Steady State Analysis of 5-Phase Symmetric Power System Networks Displaying Rotational Symmetries

Abstract

Power system network consists of generation, transmission and distribution sub networks and on the whole it is balanced i.e. symmetric. When faults occur, even though excitation may become unbalanced but the network remains normally balanced. These symmetries which are inherent in the power system satisfy mathematical group theoretical axioms. Feasibility multiphase power transmission was discussed by Stewart and Wilson (1978).

A few balanced faults occur on a real power transmission system and their fault analysis is easy. On the other hand line-to-ground faults, which are unsymmetrical in nature, are more likely to occur and their analysis requires an important tool, namely, the theory of symmetrical components. L.P.Singh and his coworkers(1979,81) employed the inherent symmetries of a power system network satisfying group theoretic axioms. This makes  possible to derive the symmetric and Clarke’s component transformation in a unified and systematic manner which can be applied for 4-phase and 6-phase networks.

Although five-phase system are not at present in practice, they serve to indicate the type of symmetrical sets which result from the resolution of a system having more than three-phases. When the number of vectors or phases of a system are prime, as in the three and five-phase cases, each component set of sequence higher than zero has n-individual vectors where as when the number of phases is not prime, as in the six-phase system, some of the component sets contain superimposed vectors and thus appear not to have an symmetrical component vectors.