disturb- 
ances which originate inside its windings; in fact the addition of 
this choke coil has the tendency to throw back the disturbance 
and thereby increase the internal voltage and destructiveness. 

Recently it has become customary to specify that transformers 
of large sizes and high voltages must not have less than ap- 
proximately 5 per cent, reactance for the protection of trans- 


formers, switches, generators and all parts of the system against 
the high mechanical stresses due to excessive currents. 

To increase the reactance of a given transformer one or several 
modifications are possible, as, for instance: 

(1) Decreasing the dimensions of the windings in the direction 
in which the leakage flux passes through the wire-space. 

(2) Decreasing the number of groups of intermixed primary 
and secondary coils, the number of turns of each group being 
correspondingly reduced. 

(3) Increasing the total number of turns in primary and 

(4) Increasing the length of turns in primary and secondary. 
From the viewpoint of safety to the transformer itself by the 

introduction of higher reactance within the transformer, little 
practical benefit is derived. 

No hard and fast rule can be given for the correct location of 
reactance. There are several reasons against making it all a 
part of the transformer. Of course, so far as the generating 
stations are concerned inductive reactance in any form in 
connection with high systems is important, but where trans- 
formers are located at the end of long transmission lines it may 
or may not be necessary to use it. To make a large transformer 
of large power with high reactance is not an easy matter, as the 
general principles of design and the economic utilization of 
materials obtain for us only low factors, and in order to make 
a transformer of high reactance we have to increase its cost and 
its ampere turns, with of course more copper and more winding 
space, and consequently a larger core and a bigger transformer 
for the same output. If it is desired to increase the reactance 
by increasing the space between the primary and secondary 
windings, the same results are obtained and the efficiency of 
the transformer is reduced. Placing reactance in the transformer 
itself is very effective on short-circuit, whereas an external 
current-limiting reactance will not generally be so effective 
because it is not on general principles designed for the short- 
circuit current and its value consequently is about frustrated by 
magnetic saturation. A reactance is required only during the 
short-circuit. In that case, why then should an expensive and 
inefficient transformer be considered when a short-circuit 
might occur only once in five years; would it not be much better 
to arrange a reactance external so that its maximum flux on 


short-circuit is about equal to its voltage flux? If a reactance 
is put in to limit the short-circuit current, the reactance must 
be there when the short-circuit occurs. All long transmission 
lines possess magnetic reactance which tend to reduce the volt- 
age so that less reactance will be required for similar trans- 
formers located at the end of the line than those at the generating 

Earthing the Neutral of Transformers. — The chief advantage 
of resistance in the neutral of a star-connected system is to limit 
the earth current on short-circuit. To arrive at a close value of 
resistance that will limit the earth current at all times is not 
easy, in fact in most cases impossible; the ideal condition being 
where the load and voltage of the system are not disturbed. 
The two extreme conditions of operation are the insulated system 
and solid-grounded system. Of these two, experience so far has 
proved the better to be the grounded system, and whether we 
ground through resistance or "dead" ground the method depends 
entirely on the system itself. Both methods will work satis- 
factory while certain conditions of operation exist and likewise 
both will vary under one particular condition, it being better or 
worse in one or the other depending on the kind of disturbance. 
It seems to appear that the best way to limit the current and 
disconnect the circuit at the same time, in preference to ground- 
ing through resistance, would be to add automatic resistance 
in the line side which would come into effect when the line 
current reached a given value and actuate the oil switches. A 
broken insulator or ground of any kind on the line, develops a 
short-circuit which will interrupt the service depending on the 
exactness of the resistance in the grounded circuit and neutral; 
generally speaking the service is interrupted whether there be 
resistance in the grounded neutral or not. It is often stated 
that with one line down and grounded in an insulated delta system 
(a non-grounded delta system), an interruption or short-circuit 
will not occur. This statement is very vague and might lead 
those who have not had experience with very high- voltage system 
(voltages above 60,000 volts) to believe that in the majority of 
cases it is correct. It may be stated that it is not correct for 
neither the non-grounded star or delta systems operate at these 
high voltages except in very unusual cases. 

The primary or secondary may be put to earth or ground through 
a group of star-connected transformers as shown in Fig. 122, or, 



if these transformers are not available and a ground connection 
must be used, a substitute might be made similar to Fig. 123. 
With this connection grounded as shown, the maximum insulation 
strain between any of its secondary or primary windings respec- 
tively to ground (whichever side might be grounded) will be 87 
per cent, of full voltage between terminals, but with the trans- 
former method of grounding and under the same operating con- 
ditions the maximum strain will not be greater than 58 per cent, 
of full voltage between terminals. Grounding the neutral point 

Fig. 122. — Method of grounding an insulated delta system through induc- 
tance coils. 

of the high-voltage windings of transformers connected to a 
transmission line will immediately operate the relays or circuit- 
breakers should one of the line conductors fall to the ground. 
Grounding the neutral point of the secondary, or low-voltage 
windings, will not operate the relays unless some special provision 
has been made, and even so, before the relays or circuit-breakers 
are actually operated the secondary or low- voltage windings are 
made subject to very high-voltage stresses. The best method of 
all is to ground the neutral points of both the high- and low-voltage 
windings necessary, and where delta-delta systems are used, ground 
the windings as shown in Fig. 123. A common condition found 
in practice is the non-grounded delta-delta system. On systems 
where the ground connection is used, the character of the ground 


connection iind the ground itself should be considered at the 
worst time of the year only, inspection and tests at other times 
of the year being of little or no value and should not enter into 
the design of the resistor and its earth resistance, and the earth 
connection itself. Grounding through a limiting resistance 
gives certain advantages, and grounding solid has the disadvan- 
tage of mterrupting the service at all times in case of any other 
ground developing in the metallic circuit. Its use is helpful in 
reducing mechanical stresses and in largely overcoming dangerous 
surges set up due to arcing grounds, etc. 

Fig. 123. — Method of direct grounding an insulated delta system. 

Earth Connections. — The old method of making earth connec- 
tions consisted in excavating a large hole, placing an expensive 
copper plate in this hole surrounding it with a load of coke. At the 
present time this method is generally considered to be not 
only a waste of money, but of less efficiency than the multiple 
pipe-earths. Their resistances are no lower even where perforated 
and treated with special compounds, their current capacity no 
greater and their life and constancy no better. 

For very small areas such as pipe-earths, the resistance of an 
earth connection depends greatly upon the exposed area of 
the metal plate to earth. 

A simple contact of a metal conductor with a normally moist 
earth will give a high resistance of enormously variable values 
due to the variations in contact. 


An ordinary pipe resting on the ground was found to give 
an average of 2000 ohms. The same pipe driven 6 feet into the 
ground gave 15 ohms, and the same pipe resting on dry pebble 
gave several thousands of ohms. 

As the pipe penetrates the earth, it is found that each addi- 
tional foot adds a conductance about proportional to the added 

The specific resistance of the earth will depend upon what 
chemicals exist around the metal plate and how much moisture 
there is present. In a dry sand-bank the resistance is prac- 
tically infinite. In a salt marsh the specific resistance is 
extremely low, being about one ohm. Resistances of earth 
connections will vary greatly even in the same locality. 

The engineer is interested mostly in the earth connection in 
the immediate vicinity of the earth pipe or plate; because in 
the main body of the earth, the area of cross-section through 
which there is current, is so enormously great that even if the 
specific resistance is very high the total resistance becomes 
negligibly small. If the earth plate should lie in the dry non- 
conducting stratum of the top layer, it is advisable to get 
some means of introducing better conductivity, not only in the 
contact between the plate and the earth, but also between the 
earth conducting layer deeper down. The best means of 
accomplishing this is to pour a salt solution around the iron 
pipe and allow it to percolate down to a good conducting 
stratum. In order that this solution may not be washed out 
by the natural filtration of rain water, it is well to leave a 
considerable quantity of crystal salt around the pipe at the 
surface, so that rain water flowing through will dissolve the 
salt and carry it continuously to the lower strata. Salt has the 
additional value of holding moisture. 

Objections have from time to time been made to the use of 
salt in stating that it would be destructive to the metal of the 
pipe. Under the usual conditions it is found that the chemical 
action on an iron pipe is of negligible value. Iron pipe is very 
cheap, and it would be better practice to use the salt, even if it 
did destroy the pipe within a period of years which it does 

If it is desired to decrease the resistance of earth connections, 
it is necessary to drive earth pipes that are separated by a distance 
sufficient to keep one out of the dense field of current of the 


other. The current density in the earth around a pipe-earth 
drops off approximately as the square of the distance. A good 
method is to drive multiple pipes at least 6 ft. apart and con- 
nect them together, and the resistance will decrease almost in 
proportion to the number of pipes. 

The more salt water placed around a pipe-earth, the less 
the potential gradient near the pipe. Inversely the drier the 
earth, the more the concentration of potential near the pipe. 

Earth pipes have a certain maximum critical value of current 
which they will carry continuously without drying out. The 
application of a high voltage might have so bad an effect that 
the earth around a pipe will be dried quickly and the earth- 
plate lose its effectiveness as a ground. As the moisture is 
boiled out and evaporated at the surface of the pipe, the sur- 
rounding moisture in the earth is being supplied, but the vapor 
generated tends to drive away this moisture from the pipe. 

The diameter of the pipe effects the resistance comparatively 
little. Doubling the diameter of a pipe decreases the resistance 
by a small percentage. 

Switching. — In laying out systems which must of necessity be 
more or less complicated, the question of continuity of service 
should be always kept in mind and placed first in importance. 
At the present time there are in operation many intricate systems 
with tie-lines between receiving stations and generating sta- 
tions. This arrangement presents difficulty in providing pro- 
tection on account of the interconnections and disturbance in 
any one line may cause an interruption of a large portion of the 

Systems are sometimes "overrelayed," relays which the oper- 
ator cannot thoroughly understand being installed. The result 
is that he oftentimes renders some of them inoperative by 
plugging with wood to prevent what he considers unnecessary 
interruptions of service, which may be at the expense of needed 
protection to the transformers. Before deciding upon the 
system of connections a careful study should be made to deter- 
mine the simplest possible arrangement, when taking into account 
not only the delivery of energy under normal conditions, but also 
continuity of service under abnormal conditions. 

Low-voltage moderate capacity transformer switching is 
simple. High-voltage power transformers connected to large 
systems are not quite so simple in their arrangement of switching 



and their protection from both internal and external short-circuits 
and other faults. 

Figs. 124, 125 and 120 show four different methods for high- 
voltage transformer protection and their switching. The series 
relays may be attached directly to the switches which thoy 
operate, while those relays energized by means of series trans- 
formers and potential transformers (differential relays) are usually 

Primary Eelay 

Disconnecting Switches 

lelay SI OH 

> Switch 
hes r^ Dteco: 



Dteconnecttog Swltcihes 

110,000 Volt Bus Bars 

-Disconnecting Switches *]; 

on Switches . 

Series Primary 
Relays ~~ 


[o] on Switch 


6. Disconnecting 
/ Switch 

Bus Bars 

Fig. 124. — Method of switching and protection of transformers. 

attached to the switchboard panels located on the operating 

Series relays, or secondary relays (relays energized from the 
secondaries of series transformers) or both, may be used on high- 
voltage circuits. The oil-switches marked A, B, C, etc., are 
operated by means of intermediate low-voltage switches which 
receive their energy from an auxiliary source of supply or the same 
source as the case may be; these small switches are located on 
the main switchboard. The disconnecting switches are of the 
air-break single-pole type and are usually located at that point 
where a break in the circuit is most desired, for interchanging, or 
isolating a circuit, bus-bar, etc. 

If a transformer is switched direct on to a high-voltage system 


there may be a rush of current equivalent in its suddenness to 
what usually occurs in high-frequency experiments, and the exact 
amount of the rush will depend largely on the local capacity of 
the high-voltage switches and their connections, that is, the 
distance they are located from the transformers to which they 
are connected. 

The usual shocks to the end turns of transformers due to 
switching are dependent upon the load, character of the load, 


110,000 Volt 

o Disconnecting 

Oil Switch 

Inverse tlme- 

Umlt series Relay 

for "A" Switch 

Tlme-llinlt over-load 
Relay for C Switch |6| 

Disconnecting ^t 
Switch (/ 

on Switch 


Power Trans^formers 


I • Keverse c 

Reverse cnrrent Relay 

I Disconnecting 

•f To Low Voltage Bus Bars t 
Fig. 125. — Two methods of switching and protecting transformers. 

type of switch (oil type or air, and single- or multi-break), the 
time allowed for opening, and the method of switching. As 
regards the switching itself, there are several ways in which 
transformers can be switched on to a line, as for example: 

(1) Switching in the transformers on an open line. 

(2) Switching non -energized transformers on an energized 

(3) Switching energized line on to energizied transformers. 

(4) Switching in the transformers and afterward raising the 
voltage at generating station. 

(5) Switching under any of the above conditions but with 
resistance or reactance in series. 



(0) Switching on the low-voltage side of transformers. 

(7) Switching on the high-voltage side of transformers. 

(8) Switching energized transformers on long transmission 
lines with transformers already switched in at the receiving 
station, but "dead." 

(9) Switching in transformers during lightning storms, 
line disturbances, etc. 

(10) Switching in transformers using oil-switches. 

(11) Switching in transformers using air-break switches. 

Series Transformer 


Vh\ Switch 
-^[pjoil Switch 

Bus Bars 

o^Si Disconnecting' 

Definite Time 
limit Relay for 
A & D Switches 

Inverse Tlme- 
lijiiit Relay for 
B & E Switches 

Oil Switch 

Series Transformer 

Oil Switch 


Generator Busses 
Fig. 126. — Another method of transformer switching and protection. 

Most of the methods above shown are bad and may lead 
to excessive surges being thrown on the windings of the trans- 
formers. Next to (4), the best method is to do all switching 
on the low-voltage side whenever possible using only 3-pole 
oil-switches in the case of three-phase circuits. The method 
(4) is generally not possible because of the necessity of lowering 


the voltage of the system. The next preferential method is 
where a receiving station is "dead" and has to be energized 
all high-voltage switches being closed first. 

A very important point about switching is the time-limit. 
If it is necessary to open a circuit instantaneously on very 
large loads, switching can be made large enough to do the work, 
but where economy of design is required, a time-limit should be 
used, and, probably, a reactance to limit the flow of current. 
The time-limit with its relay will therefore take care of that 
amount of current which it is set for and will permit the switch 
to open up to the load under which it is able to operate safely. 
If a reactance is used in connection with switches of this kind, 
it might be well to provide for some arrangement whereby it 
can be brought into use only when it is needed or, for instance, 
when the circuit is actually being opened. 

Aside from the above methods of closing circuits, there 
are two conditions of opening circuits which should be avoided, 

(1) Opening a long transmission line under heavy load, on 
the high-voltage side. 

(2) Opening a long transmission line on the high-voltage side 
with no-load. 

Method (1) refers principally to short-circuits, and method 
(2) to a high-voltage line required to be made "dead." If a 
live circuit is to be cut out at all it should be done from the low- 
voltage side no matter what the load conditions are. 

High-voltage switches for large power transformers should 
be of the most substantial mechanical construction and capable 
of safely breaking a circuit under extreme conditions. For 
comparatively small installations it is still customary to use 
expulsion fuse-switches installed inside of a delta connection, 
that is, one on each lead or 6 for a three-phase group. This 
is not good practice for the reason that with a blown-out fuse 
(leaving the delta open) a bad phase distortion may occur. 
Where connections of this kind are necessary, they should be 
made through air-break switches and not fused switches. 



The ordinary auto-transformer is a transformer having but one 
winding. The primary voltage is usually applied across the 
total winding, or in other words, across the total number of turns, 
and the secondary circuit is connected between two taps taken 
off from the same winding, the voltage ratio being equal to the 
ratio of numbers of turns. 

The auto-transformer shown in Fig. 127 has two taps brought 
out at a and h. Thus the whole or part of the winding vasiy be 





c 50 > 





Fig. 127. — Step-up auto-transformer. 

used to raise the voltage or lower the voltage simply by changing 
the connections. 

For example, the primary a b, is wound for 1000 volts, a c 
and b d each being wound for 50 volts. As will be seen, by 
taking a tap out from a and d, the secondary gives 1000-1-50 = 
1050 volts. And by moving to the far end of the winding, a, 
the voltage maybe raised from 1050-1-50 = 1100 volts. In order 
to obtain 550 volts all that is necessary is to bring two leads out 
from X and d, or x and c; the secondary then gives 1050—500 = 
550 volts. 




For pressure regulation auto-transformers are very convenient, 
being used to some extent for regulating the voltage of trans- 
mission lines. They are also used for starting induction motors; 
and lately they have been used for single-phase railway service, 
rectifiers, low voltage (5-15-27- volts), lighting, etc. 

For series incandescent systems a transformer similar to that 
shown in Fig. 127 may be used. A portion of the winding, a b, is 
common to both primary and secondary. The secondary 
voltage, c d, is greater than the primary, a b, by the voltage of 
the winding, b d and c a. The voltage, 6 d or c a, is thus added 
to the primary to form the secondary voltage of the circuit. 

By reversing the connections of the winding, 6 d and c a, how- 
ever, it may be made to subtract its voltage from the primary, 

Fig. 128. — Step-down auto-transformer. 

a 6; in which case the secondary voltage becomes less than the 
initial primary voltage; (Fig. 128). Further, by bringing a 
number of leads from parts of the winding, b d or c a, the second- 
ary voltage may be increased or decreased by successive steps as 
the different leads are connected to the secondary circuit. For a 
given transformation of energy, an auto-transformer will be con- 
siderably smaller than an ordinary transformer, and consequently 
its losses will be less and the efficiency higher. The amount of 
power delivered to the service mains at an increased voltage is 
very much greater than the power actually transformed from the 
primary to the secondary of the transformer. In fact, the power 
actually transformed is equal to the increase of voltage multiplied 
by the total current delivered; and the output, or actual rating 
of the transformer is based upon the power transformed. 

Example. — ^The voltage of a long-distance transmission line is 
to be raised from 40,000 to 45,000 volts, and the maximum 
current to be handled is 750 amperes. What is the rating of 



auto-transformer required for this service? and what will be the 
actual power delivered over the line? 

The actual rating of the auto-transformer will be, 

5000X750 = 3750 kilowatts. 
The total power delivered to the line will be, 
45,000 + 750 = 33,750 kilowatts. 

In Fig. 128 the secondary voltage is smaller than the primary. 
The voltages, b d and c a, are thus subtracted from the primary 
to form the secondary voltage of the circuit. The auto-trans- 
former may thus act as a step-up or step-down transformer. 

The action of an auto-transformer is similar to that of the 
ordinary transformer, the essential difference between the two 
lies in the fact that in the transformer the primary and secondary 
windings are separate and insulated from each other, while in 
the auto-transformer a portion of the winding is common to both 




FiG. 129. — Two-phase auto-transformation. 

primary and secondary. The primary and secondary currents 
in both types of transformers are in the opposite direction to 
each other, and thus in an auto-transformer a portion of the 
winding carries only the difference between the primary and 
secondary currents. 

In the foregoing explanation of auto-transformation the 
ordinary transformer will be used instead of the auto-transformer. 

Two-phase, four-wire, auto-transformation as shown in Fig. 
129, where the secondary winding is made to assist the primary, 
may be considered as two ordinary single-phase circuits. The 
ratio of transformation in this case is 10 to 1, therefore we obtain 
by the connection as shown, a secondary voltage of 1100. 

By reversing the secondary connection it is possible for us to 
get 1000 - 100 = 900 volts. 



If we should take one end of the secondary windhig and connect 
it as shown in Fig. 130 we would obtain 50 per cent, of the primary 
voltage plus 100, which is the total secondary voltage. Then 
assuming the primary and secondary to have a four-wire, that is 
to say, two independent single-phase systems, we would have a 







* — 1000—^ 







" 600—* 

« — occ 

— *- 

a Ob d 

Fig. 130. — Two-phase four-wire auto-transformation. 

secondary voltage of 500 plus 100= 600 volts. The points, x 
and y, are taps brought out from the middle points of the 

Another two-phase auto-transformation is represented in Fig. 
131. Both primary and secondary areconnected to a three-wire 

Fig. 131. — Two-phase three-wire auto-transformation. 

system from which we obtain a secondary voltage of 1100 
between a' h and h c' , and 1550 volts between a' and c', or 

1100X1.41 = 1550 volts. 

A very interesting combination giving a five-wire, two-phase 
transformation is shown in Fig. 132. From this arrangement it 
is seen that quite a number of different voltages and phase 



relations can be obtained, and by simply shifting the connection 
at X we increase and decrease the resultant voltages. 

At a re rf and c x d the respective phases that constitute the 
four-phase relation have been changed from 45 degrees to a 

o' 6 

-1000 > 





< 300- 

"f ^1000 » 


U — 100 — > 


FiG. 132. — Two-phase five-wire auto-tranformation. 

slightly higher value, the voltage increasing in proportion to the 
increase of phase difference. 

The three-phase arrangement shown in Fig. 133 is a method of 
auto-transformation by which we are enabled to supply approxi- 


imm J liK^^mJ 


-1000 — *■ 








FiG. 133. — Three-phase star auto-transformation. 

mately 1040 volts to the secondary mains, 1, 2 and 3, from a 
1732-volt primary source of supply, using three transformers 
with a ratio of 10 to 1, or = 1000 to 100 volts. 
Between points ah,h c, a c, we obtain 

500 X\/3= 866 volts. 


Between points 1 2, 2 3, and 1 3, there exists approximately 
500 + 100 X \/3 = 1040 volts. 

The three-phase delta connection shown in Fig. 134, with its 
three secondary windings left open-circuited, may be used where 


< 1000 *■ < ^1000 — > 


a l b c 



c a 
-500 =H 


Fig. 134. — Three-phase auto-transformation with secondaries open 


a three-phase 500-volt motor is installed. The secondary wind- 
ings, if required, may be used at the same time for lighting or 
power. To obtain a 100-volt lighting service it will be necessary 
to connect the secondary windings in delta, running a three-wire 
distribution to the source of supply, ah c. This method of 

Fig. 135. — Three-phase delta auto-transformation. 

connecting transformers is often found useful in places where 
transformers of correct ratio are not obtainable. 

