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996 ⏐⏐⏐ POLYPHASE SYSTEMS
A
N
C B
For the total load:
PT � PTD � PTY � 7200 W � 6414.41 W � 13,614.41 W
QT � QTD � QTY � 9600 VAR (C) � 4810.81 VAR (I)
� 4789.19 VAR (C)
ST � �P� 2 T��� Q� 2 T� � �(1�3�,6�1�4�.4�1� W�) 2 � �� (�4�7�8�9�.1�9� V�A�R�) 2 �
� 14,432.2 VA
PT 13,614.41 W
Fp ����� �0.943 leading
ST 14,432.20 VA
EXAMPLE 22.7 Each transmission line of the three-wire, three-phase
system of Fig. 22.26 has an impedance of 15 � �j 20 �. The system
delivers a total power of 160 kW at 12,000 V to a balanced three-phase
load with a lagging power factor of 0.86.
E AB
a. Determine the magnitude of the line voltage EAB of the generator.
b. Find the power factor of the total load applied to the generator.
c. What is the efficiency of the system?
Solutions:
VL 12,000 V
a. Vf (load) ����� 6936.42 V
�3� 1.73
P T (load) � 3V fI f cos v
and
15 � 20 �
15 � 20 �
15 � 20 �
FIG. 22.26
Example 22.7.
P T
12 k V
Z 1 = Z 2 = Z 3
160,000 W
If ��� ����
3Vf cos v 3(6936.42 V)(0.86)
� 8.94 A
c
Since v � cos �1 0.86 � 30.68°, assigning V f an angle of 0° or
V f � V f �0°, a lagging power factor results in
I f � 8.94 A ��30.68°
For each phase, the system will appear as shown in Fig. 22.27,
where
Z 2
Z 1
E AN � I fZ line � V f � 0
a
n
Z 3