Calculate the Fault Current

As fault currents usually flow in the earth conductor until such time as the circuit protective device operates, it will prove to be extraordinarily difficult.

Ahah! A formula! OK:

• Consider a phase-to-neutral fault in a single-phase system, with I_p flowing in the phase conductor. If I_n is the neutral current, then I_n = I_p, again only until the circuit protective device operates, at which point I_n=I_p=0.

Will that do?

There is no single formula since the fault current depends upon the overall system configuration (isolated, networked), what types of loads (resistive, inductive, capacitive) are in the network, the exact nature of the fault (single line to ground, three phase to ground, etc.), and the length of time the fault exists (intitiation, 5 cycles, 1 second, etc.). For simple configurations you can use symmetrical components, otherwise the best "formula" is to use a commercial software package such as ETAP.

A quick look at section 8 in this paper will give you an introduction to some of the formulas (symmetrical components) and methods (per unit system) used by power engineers to analyze the more common faults, but note that this only considers the steady state values, not the dynamic time varying values during fault initiation and decay, that's a whole other topic unto itself. Google is your friend and teacher.

There is content in British Standard 7671 on this topic. Any qualified electrician can handle the formula and carry out the calculation.