7.26 Do the same exercise as above 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?

 

Given,

The power required, 𝑃 = 800 × 103 W

Voltage to be supplied, 𝑉 = 220 V

The voltage at power generating plant, 𝑉′ = 440 V

The total resistance of two wires, 𝑅 = 2 × 15 km × 0.5 Ω per km = 15 Ω

A step-down transformer of rating 40000 − 220 V is used in the sub-station.

Input Voltage, 𝑉1 = 40000 V

Output Voltage, 𝑉2 = 220 V

rms current in the wire lines can be given by,

I=PV1=800×10340000=20A

(a) Line power loss in the form of heat,

P=I2R=202×15=6kW

(b) As there is no power loss due to leakage current. Total power,

PT=P+P=800kW+6kW=806kW

(c) Drop across the power line = IR = 20 × 15 = 300 V

Total voltage transmitted by the plant = 300 + 40000 = 40300 V

The voltage at power generating plant, 𝑉′ = 440 V

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

Percentage loss during transmission = 6806×100=0.74%

Percentage loss in the previous exercise = 6001400×100=43%

The percentage of power loss greatly reduced by high voltage
transmission.