The combination shown in Fig. 135 has its secondary windings 
connected in circuit with the primary windings. Like Fig. 133 
a tap is brought out from the middle of each winding; but instead 



of leading out to the secondary distribution, it is connected to one 
end of the secondary winding as shown at 1, 2 and 3; the result 
of which represents a phase displacement as shown in the vector 

Fig. 136. — Three-phase double-star auto-traiisformation. 

Using the same transformers as in the previous examples, 
connecting A B C to a 500X\/3=866 volt supply, it is possible 
for us to obtain a number of different voltages for the second- 
ary distribution, such as three at 1000, three at 600, three 





< ^1732- 



—1000 — >\ 



Fig. 137. — Three-phase star auto-transformation with secondaries open- 

at 520, six at 500, three at 173, and three at 100 volts, re- 
spectively (Fig. 136). According to the raito of transformation 
applied at the secondary distribution it is understood that the 
kilowatt capacity of the transformers will vary. 

Another three-phase combination is shown in Fig. 137, where 
it is shown that the primary windings are connected in star, and 



the three leads, ABC, are connected to a 1732-volt supply. 
From the middle of each primary winding a tap is brought out 
at a 6 and c. 

The secondary voltage across ab, b c and a c is 500X\/3 =866 
volts. The 100-volt secondary winding may be used for power 












FiG. 138. — Three-phase auto-transformation using primary windings only. 

and lighting, single or polyphase, depending upon the size and 
design of the transformer. 

Fig. 138 represents a three-phase transformation, using only 
the primary windings. One end of each primary winding is 
connected to the middle point of another primary winding. 
Three-phase, 1350 volts, impressed on A B C will give 500 
volts on 1-2, 2-3, and 1-3. 




For operating arc- and incandescent lighting systems from 
constant-potential, alternating-current mains, the constant- 
current transformer is frequently used. It is designed to take a 
nearly constant current at varying angles of lag from constant- 
potential circuits, and to deliver a constant current from its 
secondary winding to a receiving circuit of variable resistance. 

Thus the transformer operates automatically with respect 
to the load, making it possible to cut out any number of lamps, 
from full rated load to zero load, while still maintaining a con- 
stant current on the line. The self-regulating characteristic 
is obtained by constructing the transformer in such a manner 
that either the primary or secondary coil is balanced through 
a system of levers against a counterweight, which permits the 
distance between primary and secondary coil to vary. This 
automatically increases or decreases the reactance of the circuit 
in such amount as to hold the current constant irrespective of 
the load. 

For the majority of series incandescent systems the constant- 
current transformer will be found lower in initial cost and more 
reliable in service than the reactive coil method, as it combines in 
one element the advantages of a regulating device and an insulat- 
ing transformer. 

One type of transformer consists of a core of the double 
magnetic type with three vertical limbs and two flat coils 
enclosing the central limb. The lower coil, which is fixed, is 
the primary, while the upper one, or secondary, is carried on a 
balanced suspension, and is free to move along the central limb 
of the core. 

The repulsion between the fixed and moving windings of the 
system for a given position is directly proportional to the current 
in the windings. 

For series enclosed, arc-lighting on alternating-current circuits 
the constant-current transformer is universally used. This type 
usually consists of a movable secondary and fixed primary wind- 




ings, surrounded by a laminated iron core. Tliis core and the 
yokes at the top, bottom and sides, form a double magnetic cir- 
cuit, as shown in Fig. 139. 

The magnetic flux which passes through the primary winding, 
flows partly through the secondary winding. The secondary 
winding is made movable and partly counterbalanced by a 
weight so that an increase in the current causes the secondary 
to be pushed further away from the primary. The weight is so 
adjusted as to sustain the coil against the leakage flux, and 
simply by changing the amount of counterweight the trans- 
former can be adjusted to m'aintain any desired current. 

1J? iP 

Fig. 139. — Type of constant-current transformer for arc lighting systems. 

In small transformers, which have but one movable coil, the 
counterweight equals the weight of the coil less the electrical 
repulsion, and a reduction in the counterweight will produce an 
increase in the current. In large transformers, having two sets 
of movable coils balanced one against the other, the counter- 
weight serves merely to draw the primary and secondary coils 
together in opposition to the repulsion effect. In this case, 
a decrease in the counterweight is followed by a decrease in the 

The counterweight attachment is made adjustable because 
the repulsion exerted by a given current in the coils is not the 
same at all positions of the coils, being- greater when the pri- 
maries and secondaries are close together and less when the pri- 


maries are separated. When the primaries and secondaries are 
separated by the maximum distance, the effective force tending 
to draw them together should be less than when they are in 
full-load position; that is, when the primaries and secondaries 
are close together. 

For capacities of 100 lamps, or less, there is one primary and 
one secondary coil, the primary being stationary, and the 
secondary, or constant-current coil is suspended and so balanced 
by weights that the repulsion between it and the primary changes 
the distance between them with variations of load, the current 
in the secondary being kept constant. 

For capacities of 100, or more, there are two primary and two 
secondary coils. A separate circuit of lamps may be operated 
from each secondary, the two circuits being operated at different 
currents if desired. 

The maximum load of each circuit, when operated separately, 
will be one-half the total capacity of the transformer. However, 
when it is necessary to operate the two circuits at unequal 
loads, the load of one circuit being less, and of the other greater, 
than one-half the rated capacty of the transformer, the coils 
may be connected together in the multi-circuit arrangement, 
which will allow loads up to the total capacity of the trans- 
former to be carried upon one circuit. 

For capacities of 250, or more, there may be one or two primary 
and two secondary coils, two circuits being operated from each 
secondary, thus giving four circuits from the transformer. It is 
not necessary that the loads on the two circuits from each coil be 
balanced, and, if desired, the total load can be carried on one cir- 
cuit alone, provided the insulation of the line is such as to admit 
the high voltage which will be introduced. Constant-current 
transformers are of the air- and oil-cooled type. The air-cooled 
type is surrounded by a corrugated sheet iron or cast-iron casing 
with a base and top of cast iron. The oil-cooled type is sur- 
rounded by a cast-iron case, providing ample cooling surface. 
The working parts are immersed in oil, which assists in conduct- 
ing away the heat. 

Constant-current transformers are usually located in stations 
where electric energy is generated, received or transformed, as, 
for instance, a receiving station at the end of a long high-voltage 
line; although in large cities they are, for convenience, located 
in district sub-stations and close to distribution centers. 


They are made to operate on 60- 125-cycle and even 133-cycle 
systems, and for any reasonable primary voltage. It is cus- 
tomary to furnish a 60- 125-cycle transformer for a 125- 133-cycle 

The constant-current transformer will maintain constant 
current even more accurately than the constant potential 
transformer maintains uniform potential, and its regulation over 
a range from full-load to one-third its rated capacity will come 
within 1.5 per cent, if properly adjusted. 

The efficiencies of constant-current transformers with a full 
load of arc lamps vary at 60 cycles from about 96 per cent, for 
the 100-lamp transformer to about 94.5 per cent, for the 25-lamp 

Another constant-current transformer known as the "edge- 
wise wound" type is fast replacing the older type mentioned 

From this modern method of construction several advantages 
are derived, principal among which is the almost absolute im- 
possibility of an internal short-circuit, as the voltage between 
any two adjacent conductors consists of only the volts per turn 
of the transformer, or at the most about 10 volts. 

The construction of this type is somewhat different. The 
core is built up of thin laminations of sheet steel and has a center 
leg of cruciform shape. This form of construction not only 
tends to support itself, thereby requiring a very thin angle for 
securely clamping the laminse and decreasing the eddy current 
in the clamp, but the form of construction also gives the most 
economical flux path as well as permitting a smaller diameter 

The primary and secondary consist of four concentric edge- 
wise wound coils of double cotton covered rectangular wire. The 
four sections are assembled together concentrically with wooden 
spacing strips to maintain at all points an air-duct of sufficient 
width. Two surfaces of each conductor are therefore exposed 
to the currents of air passing through the air-ducts, thereby in- 
creasing the effective radiating surface of each coil by about three- 
fold. The large radiating surface with the consequent cool run- 
ning allows a very high current density which permits of less 
copper per ampere-turn, less weight, less floor space, and, of 
course, a cheaper transformer for the same kilowatt rating than 
the older type above mentioned. 



Construction of Transformer. — The core of this efficient and 
most modern type of constant-current transformer is built up 
of laminations of specially annealed iron, which are sheared to the 
required length and width. Each sheet or lamina) is treated by 
coating the surfaces with a species of japan, which serves to 
I'educe materially the eddy current loss in the core. This japan 
is applied by passing each individual sheet between rolls which 
are constantly kept moist with the japan. After passing the rolls, 
the pieces of iron are carried along a travelling table, where they 
are dried by passing nozzles through which air is blown. 


*•«<— >H l-x-^^J 

Fig. 140. — Connections for single, or multiple of series arc or incandescent 


Like the core-type constant potential transformer the construc- 
tion commences with the iron, the iron legs being assembled 
in a horizontal position. After all the laminations have been 
stacked together and wrapped with the necessary sheets of 
"horn-fiber," the whole assembly should be placed in a press 
under considerable pressure which will reduce the weight of the 
iron to the required dimensions. In the factory an hydraulic 
press is generally used, the pressure applied being equivalent to 
several tons; the temperature is also increased to about 250° F. 
There are three legs in each transformer — two of rectangular 
shape, and one of "cruciform" shape which is larger in cross- 
section than the two rectangular legs — each leg being assembled 
and handled separately until completed, after which the three are 
raised vertically and accurately spaced for the placing of end 
laminations. After the end laminations have been put in and 


the whole assembly made ready for the placuig of coils, the 
completed iron core is turned upside down. 

The form of coil for this modern type constant-current trans- 
former is similar in every respect to a large majority of those 
used in constant potential power and lighting transformers. It is 
cylindrical in form and consists of rectangular shaped wires, the 
width being several times the thickness. All the coils are placed 
on the center leg which is the one of cruciform dimensions. In 
all, there are four coils located concentrically with insulating 
spaces between each coil. For arc and incandescent lighting it is 
customary to make the lowest voltage coil the movable coil. For 
use with mercury arc rectifier systems the primary coil is the 
movable coil, while the secondary coil is the movable coil for 
series alternating-current lighting. 

The fabrication of this class of coil for constant-current trans- 
formers is interesting. In the winding of the coil a collapsible 
cylindrical former is used which has the same inside diameter 
as the required inside diameter of the coil. The wire is set on 
edge and wound in this manner around the former. In the 
winding, the wire is fed through a friction device to give the 
required tension, the starting end of the wire being clamped to 
a flanged collar revolving with the winding form. The wire is 
pressed firmly against the collar by another collar, which loosely 
fits the winding form and is held stationary; next follows another 
flanged collar which presses heavily against the stationary 
collar, thereby forcing the several turns of wire very tightly 
against one another. The flanged collar thus travels slowly along 
the winding former, so that for one revolution of the machine, or 
turning lathe, it travels a distance equal to the insulated thick- 
ness of one turn of the wire. After the coil has been finished and 
taken from the collapsible former it is set into a clamp and 
baked at a temperature of about 180° F. in a well-ventilated oven, 
thereby removing all moisture; and, while still hot, is dipped in 
a tank containing insulating varnish. This heating and dipping 
is repeated several times until the coil becomes self-sustaining 
and until the insulation will take up no more varnish. The 
coil is then wound with tape, each turn overlapping the pre- 
ceding turns by one-half to one-third its width. Various kinds 
of tape are used in the insulating of coils, such as cotton tape, 
which is varnished after applying, varnished cambric tape, 
which is treated after applying, and mica tape. Mica tape is 



only used on very high-voltage transformers. Where cotton 
tape is employed it receives a brushing of the best quality of 
insulating varnish, is then baked, revarnished and rebaked, 
this process being repeated several times for each tape. 

The regulation of this transformer comes within one-tenth of 
1 amp. above or below normal current from full-load to 

Fig. 140 (A), (B) and (C) show three different methods of 
connecting the secondaries of constant-current transformers for 
single, or multiple of series arc or incandescent circuits. Method 



Fig. 141. — Method of operation from three-phase primaries, using two 
constant current transformers in each case. 

(A) represents a simple circuit; (B) a single secondary winding 
with two circuits operated in series or singly as desired; (C) 
shows a multi-circuit secondary, each circuit being operated 

Fig. 141 (A) and (B) represents two methods of operating 
constant-current transformers and series-arc lighting from 
three-phase primaries. The secondaries of (A) show two inde- 
pendent circuits, each circuit being supplied from separate 
transformers, the primaries of which are wound for 2000 volts and 
2000X\/3/2 volts respectively. The secondaries of (B) also 
show two independent secondary circuits, each being in two parts 
as shown. 

Before shipment, constant-current transformers are made 
subject to an insulation test of 10,000 volts between secondary, 
primary and all parts; also between primary, secondary and all 



parts. The duration of the insulation test is one minute. If 
however, the primary voltage is above 5000, which is very rarely 
the case, the insulation test is twice normal voltage. 

The modern type of constant-current transformer referred to 
above, has a guaranteed temperature rise not exceeding 55° C. 
based on a room temperature of 25° C. If the temperature of 
the room is greater than 25° C, 0.5 per cent, for each degree' 
difference should be added to the observed rise of temperature; 
if less, subtracted. 

The record tests of a 100-lamp 6.6 amp., air-cooled constant- 
current transformer are shown below. 

Full-load =100 lamps— 6.6 amp. —60 cycles 


Lights connected 






















































Core loss in watts 

Copper loss in watts 

Sec. open-circuit voltage 

Pri. current at 2200 voltage 

(Temperature rise after 12 hours' run 

55° C.) 
Efficiency in per cent, at full-load. . . . 

At 75 per cent, full-load 

At 50 per cent, full-load 

At 33 per cent, full-load 

Power factor in per cent, at full-load . 

At 75 per cent, full-load 

At 50 per cent, full-load 

At 33 per cent, full-load 







When operating a load of 6 . 6 amp, lamps plus 7 . 5 per cent, 
line loss, the voltage and power factor at the lamp are : 
Volts per lamp 4- line loss =83 per cent. 
Power factor of lamp = 84 per cent. 



The characteristics of the series transformer are not very 
generally known. It is used in connection with alternating- 
current amnaeters and wattmeters where the voltage of the 
circuit is so high as to render it unsafe to connect the instrument 
directly into the circuit and when the current to be measured is 
greater than the capacity of the instrument, and it is also used 
in connection with relays. 

The series transformer was first considered and used in con- 
nection with street lighting systems, but was an entire failure. 




Ip ^P *• o 7^ 

Fig. 142. Fig. 143. 

Figs. 142 and 143. — ^Fundamental series transformer vector relations. 

For almost 20 years it kept in the background until it came into 
commercial use in connection with measuring instruments. 

At this time its accuracy was equal to any other instrument 
on the market and as the accuracy of instruments improved, the 
demand for a more accurate device increased. Also with the 
introduction of higher voltages better insulation was required, 
insulation that would not only protect the instruments but also 
the operator. As time went on it was found essential to use a 
magnetic circuit without joints in order to keep the magnetizing 
current within reasonable limits compared with the accuracy of 
transformation. To accomplish this a core was made of sheet- 
iron rings the primary and secondary windings being placed on 
this core. For high voltages, insulation became a serious problem. 
The number of turns of insulation had to be increased. This 
meant a considerable waste of time and money, and even after 
they were once in place it was difficult to take care of the heat 



from the windings. To overcome the necessity of using an 
extensive number of turns of insulation a new type was developed 
in which the low voltage secondary was wound on the core, 
while the insulating material consisted of telescoping tubes held 
apart by suitable spacing strips. 

Up to recent years it was considered quite sufficient to insulate 
the series transformer with the same margin of safety as that 
allowed in constant-voltage transformers; that is, double the 
line voltage. For several reasons it was deemed advisable to 
require an insulation test of three times that of the operating 
circuit. It is evident that as the secondary is usually grounded 
it is liable to receive and provide a path for a lightning discharge; 
moreover, it furnishes current to instruments, and protecting 
devices, and might be a source of danger to the attendant. 

The transformer consists of an iron magnetic circuit inter- 
linked with two electric circuits. The primary is connected in 
series with the line, the current of which is to be measured, and 
the secondary is connected to instruments, etc. It is evident that 
the meter readings will go up and down with the primary current; 
though the ratio of the instrument to the primary current may 
not be the same at all times, any one value of the current will 
always give the same reading. In well designed transformers 
the ratio of primary to secondary current is nearly constant for 
all loads within the designed limits. 

In the case of a series transformer with its primary connected 
to the line and its secondary on open circuit, the primary current 
will set up a magnetic field in the iron of the transformer, which 
will cause a drop in voltage across the primary. The same mag- 
netic flux will also cut the secondary and generate in its winding 
an e.m.f. the value of which is equal to the voltage drop across 
the primary multiplied by the ratio of the secondary to primary 
turns. When the secondary is open-circuited the iron of the 
transformer is worked at a high degree of saturation, which pro- 
duces an abnormally large secondary voltage. This condition 
gives rise to serious heating of the transformer as well as great 
strains upon the insulation. 

If the secondary circuit be closed through a resistance there 
will be a secondary current, which allows a larger resultant flux 
in the core the less the value of the current, which flux generates 
the secondary e.m.f. An increase in the secondary resistance 
does not mean a proportionate decrease in the secondary current, 


it only means such a decrease in the current as would increase the 
resulting magnetic flux and secondary e.m.f. sufficiently to main- 
tain the current through the increased resistance. Under 
ordinary conditions the resistance in the secondary circuit is low, 
so that the secondary e. m. f. is low and also the resultant mag- 
netic flux. 

If the secondary be short-circuited so that there is no magnetic 
leakage between the windings, and current put on the line, a 
magnetic flux will be set up in the primary. This flux produces 
an e.m.f. in the secondary which sets up a current opposed to 
that in the primary. The result is that the flux threading the 
windings will be reduced to a value which will produce a sufficient 

io A 

Fig. 144. — Direction of three-phase currents — chosen arbitrarily for con- 

voltage to establish current through the secondary resistance. 
Thus the magnetomotive force of the primary current is less than 
that of the secondary current, by an amount such that the flux 
produced thereby generates the voltage required to send the 
secondary current through the resistance of the secondary 
circuit, the vector sum of the secondary current and the mag- 
netizing current being equal to the primary current. 

When the secondary resistance is increased, there will be a 
decrease in the secondary current which allows a larger resultant 
flux, which in turn decreases the secondary e.m.f., which in- 
creases the secondary current. When a stable condition is 
reached there is a greater secondary e.m f. and a less secondary 
current. In order to determine the characteristics of a series 
transformer it is in general necessary to know the resistances 
and reactances of the primary and secondary windings of the 
transformer and of the external secondary circuit, and the 
amount and power-factor of the exciting current at the various 
operating flux densities in the transformer. If no magnetizing 
current were required, the secondary ampere-turns would be in 


approximate equilibrium with tlie primary ampere-turns and 
consequently the ratio of the primary to the secondary current 
would be the inverse of the number of turns. In order to attain 
this ratio as nearly as possible the iron is worked considerably 
below the "knee" of the B-H curve, so that very little magnetiz- 
ing force is required. 

The series transformer is worked at about one-tenth the 
magnetic density of the shunt transformer, due to the fact that a 
large cross-section of iron is used. It is readily understood 
that a series transformer differs very much mechanically and 
electrically from a shunt transformer; the latter maintaining a 
practically constant voltage on the secondary irrespective of the 
load, while the former must change its secondary voltage in order 
to change its secondary current. 

The fundational expression for the current of a series trans- 
former is the same as for a constant potential transformer, or 

^ = ^ = k or N s = KN V (22) 

I s N p ^ ^ ^ 


I p = primary current. I s = secondary current. 

N p = primary turns of wire in series. 

A^ s = secondary turns in series. 

K = constant = ratio of transformation. 

If the ratio of transformation is known and primary turns 

fixed, the secondary turns are equal to primary turns multiplied 

by the ratio of transformation. 

Assuming a one to one ratio and a non-inductive secondary 

load, the diagram shown in Fig. 142 is obtained. The primary 

current and e.m.f. are equal and opposite in phase to the secondary 

current and e.m.f. and as the load is non-inductive the primary 

current is in time phase with the primary voltage. 


I p = primary current. E p = primary e.m.f. 

O I s = secondary current. E s = secondary e.m.f. 

and I m = magnetizing current. 

In actual operation the secondary current is in time phase with 

the secondary e.m.f. if the secondary load is non-inductive, but 

the primary current lags behind the primary e.m.f., as shown 

in Fig. 143 by the angle 0. 

The secondary ampere-turns I s, and the primary turns 


I p being equal to the line current multiplied by the primary 
turns is made up of two components / p and / p'-O I p'. I p' 
being that part which supplies the core loss, and I p' that part 
which is equal and opposite to the secondary ampere-turns. 
The iron loss and "wattless" components ase I p' I p" and / p. 
In a well designed series transformer, the secondary ampere- 
turns for non-inductive secondary load can be taken as equal 
to / p-l p' I p", there fore secondary amperes is 

To determine this, it is merely necessary to find the ampere- 
turns I p supplying the iron loss, subtract this value from the 
primary ampere-turns / p and I p' , and divide by the secondary 
turns / s. 

To determine the iron loss it is necessary to know the loss 
in watts per unit weight of iron at a given frequency and varying 
induction. Let P represent the watts loss at a given frequency 
and induction, / the iron loss current, N s secondary turns, then 


Iron loss current = ^ (24) 


P N s 

ampere- turns (iron loss) =1 N s = — ^^ — (25) 

secondary ampere-turns = 1 p N p p— (26) 


N p P 
secondary amperes = / Pj^- — p (27) 

1 s 
If the ratio of transformation is made equal to -^— the second- 

^ 1 p 


ary current will be less than the desired value by the amount ^ 

amperes. The error in the transformation is 

As PXlOO .... 

per cent, error of rj—=i— — — -^ (28; 

^ I p I sXi^ 

To compensate for this error the secondary turns must be slightly 

I p 
diminished from the ratio j^ N s so that the secondary current 

will equal Is. 



