Chapter 2, Problem 2.14P

A 13.8-kV, single-phase generator supplies power to a load through a transmission line. The load’s impedance is $Z_{\text{load}}=500\angle 36.87°\Omega ,$ and the transmission line’s impedance is $Z_{\text{line}}=60\angle 60°\Omega .$

FIGURE P2-3

Circuits for Problem 2-14: (a) without transformers and (b) with transformers.

1. If the generator is directly connected to the load (Figure P2—3a), what is the ratio of the load voltage to the generated voltage? What are the transmission losses of the system?
2. What percentage of the power supplied by the source reaches the load (what is the efficiency of the transmission system)?
3. If a 1:10 step-up transformer is placed at the output of the generator and a 10:1 transformer is placed at the load end of the transmission line, what is the new ratio of the load voltage to the generated voltage? What are the transmission losses of the system now? (Note: The transformers may be assumed to be ideal.)
4. What percentage of the power supplied by the source reaches the load now?
5. Compare the efficiencies of the transmission system with and without transformers.