Question

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

Answer 1

Given: The total demand is 800 kW, distance between town and power plant is 15 km, resistance of the two wire line carrying power is 0.5Ω per km, the town gets power from the line through a 40,000-220 V step down transformer.

a)

The line current given by,

I= P V 1

Where, P is the total power demand and V 1 is the line voltage.

By substituting the given values in the above expression, we get

I= 800× 10 3 400000 =20 A

The line losses are given by,

P l = I 2 ( 2R )l

Where, R is the resistance of each line and l is the length of each line.

By substituting the given values in the above expression, we get

P l = ( 20 ) 2 ×2×0​.5×15 =6000 W =6 kW

Thus, the power loss in the line in the form of heat is 6 kW.

b)

The power supplied by the plant is given as,

P s =P+ P l

Where, P is the total power demand.

By substituting the given values in the above expression, we get

P s =800+6 =806 kW

Thus, the plant must supply 806 kW.

c)

Voltage drop in the line is given as,

V l =I×2R×l

By substituting the given values in the above expression, we get

V l =20×2×0.5×15 =300 V

Percentage power loss in the line is given as,

% P l = P s −P P s ×100

By substituting the given values in the above expression, we get

% P l = 806−800 800 ×100 = 6 800 ×100 =0.74%

Thus, it is observed that as the transmission voltage is increased from 4000 V to 40000 V, both the power loss in the line as well as the voltage drop in the line is decreased.