Assume that the secondary is on short-circuit, and for con- 
venience, that there is no magnetic leakage between primary 
and secondary. At the moment the current is started, flux is 
set up in the primary winding. This flux produces an e.m.f. 
in the secondary which sets up a current opposed to that 
in the primary. The result is that the flux threading the two 
windings will be reduced to a value producing only sufficient 
voltage to cause current through the secondary resistance, 
thus restoring approximate equilibrium between the primary 
and secondary currents. Thus the magnetomotive force of 

Fig. 145. — Method of obtaining equal three-phase current readings by the 
use of two- or three-series transformers. 

the primary current is less than that of the secondary current 
by an amount such that the flux produced generates the voltage 
required to send the secondary current through the resistance 
the vector sum of this current and the magnetizing current 
being equal to the primary current. 

A series transformer should maintain a practically constant 
ratio between its primary and secondary through its full range 
of load. Such a condition can only be approached but not 
absolutely reached, since the magnetizing current becomes a 


formidable factor in preventing a constant ratio. A minimum 
magnetizing current is accomplished in commercial transformers 
by having an abundance of iron in the core, thus working the 
iron at a very low magnetic density, permitting the current ratio 
of the primary to the secondary to vary approximately in inverse 
ratio to the number of turns. As iron is worked considerably 
below the "knee" of the B-H. curve, a good range of load is 
allowed for ammeters, wattmeters and relays to be operated on 
the secondary. 

In either a delta- or star-connected three-phase system the 
currents in the three leads are displaced 120 degrees from each 
other and one of the leads may be considered a common return 
for the other two. Assuming the instantaneous direction of 
current in leads A and C to follow the arrows shown in Fig. 144, 
then the direction of the current in B will follow the arrow in 
the opposite direction. With a delta-connected system the 
current in lead A is the resultant of that in the two phases B A 
and C A ; the current in lead B is the resultant of that in the 
two phases A B and C B; and the current in C is the resultant 
of that in A C and B C. With the star connection, the direction 
of the two currents A and C are in opposite directions to the 
neutral point, and the current B toward the neutral point 0. 

If all the secondaries of series transformer are not arranged in 
the same direction, it will be found that the phase relation 
between the three phases will be either 60 or 120 degrees. In 
either a delta- or star-connected group of transformers it becomes 
necessary to reverse the secondary leads with respect to the others 
when a change of phase relation is desired. A connection com- 
prising two series transformers is shown in Fig. 145 where A and 
C are connected to two ammeters, and the opposite end of second- 
ary winding connected to a common wire at 0. In the vector 
diagram it is shown that A is equal to the current in lead A 
both in magnitude and direction and C the current in lead 
C which has a phase relation oi 120 degrees. The resultant 
current that is in the common wire O is equal in magnitude 
and direction to B'. The ammeter (2) indicates the current 
in lead B, and its reading is equal to the value shown in 
Fig. 145. 

Assume that one of the transformers is reversed as at C , 
Fig. 146. Referring to the vector diagram, A represents the 
current in lead A both in value and direction, C the current 



in lead C, and the resultant current A C represents in value 
and direction the current through the ammeter (2). The re- 
sultant current A C is displaced from that of lead B by 90 
degrees, and is found to be V3 as great sls A 0, B or C. 
Thus, if the two transformers A and C are wound to give 5 
amperes on their secondaries with full load current in the primary, 
the current across A C will be 5X'\/3=8,66 amperes. So that 
in connecting series transformers and it is found that one of the 
phase currents bear V 3 relation, it is simply necessary to reverse 
one of the transformer secondary leads. 

Fig. 146. — ^Another method of using two- and three-series transformers 
with three ammeters. 

The volt-amperes on each transformer of a two-transformer 
connection like Fig. 147 are equal to \/s times the volt-amperes 
of load A B C; but the phase angle between voltage and current 
is charged 30° in the lagging direction on transformer A, and in 
the leading direction on transformer B. For power-factor of the 
secondary loads A, B and C varying from 100 per cent, to per 
cent,, the power-factor of the equivalent load on transformer A 
will vary from y/s leading to 1/2 lagging; while on transformer^ 
it will vary from \/2 lagging to a negative 1/2. 
Where (a) is for equal loads on each phase and equal power- 
(6) Equal loads and non-inductive. 




(c) Equal loads (loads A and B non-inductive) and C 50 
per cent, power-factor. 

(d) Equal loads (loads A and B non-inductive) C 10 per 
cent, power-factor. 

A tendency with lagging power-factor in load C is to increase 
the equivalent load on the transformer A which is connected to 
the leading phase, and to diminish the equivalent load on trans- 
former B which is connected in the lagging phase. Low power- 
factor on both A and B combined with high power-factor in C 
produces similar results. 

There are a number of different ways of connecting two or 

Fig. 147. — Varying phase relations due to varying loads and power factors 
through the series transformers. 

more series transformers to a polyphase system. One or more 
may be used in connection with alternating-current relays for 
operating circuits for overload, reverse power, reverse phase, 
and low voltage. Some of the connections for this purpose are 
shown in Figs. 148 to 149. 

One series transformer is sufficient for opening the circuit of 
a single-phase system, and at the same time is used in connection 
with an ammeter and wattmeter as shown in Fig. 148. For three- 
phase working, one, two or three series transformers may be 
used for relays, ammeters and wattmeters. It is often recom- 
mended that three series transformers should be used for three- 



phase systems, but in the majority of cases two are sufficient 
to give satisfactory results. In Fig. 149 one is shown connected 





Fia. 148. — Simple series transformer connection. 


KSismsuu-^ — ^itsumsu 


Fig. 149. — Method of connecting a series transformer, ammeter, and relay 
on a delta connected three-phase system. 

to one leg of a three-phase delta system. Its secondary circuit 
is connected through a relay and an ammeter. 



In connection with overload relays one series transformer 
may be used for operating a three-phase system, and when 
operating three-phase wattmeters, two are all that is 'required. 
The connection shown in Fig. 150 will be found to give good 
results, as each transformer has its own tripping arrangement. 

Three transformers are quite common operating together on a 
three-phase, star-connected system, neutral point grounded or 

If all the secondary windings are not arranged in the same 
direction the phase relations between one outside wire and the 













FiG. 150. — Method of connecting two series transformers and relays to a 
three-phase system. 

middle wire, and the middle and the other outside wire will be 
60 degrees instead of 120 degrees. In order to obtain a phase 
relation of 120 degrees between each winding, one of the second- 
ary windings must be reversed. 

Fig. 151 represents three series transformers with all the 
secondary windings connected in one direction. It makes no 
difference whether the method of connection be delta or star, it 
becomes necessary to reverse one transformer with respect to 
the others when 120 or 60 degrees displacement is required. 

A connection very much used where one relay is required, 
is shown in Fig. 152, in which the series transformers have 




-1000 s> 

* ^1000 > 


00— >j h*^ioo 




< 173 ^ 

h — 100—^ 

-* ^173- 

i_«— -i-T— i=F 


FiG. 151. — Method of connecting three series transformers, three ammeters 
and three relays on a three-phase star connected system. 



1000 — > 



< 1000- 

r-^wr»-| j-'Tnnp-| r-fws^^ 


Fig. 152. — Three-phase star arrangement showing two series transformers 
connected in opposition. 



their opposite terminals connected. The secondary phase 
relations tend to operate in parallel so that when a current 
exists in the primary of one transformer a current will also exist 
in the secondary and relay, but will not be great enough to operate 
the trip coil. If a short-circuit should occur on any one phase of 
the two outside wires A C, the secondary will become over- 
loaded and its voltage will rise to a value above that of the 
secondary of the other transformer; this will tend to reverse the 
current in the latter transformer, which in turn will allow the 


Six phase 

Fig. 153. — Method of connecting two series transformers with instruments 
and relays to a two- or three-phase system inducing six-phase secondary 

primary flux to raise the voltage to the value of the former 
transformer; this voltage will cause the additional current to 
overload and operate the relay. This current value will not be 
twice the current through the two transformers, but will be the 
algebraic sum of the currents at 120 degrees apart, or \/S times 
the current in each leg. For example: If two series trans- 
formers are wound for 5 amperes on their secondaries with normal 
current through their primaries, the algebraic sum of the two 
'currents is 

\/3X 5 = 8.66 amperes. 
Fig. 153 shows a two-phase arrangement of connecting two 



series transformers for working instruments and relays. It will 
be noticed in all the connections shown that the secondaries 
of all transformers are grounded on one side. 

In Fig. 153 the system is so arranged that two-phase or three- 
phase currents will give a six-phase secondary, depending upon 
the connection made at point x. The series transformer con- 
nections are so arranged that the instruments will work satis- 
factorily with any of the two independent phase currents. 

The Y represents the neutral point of the secondary power 













Fig. 154. — Three-phase star arrangement showing two series transformers, 
two wattmeters, and three ammeters. 

transformers, and may be used as a neutral wire in connection 
with a direct-current system of supply. 

Another interesting connection is shown in Fig. 154, in which 
currents are measured in the three phases by the use of two 
series transformers. The geometrical sum of the currents in 
the primaries where the two series transformers are installed, 
is measured by the ammeter shown connected to the grounded 
side of the transformers. The value obtained is that of the 
current through the middle wire. 

The potential sides of the two wattmeters may be connected 
to the secondary leads of two-shunt transformers; in the figure 
they are shown connected directly to the mains. 



In general, single and polyphase combinations of series trans- 
former connections are covered by the use of one to four trans- 
formers. In three-phase work either the star, delta, open-delta, 
reversed open-delta and "Z" connections might be applied. 

tM/ '*^' ^ 

y '< ^^/ > / > ^ ' K. 

' ^^^^^ ^ i 

> a 

Fig. 155. — Three transformer delta and star connections. 

(See figs. 155, 156, 157.) The connection shown in Fig. 155 is 
not unlike the ordinary constant potential transformer delta. In 
this connection the. currents in the secondary leads A and B 
are the same, but the current through C is V3. For relays 
it is thought to be much better than the delta connection. 








Fig. 156 — Two transformer " V" and inverted " V" connections. 

It is also possible to measure three-phase currents with two 
series transforiners and only one ammeter. The arrangement 
is shown in Fig. 158. To read the current through the trans- 
former on the left, the two switches, a and b, are closed. To 



read the current in the middle line, h and c are closed; the current 
through the transformer on the right is measured by closing the 
two switches, c and d. 

When measurements are not being taken it is necessary that 
the switches, a and d, should be closed; as the iron of the two 
transformers is worked at a high degree of saturation, which 
produces an abnormally large secondary voltage, giving rise to a 
serious heating of the transformer. 

Since series transformers are connected directly in series with 
the line,. if not properly installed, they will" offer a convenient 
path for the escape of high frequency charges which may occur 
on the line, and which in discharging, not only burn out the 
transformer, but are likely to form an arc and probably cause a 
fire, or loss of life. 






Fig. 157. — Three transformer special connections. 

The process of drying out air-insulated series transformers is 
accomplished by simply passing normal current through the 
winding until the transformer is thoroughly warmed. This may 
be done by short-circuiting the secondary through an ammeter 
and sending enough alternating current through the primary to 
give normal current on the secondary, the primary current being 
obtained from a low voltage source. If not convenient to obtain 
low voltage alternating current the same result may be accom- 
plished by passing normal direct current through the primary 
long enough to thoroughly warm the transformer. 

In case of oil-cooled transformers, the winding should be dried 
out by this same process before the transformer is filled with 
oil. In doing this the temperature of the coils should not be 
allowed to exceed 65° C, which may mean the use of a current 
much less than normal, owing to the fact that there is no oil 
in the transformer. 



All secondaries and casings of transformers should be grounded, 
and likewise the instruments to which they are connected. This 
serves the double purpose of protecting the switchboard attend-, 
ant and freeing the instruments from the effects of electrostatic 
charges which might otherwise collect on the cases and cause 

If for any reason it becomes necessary to remove an instru- 
ment or any current carrying device from the secondary circuit 
of a series transformer, the secondary should be short-circuited 

r^rnjr^ r^iy^jr*-! r-npsv^ 

Fig. 158. — Method of connecting two series transformers and one ammeter 
to a three-phase system, to measure the current in any lead. 

by a wire or some other means. Series transformers should be 
considered as a part of the line circuit. When it becomes 
necessary to change secondary connections, the ground wire 
should be inspected to see that it is in good condition. The 
operator should also stand in a dry board or other insulating 

By reason of phase displacement in series transformers, watt- 
meters, when used with series transformers, will have certain 
errors due to such displacement. The following table applies 
to certain types of series transformers, the actual percentage of 



error varying slightly in different manufacturers for the same 
rating in capacity. 

When a wattmeter is used in a circuit for 100 per cent, power- 
factor, the approximate errors will be: 



1-5 Watt load 

1-5 current load 

1-2 Watt 


current load 

Full watt 


current load 

(a) 2 
(6) 10 
(c) 30 
((f) 30 

+ 0.5% 
+ 0.5% 
+ 0.5% 



The current ratios remain true and cause no error when used 
with ammeters between the limits of one-tenth load and 50 per 
cent, overload. 

When potential transformers are used as well, the tendency 
of the two (series and potential transformers) is to neutralize 
the error. 

When a wattmeter is used in a circuit of 50 per cent, power- 
factor, the approximate errors may be : 




1-2 current 


watt load 

1-5 current 

watt load 

Full current 


watt load 

Double cur- 
rent or 
watt load 

(a) 2 

(b) 10 

(c) 30 
{d) 30 

+ 4.0% 
+ 4.0% 
+ 2.0% 
+ 2.0% 

+ 12.0% 
+ 7.0% 
+ 5.0% 
+ 5.0% 

+ 2.0% 
+ 1.5% 



+ 2.0% 

If the wattmeter is calibrated with the series transformer at 
100 per cent, power-factor, the error at 50 per cent, power-factor 
may become: 





1-2 current 

watt load 

1-5 current 

watt load 

Full current 


watt load 

Double cur- 
rent or 
watt load 

(a) 2 
(6) 10 
(c) 30 

+ 6.0% 

+ 4.5% 
+ 2.5% 
+ 2.5% 

+ 14.0% 
+ 6.5% 

+ 4.5% 
+ 4.5% 

+ 4.0% 
+ 3.0% 
+ 1.5% 
+ 1.5% 

+ 4.0% 

+ 1.0% 
+ 1.0% 

At power-factors of less than 50 per cent, the errors will greatly 

It will be seen that if the wattmeter is calibrated with the series 
transformer, greater accuracy may be obtained when used in 
a circuit of approximately the same power factor, but that the 
error at a lower power-factor becomes greater. 

The plus sign ( + ) means that the wattmeter will indicate more 
than the true power by the percentage shown. The minus sign 
( — ) means that the wattmeter will indicate error in the opposite 

Excepting (d) which indicates a wound primary type trans- 
former, (a), (h) and (c) are for transformers of the open type 
intended to slip over bus-bar or switch-stud as well as the wound 
primary type transformer (5 amp. secondary). 

It is sometimes desired to use for meter test and other puiposes, 
inverted series transformers; that is, "step-up current trans- 
former." Fig. 159 shows an arrangement using two series trans- 
formers of any desired ratio but equal; No. 2 transformer is 
inverted, and, depending on the ratio of transformation, may be 
employed to step up the current to any desired value. Assum- 
ing that both transformers are for 40 to 1 ratio (200-5 amp.), it is 
evident, from the diagram that the standard testing instrument 
in No. 1 transformer circuit has a 5-ampere current coil and the 
service meter 200 amperes in its current coil when a 5-ampere 
load is flowing through the circuit load b. 

For some time past, the series transformer has been used for 
low-voltage scries street lighting in connection with series arc 
lighting systems. 

For the purpose of lighting, its primary winding is connected 

Tables VI, VII and VIII are representative of a certain type of series 
transformer and should therefore not be considered general. 



in series with the series arc lighting system, so that under all 
conditions of load on the secondary the primary winding carries 
the full current of the arc circuit (see Chapter XI) which is main- 
tained at its normal value by the constant current transformer. 
Its connections are shown in Fig. 160. 

For satisfactory operation of the series incandescent lamp, it 
is desirable to obtain as near constant current as possible in the 
secondary winding. Of course, to obtain constant-current regu- 
lation under abnormal conditions of load is impossible, but it 
has been found in practice that with open circuit voltage on the 
secondary not exceeding 150 per cent, of the full-load voltage, and 
the current at 100-75 and 50 per cent, load not varying more than 
2 per cent., the regulation of the transformer and lamps on the 
secondary is satisfactory. 

.standard W, 

< «~_l In verterf 

To Load 

Fig. 159. Fig. 

Fig. 159. — Series transformer used to step-up current, as for instance, 
with a primary load of 5-40 volt lamps, 700 amperes are obtained. 

Fig. 160. — Method of using series transformer or series arc lighting cir- 
cuits for low-voltage series incandescent lighting. 

Certain classes of lighting require lower potential than that 
obtained from series arc circuits, and to provide for this, light 
and power companies are often compelled to run multiple cir- 
cuits from the central station or substation at a considerable 
expense. By using a series transformer on the series arc lighting 
circuit, a low-voltage circuit may be run when required, thus 
obviating a large item of expense and providing a very flexible 
system of distribution. 

The ratio of transformation of series transformers used for 
lighting purposes has generally been 1-1, bur there is no diffi- 
culty in winding either primary or secondary for any reasonable 
current. ' 


The core of this transformer is of the shell type, built up of 
circular punchings with two symmetrical pieces in each layer. 
On the center leg or tognue of the core are assembled the form- 
wound coils. The primary coil fits simply over the secondarp coil, 
but is so insulated that it will withstand a break-down test of 
20,000 volts to the secondary coil and also to the core. Its 
appearance is not unlike the well-known telephone line insulating 
transformer which is used in connection with long-distance 
high-voltage transmission work. 

In this series transformer there exists a drooping voltage char- 
acteristic in the secondary. Its purpose is to limit the open- 
circuit voltage on the secondary. It has been obtained by so 
proportioning the magnetic circuit that the section is contracted 
in several parts to permit saturation of the iron with no current 
in the secondary winding. 

There exist quite a number of meter connections which may be 
used on power transformer systems. Some of these are given 
below: series and potential transformers being used in each case. 

Fig. 161(A) shows the simplest three-wire three-phase meter 
arrangement, in which a single-phase wattmeter has its potential 
coil connected to the secondary of a potential transformer, and its 
current coil to the secondary of a series transformer. If the 
power transform should have an accessible neutral point, at the 
location x, the potential transformer may be connected according 
to the dotted line. 

Fig. 161(B) shows the next simplest three-wire three-phase 
wattmeter arrangement, in which two single-phase wattmeters 
are involved. This method of measuring electrical energy in 
three-phase circuits for any condition of unbalanced voltage or 
current is the correct one. 

Fig 161(C) connection is for a three-wire three-phase system. 
The wattmeter has its current coil connected to one phase through 
a series transformer (c. t.), and its potential coil to a "Y" impe- 
dance, each branch of which has equal reactance and resistance 
such as to give the proper voltage to the potential coil of the 

Fig 161(D) connection is not unlike (B). The polyphase or 
two-element wattmeter is. employed here, and should always be 
used in preference to two single-phase meters. It has a slightly 
better accuracy if we consider that the record of the meter as a 
whole is obtained without the possibility of error that comes from 






Fig. 161. — Other important uses for series transformers on three-phase 



reading the two single-phase meters separately and adding their 
sum total together afterward. 

Fig 1Q1{E) and (F) show two arrangements of the three single- 
phase wattmeter method for a three-phase three-wire system. 
The potential transformers are connected in star-star. This 
method is not recommended because of unequal loading which 
might occur on the secondary side. With unbzlanced load on the 
secondary, the voltages might become very unequal, and with an 
accidental short-circuit on one transformer its primary impedence 
may be so reduced that the remaining two transformers would be 
subjected to almost \/S times their normal voltage. 

Fig 161 (GO shows a three- wattmeter method in which three 
series transformers, and three potential transformers are used, 
the latter being connected in star-delta. This method should 
always be used in preference to methods (E) and (F) for the reason 
the balanced voltages on the primary are established by exchange 
of current through the secondary circuits of the three transformers 
in case the secondary loads are unbalanced. Abnormal voltages 
are prevented in the individual transformers and meters. 

Fig. 1Q1{H) shows a four-wire three-phase, three-wattmeter 
method. The potential transformers are connected in star-star, 
but the objection referred to in (E) and (F) is practically elimi- 
nated. The arrangement is the same as three independent single- 
phase systems with one conductor of each phase combined into a 
common return. This method of measuring energy is considered 
to be superior to the three-wattmeter method shown in (E), (F), 
and (G), for the reason that no inter-connection of potential 
transformers is required and because the wattmeters cannot be 
subjected to variations of voltage greater than those properly 
belonging to the circuit. 

Fig 161(7) shows a four- wire, three-phase, polyphase wattmeter 
method. This method is preferable to method (H) and offers 
greater simplicity and convenience. 



Potential Feeder Regulators. — Almost all regulators are of the 
transformer type, with their primary windings connected across 
the lines and their secondary windings connected in series with 
the circuit the voltage of which is to be controlled, 

A type of single-phase feeder regulator is shown in Fig. 162. 
It consists of a laminated iron ring with four deep slots on its 
inner surface, in which the primary and secondary windings 
are placed. The laminated core is mounted on a spindle and 









Fig. 162. — Type of single-phase feeder regulator. 

so arranged that it can be turned to any desired position by 
means of a hand wheel. In the position indicated by C C, the 
core carries the magnetic flux due to the primary winding, P, 
in one direction through the secondary winding, S; and in the 
position indicated by C C" the core carries the magnetic flux 
due to the primary winding, P, in the other direction through 
the secondary winding, S. That is, when the core is in the posi- 
tion C C the generated voltage in the secondary winding has its 
14 209 



highest value. When the core is midway between C C and C C 
the generated voltage in the secondary winding is zero, and the 
feeder voltage is not affected. When the core is in the position, 
C C , the generated voltage in the secondary winding is again at 
its greatest value, but in such a direction as to oppose the gener- 
ator voltage. 

