Generalized Bertotti Iron Loss Model Including Third-Harmonic Contribution and Automatic Harmonic Suppression in FCS-MPTC for Five-Phase IPMSM Drives

Iron loss in the core of multiphase machines constitutes a significant portion of the total losses, particularly at high speeds. In five-phase machines, the simultaneous presence of two rotating fields at frequencies 𝑓 (fundamental harmonic) and ۳𝑓 (third harmonic) renders classical iron loss models, such as the Bertotti equation, incapable of predicting the third-harmonic contribution. In this paper, by applying the superposition principle to the classical Bertotti model, an iron loss relationship is derived for five-phase machines that explicitly incorporates the contribution of the third-harmonic field into the total loss, with frequency-dependent coefficients of ۳ (hysteresis) and ۹ (eddy current). This model is integrated into the cost function of a finite control set model predictive torque control (FCS-MPTC) for a five-phase IPMSM drive. Unlike previous approaches that suppress the 𝑑۳–𝑞۳ currents by adding separate harmonic terms to the cost function or by introducing virtual vectors (e.g., the work of Tao et al., ۲۰۲۴), the proposed method reduces these undesirable currents automatically through a direct iron loss penalty and without the need for a dedicated harmonic suppression term. Simulation results on a ۱.۵ kW motor with a rated speed of ۳۰۰ r/min and a test torque of ۵ N·m show that, with the proposed method, the 𝑑۳–𝑞۳ currents are reduced by ۷۵%, the phase current THD improves from ۲۹.۲۷% to ۹.۸۷%, the torque ripple decreases from ۱۸.۸۳% to ۱۰.۰۷%, and the iron loss is reduced by ۲۸%. The efficiency increases from ۹۱.۲% to ۹۳.۵%, while the computational burden rises by only ۸.۳% compared to classical MPTC, which is far lower than that of methods based on virtual vectors. These achievements demonstrate that managing iron loss with a frequency-aware model can simultaneously meet multiple control objectives without increasing complexity

کلیدواژه ها:

Iron loss ، generalized Bertotti equation ، third harmonic ، model predictive torque control ، five-phase motor ، automatic harmonic suppression