When a short-circuit occurs across the terminals of a DC circuit, the current rises from the load current (y In) to the short-circuit current Isc over a period of time that depends on the value of the resistance R and inductance L of the short-circuited loop.

The equation determining the current in the loop is:
U = Ri + L Di/Dt

The curve of I versus time is defined (neglecting In) by the equation:
I= Isc (1 - exp(t/t))
where t = L/R is the time constant for the rise to Isc.

Practically speaking, after a time t = 3t, the short-circuit is considered to be established, because the value of exp(-3) = 0.05 is negligible compared to 1 (see the
curve opposite).

The lower the time constant (e.g. battery circuit), the shorter the time required for the current to rise to Isc.

To express breaking capacity, the interrupted short-circuit current with the following time constants is used:
L/R = 5 ms, fast short-circuit
L/R = 15 ms, standardised value used in standard IEC 60947-2
L/R = 30 ms, slow short-circuit.

In general, the value of the system time constant is calculated under worst-case conditions, across the terminals of the generator.

Released for: Schneider Electric India