Basic AC Power
THREEPHASE CIRCUITS
Solution:
1.
V_{L}
3 V_{f}
(1.73)(240)
V_{L}
415.2 volts
2.
P_{T}
3 V_{L}I_{L}cosq
(1.73)(415.2)(100)(0.9)
P_{T}
64.6 kW
3.
Q_{T}
3 V_{L}I_{L}sinq
(1.73)(415.2)(100)(0.436)
Q_{T}
31.3 kVAR
4.
S_{T}
3 V_{L}I_{L}
(1.73)(415.2)(100)
S_{T}
71.8 kVA
Unbalanced 3f Loads
An important property of a threephase balanced system is that the phasor sum of the three line
or phase voltages is zero, and the phasor sum of the three line or phase currents is zero. When
the three load impedances are not equal to one another, the phasor sums and the neutral current
(I_{n}) are not zero, and the load is, therefore, unbalanced. The imbalance occurs when an open or
short circuit appears at the load.
If a threephase system has an unbalanced load and an unbalanced power source, the methods
of fixing the system are complex. Therefore, we will only consider an unbalanced load with a
balanced power source.
Example: A 3f balanced system, as shown in Figure 16a, contains a wye load. The lineto line
voltage is 240V, and the resistance is 40 W in each branch.
Rev. 0
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