Instantaneous reactive power theory—A general approach to poly-phase systems

The systematic use of active power filters, APF, to compensate non-linear loads, has extended the use of the instantaneous reactive power theory. Originally, p–q theory appeared; it obtained constant instantaneous power in the source side after compensation. Later, other formulations have been developed. They have allowed different compensation objectives to be obtained. Nevertheless, all of them can only be applied to three-phase systems, i.e. those formulations frameworks cannot be used to establish versatile control strategies in multi-phase systems. This paper presents a new approach which can be applied to multi-phase power systems. Thus, a new tensorial product is introduced that allows an operative definition of the instantaneous reactive power tensor and the derived instantaneous reactive current component. According to these expressions, different compensation strategies can be defined in multi-phase systems. The powers and currents expressions derived from the formulations presented up now can be obtained applying this new approach. In this work, original p–q and modified p–q formulations expressions are derived in the new approach framework. In addition, a series of practical examples has been included to improve the understanding of the proposed formulation.