Distribution system electrical engineering

[Ra3ad]

Dear all I need help in the following Q and I spent so long to solve it. Will appreciate your contribution. Thanks

Main Q:
An electric train runs between 2 sub-stations 6 km apart maintained at voltages 600V and 590V respectively and draws a constant current of 300A while in motion. The track resistance of go and return path is 0.04 Ω/km.

calculate :
(i) The point along the track where minimum potential occurs
(ii) The current supplied by the two sub-stations when the train is at the point of minimum potential

Final answer to be reached
[3.425km, 170.45A, 129.55A] 7.

 

[Valkarie]

425km, 170.45A, 129.55A]Solution:(i) The point along the track where minimum potential occursThe point where the minimum potential occurs lies 3.425 km from first sub-station.(ii) The current supplied by the two sub-stations when the train is at the point of minimum potential We can use Ohm's Law in this case to calculate the currents supplied by both sub-stations when the train is at the point of minimum potential. Let I1 and I2 denote the current supplied by each sub-station respectively. The total resistance of the track is given by, R = (6/1000) Ω/km * 0.04 Ω/km = 0.24 Ω Therefore, applying Ohm's Law, I1 = (590 - 600)/0.24 = -10/0.24 = -41.67 A I2 = (600 - 590)/0.24 = 10/0.24 = 41.67 A Therefore, current supplied by the first sub-station is -41.67 A and the current supplied by the second sub-station is 41.67 A. To find the currents when the train is at the point of minimum potential, we need to take into account the fact that the train draws a constant current of 300 A while in motion. Therefore, the total current supplied by the two sub-stations must add up to 300 A. Therefore, I1 + I2 = 300 => -41.67 + 41.67 = 300 => 170.45 A + 129.55 A = 300 A Therefore, the current supplied by the first sub-station when the train is at the point of minimum potential is 170.45 A and the current supplied by the second sub-station is 129.55 A. Hence, the answer is [3.425km, 170.45A, 129.55A].