Application of a Multidimensional Approach in the Compensation of Industrial Loads

The instantaneous reactive power theory (IRPT) has long been utilized for load compensation through active power line conditioners (APLCs). IRPT effectively divides the current vector into two components: the instantaneous power current and the instantaneous reactive current. Among these components, only the former is necessary to transfer instantaneous real power to the load. However, the commonly adopted approach faces challenges when extended to multi-phase systems and their compensation strategy design. This challenge is particularly pertinent today due to the consensus that treating a three-phase system with a neutral wire as a four-conductor system is more appropriate. This paper introduces a formulation of IRPT tailored for multi-phase systems within the framework of geometric algebra (GA). GA is a mathematical structure that defines a single power variable, the instantaneous power multivector, encompassing both instantaneous real power and instantaneous reactive power within a unified mathematical entity. The current components can be directly derived from this power multivector. Additionally, this paper establishes a connection with the original p-q formulations and lays the foundations for time-instantaneous compensation (TIC) and time-average compensation (TAC). Finally, to validate the proposed model, simulation and experimental results from a three-phase four-wire industrial system using a novel approach are presented.