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Electric Power Engineering

Very Brief Overview of Symmetrical Components (positive, negative, & zero sequence)
Posted: 23 Jul 02

Reference Protective Relaying Principles and Applications by J. Lewis Blackburn.
Considering a three-phase system, symmetrical components (positive sequence, negative sequence, and zero sequence) allow one to analyze power system operation during unbalanced conditions such as those caused by faults between phases and/or ground, open phases, unbalanced impedances, and so on. The positive sequence set consists of the balanced three-phase currents and line-to-neutral voltages supplied by the system generator. They are always equal in magnitude and phase displaced by 120 degrees rotating at the system frequency with a phase sequence of normally a, b, c. The sequence currents or sequence voltages always exist in three's, never alone or in pairs.
The negative sequence set is also balanced with three equal magnitude quantities at 120 degrees apart but with the phase rotation or sequence reversed, or a, c, b. (If the positive sequence is a, c, b as in some power systems, then negative sequence will be a, b, c.) For the negative sequence set, again the sequence currents or sequence voltages always exist in three's, never alone or in pairs.
The members of the zero-sequence set of rotating phasors are always equal in magnitude and always in phase. Once again, if zero sequence currents or zero sequence voltages exist, they must exist in all three phases, never alone or in one phase.
In transformers, lines, etc., the phase sequence of the current does not change the impedance encountered, so positive sequence impedance equals negative sequence impedance; X1 = X2. System generators do not generate negative sequence currents, but negative sequence can flow in their windings. For rotating machines X2 = 1/2(X"d + X"q). Except for calculating faults very near machine terminals, can assume X"d=X"q, so X2 = X"d.
Zero sequence for transformers is equal to the positive & negative sequence and is the transformer leakage impedance, except in core-type transformers where Xo = .85 to .9 times X1. For estimating open lines Xo = 3 or 3.5 times X1 is commonly used. Zero sequence impedance of generators is low and variable depending on winding design.

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