Chapter 2, Problem 2.3P

Consider a simple power system consisting of an ideal voltage source, an ideal step-up transformer, a transmission line, an ideal step-down transformer, and a load. The voltage of the source is $V_S=480\angle 0°\text{V}\text{.}$

The impedance of the transmission line is $Z_{\text{line}}=3+j4\Omega ,$ and the impedance of the load is $Z_{\text{load}}=30+j40\Omega .$

1. Assume that the transformers are not present in the circuit. What is the load voltage and efficiency of the system?
2. Assume that transformer I is a 1:5 step-up transformer, and transformer 2 is a 5:1 step-down transformer. What is the load voltage and efficiency of the system?
3. What transformer turns ratio would be required to reduce the transmission line losses to 1% of the total power produced by the generator?