Permanent magnet (PM) flux linkage is a critical thermal indicator for online monitoring PM temperature. However, its estimation is compromised by rotor position error under sensorless control. In this article, a novel virtual flux linkage (VFL) injection method is proposed for online estimating PM flux linkage and temperature in a dual three-phase surface-mounted PM synchronous machine (DTP-SPMSM). The relationships among the PM flux linkage, the difference between the rotor positions estimated from two sets of DTP windings, and thedq-axis currents/voltages are first derived when a pair of positive and negative VFLs are simultaneously injected into two position observers associated with two sets of DTP windings. It is found that this relationship is independent of rotor position error, stator resistance, inductance, and inverter nonlinearity. Consequently, the PM flux linkage can be accurately identified by the least square algorithm for PM temperature estimation. It is shown that the proposed method can eliminate the influence of rotor position error and unknown parameters on PM flux linkage and temperature estimation, whilst the torque fluctuation can be avoided due to opposite VFL injections in two sets of DTP windings. The proposed method has been validated experimentally.
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Wang et al. (2025) studied this question.
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