On some misinterpretations of the instantaneous reactive power p-q theory

Document Type


Publication Date



The main features of the instantaneous reactive power (IRP) p-q Theory, considered as a power theory of three-phase systems, are analyzed in this paper using the theory of the currents' physical components (CPC). This analysis shows that the p and q powers are not associated with separate power phenomena, but with multiple phenomena. Moreover, the results of the IRP p-q Theory contradict some common interpretations of power phenomena in three-phase circuits. Namely, according to the IRP p-q Theory the instantaneous reactive current can occur even if a load has zero reactive power, Q. Similarly, the instantaneous active current can occur even if a load has zero active power, P. Moreover, these two currents in circuits with a sinusoidal supply voltage can be nonsinusoidal even if there is no source of current distortion in the load. The analysis shows that a pair of values of instantaneous active and reactive p and q powers does not enable us to draw any conclusion with respect to the power properties of three-phase unbalanced loads even in a sinusoidal situation. Thus, the Instantaneous Reactive Power p-q Theory does not identify power properties of such loads instantaneously. This conclusion may have an importance for control algorithms of active power filters. The paper reveals the relationship between the p and q powers and the active, reactive and unbalanced powers, P, Q, and D and specifies the required energy storage capability of active power filters operated under sinusoidal unbalanced conditions.

Publication Source (Journal or Book title)

IEEE Transactions on Power Electronics

First Page


Last Page


This document is currently not available here.