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 angleubetween 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 withπ/2or90◦, 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 isimax then the result of the integration yields the following
expression for the sine coefficients.

bnu=

2

un^2 π

(

sin

un

2

)(

cos

nπ

6

−cos

5 nπ

6

−cos

7 nπ

6

+cos

11 nπ

6

)

(15.18)

anu= 0

For which,

ia(ωt)=imax

∑n

j= 1

bjusinjωt

It is found from the integration that all even harmonics and those multiples of three are not
present in the waveform. Hencenhas the following value for a six-phase bridge:

n= 1 , 5 , 7 , 11 , 13 , 17 ,19 etc.

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