Question

Power is generated at 24 kV at a generating plant located 55km from a town that requires 60MW of power at 12 kV. Two transmission lines from the plant to the town each have a resistance of
0.11?/km .

What should the output voltage of the transformer at the generating plant be for an overall transmission efficiency of 97.8%, assuming a perfect transformer?

Answer 1

Power generating plant, P = 24 k V

Distance from the generating plant, d = 55 km

Two transmission lines from the plant to the town each have a resistance of R = 0.11 ? / km

Power generating plant be for an overall transmission efficiency, e = 97.8 %

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The Power produced by the transformer is

      P = 60 MW / 97.8 %

         = 60 MW / 0.978 %

         = 61.349 MW

Loss of the power during transmission is 61.349 MW - 60 MW

                                                              = 1.349 MW

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Now, use equation for power disppation:

           P = I² R

Rearrange for current, I

              I = ? P / R

                 = ? ( 1.349 x 10⁶ W ) / 2 ( 55 km)( 0.11 ? / km )

                  = 333.89 A

Use Ohm's law to find voltage

               V = P / I

                    =( 61.349 x10⁶ W ) / 333.89 A

                    = 183740.153 V

                    =183.74 kW