On account of the air-gap between the primary and secondary 
windings, inductive reactance is intro- 
duced in the line which requires com- 

The Stillwell regulator is another 
type of transformer for raising and lower- 
ing the voltage of feeder circuits. It 
consists of a primary winding which 
is connected across the feeder circuit, 
and a secondary winding in series with 
the circuit the voltage of which is to be 
varied. By means of a switch arm, 
more or less of the secondary winding 
may be introduced into the circuit, thus 
"boosting" by a corresponding amount 
the voltage of the generator. A reverse 
switch is provided to which the primary 
winding is connected, so that the volt- 
age may be added by moving the switch arm to the right, and 
subtracted by moving the switch arm to the left. 

A regulator built along the lines mentioned above, with an 
arrangement for connecting the various sections of the secondary 
winding to a dial switch and reversing switch, is shown in Fig. 
163. The feeder potential can be controlled in the following 
manner: Starting with the regulator in position of maximum 
boost, that is, with the dial switch turned to the extreme left as 
far as it will go, a continuous right-hand movement of the dial 
switch for two complete revolutions is obtained. During the 
first revolution the switch cut outs, step by step, the ten sections 
of the secondary winding. When the first revolution has been 
completed, the voltage on the feeder is the same as that of the 
generator, no secondary winding being included. A further 
movement of the switch in the same direction automatically 
throws a reversing switch; and continuing the movement of the 
dial switch, still in the same direction, the secondary windings 


163.— Type of Still- 
well regulator. 



are again switched in, step by step, this time with reversed 
polarity; so that when the second revolution is complete the 
whole secondary winding is again included in the feeder, but 
now opposing the voltage of the generator. Thus by one com- 
plete movement of the switch, covering two revolutions in one 
direction the complete range between the maximum boost and 
maximum depression of the feeder voltage is covered. 

In incandescent lighting service a potential regulator is 
particularly valuable. Within the ordinary limits of commercial 
practice the candle-power of an incandescent lamp will vary 
approximately 5 per cent, for every 1 per cent, variation in the 








I -"00-*^ 


Fig. 164. — Type of regulator used with series incandescent systems. 

voltage at the terminals. That is to say, if a 16-c-p. 100-volt 
lamp be burned at 106 volts it will give about 21 c-p., or at 94 
volts about 11 c-p. This fact shows at once the urgent necessity 
for keeping the voltage of an incandescent system adjusted 
within inperceptible degrees. A method that has given somewhat 
satisfactory service with series incandescent systems is shown in 
Fig. 164. It consists in a primary winding which is connected 
across the main lines. Attached to one end of the primary 
winding is a secondary winding. The secondary voltage, 1, 3, 
is greater than the primary, 1, 2, by the voltage of the winding, 
2, 3. The voltage, 2, 3, is thus added to the primary to form 
the secondary voltage of the circuit. By reversing the connec- 
tions of the windings, 2, 3, it may be made to subtract its 
voltage from the primary, 1, 2, in which case the secondary 
voltage, 1, 3, becomes less than the initial primary voltage; see 


Fig. 165. Further, by bringing a number of leads from parts 
of the winding, 2, 8, the secondary voltage, 1, 3, may be in- 
creased or decreased step by step as the different leads of 2, 3, 
are connected to the secondary circuit. 

In Fig. 165 is shown the connections of this form of regulator, 
or compensator. 1, 2, represents the primary winding con- 
nected across the circuit. From a portion of the secondary 
winding, 3, 4, taps are brought to the contact blocks shown in 
the diagram. The two arms, 7, 8, connect these 
ZZ contact blocks to two sliding contacts, 5, 6. 


The arms, 7, 8, may be operated by a handwheel, 
3TW55jn* one in direct contact and the other through a 
^^ gearing, so that a rotation of the handwheel 

turns one arm clockwise and the other counter- 
■* ^^ H clockwise. 

-pj^ jgg rp The secondary voltage of the circuit is that 

of series incandes- ^^ *^® primary, increased or decreased by the 
cent regulator voltage between the arms, 7, 8. In the neutral 
that reduces the position, both arms rest on one central contact 
initial primary bi^g]^^ ^nd the difference of potential between 

them is zero. In order to decrease the voltage 
at the lamps, the handwheel is turned to the right, and the volt- 
age decreased step by step, until the final position is reached 
with each arm on an extreme contact block. To increase the 
voltage at the lamps, the handwheel is turned to the left, the 
two arms being gradually separated on the contact blocks; 
and the difference of potential between the arms is effected 
step by step until in the final position, each arm rests on an ex- 
treme contact, and the secondary winding is connected into the 
circuit and its total voltage thus added to the initial voltage 
of the system. This type of regulator, as will be seen, is in the 
order of an ordinary auto-transformer with regulating taps ar- 
ranged on its secondary winding. 

The induction type regulator differs from the transformer 
type in that all the primary and secondary windings are con- 
stantly in use. There are types that vary the secondary voltage 
either by moving part of the iron core or one of the windings, 
or one of the windings (primary or secondary) and part of the 
iron core; the whole or part of the magnetic flux generated by 
the primary threads the secondary according to the position of 
the moving part. 


This type of regulator is either self-cooled oil immersed, oil- 
immersed water-cooled, or forced air-cooled depending on the 

Single-phase regulators have only one excitation winding, the 
magnetizing flux is an alternating one and its direction is always 
parallel to that diameter of the movable core which passes 
through the center of the exciting coil, but its direction may be 
varied with respect to the stationary core, and, consequently, 
with the respect to the stationary or series winding. 

With the armature in such a relation to the field that the 
primary winding induces a flux opposed to that induced by the 
secondary, the voltage induced by the primary in the secondary 
is added directly to the line voltage, but is subtracted when th6 
direction of the flux is the same, the complete range being 
obtained by rotating the armature through an angle of 180 
degrees. As the core is rotated gradually, the relative direction 
of the primary flux, and, consequently, the amount forced 
through the secondary coils, is similarly varied and produces a 
gradually varying voltage in the secondary from the maximum 
positive, through zero, to the maximum negative value. The 
induced voltage, is, however, added directly to, or subtracted 
directly from the line voltage. 

The primary or rotating core contains two windings; the active 
windings connected across the line, and a second winding short- 
circuited on itself and arranged at right angles to the active 
winding. The object of this short-circuited winding is to de- 
crease the reactance of the regulator, and its operation is as 
follows: As the primary and the short-circuited windings are 
both on the movable core and permanently .fixed at right angles 
to each other, the flux generated by the primary passes on either 
side of the short-circuited coil, and is, therefore, not affected by it 
in any way whatever; for as long as no flux passes through this 
coil there is no current in it. This condition is, however, only 
true when the armature is in the maximum boost or maximum 
lower position with current in the series winding, and in any 
position of the armature with no current in the secondary. 

With the armature in the neutral or no boost or lower position 
the flux generated by the current in the secondary passes equally 
on either side of the primary coils, which cannot, therefore, 
neutralize the flux generated by the secondary. 

If the primary core were not provided ^ith a short-circuited 


winding, and rotated from maximum position so as to reduce the 
primary flux passing through the secondary, and if the line 
current remained constant, a gradually increasing voltage would 
be required to force the current through the series windings, 
and a correspondingly increasing flux would have to be generated. 
This voltage would become a maximum with the armature in 
the neutral position, due to the fact that in this position the 
primary windings are at right angles to the series windings and 
therefore entirely out of inductive relation to them. The current 
in the secondary, therefore, would act as a magnetizing current, 
and a considerable part of the line voltage would have to be 
used to force the current through these coils. The voltage so 
absorbed would be at right angles to the line voltage, and the 
result would be a poor power factor on the feeder. 

The short-circuited coil on the armature which is in a direct 
inductive relation to the series coils when the armature is in the 
neutral position, acts as a short-circuit on the secondary winding, 


Fig. 166. — Phase positions of primary and secondary voltages of a single- 
phase induction regulator. 

and thereby reduces the voltage necessary to force full load 
current through this winding to only a trifle more- than that 
represented by the resistance drop across the secondary and 
short-circuited windings. This short-circuiting of the secondary 
is gradual, from zero to the maximum boosting position of the 
regulator to the maximum short-circuiting in the neutral position, 
so that by the combined effect of the primary and short-circuited 
coils the reactance of the secondary is kept v/ithin reasonable 

The operation of the short-circuited coil does not increase the 
losses in the regulator, but rather tends to keep them constant 
for a given secondary circuit. In rotating the armature from 
either maximum to the neutral position, the current in the 
primary diminishes as the current in the short-circuited coil 
increases, so that the total ampere-turns of the primary plus 


the ampere-turns of the short-circuited winding are always 
approximately equal to the ampere-turns of the secondary. 

In Fig. 166 there is shown graphically the values and time- 
phase position of primary and secondary voltages of a single- 
phase induction regulator. 

When the mechanical position in electrical degrees of the 
moving part is shifted to F on X following the curve of the 
semi-circle in the position of negative boost, or Y' and X' 
in the position of positive boost, the secondary voltage can be 
considered to have the values C and A respectively, and C 
and A' respectively. 

When the mechanical part occupies a mechanical position of 
90 electrical degrees from the position E s' and E s the value 
B oi the secondary voltage is zero, because the flux due to the 
primary exciting current passes through the secondary core 
parallel to the secondary windings. The resultant voltage is 
equal to the primary voltage. 

The kilowatt capacity of any regulator is equal to the normal 
line current to be regulated times the maximum boost of the 
regulator, and as the lower is always equal to the boost, the 
total range is equal to twice the kilowatt capacity or 100 per 
cent, with a 1 to 2 ratio. 

Kilowatt capacity of a single-phase regulator is maximum 
boost or lower times the current, or the maximum boost or 
lower might be expressed in terms of kilowatts divided by the 
secondary current. For a two-phase type it is one-half this 
amount. In a three-phase type the boost or lower across the 
lines is equal to the regulator capacity in kilowatts multiplied 
by V 3 and divided by the secondary current. 

Regulators of the induction type should not be used for any 
other primary voltage or frequency differing more than 10 
per cent, from that for which they are designed, because an 
increase in voltage or a decrease in frequency increases the 
magnetizing current and the losses and an increase in frequency 
increases the impedance. The deviation of 10 per cent, allowed 
must not occur in both the frequency and the voltage unless 
these deviations tend to neutralize each other. For instance, a 
regulator should not be subjected to a 10 per cent, increase in 
voltage and the same per cent, decrease in frequency, but it 
will operate satisfactorily if both voltage and frequency are 
increased within the aEiount given. 



Induction regulators may be operated by hand, either directly 
or through a sprocket wheel and chain; by a hand-controlled 
motor, or automatically-controlled motor. If operated by hand 
controlled motor, the motor may be of the alternating-current 
or direct-current type, but preferably of the alternating-current 
type and polyphase. If automatically controlled, the operating 
motor should preferably be of the polyphase type as the direct- 
current motor is not very well adapted for this purpose. When 
the regulator is operated by a motor, the motor should be con- 
trolled by a double-pole double-throw switch mounted on 
the switchboard or in any other convenient location. Closing 
the switch one way or the other will start the motor so as to 
operate the regulator to obtain a boost or lower in the line 
voltage as may be desired, and when the correct line voltage is 
obtained the regulator movement should be stopped by opening 



Tt — r 






Fig. 167. — Connections of single-phase regulators operating on a three-phase 


the switch. Generally a limit switch is provided which stops 
the movement of the regulator by opening the motor circuit as 
soon as the regulator has reached either the extreme positions 
depending on the direction of rotation, but which automatically 
closes the circuit again as soon as the regulator armature recedes 
from the extreme positions. The operation of each limit switch 
does not interfere with the movement of the regulator in the 
direction opposite to which it may be going. 

When a single-phase regulator is used in one phase of a three- 
phase system, the secondary wiring is connected in series with 
the line and the primary between the lines, see Fig. 167. Under 
these conditions there is a difference in phase between the current 
in the two windings and the effective voltage of the secondary 
is therefore reduced from its normal value. 

If three single-phase regulators are used, each phase can be 


adjusted to the range equal to the effective range of the regulator, 
so that the voltage between the phases is not that due to the 
effective voltage per regulator, but that due to the effective voltage 
of each regulator times Vo. In this case, if 10 per cent, regu- 
lation across the phases of a three-phase three-wire system is 
desired, only 57.7 per cent, of the 10 per cent, regulation per 
line is needed; thus, the boosting or lowering need not have a 
greater rating than 3 to 7,5 per cent, instead of 10 per cent, 
which is the size necessary where one regulator is used. 

In general the capacity in kw. of a three-phase regulator is rated at 
E.I.\/S, where E is the volts boost or lower and I the amperes 
in feeder circuit. For six-phase rotary converter service, kw. 
capacity of regulator is: (double-delta connection) =J5J. 7. 3.46 
(29) and (diametrical connection) =E. I. 3 (30). 

For fKjlyphase circuits the system may be regulated by intro- 
ducing the so-called "induction regulator." This form of 
regulator has a primary and a secondary winding. The primary 
winding is connected across the main line, and the secondary 
winding in series with the circuit. The voltage generated in 
each phase of the secondary winding is constant, but by varying 
the relative positions of the primary and secondary, the effect- 
ive voltage of any phase of the secondary on its circuit is varied 
from maximum boosting to zero and to maximum lowering. In 
order to avoid the trouble of adjusting the voltages when each 
phase is controlled independently, polyphase regulators are 
arranged to change the voltage in all phases simultaneously 
They can be operated by hand wheels or motors. When operated 
by hand, the movable core is rotated by means of a handwheel 
and shaft. When it is desired to operate the regulator from a 
distant point, the apparatus is fitted with a small motor which 
is arranged through suitable gearing to turn the movable core. 
The motor may be of the direct-current or induction type, 
and controlled at any convenient place. 

The theory of this form of regulator is described graphically 
in Fig. 168 in which the voltage of one phase of the regulator 
is, eo = generator voltage or the e.m.f. impressed on the primary: 
ao = e.m.f. generated in the secondary windings, and is constant 
with constant generator e.m.f. : 6' a' = secondary e.m.f. in phase 
with the generator e.m.f. :e'a' = line e.m.f., or resultant of the 
generator e.m.f. and the secondary e.m.f. 

The construction of the regulator is such that the secondary 


voltage, oa, is made to assume any desired phase relation to 
the primary e.m.f., as of, oh, oc, etc. 

When its phase relation is as represented by of, which is the 
position when the north poles and the south poles of the primary 
and secondary windings are opposite, the secondary voltage is in 
phase with the primary voltage and is added directly to that of 
the generator. 

The regulator is then said to be in the position of maximum 
boost, and by rotating the armature with reference to the fields, 
the phase relation can be changed to any extent between this and 
directly opposed voltages. When the voltage of the secondary 
is directly opposed to that of the primary, its phase relation is as 

e' I' a' 

Fig, 168. — Graphical representation of an induction regulator, 

represented by o d in the diagram, while o h represents the shape 
relation of the secondary when in the neutral position. 

The electrical design of the induction regulator is very similar 
to that of the induction motor. Its efficiency is somewhat 
higher than the average induction motor of the same rating. 
The primary winding is placed on the movable core and has either 
a closed delta or star connection, while the secondary or stationary 
winding is placed on the stationary core and is an open winding, 
each section or phase being connected in series with the corre- 
sponding phase of the line. 

The maximum arc through which the primary moves is 60 
degrees for a six-pole and 90 degrees for a four-pole. Induction 
potential regulators are built for single-phase, two-phase, three- 
phase and six-phase circuits. 

Compensators are used in connection with starting alternating- 
current motors, and to some extent they are used in connection 
with voltmeters in the generating station. 

Compensators for starting alternating-current motors consist 
of an inductive winding with taps.. For polyphase work the 



compensator consists of one coil for each phase ab c, Fig. 169 
with each coil placed on a separate leg of a laminated iron core. 
Each coil is provided with several taps, so that a number of 
voltages may be obtained, any one of which may be selected for 
permanent connection to the switch for starting the motor. 

When the three-phase winding is used the three coils are con- 
nected in star, the line is connected to the three free ends of 
the coils, and the motor when starting is connected to the taps 
as represented in Fig. 169. 


Fig. 169. — Three-phase motor 


* I Motor ' 
Fig. 170. — Two-phase induction 

As it is difficult to predetermine the best starting voltages for 
each case, for motors rated at from 5 to 15 h.p., taps of 40, 60, 
and 80 per cent, of the line voltage are provided, according to 
individual requirements. 

The most essential part of the compensator is an auto-trans- 
former, the principle of which has already been explained. 
The switch for operating the starting compensator is immersed 
in oil. In starting, the switch moves from the off position to 
the starting position, where the lowest voltage is applied to the 
motor, or the position where the starting torque is the lowest that 
can be obtained. As sopn as the motor speeds up, the switch may 


be thrown over to the running position; the compensator winding 
is then cut out and the motor is connected to the line through 
suitable fuses or circuit breakers. The switch is generally 
provided with a safety device which is used to prevent the 
operator from throwing the motor directly on the line, thereby 
causing a rush of current. 

Compensators are designed to bring the motor up to speed 
within one minute after the switch has been thrown into the 
starting position. It is important that the switch be kept in 
the starting position until the motor has finished accelerating, 
to prevent an unnecessary rush of current when the switch is 
thrown to the running position. 

In two-phase compensators the line is connected to the ends 
of the two coils, and the starting connections of the motor to 
the taps as shown in Fig. 170. 

The switch for operating the starting compensator and motor 
is the same as that used on the three-phase service. 

Other designs are used, one of which operates the compensator 
as follows: For starting the motor the switch handle moves 
from the off position to the first starting position, where a low 
voltage is applied to the motor; then to a second starting position 
where a higher voltage is applied; and then to the running 
position, where the motor is connected directly across the line, 
the compensator being disconnected from the circuit. For 
stopping, the switch handle is moved to a notch still further 
along than the running position, the movement of the switch 
handle being in the same direction as in starting. In the latter 
position the switch handle is released to that it can be moved 
back to the off position ready to start again. 

The other form of compensator used to indicate the variations 
of voltage at the point of distribution under all conditions of 
load without appreciable error between no-load and overload, 
consists of three parts: a series transformer, a variable reactance, 
and a variable resistance. The compensator is adjusted to 
allow for the resistance and inductive reactance of the line. If 
these are properly adjusted, a local circuit is obtained corre- 
sponding exactly with the line circuit, and any change in the line 
produces a corresponding change in the local circuit, causing the 
voltmeter always to indicate the potential at the end of the line 
or center of distribution, according to which is desired. It is 
well known that the drop in a direct-current circuit is dependent 



upon the resistance, but in an alternating-current circuit it is 
due not only to the resistance of the lines, but also to the react- 
ance. The reactance usually causes the drop to be greater than 
it would if the resistance were the only factor. Therefore, it is 
necessary that a compensator should give accurately the voltage 
at the load at all times, whatever may be the current and 

Fig. 171. — ^Form of compensator used to indicate the variation of voltage at 
the point of distribution under all conditions of load. 

Fig. 171 shows a series transformer in series with the line; and 
having, therefore, in its secondary circuit a current always propor- 
tional to the current in the line. The reactors and resistors are 
both so wound that any proportion of the winding can be cut in 
or out of the voltmeter circuit, so modifying the reading of the 
station voltmeter that it corresponds with the actual voltage at 
the point of consumption, regardless of the current, power- 
factor, reactance, and resistance in the line. For balanced two- 
and three-phase circuits one compensator is sufficient. 

In adjusting this type of compensator, it is advisable to 
calculate the ohmic drop for full-load and set the resistance 
arm at the point which will give the required compensation and 
then adjust the reactance arm until the voltmeter reading 
corresponds to the voltage at the point or receiving station 
selected for normal voltage. This compensator is commonly 
called the " Line-drop compensator. " 



Its connections proper, as used in practice at the present time 
are shown in Fig. 172, Each line of which the voltage at the 
center of distribution is to be indicated or recorded in the station, 
must be provided with a voltmeter as shown in Fig. 172, No. 1, 
which must be adjusted for the ohmic and reactive drop of 
each line respectively. For example, take such a line giving 
the factors shown in Fig. 173; where R is ohmic' resistance of 
10, Xs is the reactance of 10 ohms, and E is the load voltage. 
To fulfil the conditions of E = 100, it is necessary that the voltage 
of supply or generator voltage be increased to nearly 110.5, 
and the voltmeter No. 2 of Fig. 160 will indicate this value. 
With unity power factor it will be noted that the total live 
drop is due almost entirely to the line resistance R, and is prac- 
tically independent of the line reactance. 


j; fji Line Drop 
— — ■ Compensator 

Fig. 172. — Connections for live-drop compensator. 

As the power factor of the line decreases, the effective voltage 
produced by the reactance increases, until at an imaginary zero 
-power-factor load the total drop is due almost entirely to the 

The voltage diagram of such a circuit is shown in Fig. 174, 
where R and Xs and E are as before, but the line has an 80 per 
cent, power-factor load. The vector line Eg in this case represents 
114 which gives £' = 100. For the above or any other live 
conditions for which the compensator is set it is correct for all 
loads; for, as the drop m voltage in the line decreases, due to 
decreasing load, the voltage drop in the compensator decreases 
in equal measure. For other power factors a simple adjust- 
ment will be incorrect. 

Automatic regulation of single-phase feeders presents no 



diflficulties, in that there is but one definite point to regulate 
and the "boost" or "lower" of the regulator is directly added 
to or subtracted from the voltage of the feeder. If regulation 
at the station is desired, only a potential transformer is necessary 
— if regulation for compensation of drop at some distant point 
is desired, a series transformer connected in series with the 
feeder is added. 

E =10 

JP— 100 

It very often happens that one phase of a three-phase feeder 
is used for lighting and a single-phase regulator installed. In 
making such an installation, the regulator must have its seconday 
winding in series with the line, its primary being connected across 
the phase. Now, if the load on this feeder is purely lighting, 
the power factor would remain constant and approximately 
100 per cent., but should the power factor vary considerably, 



•^ Constants 

Fig. 174. 

it- may cause the current to be out of phase with the voltage to 
such an extent that satisfactory compensation may not be ob- 
tained. For such service the best arrangement would be to 
use two cross-connected series transformers, one connected in 
series with each conductor as, for instance, A and B of the phase 
across which the primary of the regulator is excited. With 
this connection (see Fig. 175) the line drop compensator is 
set to compensate for ohmic and inductive drop to the load 
center and the voltage will automatically be maintained at the 
desired value irrespective of changes in load or power factor. 



