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Appendix: Symmetrical
Components
The unsymmetrical operation of a three-phase ac system—in steady state or dur-
ing short circuit—is analyzed by resolving the unsymmetrical applied voltages and
resulting currents into symmetrical components that are orthogonal in a mathemati-
cal sense (not physical space). The method was rst developed by Fortesque and later
fully expanded by Wagner, Evans, and Clarke for applications in practical power
systems. It is analogous to resolving any space vector force into three orthogonal
components. It involves algebras of complex numbers and matrices. We study here a
brief theory and its applications in pow