Page 426 - Handbook of Electrical Engineering

HARMONIC VOLTAGES AND CURRENTS 415

Figure 15.5 Trapezoidal current in the supply side of a six-pulse thyristor bridge, with the commutation angle
◦
u = 50 .
◦
15.5 for a value of the commutation angle u between zero and 60 . This is the current in the phase A
terminal of the bridge. If the first point on the waveform is placed at the origin of the X-Y axes then
the waveform will contain both sine and cosine terms. Alternatively the waveform can be advanced,
◦
so that the centre of the positive half-wave coincides with π/2or 90 , and the centre of the negative
◦
half-wave coincides with 3π/2 or 270 . This simplifies the analysis and yields only coefficients for
the sine terms.
The Fourier integration is carried out as six sequential parts along the X-axis, i.e. A to B, B
to C, C to D for the positive half-wave and similarly for the negative half-wave. If the maximum
instantaneous value of the current is i max then the result of the integration yields the following
expression for the sine coefficients.

2 un nπ 5nπ 7nπ 11nπ
b nu = sin cos − cos − cos + cos (15.18)
2
un π 2 6 6 6 6
a nu = 0

For which,
n

b ju sin jωt
i a (ωt) = i max
j=1
It is found from the integration that all even harmonics and those multiples of three are not
present in the waveform. Hence n has the following value for a six-phase bridge:
n = 1, 5, 7, 11, 13, 17, 19 etc.

or 1, 6k ± 1for k = 1 to infinity. (15.19)