Analytical Methodology for Modelling of Circulating Current Loss in Synchronous Electrical Machines With Permanent Magnets

This paper describes a novel analytical methodology for modelling winding copper losses as a result of circulating currents (CC) in permanent magnet synchronous machines (PMSM). CCs are important to be considered at an early design stage especially in high frequency and high performance machines where sub-optimal design choices can lead to significant alternating current (AC) losses. Nowadays mainly FEM method is used for precise calculation of circulating currents. However, it suffers on significant computational time required for building models and simulation of circulating current effect that makes it inapplicable for optimization purpose. The paper demonstrates the computationally efficient methodology through comparison with FEM based models for high power density PMSM with concentrated winding and validation against experimental results for a stator section at the fundamental frequency from 500 Hz to 2000 Hz. The methodology allows simulation of CC and AC Ohmic losses when machine supplied by any current waveforms, for arbitrary size and location of the conductors in the slots. A key novelty of the proposed method is the utilization of subdomain (SDM) approach in conjunction with solution of a system of ordinary differential equations (ODE) for an equivalent electrical circuit of machine windings. This approach is precise and fast but has never been used before for circulating current loss evaluation in windings of electrical machines. The model is intended to be used at the design stage of an electrical machine where multiple geometric dimensions, winding configurations and conductor placement in the slot are considered towards an optimal design.