A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is 0.5Ω per km.
The town gets power from the line through a 4000-220 V step-down transformer at a sub-station in the town.
(a) Estimate the line power loss in the form of heat.
(b) How much power must the plant supply, assuming there is negligible power loss due to leakage?
(c) Characterise the step up transformer at the plant.
(a) Given: Power P = 800 kW
Voltage = 220 V
Voltage at which power is generated P’ = 440 V
Distance between town and power generating station = 15 km
The resistance of the two-wire line carrying power is 0.5 Ω per km.
Total resistance of wire = (15(km) + 15(km))0.5 (Ω per km)
∴ Rtotal = 15 Ω
Input voltage v1 = 4000 V
Output voltage V2 = 220 V
The root mean square current in the lines can be calculated as follows:
I = P/V1
= (800(kW) × 103)/4000(V) = 200 A
Line power loss can be calculated as follows:
P = I2Rtotal
= (200)2A × 15Ω
On calculating we get P = 600 Kw
(b) Let the power loss due to current leakage is negligible
Total power supplied by the power plant = 800kW + 600kW = 1400 kW
(c) Voltage drop V = IRTotal
Substituting the values, we get
200V × 15Ω = 3000V
Therefore, the total voltage supplied = 3000V + 4000V = 7000V
And since the power generated = 440 V
Therefore, the rating should be 440V - 7000 V