GENERALIZED instantaneous reactive power theory in poly-phase power systems

The systematic use of Active Power Filters, APFs, to compensate nonlinear loads, has extended the use of the instantaneous reactive power theory. Originally, the 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 can not be used to establish control strategies in poly-phase systems. This paper presents a new approach, based on geometric algebra, which can be applied to multiphase systems. A new tensor product is introduced that allows the operative definition of the instantaneous reactive power tensor and its derived instantaneous reactive current component. In addition, in this paper a new concept of instantaneous power multivector is introduced which allows the instantaneous reactive power theory to be encoded in an analog way as single-phase systems analysis. The new expressions are applied to a practical multi-phase system. Power and current terms are calculated and the associated waveforms are presented. Results corroborate the correspondence with the traditional electric power theory.