A cylindrical rotor generator delivers 0.5 pu power in the

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A cylindrical rotor generator delivers 0.5 pu power in the steady-state to an infinite bus through a transmission line of reactance 0.5 pu. The generator no-load voltage is 1.5 pu and the infinite bus voltage is 1 pu. The inertia constant of the generator is 5 MW-s/MVA and the generator reactance is 1 pu. The critical clearing angle, in degrees, for a three-phase dead short circuit fault at the generator terminal is

1. 53.5
2. 60.2
3. 70.8
4. 79.6

Correct Option: C

A₁ = Accelerating area, δ_cr = critical clearing angle
A₂ = Decelerating area.
Equal area acceleration states that for stability A₁ = A₂
⇒ P_eo(δ_cr - δ_o) =
⇒ P_eo (δ_cr - δ_o) = P_max(cos δ_cr - cos δ_max) - P_eo (δ_max - δ_cr)
⇒ P_eo (δ_cr - δ_o) + P_max cos δ_max = P_max cos δ_cr

⇒ cos δ_cr =	P_eo	(δ_max - δ_o) + cos δ_max
	P_max

δ_max =		π -	30° . π		rad = 2.61 rad
			180°

then, cos δ_cr = 0.5 (2.61 – 0.52) + cos 150° = 0.179
δ_cr = cos^{– 1} 0.179 = 79.6°