408 HANDBOOK OF ELECTRICAL ENGINEERING
An alternative expression forVdin terms of the commutation angleu,is,
Vd=3
√
6 E
2 π(cosα−cos(α+u)) ( 15. 2 )Hence it can be seen thatuis a function ofId, as will be shown below.
The factor 3
√
6 /πapplies to a three-phase bridge and is derived from,Vdo= 2 E(
1 −cos(
4 π
n)) 1 / (^2) (
n
π
)
sin(π
n)
Wherenis the ripple number, in the above casen= 3
andVdois the average ripple voltage at no-load.
The currentIdcan also be given as a function ofαandu,
Id=√
6 E
2 Xc(cosα−cos(α+u)) ( 15. 3 )It can be seen from (15.1) that for a given delay angleαthe 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 angleα.
Figure 15.3 Voltage versus current regulation of DC thyristor bridge used for a drilling system DC motor.