Fluctuating Power and Compensation Constraints in Unbalanced ThreePhase Systems : A Symmetrical-Component Analysis

Abstract

Résumé—This article analytically investigates the relationships between the unbalance of three-phase quantities and instanta neous power in distribution networks under sinusoidal steady state conditions. The approach is based on the decomposition of voltages and currents into symmetrical components in order to explicitly identify the terms associated with the positive-,negative-, and zero-sequence components. The resulting decom position separates the three-phase instantaneous power into an average component and an oscillating component at the angular frequency 2ω, whose amplitude depends on cross-products bet ween the symmetrical components of voltages and currents. In the particular case of a balanced supply, the expression simplifies and highlights the role of the negative-sequence current component in fluctuating power. Numerical simulations are used to illustrate the analytical relationships obtained under several unbalance scenarios and to examine their sensitivity to network parameters. This formulation provides an analytical framework for relating symmetrical components to the energy behavior of an unbalanced three-phase network.