HIGHER HARMONICS

147

Adding now the torque curves of the various voltage harmonics,
jF3, Tz, Ty, to the fundamental torque curve, TI, of the induction
motor, gives the resultant torque curve, T.

As seen from Pig." 55, if the voltage harmonics are consider-
able, the torque curve of the motor at lower speeds, forward
and backward, that Is, when used as brake, is rather irregular,
showing depressions or "dead points."

89. Assume now, the general voltage wave (1) is one of the
three-phase voltages, and is impressed upon one of the phases
of a three-phase induction motor. The second and third

phase then is lagging by -5- and -5- respectively behind the first

o o

phase (1) :

e = ei cos - ~ + e3 cos- (3 <£ -- j- —

. /- , 10 TT \ . /_ , 14 TT \

+ e5 cos (5<p ---- 3 - a5j + ei cos (7 <t> — ^ - a7j

69

/0 . 18 T \

3(90— v;-------<*9)

\ o /

+ . . .

= ei cos (<f> — YJ + e3 cos (3 <j) — a3)

cos

?7 cos I 7 <t> — <*7-------«—

\ •

+ eg cos (9 <t> — as) + •
e" = ei cos {<t> — -TT- ) + ez cos (3 <^> — az)

4- 65 COS (S <t> - a5 + -j~ j + 67 COS (?(#>- a7 — y j

+ 69 COS (9 $ — a9) + .

Thus the voltage components of different frequency, impressed
upon the three motor phases, are:

(6)

r\ COS 0
es cos
e& cos
e? cos
CD cos

(3 <A ™ aa)
(50 — as)
(70 - a?)
(90- an)

fj COS

es cos
C7 COS

(-¥)
ea cos (3 0 - as)

(7*-«'-2f)
£9 coa (9 0 — as)

ei cos

es cos
e? cos

(-¥)
<?3 COS
(3 0 - a3)
/ ^ 4r\
. (,.-.-9
69 C08
'(90 - as)

Fundamental....
-Jd ! 5th
7th
9th