Hand regulation has long been replaced with automatic 
regulators. With the development of the automatic regulator 


Fig. 175. — Single-phase regulator and voltage-drop compensator connections 
to a three-phase system. 





-o o 

9 <? 


y Y y 

Fig. 176. — Two single-phase regulators on three-phase system, showing the 
use of the contact making voltmeter. 

there has followed a perfection of the contact-making volt- 
meter, which displaces the operator and regulates the voltage 


automatically. This instrument is composed of a solenoid 
with two windings; a shunt winding which is connected in 
parallel with the secondary of a potential transformer, and a 
series winding (differential with respect to the shunt winding) 
which is connected in series with the secondary of the series 
transformer, the primary of which is in series with the feeder 
circuit. A movable core passes through the center of the 
solenoid, and to the top of this core is attached a pivoted lever. 
The lever carries at its other end a set of contacts which make 
contact with an upper and a lower stationary contact. The 
lever is set by means of a spring acting against the core, so that 
its contacts are midway between the upper and lower stationary 
contacts when normal voltage is on the shunt coil of the meter. 
The stationary contacts form, when closed, a circuit to one or 
the other of two coils of a relay switch, which in turn controls 
a motor on the regulator cover. Any deviation of voltage from 
normal causes contact to be made and the regulator corrects 
for this change, bringing the voltage back to normal. When 
compensating for line drop to a distant point the current coil 
is used and as the load increases, the regulator boosts the voltage 
by the proper amount. In this manner the meter can be set 
so that constant voltage can be maintained at a great distance 
from the regulator. 

The connections of this instrument for a feeder circuit where 
lighting is connected on only two phases of a three-phase system 
and motors connected to the same, are shown in Fig. 1 76. Two sin- 
gle-phase regulators and three series t{||hsf ormers (one transformer 
in each conductor) are necessary. If the series transformer in 
the middle conductor or phase were not installed, proper com- 
pensation could not be secured, owing to both phase displace- 
ment and an unbalancing of current in the three phases. 

Three single-phase regulators are usually employed when 
lighting and power are taken from all the three phases of a 
three-phase system. One three-phase regulator may be used, in 
which case it is better to employ only two series transformers 
cross-connected, so as to get an average of unbalanced current. 
With single-phase regulators as shown in Fig. 177 each phase can 
be adjusted independently of the others and constant voltage 
established at the load center of each. For this reason it is better 
to use three single-phase regulators in preference to one three- 
phase regulator. 




For three-phase four-wire systems, three single-phase regula- 
tors are employed having their secondaries connected in series 
with a phase conductor and their primaries excited from phase 
conductors to neutral. This method is equivalent to three 
independent single-phase circuits. 


y y 

Fig. 177. — An installation giving perfect regulation when properly installed 

and operated. 




In order to determine the characteristics of a transformer 
the following tests are made: 

1. Insulation. 

2. Temperature. 

3. Ratio of transformation. 

4. Polarity. 

5. Iron or core loss. 

6. Resistances and P R. 

7. Copper loss and impedance. 

8. Efficiency. 

9. Regulation. 

10. Short-circuit test. 

Insulation. — The insulation of commercial transformers should 
be given the following tests : 

a. Normal voltage with overload. 

b. Double voltage for 30 minutes and three times the normal 
voltage for five minutes. (Distribution 2000 to 6000 volt 
transformers only.) 

c. Between primary, core and frame. 

d. Between primary and secondary. 

e. Between the secondary, core and frame. 

The National Board of Fire Underwriters specify that the 
insulation of nominal 2100-volt transformers, when heated, 
should withstand continuously for one minute a difference of 
potential of 10,000 volts alternating current between the primary 
and secondary coils and the core. 

For testing the insulation of transformers, a high-potential 
testing set with spark-gap is required. The testing set should, 
preferably, have low reactance so that the variation in voltage, 
due to leading and lagging currents, will not be large. The 
voltages will be practically in the ratio of the turns, and the 
high-tension voltages may be determined by measuring the low- 
tension voltages and multiplying by the ratio of transformation. 




Where a suitable electrostatic voltmeter is available the high- 
tension voltage is obtained by direct measurement. 

In applying insulation tests, it is important that all primary 
terminals should be connected together as well as all secondary 
terminals, in order to secure a uniform potential strain throughout 
the winding. In testing between the primary and secondary or 
between the primary and core and frame, the secondary must 
be connected to the core and frame, and grounded. 

In making the test, connect as shown in Fig. 178. The spark- 
gap should be set to discharge at the desired voltage, which 
may be determined directly by means of test with static volt- 
meter, or by the spark-gap table giving sparking distances in air 
between opposed sharp needle-points for various effective sinu- 
soidal voltages in inches and in centimeters. 


Table of Sparking Distances in Air between Opposed Sharp Needle- 
Points, for Various Effective Sinusoidal Voltages, in inches and in 

(Sq. root of 
mean square) 


(Sq. root of 
mean square) 



























35 4 






40 7 






46 1 









54 1 






























Testing Transformer 

After every discharge the needle points should be renewed. 
The insulation test which should be applied to the winding of a 
transformer depends upon the voltage for which the transformer 
is designed. For instance, a 2100-volt primary should with- 
stand a difference of potential of 10,000 volts, and a 200-volt 
secondary should therefore be tested for at least 2000 volts. 
The length of time of the insulation test, varies with the magni- 
tude of the voltage applied to the transformer, which, if severe, 
should not be continued long, as 
the strain may injure the insula- 
tion and permanently reduce its 

Transformers are sometimes 
tested by their own voltage. One 
side of the high-tension winding 
is connected to the low-tension 
winding, and the iron, and the 
transformer operated at a voltage 
above the normal to give the 
necessary test voltage. The same 
test is repeated when the other 
end of the high-tension winding is 
connected and the one side dis- 

In making insulation tests great 
care should be taken to protect not only the operator but others 
adjacent to the apparatus under test. If it is necessary to 
handle the live terminals, only one should be handled at a time, 
and whenever possible, it should be insulated beyond any possi- 
bility of the testing set being grounded. 

Another insulation test called "over-potential test" is made 
for the purpose of testing the insulation between adjacent turns 
and also between adjacent layers of the windings. In applying 
the over-potential test, the exciting current of a transformer is 
always increased. 

This test usually consists of applying a voltage three to four 
times the normal voltage to one of the windings with the other 
winding open-circuited. If this test is to be made on a 2000- 
volt winding, at three times its normal voltage, 6000 volts may 
be applied to one end of the winding in question, or: 

Fig. 178. — Method of connecting 
apparatus for insulation test. 


3000 volts to a 1000-volt winding, 
1200 volts to a 400-volt winding, 
300 volts to a 100-volt winding. 
In general, this test should be applied at high frequency so that 
the exciting currents referred to above may be reduced. The 
higher the frequency the less will be the amount of current 
required to make the test. It is recommended that 60 cycles 
be the least used, and for 60-cycle transformers 133-cycle cur- 
rents be applied, and for 25-cycle transformers 60 cycles. 

The highest voltage transformer built up to the present time 
for power and industrial purposes was tested at 280,000 volts, or 
double voltage for which it was designed. 

Double voltage is applied to test the insulation between turns 
and between sections of coils, these being the cause of practically 
85 per cent, of transformer burnouts. A better and surer test 
than this would be to apply twice the normal voltage for one 
minute followed by another test for five minutes at one and one- 
half times normal voltage. The latter test is to discover any 
defect that may have developed during the double-voltage test, 
and yet not have become apparent in the short time the double 
voltage was applied. 

The application of a high voltage to the insulation of a trans- 
former is the only real method of determining whether the 
dielectric strength is there. Mechanical examination of the keen- 
est kind is false, and measurement of insulation resistance is not 
very much better; since insulation may or may not show resist- 
ance when measured by a voltmeter with low voltage, but offer 
comparatively little resistance to a high-voltage current. 

In working the high-voltage test between the primary and the 
core or the secondary, the secondary should always be grounded 
for the reason that a high voltage strain is induced between the 
core and the other winding which may be greater than the 
strain to which the insulation is subjected to under normal 
operation, and, of course, greater than it is designed to stand 
constantly. When testing between the primary or high-vol- 
tage side of, say, a high ratio transformer, and the core, the 
induced voltage strain between the low-voltage winding and 
core may be very high and the secondary may be broken 
down by an insulation test applied to the high-voltage side 
under conditions which would not exist during normal operation 
of the transformer. The shorter the time the voltage is kept 


on, with correspondingly higher voltage to get the desired 
severity of test, the less will be the deterioration of the insu- 
lation. Every transformer should be tested with at least 
twice its rated voltage, the reason for this being necessary is 
because of the many abnormal conditions of operation which 
occur. On a very high voltage system, if one side of the winding 
becomes grounded, the whole rated voltage is exerted between 
the winding and the iron core; and sometimes during normal 
operation (so far as exterior observtion indicates) a difference of 
potential will occur, lasting but a small fraction of a second or 
minute, which might be as high as the testing voltage required. 

Practically all high-voltage transformers are wound with copper 
strip or ribbon, one turn per layer, the coils being insulated 
uniformly throughout excepting the end turns which are some- 
times insulated to withstand voltages of 5000 volts between 
turns. Take the case of a transformer with a normal voltage 
between turns of 80 volts, it would mean that in applying the 
standard voltage test, i.e., twice the rated high-tension voltage 
between the high-voltage winding and low-voltage winding 
connecting the latter to the core we shall receive 220,000 volts 
across a 110,000-volt winding, or an induced voltage of 160 volts 
between turns. 

Several years ago it was agreed to lower the standard high- 
voltage test specifications to 1.5 times the rated voltage, and all 
sorts of breakdowns happened until a change was made to the 
higher test. The double voltage test is not too high and not too 
severe a test no matter how high the rated voltage of the trans- 
former might be for power and industrial purposes. For com- 
mercial testing transformers it will not apply. Such a trans- 
former was recently made for 400,000 volts and before it was 
shipped from the factory it was given a full half-hour test at 
650,000 volts with the center of the high-voltage winding grounded. 
Since then one has been made for 750,000 volts. About the 
highest test made so far, on commercial power transformers 
was that of a 14,000 kv-a 100,000 volt transformer which was 
given 270,000 volts across its high-voltage winding to all other 
parts. This transformer was for a 60-cycle system and covered 
a floor space of 23 ft. X 8.5 ft,, it being 18 ft. high. Another 
transformer of 10,000 kv-a at 70,000 volts operating on a 25-cycle 
system was give a high-voltage test of 180,000 volts. The 
former transformer was fitted with oil-filled terminal bushings 


and during the test of these bushings at 270,000 volts, no corona 
was visible even when in utter darkness. The latter trans- 
former was fitted with the condenser type of terminal bushings 
which is made up of alternate layers of insulating and conducting 

In the operation of transformers it has been found that we are 
confronted with the difficult problem of taking care of the voltage 
rise between turns that may not increase the line voltage suf- 
ficient to be noticeable but be so high in the transformer itself 
and only effective across a few turns as to short-circuit and 
burn-out that part where the excessive voltage is concentrated. 
In fact it is quite possible to get 100 times normal voltage across 
a small percentage of the total turns and at the same time have 
no appreciable increase in voltage at the terminals of the 

With or without extra insulation on the end turns of trans- 
formers operating on high-voltage systems, the voltage difference 
on the end turns due to switching, etc., is there, and the only 
way out of the difficulty is to provide sufficient insulation to 
make it safe irrespective of the external choke coils which are 
always provided. 

This double voltage test is made after the transformer has 
been thoroughly dried out and the quality of oil brought up to 
standard. In the past some makers placed too much reliance on 
oil as an insulator and consequently left out much solid insula- 
tion; the result was that many burnouts occurred, because the 
oil could not be relied upon always, its insulating proportions 
decreasing with age. In many cases burnouts occurred immedi- 
ately the transformers were put into service after the drying-out 
process had been completed, and the voltage slowly brought up 
to the desired value. 

Temperature. — The temperature or heat test of a transformer 
may be applied in several ways, all of which' are arranged to 
determine as nearly as possible the working temperature condi- 
tions of the transformer in actual service. 

Before starting a temperature test, transformers should be 
left in the room a sufficient length of time for them to be affected 
alike by the room temperature. 

If a transformer has remained many hours in a room at con- 
stant temperature so that it has reached approximately uniform 
temperature throughout, the temperature of the surface may 


be taken to be that of the interior, or internal temperature. If, 
however, the transformer is radiating heat to the room, the 
temperature of the surface will be found to give little indication 
of the temperature of the interior. 

To ascertain the temperature rise of a transformer, thermom- 
eters are sometimes used, which give only comparative results 
in temperature and such measurements are, therefore, useful only 
in ascertaining an increase in temperature during the heat run. 
If thermometers are used they should be screened from local air- 
currents and placed so that they can be read without being 
removed. If it is desired to obtain temperature curves, ther- 
mometer readings should be taken at half-hour intervals through- 
out the test and until the difference between the room temper- 
ature and that of the transformer under test is constant. 

In order to determine temperature rise by measurement of 
resistance, it is necessary to determine first what is called "cold" 
resistance by thermometer measurements after the trans- 
former has remained in a room of constant temperature for a 
sufficient length of time to reach a uniform temperature through- 
out its windings. 

The temperature rise by resistance gives the average rise 
throughout the windings of the transformer, and to obtain 
average temperature rise of each of the windings, separate 
resistance readings should be taken of each. 

The temperature rise by means of resistance may be deter- 
mined by the use of the following equation: 

R = Ro(l +0.0040; (31) 

or by equation 

Resistance at S°C = ~^^^~R' (32) 

where R' is the resistance at any temperature t. 
where R^ is the resistance at room temperature; R the resistance 
when heated, and t the rise in temperature. The temperature 
coefficient of resistance is taken at 0.004 as 25° C. Considering 
the above equation, the temperature rise corrected to 25° C. may 
be determined in the following manner. 

Example: Let room temperature be 20° C, and absolute 
temperature of transformer 60° C. Ascertain correct tem- 
perature rise. 



The temperature is apparently 60 — 20 = 40° C, but since the 
room temperature is 5° lower than the standard requirements, 
a correction of 0.5X5 = 2.5 per cent, must be added giving a 
corrected temperature of 


= 41° C. 


Thus with a room temperature of 20° C. the rise in temperature 
calculated from the above equation should be added by 2.5 per 
cent., or with a room temperature of 35° C, the rise in temper- 
ature should be decreased by 5 per cent.; and with a room 

temperature of 15° C, the rise in 

temperature should be increased 
by 5 per cent., and so on. 

If the room temperature differs 
from 25° C. the observed rise in 
temperature should be corrected 
by 0.5 for each degree centigrade. 
This correction is intended to com- 
pensate for the change in the radia- 
tion constant as well as for the 
error involved in the assumption 
that the temperature coefficient is 
0.004, or more correctly, 0.0039, 
remains constant with varying 
room temperatures. 

To measure the increase of re- 
sistance let us take the follow- 
ing example. The primary resis- 
tance of a certain transformer is 
8 ohms, and at its maximum operating temperature, 9 ohms. 
Temperature of room during test is 30° C. Ascertain cor- 
rected temperature rise. 

The primary resistance taken at a temperature of 30° C, 
when referred to temperature coefficient of 0.4 per cent, per 




Umj!jImJ UjiMWHL 




Fig. 179. — Method of con- 
necting transformers and instru- 
ment for an over-potential test 

For water-cooled transformers, the standard temperature of reference for incoming cooling 
water should be 25° C, measured at thfe intake of the transformer. In testing water-cooled 
transformers it is important to maintain the temperature of the ingoing water within 5° C. 
of the surrounding air, but where this is impracticable, the reference ambient temperature 
should be taken as that indicated by the resistance of the windings, when the disconnected 
transformer is being supplied with the normal amount of cooling water and the temperature of 
the windings has become constant. 


degree, represents a rise of 30X0.4 = 12 per cent, above its value 
at zero centigrade, which is 

8X100 ^,, , 
— 11 o~ = ♦ • 14 ohms. 

The maximum operating temperature of 10 ohms represents 

a rise of 

(9-7.1 4) 100 

if-jT- = 26.05 per cent. 

above value at zero, and is equal to 

absolute temperature. 

Deducting from this the room temperature at 30°, the apparent 
rise = 35° C. Since the room temperature during test was 5° 
above standard requirements, a correction of 0.5X5, or 2.5 per 
cent, must be substracted, giving a corrected rise of 



= 3.15° C. 

It is well known that high temperatures cause deterioration 
in the insulation as well as increase in the core loss. 

The average temperature rise of the coils of transformers can 
be more accurately determined from the hot and cold resist- 
ances, and is calculated as follows: 

Temp, rise (°C) = (238. l + r)(^'>°^R^-l) (33) 

T = temperature at which cold resistance is taken. 

As already stated above, if the final room temperature is less 
than 25° C, the temperature rise should be corrected by adding 
0.5 of 1 per cent, for each degree less; if room temperature is 
greater than 25° C, subtract 0.5 of 1 per cent., for each degree 
greater. While these readings are being taken the exciting 
current and the load current are held constant and the ther- 
mometers are read at 30 or 60 minute intervals for a period 
of several hours and until the constant temperature has been 
reached. The thermometers should be placed in the room, 

The A. I. E. E. recommend that in the case of resistance measurements, the temperature 
coefficient of coMer siiall be deduced from the formula 1/(234. 5-T). Thus, at an initial tem- 

Ferature T is 4Cr C. the temperature coefficient or increase in resistance per degree C. rise is 
/(274.5) b0..00364. 



in the oil, on the cores, tank and various other parts of the 
transformer when possible, 

A method of heat-run used to some extent, and known as the 
^'Opposition" test, is shown in Fig. 180. In this test two trans- 
formers of the same capacity, voltage and frequency are required 
and connected as shown in diagram. The two secondary wind- 
ings are connected in parallel, and the two primary windings 
connected in series in such a way as to oppose each other. The 
two secondary leads receive exciting current at the proper voltage 
and frequency, while the primary leads receive a current equal 
to the desired load current ; the wattmeter in the primary circuit 



Fig. 180. — Method of connecting apparatus for heat test, known as "oppo- 
sition" test. 

measures the total copper loss, and that in the secondary the 
total core loss. 

Another method often used and called the "motor generator 
test" is shown in Fig. 181. In this test two transformers are 
used, having their high-tension windings connected together. 
Proper voltage is applied to the low-tension winding of one of the 
transformers, and the low-tension winding of the other trans- 
former is connected to the same source. Then with the switch 
s open, the wattmeter reads the core losses of both transformers, 
and with s closed, it reads the total loss. Subtracting the core 
loss from the total, the copper loss is obtained. This method 
requires (as is also the case in the opposition test) that only the 
losses be supplied from the outside. 


At the present time the flow point of the impregnating com- 
pounds gives a temperature limit of about 90° C. It is possible 
that the development of synthetic gums will soon reach a stage 
to permit of actual operating temperatures of at least 125° to 
150° C. The only difficulty with such an operating temperature 
will be with the oil. 

Certain practices of drying out transformers are applicable 
to temperature tests (see Chapter IX). In drying out trans- 
formers it is always more convenient to short-circuit the low- 
voltage winding and impress sufficient voltage on the high- 

FiG. 181. — Another method of connecting apparatus for heat test known 
as "motor generator" test. 

voltage winding to cause about 20 to 30 per cent, current to flow 
through the transformer coils. This current is found quite suffi- 
cient to raise the temperature of the coils to the desired limit. 

To make normal current flow through the windings when the 
secondary is short-circuited requires a voltage of about 3,3 per 
cent, of the high voltage winding, according to the way the wind- 
ings are connected (series or parallel). For example: It is 
desired to dry out a 100,000 volt, 10,000 kw. single-phase trans- 
former; a 5000 kw., a 2500 kw., and a 1250 kw. of the same 
voltage, etc. What will be the voltage necessary to circulate 
20 and 30 per cent, of noiynal current through the coils of the 
transformers? The answer to this is best given in the following 
table : 



Conditions of test 

Capacity of transformers in kw. 























Normal high-voltage current at 100,- 
000 volts on full-load. 

Voltage required to circulate same 
when low-voltage winding is short- 

At 20 per cent, normal current. . . . 

Voltage required for 20 per cent. . . 

At 30 per cent, normal current 

Voltage required for 30 per cent. . . 

12.5 amp. 
3300 volts 

2.5 amp. 

660 volts 

3.75 amp. 

990 volts 

If one is obliged by circumstances to short-circuit the high- 
voltage winding, the same per cent, voltage holds good. As- 
suming the low voltage to be 5000 volts, it will require 33 volts 
for 20 per cent, normal current, and 50 volts for 30 per cent, 
normal current. With the high-voltage winding connected for 
50,000 volts, the current values given above will be doubled but 
the temperature conditions will remain about the same. 

The maximum values of temperature for large transformers is 
a rise of 40° C. under rated load, this value having for its basis a 
room temperature of 25° C, For rated overloads the limiting 
temperature rise is 55° C. In an earlier part it has been stated 
that, in general, it is found that transformers will operate quite 
,satisfactorily when worked at their limiting temperatures; that is 
to say, around that point where the best efficiency and full-load 
is obtained. A condition of this kind might mean that for short 
periods of time an overload is required, hence a high ratio of 
copper and iron loss, and decreased first cost of transformers. 

High temperatures are objectionable in transformers. Their 
effect on the insulation at temperatures about 100° C. means 
gradual deterioration; their effect on the copper loss is a decided 
objection, this loss increasing about 10 per cent, with an increase 
of 25° C. in the temperature; their effect on the oil is to increase 
the deposition of hydrocarbon on the windings and internal 
cooling apparatus, and a further bad effect is their tendency to 


increase the "aging" of the iron (not including the present 
improved silicon steel). 

To get at, and measure, the maximum temperature affect- 
ing the insulation is almost impossible and only the average 
temperature is measured during a regular test, the temperature 
being taken at the top of the oil and not at the immediate 
surface of contact with the coils or core of the transformer. 

