Two-phase co-ordinates of a three-phase circuit

IN RECENT years there has been an increasing interest in the use of substituted variables in the analysis of unbalanced three-phase circuits and machines. The best known and most widely used of the substituted variables are symmetrical components, introduced by Fortescue in 1918. In the method of symmetrical components the actual currents and voltages of the three phases of a three-phase circuit are replaced by the zero-sequence, positive-sequence, and negative-sequence currents and voltages, and, furthermore, the three-phase circuit itself is replaced for purposes of analysis by three fictitious single-phase circuits known as the sequence networks. This method has achieved extensive use in the analysis of polyphase machinery and in the making of fault studies on three-phase power systems. Another example of substituted variables is furnished by the direct-axis and quadrature-axis quantities as defined by Park² in 1929, which have greatly facilitated the mathematical analysis of salient-pole synchronous machines.