A Voltage-Behind-Reactance Model of Five-Phase Induction Machines Considering the Effect of Magnetic Saturation

Five-phase induction machines are generally modeled using multiple dq planes or using a phase variable model. This paper considers modeling five-phase induction machines using a voltage-behind-reactance (VBR) configuration. This configuration lends itself suitable for time-domain circuit-based simulators as the MATLAB/Simulink SimPowerSystems (SPS) toolbox. The stator electrical dynamics are represented in five-phase coordinates, while the rotor electrical circuit is modeled using rotor flux linkage as the state variable and expressed in the dq stator reference frame. The VBR model is equivalent to a conventional dq model; however, it facilitates the connection of an external inductance without affecting numerical accuracy and calculation efficiency. It also facilitates the simulation of different winding connections, series-connected multimotors, and open phase(s) conditions. The model is, first, derived for a magnetically linear system and then it is extended to include the effect of magnetic saturation. The flux correction method is used to represent the effect of magnetic saturation with a simple modification to represent the effect of cross coupling between fundamental and third sequence planes due to saturation effect. The dynamic cross saturation is considered by adding compensating terms that depend on magnetizing inductance variation. The proposed model is experimentally verified using a prototype 1.5-hp five-phase induction machine under different operating conditions.