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 at this operation mode will be _________________

To find the new power factor at the reduced voltage regulation, we can follow these steps:

1. Determine the current (I) at the receiving end:

[

P = V cdot I cdot text{pf}

]

Rearranging gives:

[

I = frac{P}{V cdot text{pf}} = frac{5,000,000}{10,000 cdot 0.8} = 625 , text{A}

]

2. Calculate the voltage drop (VD) over the transmission line:

[

V_D = I cdot (R + jX) = I cdot R + I cdot jX

]

Where:

– (R = 0.39 , Omega)

– (X = 3.96 , Omega)

[

V_D = 625 cdot (0.39 + j3.96) = 243.75 + j2475 = 243.75 + 2475j , text{V}

]

The magnitude of the voltage drop is:

[

|V_D| = sqrt{243.75^2 + 2475^2} approx 2476.59 , text{V}

]

3