Problems solved about Ideal Transformer

Problem 91-4 Source: Adapted from example 2-1 - page 73 - CHAPMAN, Stephen J. - Book: Fundamentals of Electric Machines - 5th Edition - Ed. McGrawHill - 2013.

A single-phase power system consists of a generator with voltage V_G = 480∠0° V that supplies a value load Z_L = 4 + j3 Ω through a transmission line that has an impedance Z_line = 0.18 + j0.24 Ω, as shown in Figure 91-04.1. It is asked:

a) Determine the voltage V_L on the load.

b) Calculate the real and reactive power that the load consumes.

c) Calculate the losses in the transmission line.

Solution of the Problem 91-4

Item a

This problem will be compared with the next one to show the advantages of using transformers when we have to supply loads that are at a certain distance from the power source, when a transmission line is used for link source/load.

To solve this problem we must sum all the impedances of the circuit and calculate I_L. Then

I_L = V_G / (Z_L + Z_line) = 480∠0° / (4.18 + j3.24)

Carrying out the calculation, we find:

I_L = 480∠0° / 5.29∠37.78° = 90.8∠-37.78° A

So the load voltage is:

V_L = Z_L I_L= 5∠36.86° x 90.8∠-37.78° V

Carrying out the calculation, we find:

V_L = 454∠-0.92° V

Item b

To calculate the requested powers in the problem, the equations below are used:

P_L = V_L I_L cos φ = 454 x 90.8 x cos 36.86°

Where φ is the phase shift angle between voltage and current and is the impedance angle itself. Z_L. Carrying out the calculation, we find:

P_L = 32,983 W

To calculate the reactive power we use:

Q_L = V_L I_L sen φ = 454 x 90.8 x sen 36.86°

Carrying out the calculation, we find:

Q_L = 24,728 VAr

Item c

The line losses are due to the electrical resistance of the transmission line and its value is R_line = 0.18 Ω . Therefore:

Loss_line = R_line I_L² = 0.18 x 90.8²

Carrying out the calculation, we find:

Loss_line = 1,484 W

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