Handbook of Electrical Engineering

FAULT CALCULATIONS AND STABILITY STUDIES 287

Figure 11.10 Short-circuit current waveform of a series-connected R-L circuit that is fed by a sinusoidal
voltage. The switching angleθis−90 degrees, which represents the worst case. The responses are for eight
values of the circuit X-to-R ratio.

is small i.e. X-to-R ratios greater than about 5.0. Hence substituting forωt=πgives the doubling
factor (DF) as,

DF∼=e

−Rπ

x + 1. 0

For intermediate X-to-R ratios i.e. 0.1 to 5.0, the equality in (11.7) must be satisfied, which
is best achieved by iteration for a solution in the vacinity ofωt= 3 π/4, e.g. by Newton’s method,
see Reference 4.

Figure 11.10 shows ‘worst-case’ responses ofifor different values of the ratio X to R.

11.7 Application of the Doubling Factor to Fault CurrentIfrms′′ found in 11.6

Ifrms′′ FOUND IN 11.6

Now returning to the rms equations forIg′′,Ihm′′ andIlm′′in sub-section 11.6 it can be seen that each of
these currents can have different X-to-R ratios and will therefore decay at different rates. The peak
fault current is,
Ifpk′′ =

√

2 (DFgIg′′+DFhmIhm′′ +DFlmIlm′′)

Where the doubling factorsDFg,DFhmandDFlmare evaluated from the X-to-R ratios of
each component using equation (11.5) or their nearest ratio given in Table 11.3 asI 1 (pu) or in
Table H.1b.