Handbook of Electrical Engineering

SWITCHGEAR AND MOTOR CONTROL CENTRES 153

Let,

ylhs=

[

1

Xd′

−

1

Xd

]

exp

−t

T′d+

[

1

Xd

]

( 7. 4 )

and

yrhs=

[

1

Xd′′

]

exp

−t

Ta ( 7. 5 )

If these two functions are plotted on a graph which has a common base of time, then they
will cross each other at the critical time. Figures 7.2 and 7.3 show critical times for several ranges
of values forTd′,Ta,X′′dandX′d. The parameter that has the greatest sensitivity is the armature time
constantsTasince it moves the crossing point from the left to the right very noticeably. Changes in
the value of the sub-transient reactanceX′′dmove the curves 4 and 8 in (7.5) vertically. The higher
the value ofX′′dthe lower is the critical time. It can be seen that in order to achieve low values of the
critical time, or to keep the number of cycles to the first current zero to a low number, it is necessary
to have a low value ofTaand a high value ofXd′′.

7.2.12 Fault withstand duty

So far particular conditions have been considered, initial reaction to the severest fault and what
happens at the time of clearing the fault. What happens during the fault is also of importance since

Figure 7.2 Functions pertaining to the calculation of the critical switching time of circuit breaker that discon-
nects a generator from a switchboard. The generator has low values of sub-transient and transient reactances.
The sensitivity of the time constantTais shown.