Page 12 IM02601004E www.eaton.com1 IntroductionSYMMETRICAL COMPONENTSSymmetrical components are commonly used for analysis of three-phase electrical powersystems. Phase vectors are expressed as sets of phasors, either as real or quadrature ormagnitude and phase. For example, a vector for three-phase voltages could be written asVabc..and the three symmetrical component phasors arranged into a vector as V012.:where Vo is the zero-sequence of component (the portion of voltage with no rotation)where V1 is the positive-seqience component (the portion of voltage with abc rotation)where V2 is the negative-sequence component (the portion of voltage with abc rotation).A phase rotation operator ...... is defined to rotate a phasor vector forward by 120 de-grees. As a result ...... 2 is a phase rotation of 240 degrees.A matrix “A” can be defined using this operator to transform the phase vector into sym-metrical components.The phase voltages are generated by the sequence equation: Vabc = A • V12.Conversely, the sequence components are generated from the analysis equationsV012 = A-1 • Vabc .While the analysis of symmetrical components is primarily focused on voltage, the analy-sis of current is equally valid.VOLTAGE AND CURRENT UNBALANCEWhen individual phases of a three-phase system differ, an unbalance results. Further-more, harmonic distortion can also result in unbalance. The measure of unbalance is theratio of the negative-sequence to the positive-sequence components and is representedas a percentage.
