Apparent Power and Energy Characteristics of a Multiphase Power Supply System

Increasing the power factor is one of the most important tasks of active filtering. For its successful solution, it is necessary to correctly determine the multiphase power supply system’s apparent power and active current. This paper considers a generalized case of a multiphase power supply system with different values of transmission line resistances, periodic currents and voltages of arbitrary shape. Using Schwartz’s integral inequality, applied in the reduced coordinate basis, the formulas of the apparent power and the corresponding active current in the matrix-vector form were obtained. The interdependence of the current and voltage multipliers of the apparent power formula on the transmission line resistance ratio is shown. When using energy-saving active filtering, the formulas for the minimum power loss and efficiency of a multiphase power supply system were derived. The obtained apparent power formula was compared with that given in IEEE Std. 1459-2010 for a three-phase, four-wire power supply system and the area of transmission line parameters for their convergence was established.