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 ______

To find the sending end voltage, we can use the formula for the sending end voltage in an AC system:

[ V_s = V_r + I cdot (R + jX) ]

Where:

– ( V_s ) = sending end voltage

– ( V_r ) = receiving end voltage (10 kV)

– ( I ) = current through the line

– ( R ) = resistance of the line (0.39 Ω)

– ( X ) = reactance of the line (3.96 Ω)

First, we calculate the current using the power formula:

[

P = V_r cdot I cdot text{pf}

]

Rearranging gives:

[

I = frac{P}{V_r cdot text{pf}}

]

Plugging in the values:

[

I = frac{5,000,000}{10,000 cdot 0.8} = frac{5,000,000}{8,000} = 625 , text{A}

]

Now, we can calculate the voltage drop due to resistance and reactance:

[

V_d = I cdot (R + jX) = 625 cdot (0.39 + j3.96) = 625 cdot 0.39 + j625 cdot 3.96

]

Calculating the