Page 49 - Electrical Equipment Handbook _ Troubleshooting and Maintenance

TRANSFORMERS

3.6 CHAPTER THREE

transformer present) can be solved for its voltages and currents. The process of replacing
one side of a transformer by its equivalent at the second side’s voltage level is known as
reflecting or referring the first side of the transformer to the second side.
The solution for circuits containing ideal transformers is shown in Example 3.1.
EXAMPLE 3.1 A single-phase power system consists of a 480-V 60-Hz generator supply-
ing a load Z 4 j3 through a transmission impedance Z 0.18 j0.24 .
load line
Answer the following questions about this system.
1. If the power system is exactly as described above (Fig. 3.4a), what will be the voltage
at the load? What will the transmission line losses be?
2. Suppose a 1:10 step-up transformer is placed at the generator end of the transmission
line and a 10:1 step-down transformer is placed at the load end of the line (Fig. 3.4b).
What will the load voltage be now? What will the transmission losses be now?

Solution
1. Figure 3.4a shows the power system without transformers. Here I I I . The
G line load
line current in this system is given by
V
I
line
Z Z
line load
480 0° V

(0.18 j0.24 ) (4 j3 )
480 0°

4.18 j3.24

480 0°

5.29 37.8°
90.8 37.8° A
Therefore the load voltage is
V I Z
load line load
(90.8 37.8° A)(4 j3 )
(90.8 37.8° A)(5 36.9° )

454 0.9° V
and the line losses are
2
P (I ) R
loss line line
2
(90.8 A) (0.18 )
1484 W
2. Figure 3.4b shows the power system with the transformers. To analyze this system, it is
necessary to convert it to a common voltage level. This is done in two steps:

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