Given:

Supply voltage, V = 220 V

Total electric power required, P = 800 kW = $$800 × 10^{3} W$$

The voltage at which the electric plant is generating power, V’ = 440 V

Distance between the town and power generating station, d = 15 km

The resistance of the two wireline carrying powers = 0.5$$\omega /km$$

Total resistance of the wires, R = (15 + 15)0.5 = 15 $$\omega$$

A step-down transformer of rating 4000 − 220 V is used in the sub-station.

Input voltage, V1 = 4000 V

Output voltage, V2 = 220 V

RMS current in the coil, $$I = \frac{P}{V_{1}}$$ $$\Rightarrow 800 * \frac{10^{3}}{4000}$$ $$\Rightarrow 200 A$$

(A) Estimate The Line Power Loss In The Form Of Heat.

$$Power Loss = I^{2}R$$ $$\Rightarrow 200^{2} * 15$$ $$\Rightarrow 600 KW$$

(B) How Much Power Must The Plant Supply, Assuming There Is Negligible Power Loss Due To Leakage?

Total power supplied by the path – P = 800 + 600

$$\Rightarrow 1400 KW$$

(C) Characterise The Step Up Transformer At The Plant.

Voltage drop is IR = 3000 V

The secondary voltage is 3000 + 4000

$$\Rightarrow 7000 V$$

Power generated is at a primary voltage of 440 V

Hence the transformer rating is 440 V − 7000 V

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