Calculation of derating factors based on steady-state unbalanced multiphase induction machine model under open phase(s) and optimal winding currents

Multiphase machines have become a promising candidate in high-power applications as they offer many advantages over their three-phase counterparts. The main salient feature is the high fault tolerance capability. During faults, two alternatives for machine operation are possible, namely; open loop control and optimal current control. While the former corresponds to higher torque ripple and unbalanced winding currents, the latter option necessitates unbalanced phase voltages and typically an increased DC-link voltage to source the required optimal currents. Consequently, an increase in the employed semiconductor device rating is required, which is a critical design factor especially in medium voltage applications. This paper investigates an eleven-phase induction machine with concentric windings under fault conditions. An unbalanced steady-state machine model based on symmetrical components theory is developed as a mathematical tool to estimate different machine currents and total developed torque under open circuit phase(s). The effect of different sequence planes is also included in the derived model. This model is then experimentally verified. It is shown that the application of optimal current control in multiphase induction machines with open circuited phase(s) optimizes torque production while maintaining minimum stator copper loss and torque ripples. This optimization problem usually incorporates solving complicated nonlinear equations that increase in complexity with higher numbers of phases. Alternatively, a genetic algorithm is used in this paper to provide a simple method to obtain the optimum currents in the remaining healthy phases. Based on the derived optimal currents, the steady-state model is used to estimate the required DC-link voltage reserve that ensures no machine de-rating. Finally, the required derating factors to avoid machine overheating are calculated for different numbers of disconnected phases when DC-link voltage limitation is introduced.