Electrical Power Systems

292 Electrical Power Systems
angle (or clearing time) larger than this value, the system would be unstable. The maximum
allowable value of the clearing angle and clearing time for the system to remain stable are
known as critical clearing angle and critical clearing time respectively.
rom ig. 11.11, d m = p – d 0, we have upon substitution into eqn. (11.49)
cosd cr = cosd m + (d m – d 0 ) sind 0
\ cosd cr = cosd m + (p – d 0 – d 0) sind 0
\ cosd cr = cos (p – d 0) + (p – 2d 0) sind 0
\
cosd cr = (p – 2d 0 ) sind 0 – cosd 0
\ d cr = cos –1 [(p – 2d 0) sind 0 – cosd 0] ...(11.53)
Using eqn. (11.52), critical clearing time can be written as:
t cr =
d i ...(11.54)
2H dcr – d0
p fP
i
d cr can be computed using eqn.(11.53).
Let us consider the double circuit line as shown in ig. 11.12. A three-phase short-circuit
fault occurs on one of the line as shown in
ig.11.12. Because of the rotor inertia,
the power angle can not change instantly.
Also, some power could still be
transmitted during the fault because the
terminal voltage of the generator will not
be zero.
ig. 11.12: Double circuit transmission line.
ig. 11.13: Determination of d cr during fault conditions.
In ig. 11.13, curve A before a fault, B during the fault and C after the fault–such that
A = P max sind, B = K 1 A, and C = K 2 A with K 1