Question

Do the same with the replacement of the earlier transformer by a 40,000-220 V step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred?

Answer 1

The rating of a step-down transformer is 40000 V − 220 V.

Input voltage, V₁ = 40000 V

Output voltage, V₂ = 220 V

Total electric power required, P = 800 kW = 800 × 10³ W

Source potential, V = 220 V

Voltage at which the electric plant generates power, V‘ = 440 V

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

Resistance of the two wire lines carrying power = 0.5 Ω/km

Total resistance of the wire lines, R = (15 + 15) 0.5 = 15 Ω

P = V₁I

Rms current in the wire line is given as:

I = `"P"/"V"_1`

= `(800 xx 10^3)/40000`

= 20 A

(a) Line power loss = I²R

= (20)² × 15

= 6 kW

(b) Assuming that the power loss is negligible due to the leakage of current.

Hence, power supplied by the plant = 800 kW + 6kW = 806 kW

(c) Voltage drop in the power line = IR = 20 × 15 = 300 V

Hence, voltage that is transmitted by the power plant

= 300 + 40000 = 40300 V

The power is being generated in the plant at 440 V.

Hence, the rating of the step-up transformer needed at the plant is 440 V − 40300 V.

Hence, power loss during transmission = `600/1400 xx 100` = 42.8%

In the previous exercise, the power loss due to the same reason is `6/806 xx 100` = 0.744%. Since the power loss is less for a high voltage transmission, high voltage transmissions are preferred for this purpose.