A single phase 50 hz, generator supplies an inductive load of 5 MW at a power factor of 0.8 lagging using OHTL over 20 km. The resistance and reactance are 0.39Ω and 3.96 Ω. The voltage at receiving station is maintained at 10 KV. The sending end voltage is 11.68 kV. If the voltage regulation is reduced to 50%, then the power factor angle at this operation mode will be _______

To calculate the power factor angle at the reduced voltage regulation of 50%, we can follow these steps:

1. Calculate the apparent power (S):

[

P = 5 , text{MW} quad text{power factor (pf)} = 0.8

]

[

S = frac{P}{pf} = frac{5 , text{MW}}{0.8} = 6.25 , text{MVA}

]

2. Calculate the current (I):

Using the receiving end voltage (Vr = 10 kV):

[

S = V_r cdot I implies I = frac{S}{V_r} = frac{6.25 times 10^6 , text{VA}}{10 times 10^3 , text{V}} = 625 , text{A}

]

3. Calculate the voltage drop (V_drop) across the line:

[

V_{drop} = I cdot (R + jX) = 625 , text{A} cdot (0.39 , Omega + j3.96 , Omega)

]

[

V_{drop} = 625 cdot 0.39 + j(625