A 220 kV transmission line has the following line constants:
$A = 0.85 ∠ 5^{o}, B = 200 ∠ 75^{o}$
If the voltage at each end is to be maintained at 220 kV. The power angle (in degrees) at unity power factor is____________.
22

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Solution

The correct option is A 22
Given, $| V_{S} | = | V_{R} | = 220 k V$
$α = 5^{o}$
$β = 75^{o}$

Since the power is received at unity power factor.

$Q_{R} = 0$
$0 = \frac{220 \times 220}{200} s i n (75^{o} - δ) - \frac{0.85}{200} \times (200)^{2} s i n (75^{o} - 5^{o})$

$= 242 s i n (75^{o} - δ) - 193.29$
$193.29 = 242 s i n (75^{o} - δ)$
$75^{o} - δ = 53^{o}$
Power angle $δ = 22^{\circ}$

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A 220 kV transmission line has the following line constants: A=0.85∠5o,B=200∠75o If the voltage at each end is to be maintained at 220 kV. The power angle (in degrees) at unity power factor is____________.22

The correct option is A 22Given, |VS|=|VR|=220 kV α=5o β=75o Since the power is received at unity power factor. QR=0 0=220×220200sin(75o−δ)−0.85200×(200)2 sin(75o−5o) =242 sin(75o−δ)−193.29 193.29=242 sin (75o−δ) 75o−δ=53o Power angle δ=22∘

A 220 kV transmission line has the following line constants:
$A = 0.85 ∠ 5^{o}, B = 200 ∠ 75^{o}$
If the voltage at each end is to be maintained at 220 kV. The power angle (in degrees) at unity power factor is____________.
22