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Question

# A 60 Hz generator, connected directly to an Infinite bus operating at a voltage of 1∠0∘ p.u., has a synchronous reactance of 1.35 p.u. The generator no load voltage is 1.1 pu. and its inertia constant H is 4 MJ/MVA: The generator is suddenly loaded to 60 percent of its maximum power limit. The frequency of the resulting natural oscillations of the generator rotor is

A
1.246 Hz
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B
0.882 Hz
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C
0.921 Hz
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D
1.16 Hz
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Solution

## The correct option is B 0.882 Hz0.6 Pmax=Pmax sin δ δ=sin−1(0.6)=36.8698∘ ∂Pe∂δ∣∣∣δ=36.8698∘=Pmax cos(36.8698∘) =1.1×11.35cos(36.8698∘)=0.6518 p.u./rad Frequency of oscillations=√(∂Pe/∂ δ)36.8698∘M Where, M=Hπf=4π×60=0.0212 p.u. s2/rad fu=√0.65180.0212 fn=5.54 rad/sec=0.882 Hz

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