Symmetrical components

In electrical engineering, the method of the symmetrical components is used to make a simplified analysis of a fault in an unbalanced three-phase system ( three-phase AC system ). In this case, an unbalanced system of phasors in positive sequence, negative sequence and zero sequence is split.

Causes

Reason for an unbalanced error can be, for example, an unbalanced short circuit ( phase-to- ground, phase-to- phase conductor, phase-to- phase-to- ground), which does not affect all three phases equally in contrast to a symmetric error. Unlike a balanced three-phase system, wherein the phasors are symmetrical, the phasors of the currents or voltages are added together in an unbalanced system of Figure 2 possible reasons not null:

  • Different sizes of the three phasors
  • Deviation from the normal 120 ° phase difference ( phase angle between two pointers, see phasor diagram )

History

Charles Legeyt Fortescue showed in a 1918 paper presented ( Method of Symmetrical Co - Ordinates Applied to the Solution of Polyphase Networks) that any unbalanced three-phase system can be represented as a sum of three balanced phasors sets. This analysis was taken up and improved by engineers at General Electric and Westinghouse. After the Second World War, it was a widely accepted method for the analysis of asymmetric errors in three-phase networks. (see Earth-fault )

Method

Fortescue showed first, that an unbalanced Phasorenset that does not add to zero, can be in an unbalanced set, but that adds up to zero and disconnect a system of equal phasors. Then he showed secondly, that any unbalanced, but at zero cumulative set of phasors in two symmetrical sets of opposing sequence ( considered in the same rotational direction: abc = positive, acb = negative) can be subdivided. Thus he found the division of any unbalanced, not to zero summing Phasorensets in a:

  • Positive sequence (positive sequence component): This is the same direction of rotation as the original system.
  • Negative phase (negative -sequence component): Has an opposite direction to the original system. It compensates for the deviation of the phasors of the usual 120 ° phase shift.
  • Zero system ( zero sequence component): All phasors have the same direction and the same length. This system compensates for the "non- addition" of the original system to zero.

With the extension of a single-pole representation to show the positive, negative and zero sequence systems of generators, transformers and other equipment, the analysis of unbalanced conditions ( eg ground faults ) is greatly simplified. Thus, a supply network operators quickly identify and fix the source of the error. The division into symmetrical components can also be extended to higher orders of phase.

Calculation

With the help of Fortescue matrix, the phasors of symmetrical components ( positive sequence ), ( NPS ), ( zero system ) can be calculated from the phase currents.

As a result of the positive sequence:

For the negative-sequence applies:

And for the zero system:

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