System Studies

Stanley E. Zocholl
Schweitzer Engineering Laboratories, Inc.

C. L. Fortesque in his 1918 paper [1] states the most striking thing about the results of his mathematical investigation of induction motors under unbalanced conditions was their symmetry.
The solution always reduced to the sum of two or more symmetrical solutions. He was led to inquire if there were no general principles by which unbalanced polyphase systems could be reduced to the solution of two or more balanced cases. The result of his inquiry is the method of symmetrical components, the essential means for analyzing fault conditions in power systems.
Today they are routinely measured and used as operating quantities in protective relays. This article reviews the classical solutions using the impedance transposed transmission lines and then examines the symmetrical components method when applied the impedance of untransposed lines.

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