Page 419 - Handbook of Electrical Engineering

408 HANDBOOK OF ELECTRICAL ENGINEERING

An alternative expression for V d in terms of the commutation angle u,is,

√
3 6E
V d = (cos α − cos(α + u)) (15.2)
2π
Hence it can be seen that u is a function of I d , as will be shown below.
√
The factor 3 6/π applies to a three-phase bridge and is derived from,

π
n
4π 1/2
V do = 2E 1 − cos sin
n π n
Where n is the ripple number, in the above case n = 3
and V do is the average ripple voltage at no-load.
The current I d can also be given as a function of α and u,

√
6E
I d = (cos α − cos(α + u)) (15.3)
2X c
It can be seen from (15.1) that for a given delay angle α the output voltage has declining or
‘drooping’ value as the DC current rises, for example as the load on a motor is increased causing it
to slow down and to reduce its emf. Figure 15.3 shows a family of curves of output voltage against
current, as a function of angle α.

Figure 15.3 Voltage versus current regulation of DC thyristor bridge used for a drilling system DC motor.