226
Electrical Power Systems
9 Symmetrical Components 9.1 INTRODUCTION In a balanced system, analysis can be done on a single phase basis. The knowledge of voltage and current in one phase is sufficient to determine the voltages and current in other two phases. Real and reactive powers are three times the corresponding per phase values. When the system is unbalanced, the voltages, currents and the phase impedances are in general unequal. Unbalanced system operation can result due to unsymmetrical fault, e.g., line to line fault, double line to ground fault or single line to ground fault. Unbalanced operation may also result when loads are unbalanced. Such an unbalanced operation can be analyzed through symmetrical components where the unbalanced three phase voltages and currents are transformed into three sets of balanced voltages and currents called symmetrical components.
9.2 SYMMETRICAL COMPONENTS OF AN UNBALANCED THREE PHASE SYSTEM The unbalanced phasors of a three-phase system can be resolved into following three component sets of balanced phasors which possess certain symmetry: 1. A set of three phasors equal in magnitude, displaced from each other by 120º in phase, and having the same phase sequence as the original unbalanced phasors. The set of balanced phasor is called positive sequence component. 2. A set of three phasors equal in magnitude, displaced from each other by 120º in phase, and having the phase sequence opposite to that of the original phasors. This set of balanced phasors is called negative sequence components. 3. A set of three phasors equal in magnitude with zero phase displacement from each other. This set is called zero sequence components. The components of this set are all identical. These three sets of balanced phasors are called symmetrical components of the original unbalanced phasors. Assume that the three phases are represented a, b and c such that the phase sequence is abc (positive sequence). Say, Va, Vb and Vc are balanced voltages (phasors) characterized by equal magnitudes and interphase differences of 120º, then the set is said to have a phase sequence abc (positive sequence) if Vb lags Va by 120º and Vc lags Vb by 120º. Assume Va is reference phasor, Va = Va, Vb = b2Va, Vc = b Va where the complex operator b is defined as b = e j120º