Power definitions for three-phase systems in terms of instantaneous symmetrical components

This paper considers power definitions for three-phase power systems with non-sinusoidal and unbalanced voltages and currents. By applying the Lyon transformation to three-phase voltages and currents, instantaneous symmetrical components are obtained and used to define powers. Definitions of instantaneous apparent and reactive powers are derived, as well as definitions of well-known quantities based on rms values, such as apparent and reactive powers. The introduced set of power definitions based on the same mathematical framework could be used for time-instantaneous and time-average compensation types. To provide correct calculation of powers for unbalanced three-phase four-wire systems, all wires and related quantities of the three-phase four-wire system are treated equally. The instantaneous apparent and reactive powers are also expressed in terms of instantaneous symmetrical components derived from the Clarke transformation. The proposed defini-tions are compared with other power definitions. In the case of a three-phase three-wire system, the proposed definitions give the same values of powers as the most known power definitions. In the case of a three-phase four -wire system, the proposed definitions give the same value of the apparent power as the DIN 40110 Standard and the same value of reactive power as the Currents' Physical Component theory. (c) 2017 Elsevier Inc. All rights reserved.