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Question

The figure shows the single line diagram of a single machine infinite bus system.

The inertia constant of the synchronous generator H=5 MW-s/MVA.
Frequency is 50 Hz. Mechanical power is 1 p.u. The system is operating at stable quilibrium point with rotor angle δ=30. A three phase short circuit fault occurs at a certain location on one of the circuits of the double circuit transmission line. During fault, electrical power in p.u. is 0.23sinδ. If the value of δ at the instant of fault clearing is 45 then,dδdt=_____radians/sec.
  1. 3.76

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Solution

The correct option is A 3.76
We know that,

Acceleration of machine,

d2δdt2=PaM=10.23sin(45)(Hπ×50)

d2δdt2=(10.1626)×π×505=26.3077radians/sec2

The fault is cleared at ωt=45

t=452π×50=0.143sec,

dδdt=26.3077×t=26.3077×0.143

=3.762radians/sec

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