The Standardization Rules of the A.I.E.E. state that the 
rise in temperature of a transformer should be based on the 
temperature of the surrounding air. The cooling medium for 
oil-insulated self-cooled and for forced-air cooled transformers 
is the surrounding air, but for oil-insulated water-cooled trans- 
formers the cooling medium is water, and the temperature 
rise to be considered in this type is that of the ingoing water and 
not the temperature of the surrounding air. On this basis a 
transformer of this type will be about 10° C. less than one 
specified on the basis of the temperature of the surrounding air. 

The class of oil used for insulating purposes has a great 
effect on the temperature. An increase in the viscosity of the 
oil means an increase in the frictional resistance to its flowing. 
The velocity of circulation is reduced, thereby causing an in- 
creased rise in the temperature. 

As yet it has not been possible to formulate a correct theory 
of the laws of cooling for general cases which will indicate 
once for all that combination of conditions which is most favor- 
able to cooling, and enable one to say with considerable accuracy 
not only what will be the average temperature rise in any 
given case, but also what will be the maximum rise. 

Ratio of Transformation. — The ratio of a transformer is tested 
when the regulation test is made. It is the numerical relation 
between the primary and secondary voltage. The ratio of a trans- 
former must be correct, otherwise the service will be unsatisfac- 
tory, because the secondary voltage will be too high or too low. 

For successful parallel operation, correct ratios are essential; 
otherwise cross-currents will be established through the windings. 

A method of ratio test is shown in Fig. 182, where the primary 
of the transformer under test is in parallel with the primary 
of the standard ratio transformer, and the two secondary wind- 
ings are connected in series^ 

Standard transformer ratios are usually an exact multiple 
of 5 or 10. 









Temp, coefficient 

in per cent, per 

degree cent. 




Temp, coefficient 

in per cent, per 

degree cent. 


1 0.4182 

25 0.3801 
























. 3983 






















n .'^Sl.'^ 

26 0.3786 

27 0.3772 




n .-^744 








































. 3482 



Low-voltage distribution transformer ratios are (low-voltage 
windings) 110, 220, 440 or 550 volt to (primary voltage wind- 
ing) 1,110/2,200, 3,300, 6,600 and 10,000 volts. 


High-voltage transformers are wound for 11,000, 22,000, 33,000, 
44,000, 66,000, 88,000, 110,000 and 140,000 volts. 

Occasionally transformers are required with ratio-taps on 
the primary winding so that they may be operated at the maxi- 
mum, intermediate or minimum ratio. 

7 7 

ImAMOAMmJ lQfi.Q.0QQ.O.QO.Q.Qj Primary 
— ^DqOO^ I ^^^'^ — I Secondary 

S.E D.T. 

Sw tch 

Fig. 182. — Method for ratio of transformation test. 

The advantages of such taps are (a) voltage compensation due 
to line drop; (6) the possibility of operating the complete system 
on any of the intermediate ratios, (assuming neutralized system). 

Both of these advantages are sometimes desirable but it would 
be better to obtain them by other means than cutting down 
the normal rating of the transformer. 

It is evident that if the primary voltage is maintained constant 
while operating on any of the intermediate taps, the transformer 
is operated at a greater voltage per turn and therefore at a 
greater iron loss than when the total winding is used. The 
copper loss is reduced somewhat so that the total full-load 
losses are not materially increased. The all-day efficiency is re- 
duced very materially since the iron loss exists for 24 hours 
of the day and the copper loss only about three to four or five 
hours. And, as regards compensating for excessive line drop, 
it is true that if the transformer is connected for a lower ratio 
and at such places as have excessive line drop, the decreased 




primary voltage impressed upon the decreased primary turns 
will produce approximately normal core loss and the desired 
secondary voltage during the period of full-load on the system. 
However, during light load, when a heavy current is no longer 
in the primary and an excessive drop no longer exists, the 
transformer connected and operating on any of the intermediate 
or lower ratio taps will be subjected to full primary voltage 
impressed on the reduced primary turns, and the core loss 

of the transformer will become ex- 
cessive and the secondary voltage in- 
creased to a dangerous limit, that is to 
say, dangerous so far as burn-outs of 
incandescent lamps are concerned, for, 
whoever should happen to turn on their 
lamps during the period of light-load 
operation, is sure to suffer from exces- 
sive lamp burn-outs. Operation at 10. 
per cent, above normal voltage for which 
the lamp is designed, reduces its life to 

-n 100 T.^ X r 15 per cent, of its normal value. Conse- 

FiG. 183. — Effect of con- ^,1 . . 

necting two transformers of q^ently by operatmg a transformer on 
different ratios in parallel, its intermediate ratio-taps, offers the 

disadvantage of excessive core loss for 
at least 20 to 21 hours in the day, and excessive burning out of 
lamps during the same period of time. 

Decreasing the ratio of a transformer from, say, 10-1 to 9-1 
and maintaining the voltage constant, increase the core loss ap- 
proximately 20 per cent. 

A difference of about 10 per cent, in ratios of primary and sec- 
ondary voltages will result in a circulation of about 100 per cent, 
full-load current. And a difference of 2 per cent, in the ratios 
may result in a circulation of 20 per cent, full-load current, or a 1 
per cent, difference in ratio may result in a 10 per cent, circula- 
tion of full-load current; thus showing the absolute necessity 
for having the ratios always exactly the same. For example; 
take Fig. 183 and assume that the percentage impedance volts 
of each transformer is 5 per cent., and the measured difference 
between points a and h shows 21 volts. What will be the 
circulating current with open secondaries? 

The 21 volts is effective in circulating current through the trans- 
former windings against the impedance of the transformers the 


amount of current being expressed in per cent., as 

I per cent. = — y^— (34) 

where k is the difference in voltage ratio and Z° the total imped- 
ance volts of the two transformers. 

The circulating current in this case will be 100 per cent., or 




= 100 



Taking the transformers at 2000 kv-a each, it is evident that 
there will be 10,000 amp. flowing through the secondary windings 
of one transformer and 9100 amp. through the secondary wind- 
ings of the other when a and b are connected together. 

Before connecting any two trans- 
formers in parallel it is advisable first to 
measure the voltage difference between 
a and b points shown in Fig. 183. 

Polarity. — The most simple method 
for testing the polarity is to connect the 
primary and secondary windings of 
the transformers in parallel, placing a 
fuse wire in series with the secondary 
winding. If the transformers are of 
opposite polarity the connection will 
short-circuit the one transformer on 
the other, and the fuse will blow. 
Many burnouts are due to wrong con- 
nections of this kind. 

Transformers are generally assembled 
so that certain selected leads are 
brought out the same in all trans- 
formers of the same type. See Fig. 184, 

The primary terminal (a) should be of opposite polarity to the 
secondary terminal (A). If we apply 200 volts to the primary, 
a b, of the transformer, the voltage between a B should be 
greater than the voltage applied to a b, if the transformer is of 
the correct polarity, or less if of opposite polarity; that is to say. 

-200 +z- 


Fig. 184. — Simple method 
for testing the polarity of 

The A. I. E. E. recommend that the terminals of single-phase transformers shall be marked^ 

A B 

X Y 

A B 

(1) High- and low-voltage windings in phase: 

(2) High- and low-voltage windings 180° apart in phase: 

(3) High- and low-voltage windings in phase possessing more than two 


(4) An out-going neutral tap (50 per cent.) as: 

(5) For three-phase transformers as: 












if two single-phase transformers, both of positive polarity or both 
of negative polarity, are to be operated in parallel, they should be 
connected together as shown. If all traiisformers are alike, they 
may have the same polarity, but if some are of different designs 
or are made by different manufacturers, their polarity may be 

Single-phase polarity is very easily determined; not so with 
polyphase transformers since both phase relation and rotation 

Polarity = 



NO 2 

I Negative 

VJ Polarity — 


Fig. 185. — ^Positive and negative polarity of single-phase transformers. 

must be considered; in fact polyphase polarity may mean a large 
number of possible combinations. 

Considering first, the test for polarity of single-phase trans- 
formers, it is best to consider the direction of voltages to know 
whether they are in phase or in opposition, that is, 180 degrees 
out of phase. Positive polarity means that if, during the test, 
A-b is the sum of voltage A-B and a-h, positive polarity is ob- 

' ■ i 


iryivn ryyv-n 


Fig. 186. — Method of finding threee-phase polarity. 

tained. Negative polarity means that if, the voltage between 
A-b is the value of secondary voltage less than A-B and a-h 
negative polarity is obtained. See Fig. 185. 

In Fig. 185 we have: 
Positive polarity = No. 1 transformer ={A — B)-\-(a—h)=E->re. 
Negative polarity = No. 2 transformer ={A — B) — {a—h)=E — e. 


This means that, in order to connect No. 1 and No. 2 in parallel, 
different leads must be connected together. A A, BB on one side 
and aa, bb on the other side. It is always better, however, when 
a positive polarity transformer is to be connected in parallel with 
a negative polarity transformer, to reverse the connections of 
cither the high-voltage winding or the low-voltage winding of one 
of the transformers. 

Fig. 186 shows the method of finding whether two three-phase 
transformers have the same polarity. 

In making the above test similarly located terminals should be 
connected together as shown. If no voltage is indicated between 
leads x' and x or between y' and y, the polarities are the same and 
the connections can be made and if desired, put into regular 
operation. If, however, there is a difference of voltage between 

a c 

Fig. 187. — Testing for polarity in .three-phase systems. 

y' — y or x' — x, or both, the polarity of the two groups is not the 
same and parallel operation is impossible. It is necessary to 
determine the polarity of each three-phase transformer separately. 

The correct connections under these circumstances, are given 
in Fig. 187. 

Iron or Core Loss. — The core loss includes the hysteretic and 
eddy-current losses. The eddy-current loss is due to currents 
produced in the laminations, and the hysteretic loss is due to 
molecular friction. The core loss remains practically constant 
at all loads, and wUl be the same whether measured from the 
primary or secondary side, the exciting current in either case 
being the same per cent, of the full load. The economical opera- 
tion of a lighting plant depends in a large measure on the selection 
of an economical transfornjer. An economical transformer is 
seldom the one of lowest first cost, nor is it necessarily the one 
having the smallest full-load losses. It is the one which has the 


most suitable division of losses for the service for which it is to be 

The hysteresis loss is dependent on the iron used, and in a given 
transformer varies in magnitude with the 1.6 power of the 
(induction) or magnetic density. An increase in voltage applied 
to a transformer causes an increase in core loss (see following 
table), while an increase in the frequency results in a corre- 
sponding decrease in core loss — the density varying directly as 
the voltage and inversely as the frequency. The eddy current 
loss varies in magnitude with the conductivity of the iron and 
the thickness of laminations. Both the hysteresis and eddy 
current losses decrease slightly as the temperature of the iron 
increases, and if the temperature be increased sufficiently the 
hysteresis loss might disappear entirely while the eddy current 
loss will show a decrease with increased resistance of the iron due 
to this temperature. Thus at full-load, or in other words, an 
increase in temperature to the limiting temperature rise of 40° C. 
may cause a decrease in core loss of about 5 per cent, depending 
on the wave form of the impressed voltage. For ordinary steel 
used in transformers, a given core loss at 60 cycles may consist of 
72 per cent, hysteresis and 28 per cent, eddy current loss, the 
hysteresis loss decreasing with increased frequency while tlie eddy 
current loss is increased with increased frequency. 

Low power factor of exciting current is not in itself very 
objectionable. This can best be explained by taking two trans- 
formers, one made up of ordinary iron and the other of modern 
silicon steel or "alley-steel," Take, for example, two 5kw, 
transformers. The one made up of ordinary iron will have a core 
loss of about 64 watts while that made of silicon steel will have a 
core loss of only 45 watts; and, taking the exciting current of 
both to be 2 per cent, of the full-load current, we have the follow- 
ing power factors: 

Transformer with ordinary iron: 


= 64 per cent, power factor 



Transformer with silicon steel 

5000x0.02 ^^^ P^^ ^^^*" P^^^^' factor. 


which means that on no-load the one using ordinary iron has 
19 per cent, better power factor. 

As stated above, the lower the frequency the greater will be 
the iron loss. In ordinary commercial transformers a given core 
loss at 60 cycles may consist of 72 per cent, hysteresis and 28 
per cent, eddy-current loss, while at 125 cycles the same trans- 
former may have 50 per cent, hysteresis and 50 per cent, eddy- 
current loss. The core loss is also dependent upon the wave- 
form of the applied e.m.f. A flat top wave gives a greater loss 
than a peaked wave and vice versa. 

With a sinusoidal wave of e.m.f. applied on a transformer, the 
exciting current is distorted, due to the effect of hysteresis. If 
resistance is introduced into the primary circuit, however, the 

HjiJiJlftiiiL^ Transformer 

Fig. 188. — Iron or core loss transformer test. 

exciting current wave becomes more sinusoidal and the generated 
e.m.f .-wave more peaked, the effect of these distortions tending 
to reduce the exciting current and core loss. Since the magnetic 
density varies with the voltage and inversely with the frequency, 
an increase in voltage applied. to the transformer causes an 
increase in core loss, while an increase in frequency results in a 
corresponding decrease in core loss. 

Of the several methods in use for determining core loss, the 



following method is the simplest to apply and gives very accurate 
results. See Fig. 188. 

There are occasions when the core losses of a transformer are 
known while operating at a given frequency and voltage but 
when it is desired to correct these results for operation under 
other conditions other figures are necessary. In order to deter- 
mine approximately the losses of a 60-cycle transformer when 
operating at other than rated voltage, the losses at rated voltage 
may be multiplied by the factors given in the following table: 


Rated voltage of transformer 

Operating voltage 















. 2080 


1 00 

The values given in the above table are only approximate 
-because the variations with varying voltage depend largely 
upon the quality of steel and the density at which the trans- 
formers are operated. 

Resistances. — ^The resistance of the primary and the secondary 
of a transformer may be determined by several different methods, 
the most common of which are "fall of potential" and "wheat- 
stone bridge" methods. For commercial use the most satis- 
factory method is the fall of potential. In this method the 
resistance may be determined by Ohms law: 

Resistance =-r . (38) 



The measurement requires continuous current and a continu- 
ous-current voltmeter and ammeter. With the connection 
shown in Fig. 189, assume, for example, the ammeter reading to 
be 2.5 amperes, and voltmeter reading to be 11 volts. What is 
the resistance of coil? 

The resistance of voltmeter used in test is 500 ohms, and the 
temperature of transformer coil is 30 degrees centigrade. There- 
fore, current taken by voltmeter at 1 1 volts is, 

^ = 0.022 amp. 

Current in transformer coil =2.5 — 0.022 = 2.478 amp. 

The ammeter reading includes the current in the voltmeter, 

lJ I 

—*< Res. 


Fig. 189. — Method of finding the resistance of a transformer. 

and in order to prevent error the resistance of the voltmeter 
must be much greater than that of the resistance to be measured. 
Resistance of transformer coil at 30 degrees centigrade is, 



= 4.48 ohms. 

It is important that measurements be taken as quickly as 
possible, especially if the current be near the full-load values, and 
it is equally important in alJ cases that the voltmeter needle be 
at rest before the observation is taken, otherwise the values 
obtained will not be reliable. It is possible to have a current of 



sufficient strength to heat the coil so rapidly as to cause it to 
reach a constant hot resistance before the measurement is taken. 
The resistance of the transformer coil at 25° C, which is the 
temperature coefficient of 0.42 per cent, per degree from and at 
0°C., is, 


(0.42X5) +100 

i:-^ v^^ = 4.39 ohms. 

If the temperature of windings is different for each observation, 
then resistance must be calculated for each and the average taken. 
If the temperature of the windings is the same for air observa- 
tions, then the average voltage and current may first be deter- 
mined and the resistance calculated from the average values. 

Copper Loss and Impedance. — ^When a transformer is delivering 
power, copper loss takes place, varying as the square of the 


Fig. 190. — Copper loss and impedance. 

current. It is due to the resistance of the windings and to the 
eddy currents within the conductors themselves. 

The copper loss may be measured at the same time as the 
impedance-drop measurement by introducing a wattmeter as 
shown in Fig. 190. It may also be calculated from currents 
through conductors and resistance of conductors, as follows: 

P = h^Ri + h^R2, in watts, 


wherein P is the power lost; /j, the primary current; 1 2, the 
secondary current; j^i the primary resistance; and R2 the second- 
ary resistance. 

The variation of copper loss with varying voltage on 2200 to 
2600 volt 60-cycle transformers is given in the following table: 


Ratio voltage 

























In testing a three-phase transformer for copper loss and 
impedance the measurements can be made conveniently by 
connecting both the high-voltage and the low-voltage windings 
in delta and opening up any one corner of the delta on either the 
high-voltage or low-voltage side as desired and convenient for 
supply voltage, and inserting a wattmeter, voltmeter and ammeter 
and impressing sufficient single-phase voltage across this corner 
at the proper frequency to cause normal full-load current to flow 
through the windings. The wattmeter reading will give the 
copper loss, and this reading divided by the normal full-load 
input in the transformer will represent the per cent, copper loss. 
One-third of the voltage measured on the voltmeter divided by 
the normal voltage of the winding of one phase represents the 
percentage impedence drop. 

The impedance in alternating-current circuits is similar to re- 


sistance in continuous-current circuits, that is to say, the ex- 

r ^ r^ x G.m.f. .^^^ 

/ = D = Current = ~ . (42) 

R Resistance ^ ^ 

for continuous-current circuits is replaced in alternating-current 
circuits by the equivalent expression, 

~ \/R^+{X's^ ~ ~ i mpedance ~R-jx~Uj^^ -fhw ^^"^ ^ 

where / is the current; E the impressed e.m.f. ; Xg the inductive 
reactance; and J^ the resistance of the circuit. 

The impedance of a transformer is made up of two components 
at right angles to each other. (Reactance and resistance.) It 
is expressed as 

Z = \/R^+X^= {R-jx)R + v'^T Lw (45) 

Reactance may be inductive, Xg, or condensive Xc', this latter 
factor is never considered when dealing with transformers. 

X. = 2.fL and X, =^-l_ = _J__ (46) 

wherein /is the frequency in cycles per second; L is the induct-, 
ance in henrys; and C is the capacity in farads. 

The impedance of a transformer is measured by short-circuiting 
one of the windings, impressing an e.m.f. on the other winding 
and taking simultaneous measurements of voltage and current. 

The impedance voltage varies very nearly with the frequency. 
In standard transformers the impedance voltage varies from 
1 to 4 per cent., depending upon the size and design of the 

Efficiency. — ^The efficiency of a transformer is the ratio of its 
net output to its input. The output is the total useful power 
delivered and the input is approximately the total power delivered 
to the primary; and consists of the output power plus the iron 
loss at the rated voltage and frequency, plus the copper loss due 
to the load delivered. 

Example: Find the full-load, and half-load efficiency of a 
5-kw., 2000 to 200-volt, 60-cycle transformer having an iron 
loss of 70 watts, a primary resistance of 10.1 ohms, a secondary 
resistance of 0.066 ohms. 


The efficiency of the transformer under consideration is taken 

as follows: 

Full Load: 

Primary I^ R 63 watts 

Secondary PR 42 watts 

Core loss 70 watts 

Total Losses 175 watts 

Output = 5,000 watts 

Input = 5,000 + 175 5,175 watts 

Full load efF. = t^v?==96.6 per cent. 

Half Load: 

Primary and Secondary 26 watts 

Core loss 70 watts 

Total Losses 96 watts 

Output = 2,500 watts 

Input = 2,500 + 96 2,596 watts 

One-half load eff. =^^^-=96.2 per cent. 

It will be noted that the iron loss remains constant at all 
loads but the copper loss varies as the square of the load current. 
The copper loss remains the same in all transformers of a given 
design and size, it is, therefore, only necessary to make these 
tests on one transformer of each rating and type. 

The copper loss should preferably be determined from the 
resistances of the windings, rather than from the copper loss 
test by wattmeter. For other than full-load, the copper loss 
varies as the square of the load, the core loss remaining constant 
at all loads. The all-day efficiency takes into account the time 
during which these losses are supplied and is expressed as: 

Per cent, all-day eff. = 

100 +watthours output . .„v 

w.-hrs. output +w.-hrs. copper loss-j-w.-hrs. core loss ^ 

The exact copper loss of a transformer must be known in order 
to calculate the efficiency. The core loss should be taken at 
exactly the rated voltage of the transformer and, when possible, 
with a sine wave current, otherwise considerable discrepancies 
may occur. 

Regulation. — ^The regulation of a transformer with a load of 
given power-factor is the percentage of difference of the full 
load and no load secondary voltages with a constant applied 


primary voltage. It may be ascertained by applying full load 
to the transformer and noting the secondary voltage, then 
removing the load and noting the secondary open-circuit voltage. 

The secondary voltage drop will be very much greater with 
an inductive load, such as induction motors or arc lamps, than 
it will be with incandescent lamps. 

The regulation can be determined by direct measurement or 
calculation from the measurements of resistance and reactance 
in the transformer. Since the regulation of any transformer is 
only a few per cent, of the impressed voltage, and as errors of 
observation are liable to be fully 1 per cent., the direct method of 
measuring regulation is not at all reliable. By connecting the 
transformer to a circuit at the required voltage and frequency, 
using a lamp load or water rheostat on the secondary the regula- 
tion may be determined. This method, is, however, unsatis- 
factory, and much more reliance can be placed on the results of 

Several methods have been proposed for the calculation of 
regulation, but the following is found quite accurate for inductive 
and non-inductive loads. 

For inductive loads: 

% regulation =%X smd+%1 R cos d. (48) 

= % E:, sin d+%Er cos 0. 

Per cent. Ex =the per cent, reactance drop. 

Per cent. Er =per cent, total resistance drop. 

^ = the angle of lag of load current delivered. 

Example. — ^Find the regulation of a transformer which has 
a reactance drop of 3.47 per cent, and a resistance drop of 2.0 
per cent, when delivering a load to a circuit having a power- 
factor of 87 per cent. 

The cos ^ = 0.87 is 30 degrees. The sine of angle 30 degrees is 
0.5. Then from the above formula: 
Per cent, regulation = 3.47x0.5 + 2X0.87 = 3.48. 

