TABLE OF CONTENTS Several specialized analytical tools have been developed to aid in the solution of power and power electronics circuits. Learning these tools can make the design job easier, especially when studying the interaction between a power electronics system and the supplying utility system. Also, it is necessary to understand these analytical tools and their nomenclature to converse with utility and vendor engineers associated with the power electronics field.
Analysis of a three-phase AC circuit with unbalanced currents or voltages gets into some rather messy complex numbers. In 1918, Dr. C. L. Fortesque delivered a paper before the AIEE, predecessor organization to the IEEE, that laid the groundwork for symmetrical components, a method of representing unbalanced voltage or current phasors by symmetrical sets of phasors. These symmetrical components are positive- and negative-sequence three-phase components as well as a zero-sequence single-phase component. This latter phasor is involved with four-wire systems, usually involving ground circuits. The network can be solved in the usual fashion with each of the symmetrical components, and then the individual solutions combined to represent the unbalanced system. Symmetrical components are universally used by power company engineers for system parameters.
Symmetrical component analysis uses a complex operator, a, where a = ?0.5 + j 0.866, a unit phasor at 120 . Then, a 2 = ?0.5 j 0.866, and a 3 = 1.0. If a set of asymmetric phasors are given as x, y, and z, then
