For the power system of Figure Q4.1, all per unit quantities have been calculated using a common base. The generator delivers power p∞ = 1 p. u. at a lagging power factor of cos= 0.93.   i) Calculate the internal voltage of the generator, the maximum electrical power that the generator can deliver to the system during the steady state operation and the steady state rotor angle, σ0, of the generator. ii) A three-phase fault occurs at busbar 3 and it is cleared by simultaneously disconnecting lines 13 and 23. Following the fault clearing, the system continues to operate with only line 12 in service. Determine the new steady state rotor angle, σ1, of the generator and the maximum power the generator can deliver to the system post fault. iii) Assuming that the post fault condition is small disturbance stable and that there is no negative interaction among system controllers, calculate the critical clearing angle, σcr, at which the fault should be cleared to ensure the generator reaches a new steady state operating condition defined by σ1.

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For the power system of Figure Q4.1, all per unit quantities have been calculated using
a common base. The generator delivers power p∞ = 1 p. u. at a lagging power factor of
cos= 0.93. 

 i) Calculate the internal voltage of the generator, the maximum electrical power
that the generator can deliver to the system during the steady state operation
and the steady state rotor angle, σ0, of the generator.

ii) A three-phase fault occurs at busbar 3 and it is cleared by simultaneously
disconnecting lines 13 and 23. Following the fault clearing, the system
continues to operate with only line 12 in service. Determine the new steady
state rotor angle, σ1, of the generator and the maximum power the generator
can deliver to the system post fault.

iii) Assuming that the post fault condition is small disturbance stable and that there
is no negative interaction among system controllers, calculate the critical
clearing angle, σcr, at which the fault should be cleared to ensure the generator
reaches a new steady state operating condition defined by σ1.

iv) If the rate of acceleration of the rotor during the fault is Cacc = 39 rad/sec^2
calculate the corresponding critical clearing time of the circuit breakers.

G
XG
=
∞
0.3 p.u. XT = 0.1 p. u.
X12 = 0.2 p. u.
X13 = 0.1 p.u.
3
X23
= 0.2 p. u.
P 00
V ∞o
8
Transcribed Image Text:G XG = ∞ 0.3 p.u. XT = 0.1 p. u. X12 = 0.2 p. u. X13 = 0.1 p.u. 3 X23 = 0.2 p. u. P 00 V ∞o 8
i) E= 1.3127/23.33°
= 2.5244 p. u.
e,pre
8⁰ = 0.4073 rad
ii) 8¹ = 0.44747 rad
iii) Ser = 115.89° rad
iv) ter = 0.0162 sec
Transcribed Image Text:i) E= 1.3127/23.33° = 2.5244 p. u. e,pre 8⁰ = 0.4073 rad ii) 8¹ = 0.44747 rad iii) Ser = 115.89° rad iv) ter = 0.0162 sec
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