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 +

To analyze the given problem, we can approach it in a structured manner.

1. Calculate the apparent power (S):

The real power (P) is given as 5 MW and the power factor (pf) is 0.8.
[

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

]

2. Calculate current (I):

The voltage at the receiving end (V_R) is 10 kV.

[

I = frac{S}{sqrt{3} cdot V_R} = frac{6.25 times 10^3 , text{VA}}{sqrt{3} cdot 10 times 10^3 , text{V}} = frac{6.25}{sqrt{3} cdot 10} approx 0.361 , text{A}

]

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

Given the resistance (R) is 0.39 Ω and the reactance (X) is 3.96 Ω, we can calculate the voltage drop using:

[

V_{drop} = I cdot Z

]

Where

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