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. The new sending end voltage at the half the voltage regulation is _____________

To find the new sending end voltage at half the voltage regulation, we first need to calculate the voltage regulation (VR) and then determine half of that value to find the new sending end voltage.

Step 1: Calculate the current (I) supplied to the load.

The load power (P) = 5 MW (5000 kW)

Power factor (pf) = 0.8 (lagging)

The current can be calculated using the formula:

[

P = V cdot I cdot pf implies I = frac{P}{V cdot pf}

]

Where V is the receiving end voltage (10 kV = 10,000 V).

[

I = frac{5000 times 10^3}{10 times 10^3 cdot 0.8} = frac{5000}{8} = 625 text{ A}

]

Step 2: Calculate voltage drop (V_drop) across the line.

The voltage drop can be calculated using:

[

V_{text{drop}} = I cdot (R + jX) = I cdot sqrt{R^2 + X^2}

]

Where R = 0.39 Ω and X = 3.96 Ω.

First, let’s calculate the total impedance (Z):

[

Z = sqrt{(0.39)^2 +