## THREE PHASE VS. SYMMETRICAL COMPONENTS REPRESENTATION

It is customary for three-phase electrical systems to be represented on a single-phase basis. This simplification, successfully employed for power flow and transient stability studies, rests on the premise that the system is balanced or at least can be assumed to be so for practical purposes (Anderson [B1], Blackburn [B3] Stevenson [B10], Wagner and Evans [B13]).

Modeling the system, however, on a single-phase basis is inadequate for analyzing phenomena that involve serious system unbalances (Anderson [B1], Arrilaga, Arnold, and Harker [B2]). Within the context of short circuit analysis, only the three-phase shunt fault lends itself to single-phase analysis, because the fault condition is balanced involving all three phases, assuming a balanced three-phase system.

Any other fault condition will introduce unbalances that require including in the analysis the remaining two phases. There are two alternatives to address the problem:

a) Three-phase system representation. When the system is represented on a three-phase basis, we explicitly retain the identity of all three phases. The advantage of threephase representation is that any kind of fault unbalance can be readily analyzed, including simultaneous faults.

Furthermore, the fault condition itself is specified with somewhat greater flexibility, particularly for arcing faults. The main disadvantages of the technique are the following:

1) It is not tractable for hand calculations, even for small systems.
2) Supposing that a suitable computer program is used, it can be data-intensive.

b) Symmetrical components representation. The symmetrical components analysis is a technique that, instead of requiring analysis of the unbalanced system, allows for the creation of three subsystems, the positive, the negative, and the zero-sequence systems, properly interconnected at the fault point, depending on the nature of the system unbalance.

Once modeled, the fault currents and voltages, anywhere in the network, are then obtained by properly combining the results of the analysis of the three-sequence networks (Anderson [B1], Blackburn [B3] Stevenson [B10], Wagner and Evans [B13]). The distinct advantage of the symmetrical components approach is that it allows modeling unbalanced fault conditions, while still retaining the conceptual simplicity of the single-phase analysis.

Another important advantage of the symmetrical components method is that system equipment impedances can be easily measured in the symmetrical components reference frame. This simplification is only true if the system is balanced in all three phases (except at the fault location which then becomes the interconnection point of the sequence networks), an assumption that can be entertained without introducing significant modeling errors for most systems.

The main disadvantage of the technique is that for complicated fault conditions, it may introduce more problems than it solves. The symmetrical components technique remains the preferred analytical tool today for fault analysis for both hand and computer-based calculations.