Fault analysis
A fault is an unintended short circuit — a tree branch bridging two lines, a lightning strike flashing a wire to ground, an insulator failing. Suddenly the impedance that limited the current nearly vanishes, and current that was a polite few hundred amps explodes to tens of thousands of amps in milliseconds, a torrent that can melt copper and explode equipment. Fault analysis is the calculation of exactly how big that surge will be at every point in the network, for every type of fault.
You can't design protection without it. The breaker that clears a fault must be rated to interrupt the full fault current without welding shut or arcing over — undersize it and it fails catastrophically the one moment it matters. Engineers compute fault levels using symmetrical components (splitting an unbalanced fault into balanced positive-, negative-, and zero-sequence networks) so even a messy single-line-to-ground fault becomes solvable. The results set breaker ratings and tell every protection relay how to tell a genuine fault from a heavy but normal load.
Counterintuitively, the worst-case fault current isn't always a three-phase short — depending on grounding, a single-line-to-ground fault can produce a higher current, which is why all fault types are studied.