Page 436 - Handbook of Electrical Engineering

HARMONIC VOLTAGES AND CURRENTS 425

◦
Assume the inverter equivalent output phase-to-neutral voltage consists of a 180 rectangle
◦
waveform plus a 60 rectangle waveform. The complete waveform has a harmonic content of,

4 2 2πn 4πn 8πn 10πn
b n = + cos − cos − cos + cos
πn πn 6 6 6 6
4 2
= + (1.155) for n = 1, 5, 7, 11, 13, etc.
πn πn
6.31 2.0085
= =
πn n
4 2
And = + (−2.309) for n = 3, 9, 15, 21 etc.
πn πn
−0.618 −0.1967
= =
πn n
√
The rms value of the fundamental phase-to-neutral voltage is 415/ 3 = 239.6 volts. Therefore
√
its peak value is 239.6 2 = 338.85 volts which corresponds to b 1 having a value of 2.0085. The
peak values of the first 17 harmonic components of the phase-to-neutral voltage are given below in
Table 15.3.
The triplen harmonics can be ignored because the motor has a star-wound stator winding.
Consider the fifth harmonic situation

The rotor resistance becomes 0.0045/1.2 = 0.00375
The rotor reactance becomes 0.1113 × 5 = 0.5565
The stator reactance becomes 0.0470 × 5 = 0.2350
The magnetising reactance becomes 2.9310 × 5 = 14.655
Assume the stator resistance to be constant.

Table 15.3. Peak values of harmonic
voltage components
Harmonic Peak value and sign of
number the component voltage

1 338.85
3 −11.06
5 67.77
7 48.41
9 −3.69
11 30.80
13 26.06
15 −2.21
17 19.93
19 17.83