Page 425 - Handbook of Electrical Engineering

414 HANDBOOK OF ELECTRICAL ENGINEERING

The value of the fundamental coefficient b 1 is,
√
√
1 3 2 3
b 1 = 4 =
π 2 π
15.3.2 Simplified Commutation Delay

In practice the commutation delay angle is in the order of a few degrees. When the waveform of
AC current is drawn it is difficult to distinguish a difference between a sloping straight line and an
exponential line for the ‘vertical’ faces of the waveform. For this reason it is acceptable to assume
a straight line and treat the waveform as a trapezium, as for example, in Reference 1, Chapter 9.
Figures 15.4 and 15.5 show a trapezoidal waveform for two values of commutation angle u = 20 ◦
◦
and u = 50 . It can be seen that as u increases from zero the right-hand side face moves to the
◦
right and reduces the zero valued gap from 60 to zero. As a result the coefficient of each harmonic
2
component diminishes from 1/n to 1/n , which may be expected because a trapezium is a closer
approximation to a sine wave than the rectangular pulse. Table 15.2 shows the reduction in coefficient
magnitudes as the commutation angle u increases over its theoretical range. The method of calculation
was by numerical integration, as described for example in References 10 and 11, which is sufficiently
accurate for practical purposes. It can be seen that for practical values of u the approximation of
commutation by a sloping straight line can even be ignored, and the simple rectangle pulse is adequate
for all practical steady state loading of the bridge.

15.3.3 Fourier Coefficients of the Line Current Waveform

The Fourier coefficients of the line current waveform for the sine and cosine components can be found
◦
by integrating the waveform over any period of π, or 360 . The waveform is shown in Figure 15.4 or

Figure 15.4 Trapezoidal current in the supply side of a six-pulse thyristor bridge, with the commutation angle
◦
u = 20 .