AC Circuits and Power Systems in Practice

5Symmetrical Components

Generators supplying a distribution network are carefully designed to produce a balanced three‐phase supply, which means that each phase voltage has the same amplitude and is separated from its neighbours by exactly 120°. Unfortunately the connected load is seldom exactly balanced, and therefore the magnitude and phase of the load currents may not be quite equal. This causes differing potential drops across the phase impedances, and a proportionally unbalanced supply is seen throughout the network as a result.

The situation becomes considerably worse when faults occur in a network, the most disturbing of which tend to involve short circuits, either between individual phase conductors or between one or more phases and either the neutral terminal or ground potential. Under these conditions the degree of unbalance present in a network becomes extreme, and close to the fault the affected phase voltage(s) may vanish entirely. High fault currents flow as a consequence, and the protection system must quickly detect and clear such faults before permanent damage occurs.

The analysis of balanced three‐phase systems is straightforward, and can be done using phasor analysis, but when the degree of unbalance becomes substantial another approach is generally used. This technique, called the method of symmetrical components, relies on the fact that the faulted network remains essentially linear. Linear or near linear systems are common in engineering and there are general ...