For non-inductive loads: 

% Regulation =%IR- ^^~q^^^ (49) 

Per cent. I R = per cent, resistance drop. 
% X = 'V% impedance drop^— % resistance drop^= % react- 
ance drop. 
I = V% exciting current^— % iron loss currents 



For non-inductive load O — O, sin O — O, cos = 1, we have, 

% regulation =% Er 

The above formula is practically correct for small values of 
angle 6, but the error becomes greater as increases. 

Another simple and accurate method in use for calculating 
regulation is, 

For non-induction loads: 

TV 2 

% regulation =7 7^20^ ^^°^ 

and for inductive loads: 

% regulation =d 4- 2QQ (51) 

where d is component drop in phase with the terminal voltage 
and k is the component drop in quadrature with the terminal 
voltage, IR is total resistance drop in per cent, of rated voltage 
and IX is reactance drop in per cent. 

Take for example a 7.5 kw. 60-cycle single-phase transformer 
with a 10 to 1 ratio, secondary voltage at full load = 208 volts and 

Sec. resistance =0.0635 ohms. Primary resistance =4.3 

Sec. 7/2 = 2.165 volts = 0.985 %. Primary 772 = 14.65 volts = 
0.667 %. 

IX = V{% impedance drop) 2- 77^2= 1.8 % 

For non-inductive load, using the formula above, we have 

% regulation = 1.65 +^|^ = 1.67 % 


For inductive load with a power factor of, say, 80%, we have 

% regulation = 2.3 + ^^ = 2.33 % 

where 2.3 is taken from formula, and is: — 

d = w 7X + 772 Cos ^ = (0.6 X 1 .8) 4- (1 .65 X 0.8) = 2.3 

The value IX (reactance drop in volts) may also be expressed by the formula 


where E is the rated primary voltage, E^ being the impedance voltage and is found by short- 
circuiting the secondary winding and measuring the volts necessary to send rated-load current 
through the primary. P is the impedance watts as measured in the short-circuit teat. 



0.46 is from formula, and is: — 

k = w IR- IX Cos ^ = (0.6 XI. 65) -(1.8X0.8) =046 

where w is the wattless factor of load. 

Short-circuit Test. — For some time past it has been the practice 
of certain transformer-testing departments in America to subject 
certain types of transformers over a given k-v-a. capacity to 
short- circuit tests of from 5 to 25 times rated current. 

It is now well known that the cause of many burn-outs is 
due to the large amount of power back of the transformers. It 
has also been shown that a certain milling occurs in transformers, 
and after repeated short-circuits the transformer breaks down, its 
coils being twisted in the shell type and displaced in the core 


The short-circuit test is usually done at special times of the 
night so as not to affect the voltage regulation of the system. 
One winding of the transformer is connected to the power system 
(always many times the capacity of the transformers) and the 
other winding suddenly short-circuited. The tendency of the 
coils to flare out due to the excessive magnetic repulsion is the 
most important point of the test. This test is of very short 
duration, as the current sometimes reaches as high a value as 
25 to 30 times full-load current. 



High-voltage transformer specifications are always interesting 
in that other more severe mechanical and electrical stresses have 
to be considered in their design, and the arrangement of coils, 
their form and make-up are so different. Below is given a wind- 
ing specification of a high-voltage transformer which was 
specially made for an existing transformer operating at a lower 
voltage (the same iron being used over again). 

60-CYCLE 900-KW. 22,700-39,300 TO 2200-VOLT SINGLE- 

Primary Winding 

Conductor cross-section, two 0.170 in. X 0.080 in. double cotton 

Weight, 750 lb. double cotton covered. 

Inside Section. Outside Section. 

Turna / 8 B.T. coils of 32 and 32 \ / pz, pa, pt, p&, pe, p?, pa, 

618 in. \ 2 B.T. coils of 27 and 26 / "• \ p^, pi, and pn,. 

Winding taps made at end of fifth turn inside end of outside 

section ps, p^. 
Insulation between turns (8300 ft.) 0.015 in. thick by 3/16 in. 

wide, consisting of two 0.005 in. hercules parchment and one 

0.005 in. mica. 

Reinforced Turn Insulation 

26-turn section, last 12 turns (triple) turn insulated, and all turns 

0.012 \.CK 
26-turn section, all other turns (double) turn insulated, and all 

turns 0.012 V.C. 
26-turn section, all turns (double) turn insulated, and all turns 

0.012 V.C. 

1 V.C. = varnish cambric. 



Coils pi and pio special collars of 1 3/32 in. pressboard. 
All wood strips to be of 3/4 in. wide by 3/16 in. 
Pressboard strips to be of 1 1/2 in. wide by 3/16 in. 
Taping of coils to be of 0.229 in. 
Wire vacuum, 1. 
Coil dimensions: bare, 7 5/16 in. by 1/2 in.; insulated, 

7 3/8 in. by 9/16 in. 
Dimensions of coils with special collars: bare, 7 5/16 in. 
by 5/8 in.; insulated, 7 3/8 in. by 11/16 in. 

Secondary Winding 

Conductor cross-section, four 0.300 in. X 0.115 in., two 
of double cotton covered and two of bare. 

Weight, 370 lb. double cotton covered and 370 lb. bare. 

60 turns in 8 S.S. coils of 15 turns each, 4 coils in series, 
2 in parallel. 

Insulation between turns, 1340 ft., 0.025 in. thick by 
5/16 in. wide, consisting of two 0.010 in. hercules parch- 
ment and one 0.005 in. mica. 

Coil dimensions: bare, 7 3/4 in. X 5/16 in.; insulated, 
7 13/16 in. X 3/8 in. 

Coils for special collars of 1 3/32 in. 

Insulation Specification 

After winding the coils they must be securely clamped to 
dimensions called for in the winding specifications, after which 
they are to have the terminals attached. 

Before the coils are dipped they should have a preliminary 
baking for 12 hours at 250° F. (120° C), or longer if necessary, 
thoroughly to dry out any moisture and shellac in the turn 
insulation and collars. The coils should be twice dipped when 
hot in 0.07-B japan and baked 12 hours at 250° F. after each 

After the coils have been dipped they are to receive one pintag 
of 0.007 in. cotton tape for varnish treatment. The taping is 
to be put on according to directions given below. 

Before putting on the taping the coils should be brushed over 
with a thin coat of 0.028 in. sticker to hold the tape to the coils. 
The taping should receive five brushings of 0.094 in. varnish of 
specific gravity 875, and should be baked after each brushing at 
least five hours, or until hard, at a temperature of 180° F. (85 to 


95 °C.). After each taping the coils should be allowed to cool to 
at least 100° F. (38" C.) before the next varnishing is given. 

The taping should be put on with one-half lap, except at the 
corners of the coils, where it should overlap not more than one- 
eighth at the outside edge. 

With single section coils there should be added, before the taping 
is put on, one thickness of No. 2 cotton drill, which is to be placed 
over the connecting straps. The drill should extend at least 
1 1/2 in. each side of the strap, and must be neatly and firmly- 
tied down with twine and sewed together at the outside edge of 
the coil, A tongue of the drill should extend up the outside of 
the strap as far as the terminal, and should be secured to the 
strap with a wrapping of cotton tape. 

Below is given a form of general specification as presented to 
purchasers of transformers. The former is for a high-voltage 
shell-type transformer and the latter for a high-voltage core-type 




General Construction. — Each transformer to consist of a set of 
flat primary and secondary coils, placed vertically and surrounded 
by a built-up steel core, the coils being spaced so as to admit of 
the free circulation of oil between them, which acts not only as 
an insulator but as a cooling medium by conveying the heat 
from the interior portions of the transformer to the tank by 
natural circulation. 

The transformer to be enclosed in a boiler-iron tank, the base 
and cover being of cast iron. The tank to be secured to the base 
with a joint made oil-tight by heavy riveting and caulking. 

A coil of pipe for water circulation to be placed in the oil in the 
upper part of the tank over the cover and surrounding the ends 
of the windings, the combined surface of the coil and tank being 
sufficient to dissipate the heat generated and thus maintain the 
oil and -all parts of the transformer at a low temperature. 

Core. — The core to be built up of steel laminations of high per- 
meability and low hysteresis loss. The laminations also to be 
carefully annealed and insulated from each other to reduce 
eddy-current losses. 


Windings. — The primary and secondary windings to be sub- 
divided into several coils, each built up of fiat conductors, wound 
with one turn per layer so as to form thin, high coils which will 
present a large radiating surface to the coil. The conductors to 
be cemented together with a special insulating compound, after 
which an exterior insulating wrapping to be applied and separately 
treated with an insulating varnish, making a very durable 

A solid insulating diaphragm to be placed between adjacent 
primary and secondary coils, and to be rigidly held in position 
by spacing channels covering the edges of the coils. 

The assembled coils, except at the ends, to be completely 
enclosed by sheets of solid insulation, which will interpose a sub- 
stantial barrier at all points between the winding and the core. 

Oil. — Each transformer to have sufficient oil completely to 
immerse the core, windings, and cooling coil. In order to secure 
the best insulating qualities and a high flashing-point, the oil 
to be specially refined and treated and tested for this use. 

A valve for drawing off the oil to be located in the base of the 

Water-cooling Coil. — To consist of heavy wrought-iron lap- 
welded pipe with electrically welded joints, and to stand a test 
of at least 1000 lb. pressure per square inch. 

The duty of the cooling coil is to absorb that portion of the heat 
that cannot be dissipated by natural radiation from the tank, 
which will be made to fit the transformer closely, and thus 
minimize the amount of oil and floor space. 

Leads. — The primary and secondary leads to be brought out 
through the cover, and to consist of heavy insulated cables 
brought through porcelain bushings of ample surface and thick- 

Performance. — After a run of 24 hours at rated load, frequency, 
and voltage, the rise in temperature or any part of the trans- 
former, as measured by thermometer, and the rise in temperature 
of the coils, as measured by the increase in resistance, not to 
exceed 40° C, provided the temperature of the circulating water 
is not greater than 25" C, and that the supply of water is normal. 
If the temperature of the water differs from 25° C, the observed 
rise in temperature shoul^ be corrected by 0.5 per cent, for each 

The insulation between the primary coils and the core, and 


that between the primary and secondary coils, to stand a test of 
140,000 volts alternating current for 1 minute, and between the 
secondary coils and the core a test of double the normal voltage 
for the same length of time. 

The transformer to carry an overload of 25 per cent, for two 
hours without the temperature rise exceeding 55° C. 

The transformer to give full kilowatt output when operating 
at 90 per cent, power factor without exceeding the above tem- 
perature rise. 


Core. — The cores to be built up with laminated iron sheets 
of high permeability, low hysteretic loss, and not subject to ap- 
preciable magnetic deterioration. The sheets to be carefully 
annealed and insulated from each other in order to reduce eddy- 
current losses. 

Windings. — The primary and secondary windings to be thor- 
oughly insulated from each other and from the core and frame, 
and to stand a potential much greater than the rated voltage of 
the transformer. 

Oil. — Each transformer to have sufficient oil to cover the core 
and winding when placed in the tank. The oil to be specially 
treated and refined in order to secure good insulating qualities 
and a high flashing-point. 

Terminals and Connections. — The primary and secondary leads 
to be carefully insulated and taken from the tank through por- 
celain bushings, which shall have sufficient surface to prevent 
perceptible leakage to the frame of the transformer. 

Performance. — After a run of twenty-four hours at rated load, 
voltage, and frequency the rise in temperature of any part of the 
transformer as measured by thermometer, and of the coils as 
measured by the increase in resistance, not to exceed 45° C, 
provided the temperature of the surrounding air is not greater 
than 25° C. and the conditions of ventilation are normal. If 
the temperature of the surrounding air differs from 25° C. the 
observed rise in temperature should be corrected by 0,5 per cent, 
for each degree. 

Insulation between the primary winding and the core, and be- 
tween the primary and secondary windings, to stand a test of 
140,000 volts alternating-current for one minute, and between 


the secondary winding and the core a test of 10,000 volts alter- 
nating current for the same length of time. 

The transformer to carry an overload of 50 per cent, for two 
hours without undue heating of any of the parts. 

Every manufacturer has his own particular way of arranging 
transformer specifications. One finds it suits his purpose to 
give but a general description while another will sometimes present 
useful information and give a detailed specification covering the 
complete characteristics of the transformer, including a complete 
test record and general mechanical and electrical description. 

One of the best specifications and one of great interest to all 
operating engineers is made up as follows: 

Transforyner Detailed Specification.' — Form X X 

Tank Cribs Total I^R per cent. IR 

H.T. cable No long. L. T. cable 

No. long. H.T. brushing (terminal) No L.T. bush- 
ing (terminal) No Winding Length Depth 

....... Width. ...... Weight of coils and core ....... Net 

weight of oil Weight of tank and cribs Total weight 

Gallons of oil Steel curve K. V. A Type 

Frequency Volts ^.T Phase VoltsL.T. 


Iron Core. — Steel End irons X Iron clusters 

per leg Core irons X Narrow iron clusters 

per leg Corners Weight of core Window ..... 

X Volume of core Exciting current Core 

section X and square inches. Length 

of mag. path Core loss, amperes Mag. amperes 

per. cent. 

H. T. Winding — Amperes Volts Turns Tap- 
outs No. of layers Sections per lag Insula- 
tion coil to core Insulation between layers Turns 

in each layer per section Length of section Space 

of ends Space between sections Insulation exten- 
sion Space around core Size of conductor 

Diam. of conductor Lbs. per M. ft Weight 

Thickness of coil Mean turn Copper density 

Resistance (R) Volts per turn Max, volts per layer 

/2/2 IR 

L. T. Winding. — Volts Amperes Taps No. 

of layers Insulation between layers ...... Section per 


leg Turns in each layer per section Space between 

sections Space at ends Diam. of conductor 

Space around core Length of sections Weight 

Insulation extension Size of conductor Lbs. per M. 

ft Mean turn Thickness of coil (R) Resist- 
ance Max. volts per layer Copper density 

Volts per turn IR im 

Like all customers' specifications these two are not complete 
as they do not specify the efficiency and regulation (these two 
important factors being on the test record sheet only); the 
dielectric test of the oil; the temperature of the water necessary 
to cool the oil; the method of supporting the transformer; lifting 
the transformer, nor the method employed in moving the trans- 
former whether it be on steel-rails, a four-wheel truck or on a 

The general characteristics of a transformer are always given 
in the test record sheets. A good example of such a sheet is 
given below and is for a high-voltage power transformer. 


1000 kw., 25 cycle, 60,000-volt shell-type, single-phase 

transformer (water cooled). 
H. T. winding 30,000 60,000 volts; L.T. winding 2300 volts. 
H. T. amperes 16.66; L. T. amperes 435. 
Heat Run. — 

Run for 8 hours at 2300 volts L. T., and 18.5 amperes H. T. 

Run for 2 hours at 2300 volts L. T,, and 23.2 amperes 

H. T. (6). 
■Temperatures (degrees C. at end of run). — 

H. T. by resistance 35.0 for (a) and 50.0 for (6). 
L. T. by resistance 37.0 for (6) . 
Temperature of oil 18.0 for (a) and 23.5 for (b). 
Temperature of water leaving the transformer 10.0 for (a) 

and (6). 
Temperature of frame of transformer 12.0 for (a) and 16.5 

for (b). 
Resistances. — 

H. T. resistance at 25° C. is 1796, and for (b) is 21.32 ohms. 
L. T. resistance at 25° C. is 0.0223 and for (b) is 0.02545 ohms. 


Insulation. — 

Voltage applied to primary and secondary and core for one 
minute is 120,000 volts. 

Voltage applied to L. T. and core for one minute is 5000 

(Application of alternating current). 

Efficiency. — 
At 125% full-load, guaranteed eff. 98.0% and commercial eff. 98.38%. 
At 100% full-load, guaranteed eff. 97.8% and commercial eff. 98.36%. 
At 75% full-load, guaranteed eff. 97.4% and commercial eff. 98. 11%. 
At 50% full-load, guaranteed eff. 96.7% and commercial eff. 96.93%. 
At 25% full-load, guaranteed eff. 93.9% and commercial eff. 94.52%. 
Regulation (100 per cent. P. F.). — 

Guaranteed regulation = 1.0 per cent. 
Commercial regulation = 1.037 per cent. 

General. — 

Core loss in watts = 7.335 watts. 

Excitation in amperes = 14.3. 

Impedance volts = 1.653. ((a) =1.822 volts.) 

Impedance watts = 9.560. ((a) =11.720 watts.) 

Water per minute = 2.6 gallons. 

(ingoing water 25° C). 

Detailed Specifications. — 

Height over cover = 135 in. 

Floor space = 110 in. X59 in. 

Total weight (without oil) =30,000 lb. 

Gallons of oil required = 1300. 

Weight of oil = 10,400 lb. 

Weight of tank and base = 7500 lb. 

Weight of large cover = 2450 lb. 

Weight of small cover = 550 lb. 

Weight of cooling coils and casing = 2500 lb. 

Dimensions of coils and casing = 70 in. X37 in. X32 in. 

Cooling coil (size of pipe) =1.5 in. 

Length of cooling coil pipe = 830 ft. 

Cooling coil pipe dimensions = 30 in. X53 in. X96 in. 

Weight of cooling coil = 2200 lb. 

Weight of iron cover =14,000 lb. 



200-kw., 25 cycle, 57,500 volts core type, water-cooled 

single-phase transformer. 
H. T. winding 28,750, 57,500 volts; L. T. winding 2300 volts. 
H. T. amperes = 3.5; L, T. amperes = 87. 
Heat Run. — 

Run for 11 hours at 2300 volts L. T., and 87 amperes L. T. 

current (a). 
Run for 2 hours at 2300 volts L. T., and 130.5 amperes L. T. 

current (6). 
Temperatures (degrees C. at end of run) . — 

H. T. by resistance 30.0 for (a) and 49.5 for (b). 
L. T. by resistance 38.5 for (6). 
Temperature of oil 21.5 for (a) and 28.0 for (6). 
Temperature at top of frame is 19.5 for (a) and 25.0 for (6). 
Temperature at bottom of frame is 9.5 for (a) and 12.5 for (6), 
Room temperature for (a) is 18.5 and for (b) 17.5° C. 

H. T. resistance at 25° C. is 56.6 ohms on winding connected 

for 28,750 volts. 
H, T. resistance for (6) is 68.1 ohms. 
L. T. resistance for 25° C. is 0.1168 ohms, and for (b) is 

0.1307 ohms. 
Insulation. — 

H. T. to L. T. and core 115,000 volts alternating current 

for one minute. 
L. T. and core 10,000 volts alternating current for one minute. 

At 100% load guaranteed eff. 96.7% and commercial eff. 97.9%. 
At 75% load guaranteed eff. 96.2% and commercial eff. 97.8%. 
At 50% load guaranteed eff. 95. 0% and commercial eff. 96.8%. 
At 25% load guaranteed eff. 91.2% and commercial eff. 94.5%. 

Regulation (100 per cent. P. F. =1.6 per cent.). — 

Core loss in watts =2.865. 

Excitation in amperes =10.3. 

Impedance volts (57,500 volt winding) =1.017. 

Impedance watts =1.750. 


Detailed Specifications. 

Height over all =103 in. 

Floor space =47 in, X64 in. 

Total net weight (without oil) = 10,000 lb. 

Weight of oil =3,000 lb. 

Gallons of oil required =150. 

H. T. voltage taps =57,500, 55,000, 47,500 and 45,000 volts. 
Up to the present time natural-cooled oil-insulated single-phase 
transformers have been built in sizes of 3000 kv-a, and air-cooled 
transformers up to 4500 kv-a at 33,000 volts. 

Comparing the various types of European and American made 
transformers in so far as their over-all dimensions, kilowatts per 
square foot, kilowatts per cubic foot, cubic foot of air per minute, 
gallons of oil for a given size, etc., we find there exists quite a 
difference. For instance, taking two of the largest sizes made in 
the respective countries, we have, for the air-cooled type: 


(American manufacture) 
(Dimensions, 90 in. X74 in. X137 in. high) 

Kilowatts per square foot 86 . 5 

Kilowatts per cubic foot 7 6 

Cubic feet of air per minute 6. 750 

Frequency 25 


(European manufacture) 
(Dimensions, 86 in. X25 in. X98 in. high) 

Kilowatts per square foot 55 

Kilowatts per cubic foot 6.r 

Gallons of oil 640 

Gallons per kilowatt 0. 376 

Cubic feet of air per minute 7 . 500 

Frequency 25 

The European type referred to here is oil-insulated and cooled 
by means of an air blast at the outside of the tank. The Ameri- 
can type referred to here is commonly known as the air-blast 
transformer and is cooled by forced air circulation through core 
and coils. 


Also, comparing the largest water-cooled oil-insulated trans- 
former made in Europe with an ordinary 4000 kw. standard 
American design of the same type, we have: 


(American manufacture) 
Dimensions, 107 in. X63 in. X150 in. high) 

Kilowatts per square foot 86 

Kilowatts per cubic foot 6 . 85 

Gallons of oil 1950 

Gallons per kilowatt 0.49 

Full-load efficiency 98.9 per cent. 

Half -load efficiency 98 . 5 per cent. 

Gallons of water per minute 19 . 5 

Frequency 25 


(European manufacture) 
(Dimensions, 82 in. X59 in. X136 in. high) 

Kilowatts per square foot 162 

Kilowatts per cubic foot 14.2 

Gallons of oil 1130 

Gallons per kilowatt 0. 215 

Efficiency at full-load 98 . 95 per cent. 

Efficiency at 50 per cent, load 98.85 per cent. 

Regulation (P. F. = 1.0) 0. 62 per cent. 

Regulation (P. F. =0.8) 3 . per cent. 

Frequency 50 

Transformers of a much greater size than 5,000 kv-a at 45,000 
volts have not yet been built in Europe. In American single- 
phase units of 7500 kw., and three-phase units of 14,000 kw, 
are in operation at voltages above 100,000 volts. 

The three following high-voltage power transformers will 
serve to show what is being done in this direction: 


Kilowatts per square foot 80 

Kilowatts per cubic foot 5.65 

Gallons of oil 4000 

Gallons of oil per kilowatt. 0.53 

Efficiency at full-load 98 . 95 per cent. 

Weight without oil 42 . 5 tons. 

