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: Rating of step down transformed = 40,000-220 V
Input voltage V1 = 40000 V
Output voltage V2 = 220 V
Total electric power P = 800 KW
In watt, P = 800 × 103 W
Potential V = 220 V
Voltage of power generated by the plant V’ = 440 V
Distance between town and power generating station = 15 km
The resistance of the two wire line carrying power is 0.5Ω per km.
Total resistance of wire = (15(km) + 15(km))0.5 = 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 × 103W)/40000V = 20 A
Line power loss can be calculated as follows:
P = I2R
= (20A)2 × 15Ω = 6 kW
B. Let the power loss due to current leakage is negligible
Total power supplied by the power plant = 800kW + 6kW = 806 Kw
C. Voltage drop V = IR
Substituting the values, we get
20A × 15Ω = 3000V
Therefore, the total voltage supplied = 300V + 40000V = 40300V
And since the power generated = 440 V
Therefore, the rating should be 440 V- 40300 V