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Symmetrical components
In electrical engineering, the method of symmetrical components simplifies the analysis of a three-phase power system exhibiting an electrical fault or other unbalanced condition.
The symmetrical components corresponding to an asymmetrical set of three phasors are:
The analysis of power system is much simpler in the domain of symmetrical components, because the resulting equations are mutually linearly independent if the power system itself is balanced. In this case, each symmetrical component can be analyzed separately, similar to the per-phase analysis.
The protective relays utilize the symmetric components for fault detection. For example, during the normal operation, the zero-sequence current is very small, so a high current value is a convenient and reliable indicator of a ground fault.
The basic idea dates back to 1895, when Ferraris et al. produced an analysis of a single-phase motor by splitting a field set inside it into two components revolving in the opposite directions. The concept now known as the positive and negative sequences was published by Ernst Alexanderson in 1913 in his work on phase balancers, and by L. G. Stokvis in 1912-1915 while investigating the voltage regulation. These works lacked the clear definition of a zero sequence.
In 1918 Charles Legeyt Fortescue presented a paper which demonstrated that any set of N unbalanced phasors (that is, any such polyphase signal) could be expressed as the sum of N symmetrical sets of balanced phasors, for values of N that are prime. Only a single frequency component is represented by the phasors.
In 1943 Edith Clarke published a textbook giving a method of use of symmetrical components for three-phase systems that greatly simplified calculations over the original Fortescue paper. In a three-phase system, one set of phasors has the same phase sequence as the system under study (positive sequence; say ABC), the second set has the reverse phase sequence (negative sequence; ACB), and in the third set the phasors A, B and C are in phase with each other (zero sequence, the common-mode signal). Essentially, this method converts three unbalanced phases into three independent sources, which makes asymmetric fault analysis more tractable.
By expanding a one-line diagram to show the positive sequence, negative sequence, and zero sequence impedances of generators, transformers and other devices including overhead lines and cables, analysis of such unbalanced conditions as a single line to ground short-circuit fault is greatly simplified. The technique can also be extended to higher order phase systems.
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Symmetrical components
In electrical engineering, the method of symmetrical components simplifies the analysis of a three-phase power system exhibiting an electrical fault or other unbalanced condition.
The symmetrical components corresponding to an asymmetrical set of three phasors are:
The analysis of power system is much simpler in the domain of symmetrical components, because the resulting equations are mutually linearly independent if the power system itself is balanced. In this case, each symmetrical component can be analyzed separately, similar to the per-phase analysis.
The protective relays utilize the symmetric components for fault detection. For example, during the normal operation, the zero-sequence current is very small, so a high current value is a convenient and reliable indicator of a ground fault.
The basic idea dates back to 1895, when Ferraris et al. produced an analysis of a single-phase motor by splitting a field set inside it into two components revolving in the opposite directions. The concept now known as the positive and negative sequences was published by Ernst Alexanderson in 1913 in his work on phase balancers, and by L. G. Stokvis in 1912-1915 while investigating the voltage regulation. These works lacked the clear definition of a zero sequence.
In 1918 Charles Legeyt Fortescue presented a paper which demonstrated that any set of N unbalanced phasors (that is, any such polyphase signal) could be expressed as the sum of N symmetrical sets of balanced phasors, for values of N that are prime. Only a single frequency component is represented by the phasors.
In 1943 Edith Clarke published a textbook giving a method of use of symmetrical components for three-phase systems that greatly simplified calculations over the original Fortescue paper. In a three-phase system, one set of phasors has the same phase sequence as the system under study (positive sequence; say ABC), the second set has the reverse phase sequence (negative sequence; ACB), and in the third set the phasors A, B and C are in phase with each other (zero sequence, the common-mode signal). Essentially, this method converts three unbalanced phases into three independent sources, which makes asymmetric fault analysis more tractable.
By expanding a one-line diagram to show the positive sequence, negative sequence, and zero sequence impedances of generators, transformers and other devices including overhead lines and cables, analysis of such unbalanced conditions as a single line to ground short-circuit fault is greatly simplified. The technique can also be extended to higher order phase systems.