Frequency 25 



Kilowatts per square foot 71 

Kilowatts per cubic foot 5.3 

Gallons of oil 2500 

Gallons of oil per kilowatt 0.7 

Efficiency at full-load 98 . 8 per cent. 

Efficiency at 75 per cent, load 98.7 per cent. 

Efficiency at 50 per cent, load 98.3 per cent. 

Efficiency at 25 per cent, load 96.9 per cent. 

Total weight in tons 28 

Frequency 60 

Test voltage 280,000 volts. 

(Length of high-voltage winding is 4 miles) 


Kilowatts per square foot 58 . 7 

Kilowatts per cubic foot 3 . 25 

Gallons of oil 1500 

Gallons of oil per kilowatt 0.75 

Efficiency at full-load 99 per cent. 

Weight without oil 60 tons. 

Frequency 60 

(The primary winding (high-voltage winding) consists of 10 miles of copper 


Practically every high-voltage alternating-current three-phase 
system operating at 55,000 volts and above are given in the 
table "Modern High-voltage Power Transformers operating at 
the Present Time." The transformer connections are as 38 for 
star against 21 for delta (the star connections being in some cases 
solid grounded and in others grounded through a high resistance 
— while the delta connections are all insulated). In Chapter IV 
several important advantages and disadvantages are given for 
delta and star connections, in looking through the list of the 
highest voltage transformer installations practice appears to 
point toward the star connection. 



Operating systems 

§ I ° S 

i! £ as 

X I « C8 P 

1. Sierra and San Francisco 

2. Power Company 

3. Eastern Michigan Power Co. . . . 

4. Hydro-pjlectric Power Comm-n. 
Hydro-Electric Power Comm-n. 

5. Mexican Northern Power Co. . . 

6. Great Western Power Company. 
Great Western Power Company. 

7. Mississippi River Power Co. . . . 

8. Grand Rapids Mich. Power Co. 

9. Georgia Power Company 

10. Truckee River G. E. Company. . 

11. Yadkin River Power Company. . 

12. Great Falls Water P. & T. Co.. 

13. Southern Power Company 

14. Central Colorado Power Co. . . . 

15. Tata Hydro-Electric Power Co. . 

16. No. State Hydro-Electric Co. . . 

17. Yadkin River Power Company. . 

18. Shawinigan Power Company. . . . 
Shawinigan Power Company. . . . 

19. Central Colorado P. Company.. 

20. Rio de Janeiro L. & P. Co 

21. Appalachian Power Company. . . 
Appalachian Power Company. . . 

22. Sao Paulo Electric Company. . . 

23. Tata Hydro-Electric Company.. 

24. Mexican L. & P. Co. Ltd 

Mexican L. & P. Co. Ltd 

25. Madison Riven Power Company 

26. Utah Light & Power Company . 

27. Butte Elect. L. & P. Company . , 

28. Telluride Power Company 

29. Katsura-Gawa Hydro-Elect. Co. 

30. Southern Calif. Edison Co 

31. Pennsylvania W. & Power Co . . 


Star. . . 



Star. . . 



Delta . 



Delta . 



Delta . 



Star. . . 



Delta . 



Delta . 






Delta . 






Star. . . 



Star. . . 



Delta . 



Delta . 






Star. . . 



Star. . . 



Star. . . 



Delta . 



Delta . 



Delta . 



Star. . . 



Delta . 



Delta . 



Star. . 



Star. . . 



Star. . . 



Star. . . 



Delta . 



Delta . 



Delta . 



Star. . . 



Star. . . 



Star. . . 



Star. . . 



1 10,000 

•The connection of systems given here is not strictly correct «is changes from delta 
to star and from star to delta are constantly being made to suit new conditions. 

t This denotes single or three-phase transformer — the systems themselves in all the 
above cases being three-phase. 





Operating systems 

32. Missouri River Power Co 

33. Southern Wisconsin Power Co. . 

34. Kern River Power Company. . . . 

35. Northern Calif. Power Co 

36. Yakima Valley Power Company 

37. Central Georgia Power Co 

38. Northern Hydro-Electric Co 

39. Eastern Tennessee Power Co. . . 

40. Idaho-Oregon L. & P. Company 

41. Spokane & Inland E. R. Co . . . 

42. Nagoya Electric Power Co 

43. Toronto Power Company , 

44. Washington Water Power Co. . . 

45. Mexican L. & P. Co. Ltd 

46. East-Creek L. & P. Company. . . 

47. Great Northern Power Co 

48. Niagara-Falls Power Company. 

49. Pacific Coast & Electric Co 

50. Guanajuato Power & E. Co. . . . 

51. Jhelum River Electric Co 

52. Michiacan Power Company. . . . 

53. Elect. Development Company. . 
61. Puget^Sound Power Company. . 

55. Canadian-Niagara Power Co 

50. Portland L. & P. Company 

57. Calif. Gas & Electric Co 

58. Pacific Coast Power Company . . 
69. Winnipeg L. & P. Company. . . . 



" IS 


Star. . . 


Delta . 


Star. . . 


Star. . . 


Star. . . 


Star. . . 


Star. . . 


Star. . . 


Delta . 




Star. . . 


Star . . 


Star . . 


Star. . . 


Delta . 


Delta . 


Delta . 




Star. . . 


Delta . 


Star. . . 


Delta . 


Star. . . 




Star. . . 


Star. . . 


Star. . . 
Delta . 

a . a 



u ^ O 

O M V 

"S * to 

O — >> 

« o « 



The subject of transformers cannot very well be concluded 
without a reference to the effects of altitude on their operation. 
It is deemed safe to say that not one of the above mentioned 
systems took this effect of altitude into consideration when 
specifying their system requirements, yet each and all were 
careful to note that the common every day specifications and 
tests were complied with. 

With the exception of water-cooled oil transformers, manu- 
facturers should specify the temperature rise and efficiency of 
transformers at service-altitudes. This is very important for 
the reason that insulation, temperature and efficiency values 
are quite different at high altitudes to those at sea level. For 
example, at an altitude of 3,500 ft. above sea level a higher 
kv-a rating should be allowed a given unit and, when a trans- 


former is rated for operation at this altitude, the normal per- 
missible temperature rise should be reduced by approximately 
1 per cent, for every additional 350-ft. rise at which it is put 
into service, that is to say: at an altitude of 10,500 ft. the per- 
permissible temperature rise would be approximately 10,500 
•V- 350 =30 per cent. LESS, thus we see that for higher altitudes 
a given transformer will have a different rating for a given 


Ability of a transformer to deliver Centralized system over 200,000 kw., 
current at a constant volt- 3 

age, 16 

Admittance, 31, 32 

Advantage of the delta-delta to 
delta-delta, 74, 75 
delta-star to star-delta system, 
74, 75 

Advantages of iron and air reactance 
coils, 159 

Aging of the iron, 11, 15 

Air and iron reactance coils, 159 

Air-blast transformers, 7, 120, 144 

Air-chambers for transformers, 144 

Air-cooling of transformers, 120-122 

All-day efficiency, 14, 15 

Alloy steel in transformers, 11, 246 

Alternating currents dangerous and 
impracticable, 3 
fought in the Law Courts, 3 

American and European engineers, 

American I. E. E., 239 

Amount of heat developed in a 
transformer, 6 
hysteresis in a given steel, 8 

Anhydrous copper sulphate, 132 

Arc-series lighting, 178-185 

Assembly of large power transform- 
ers, 136-148 

Auto-transformers and transforma- 
tion, 33, 170-177 

Automatic regulators, 224-226 

Balancing transformer, 26, 27 

Best shape of transformer core, 11 

Best operated system, 74 

Blotting paper, 133 

Breathing action, 125 

Building of fire-proof construction, 8 

Capacity in kw., 3, 52 
Causes of transformer failure, 145, 

Central station engineers and man- 
agers, 153 

Cheap copper space and alloyed 
iron, 153 

Cheapest cost of system, 74 

Changing of frequency (using trans- 
formers), 83 

Change any polyphase system into 
any other system, 35 

Chief danger of fire, 8 

Choice of transformer system con- 
nections, 70, 74 

Cleaning of transformer cooling- 
coils, 125 

Close regulation, 156 

Coefficients of resistivity in copper 
—Table, 240 

Comparison of shell and ore type 
transformers, 150-153 

Comparison of single-phase and 
polyphase transformers, 43 

Comparative weights of transform- 
ers, 42 

Commercial manufacture of 175,000 
volt power transformers, 3 

Common return wire, 32, 39, 49 

Combination method of cooling 
transformers, 122 

Compensators, 218-220 

Connections for grounding three- 
phase transformers, 81 

Connections for grounding two- 
phase transformers, 39 

Consolidation and concentration of 
systems, 158 

Constant current transformers, 14, 
178, 185 
potential transformers, 4, etc. 

Construction of large power trans- 
formers, 136 144 
of constant current transform- 
ers, 182-184 





Contact-making voltmeter, 224-226 
Control of the designer, 9 
Conversion of one polyphase system 

into another, 20 
Conventional connections for trans- 
formers, 56 
Cooling of transformers, 6, 117-130 
Cooling-coil cleansing, 125 
Cooling medium, 153 
Copper or I^ R loss in transformers, 

9, 16, 250-252 
Cost of a given volume and area, 9,11 
Core of the transformer for a given 

service, 5, 75, 153 
loss or iron loss, 8, 11, 14, 245- 

type transformers, 10, 24, 125, 

136, 137-139, 150-153, 158, 

Cost of total losses, 6 
Current, short-circuit, 154, 156, 257 
transformers, 186-208 

Dangerous and impracticable cur- 
rent, 3 
'Dead," short-circuit, 154 
Dear copper space and ordinary 

iron, 153 
Delta-connected systems, 42, 53 
-star systems, 47, 53, 73 
-star merits, 53, 73 
-delta systems, 47, 54, 73 
-delta merits, 48, 53, 73 
Demerits of the delta-delta system, 

-Design of oil-insulated transformers, 

Determination of temperature rise, 7 
Development of transformers, 2 

of the art of transformer con- 
struction, 1 
Diametrical system, 116 
Difference of potential, 34 

of opinion as regards grounding, 
Difficulties of three-phase operation, 

Different ways of applying trans- 
formers, 22 

Disadvantage of the delta-delta 
system, 74, 75 
of the "T" (two transformer) 
system, 80 
Disc-shape coils, 129 
Distribution transformers, 28 
Disturbed system due to incoming 

surges, 75 
Dividing each secondary coil of 

transformers, 24 
Double-delta system, 109, 113, 116 
-star system, 109, 114, 116 
-tee, system, 114, 116 
Drop due to load, 31, 32 
Drying of insulation, 145 

out of power transformers, 146- 
Duration of tests, 13 

Early development of transformers, 

Earth connections, 163 

Earthing of the neutral of trans- 
formers, 161 

Economy of copper, 30 

Eddy-current loss, 8, 245-247 

Edison, Thos. A., three-wire system, 

Effect of various iron substances, 1 1 

Efficiency of transformers, 14, 16, 
153, 252, 253 

Electrical characteristics of a trans- 
former, 5 

Electro-magnetic properties of alloy- 
steel, 11 

Electro-static capacity of parts too 
high, 95 

Equal output and change in copper 
loss, 9 

Engines, 3 

Exciting current, 9, 10 

External and internal choke-coils, 159 

Factory, transformers from the, 26 
Faraday's historic experiments, 1 
Favor of the shell-type transformer, 

of the core-type transformer, 




Feeder-regulators, 209-220 
Ferranti's S. Z. de., modification of 

Varley's method, 1 
Filter-paper, 125 

Fire-risks of air-blast transformers, 7 
Five-wire two-phase system, 34 
Fluid of some impregnating com- 
pounds, 12 
Fluxes (magnetic) in transformers, 42 
Forced current of air-cooling, 120 

current of water-cooling, 122 

oil circulation, 127 
Form of transformer coil, 9 
Four-wire two-phase system, 30, 33 
Freezing of water, 124 
Frequency changer (using trans- 
formers), 83 
Fundamental equations in design, 13 

principals, 3 
Fused-switches, 169 

General construction, 260 

Generators, 3 

Generating and receiving stations, 

Governing factors of systems, 74 
Grading of insulation on the end 

turns, 151 
Graphical methods, 17, 23, 40, 43, 44, 

46, 53, 111 
Greater coal consumption due to 

exciting current, 9 
generating station equipment, 

Ground connections, 163-165 
Grounded systems, 28, 37, 29, 74, 

81-82, 84, 161 
Grounding of the neutral point, 39, 

74, 76, 81, 161 

Heat test of transformers, 232, 233 
High frequency currents, 159 

voltage operation of transform- 
ers, 2 
stresses, 76, 79, 86 
surges, 74, 75 
transformer troubles, 94 
installations, 125, 136-144 
specifications, 258, 267 

History of alternating currents, 3 
of delta and star systems, 3 
of 50,000 and 60,000 volt 
systems, 3 
Hourly temperature readings, 153 
Hydrochloric acid-cleaning of coils, 

Hysteresis, 8, 10, 245-248 
loss, 8 

I R drop, 18, 19, 67, 91 
12 R loss, 9, 16, 20 
Incoming surges, 75 
Increased hysteresis and higher 
temperatures, 9 
temperatures due to excessive 
iron losses, 9 
Inductive load on transformers, 10, 
reactance (XJ, 18 
Inherent reactance, 154 
Impedence (Z), 19, 24, 31, 67, 91, 

Important advantages of the delta- 
star to star-delta, 74, 75 
factors in the make-up of a 
transformer, 8 
Impregnating of transformer coils, 

Improper drying out of trans- 
formers, 95 
Impulses from transmission line, 75 
Installation of large power trans- 
formers, 144—148 
Instantaneous values of the currents, 

40, 47 
Insulation, 11, 117, 227, 228 

specification, 259 
Internal and external choke-coils, 

Iron and air reactance coils, 159 

or core loss, 8, 9, 11, 14, 245-248 

Joints of ground wire, 162, 164 

Kirchhoff's law, 44 
Kv-a capacity of transformers, 3, 52 
K-w capacity of transformers, 69, 74, 



Lamps, arc and incandescent, 178- 

Large commercial power trans- 
formers, generators, etc., 3 

Law courts and alternating currents, 

Leakage reactance of the trans- 
former, 154 

Least potential strain on system, 74 

Liberal oil ducts between the vari- 
ous parts, 6 

Lighting transformers, 31 

Limiting feature of transmission, 2 
resistance, 163 

Limit of temperature rise in trans- 
formers, 6 

Line-drop compensator, 221-225 

Long-distance transmission lines, 151 

Losses, 8, 79 

Loss due to magnetic leakage, 10 
to magnetizing current, 10 
in revenue due to transformer 
failure, 6 

Low average operating temperature, 

Lowering the frequency of supply, 9, 

Lowest price for transformers, 74 

Magnetic densities of transformers, 
leakage, 16 

Magnetizing currents in transform- 
ers, 11 

Mechanical failure of transformers, 
76, 152, 153, 155, 160 

Mercury thermometers for tem- 
perature readings, 147 

Merits of the delta-star to star-delta 
system, 74, 75 
of three-phase units, 43 

Method of connecting three-phase 
systems, 42 
two-phase systems, 30, 33 
of insulating transformers, 11 

Methods of cooling transformers, 

Meyer and Steinmetz systems the 
same thing, 106 (Fig. 101 A) 

Modern high voltage power trans- 
formers, 270, 271 

Moving of coils and core, 94, 154, 

Motor auto-starters, 219, 220 

National Board of Fire Under- 
writers, 227 
National Electrical Code, 28 
Negative direction, 40, 56, 244, 245 
Neutral point, 39, 49, 76, 81, 86, 161 

Ohm's Law, 248, 252 

Ohmic drop, 16, 42 

Oil for transformers, 127, 130-135 
-filled self-cooled transformers, 7 
transformers in separate com- 
partments, 8, 144 

Open-delta "V" system, 51, 52, 53, 

Operation of transformers, 153-169, 

Operating at the end of long lines, 1 1 
engineer's difficulties, 64 

Operation of constant current trans- 
formers, 178-185 

Opposition-test, 236 

Over-potential test, 229 

Parallel operation, 22, 38, 56, 64, 66, 

78, 91, 239 
Phase relations, 22, 59, 68, 74, 87 
Phase-splitting methods, 21 
Points in the selection of trans- 
formers, 5 
Polarity of transformers, 55, 58, 59- 

64, 243-245 
Polyphase regulators, 220-226 
Positive direction, 40, 56, 244-245 
Power (P) or electrical energy, 31 
factor, 10, 16, 19, 22, 203-204 
limiting capabilities of react- 
ance, 158 
transformers, 43, 56, 66, 123, 
145, 153, 267-271 
Practicable 50,000 and 60,000 volt 

systems, 3 
Primary windings of transformers, 
with R and X., 5 



Principal argument for grounding 

transformers, 28 
Puncturing of the insulation between 

turns, 94, 117 

Raising current, 205 
Ratio of high voltage to low voltage 
turns, 65, 67 
of iron and copper loss, 5 
of transformation, 65, 67, 239- 
Reactance, internal and external, 

154, 160 
Recognized commercial operation of 

60,000 volts, 3 
Receiving station transformers, 74 
Record sheet of tests, 264-269 
Regulation, 10, 16, 22, 155, 223, 253- 

Regulators and compensators, 209, 

Relays for protection of trans- 
formers, 165-167 
Reliability of transformers in service, 

80, 151, 154 
Resistance (R), 18, 41, 248-250 
per phase, 31 
of wiring, 31 
Revenue effected imperfect iron of a 
low grade, 1 1 
loss due to transformer failure, 6 
Roasting of oils due to over-load, 

Safety to life and property, 5, 154 
Salt for the earth connections, 165 
Scott, Chas. F., system, 53, 80, 98, 

Secure the desired copper loss, 9 
Self-cooling transformers, 117-120, 

induction, 18 
Short-circuits, 28 

-circuit stresses, 154, 156, 257 
Shell type transformer, 2, 10, 73, 79, 

128, 139-144, 260 
Series enclosed arc lighting, 178-180 
lighting from constant current 

transformers, 205 

Series-pai'allel operation, 152 
step-up transformer, 205 
transformers, 186-208 
Simple transformer manipulations,22 
Single-phase systems, 22, 42, 83 

from three-phase, 82, 83 
Six-phase transformation and opera- 
tion, 109-116 
Solid compounds for impregnation 
of windings, 11 
insulation, 11 
Spark-gap— Table, 228 
Specifications of transformers, 258- 

Star or "Y" system, 41-53 

-delta system, 47, 53, 73, 74 
merits, 47, 73, 74 
-star system, 47, 53, 55 
versus delta, 71, 73, 74 
Station equipment and transmission 

lines greater, 10 
Standard rules of the A. I. E. E., 
voltage test, 231 
Steam turbines of 40,000 h.p. ca- 
pacity, 3 
Steinmetz, Chas. P., system, 100, 

Step-up current transformers, 205 
-down transformers, 4 
-up transformers, 4, 23 
Strain between high and low voltage 

windings, 27 
Stillwell, Lewis B., regulator, 210 
Surges, 75, 159, 163 
System giving cheapest cost, 74 
Switches, 76, 165 

Switching and its advantages, 76, 
165, 109-116 

Taylor, William T., system, 37, 71, 

80, 106, 255 
"T" two-transformer system, 37, 53, 
71, 80, 98 
three-transformer system, 37, 
71, 80 
Telephone transformers, 206 
Temperature rise of the oil, 128 
of electrical apparatus, 7, 147 



Temperatures, 123, 125, 128, 152, 

Terminals and connections, 262 
Test record sheets, 264-267 
Testing cooling coils for transform- 
ers, 146 
Tests specified by the National 
Board of Fire Underwriters, 
of copper loss and impedence, 

of efficiency, 252, 253 
of iron or core loss, 245-252 
of insulation, 13, 227-232 
of polarity, 243-245 
of ratio of transformation, 239- 

of regulation, 253-256 
of resistance and I R., 248- 

of short-circuits, 257 
of temperature, 232-239 
Third harmonics, 75 
Three-phase systems, 22, 39, 53 
to single-phase, 82, 104, 105 
to six-phase, 109-116 
to two-phase, 53, 97-109 
two-phase methods, 107, 109 
group of 18,000 kw., 3 
Three-wire service transformers, 24, 
two-phase systems, 30, 33 
Time-limit relays, 169 

-phase, 40 
To secure the desired copper loss, 9 
Tra,nsmis8ion engineers, 153 
Transformer development, 1 
of 14,000 kw capacity, 3 
regulation, 10, 16, 17 
Transformers of identical character- 
istics, 22 
in separate compartments, 8 
Troubles experienced with high volt- 
age transformers, 94 
Turbines, 3 

Turbo-generators of 30,000 kw., 3 
Two-phase systems, 22, 30, 33 
to three-phase, 22, 53 
three, four and five wire, 34 

Two-phase, to single-phase, 35, 36 
multi-wire distribution, 36 
parallel combinations, 38 
three-phase methods, 107, 109 

Unbalancing, 32, 52, 68, 75, 85 
Unduly moist transformers, 145 
Unlimited power behind transform- 
ers, 156 
Use of reactance, internal and ex- 
ternal, 154 
of resistance in the neutral of 
grounded systems, 154 
Useful energy delivered, 9 

Vacuum process of impregnation, 11 

Varley's method, 1 

"V" or open-delta system, 42, 51, 

53, 72 
Variation of core loss, 248 

of copper loss, 251 
Vector representation, 17, 30, 33, 40, 

44, 46, 53, 116 
Viscosity, 130, 132 
Voltage compensator, 221-224 
Voltmeter — contact-making, 224, 225 

Water available and not expensive, 7 

-cooled transformers, 7, 122, 
144, 258, 261 

-freezing difficulties, 124 

-wheels, 3 
Wattmeter, 203, 204, 207 
Watts radiated per square inch of 

surface, 119 
Weak link in the insulation, 152 

mechanically, transformers, 154 
Weight, comparative, 42, 79 
Windings, specifications, 261, 262 

Xg or inductive reactance, 18 

Y or admittance, 31 

"Y" or star connection, 41 

three-phase to two-phase sys- 
tem, 98 

"Z" (series transformer) connection, 
200, 201