Power system calculations can be done using actual voltages and currents or using per-unit representations of actual quantities. While performing a calculation in actual quantities makes sense occasionally, the vast majority of calculations are done in per-unit.
The discussion in this assumes a familiarity with the per-unit method; but, to avoid confusion, definitions of important parameters are given in Table 1. Equivalent three-phase values are usually used in practice, but an understanding of the mathematics presented in Table 1 relies on a careful interpretation of base values as single-phase quantities.
Example A: Calculate the maximum three-phase current measured by an instantaneous relay, fuse, or series trip device on the 13.8 kV feeder serving the 2 Mvar power factor capacitor on Bus 4.
Figure 2 depicts a portion of the system one-line diagram and shows a fault in the 13.8 kV, 2 Mvar capacitor feeder on Bus 4. The calculated current magnitudes are
Distribution of instantaneous currents for fault on capacitor feeder in sample system
— 19 203 A, rms asymmetrical
— 12 410 A, rms symmetrical
A moderate asymmetrical offset (X/R = 15.65) is present due primarily to the close proximity of the generator, which contributes 4080 A of symmetrical current. The largest contributor, of course, is the utility, with other sources making up the difference.
The capacitor itself does not contribute current to the fault. Present practice ignores any capacitor contribution to system short-circuit currents on the basis that it occurs so quickly and is out of phase with system currents.
In this instance, also, a protective device in the capacitor feeder would detect currents flowing from the system to a fault on the feeder, or current flowing from the capacitor to the system, but not both, again illustrating that the analyst should carefully consider what constitutes the branch current measured by the protective device of interest.
Figure 3 shows this same fault condition, but with the impedances adjusted to calculate the long-time fault magnitude. The current has decayed to less than 9185 A symmetrical and the generator contribution is down to 2721 A. Also, the contributions from motors on the system have dropped to zero.
Figure 3 Calculated distribution of long-time relay current to fault on capacitor feeder in sample system
NOTE—The current is purely symmetrical and the contributions from sources other than the generator and utility have decayed away.
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