Determination of active and reactive powers in multiphase machines

A method for the determination and measurement of the real and reactive powers of multiphase electric machines is proposed using the geometrical algebra and the power invariant stationary reference frame transformations of the phase voltages and currents. Geometrical Algebra provides the expressions for the calculation of the powers. A four-wattmeter method to determine the active and reactive powers for the 5-phase induction motor by using the line-to-line voltages and line (or phase) currents is set forth in some details. Expressions for the calculation of the real and reactive power components for 7 and 9-phase machines are set forth. Furthermore, it is revealed that when there is an imbalance in the supply voltages or in the machine, the reactive power exists in three components, as ij, ik and jk bivectors which must be individually compensated to improve input power factor or reduce torque pulsations. Simulation and experimental results on a 5-hp, 4-pole, five phase induction machine fed with balanced and unbalanced input voltage converter source provide the justification for the proposed methodology.