Bus Impedance Matrix

The calculation of subtransient fault currents for three-phase faults in an N-bus power system is modeled by the positive-sequence network. A three-phase short circuit at bus n requires analysis of two circuits via the superposition method.

The first circuit, with all machine-voltage sources short-circuited, leaving only the pre-fault voltage source at the fault. Solving its nodal equations, including the positive-sequence bus admittance matrix, yields the positive-sequence bus impedance matrix.

With a single source at the faulted bus in the first circuit, the matrix solution of nodal equations determines the fault current and voltage at any bus.

The second circuit represents prefault conditions. Neglecting prefault load current equates all voltages to pre-fault voltage. The equivalent circuit of the short-circuit currents shows self-impedances and mutual impedances.

Neglecting prefault load currents implies equal internal voltage sources of all synchronous machines. These are replaced by one equivalent source.

With the switch open, all currents are zero, and each bus has equal voltage. Closing the switch results in a short circuit at bus n, reducing its voltage to zero.