A synchronous generator is connected to an infinite bus with excitation voltage Ef = 1.3 pu. The generator has a synchronous reactance of 1.1 pu and is delivering real power (P) of 0.6 pu to the bus. Assume the infinite bus voltage to be 1.0 pu. Neglect stator resistance. The reactive power (Q) in pu supplied by the generator to the bus under this condition is _________.Correct answer is '0.109'. Can you explain this answer?

Question

Answer

Solution:

Given data:

Excitation voltage, Ef = 1.3 pu

Synchronous reactance, Xs = 1.1 pu

Real power delivered to the bus, P = 0.6 pu

Infinite bus voltage, V = 1.0 pu

Neglecting stator resistance

Reactive power supplied by the generator, Q = ?

We know that the power delivered by the generator to the bus is given by,

P = (EfV/Xs)sin(δ)

where δ is the load angle.

Given that P = 0.6 pu, Ef = 1.3 pu, Xs = 1.1 pu and V = 1.0 pu

0.6 = (1.3 * 1.0 / 1.1)sin(δ)

sin(δ) = 0.517

cos(δ) = √(1 - sin^2(δ)) = 0.856

The reactive power supplied by the generator is given by,

Q = (EfV/Xs)cos(δ) - (V^2/Xs)

Q = (1.3 * 1.0 / 1.1) * 0.856 - 1.0 / 1.1

Q = 0.109 pu

Therefore, the reactive power supplied by the generator to the bus under this condition is 0.109 pu.

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