Hybrid Physics–Data-Driven Digital Twin of a Six-Phase PMSM with Experimentally Identified Parameters and Saturation Maps

Accurate digital twins (DTs) of multiphase permanent-magnet synchronous machines (PMSMs) remain challenging because nonlinear magnetic saturation, cross-coupling, iron-loss effects, and inverter non-idealities must be represented despite limited machine parameter information. This paper proposes a hybrid physics–data-driven DT for a six-phase PMSM drive, in which experimentally identified parameter maps are directly integrated into an analytical machine-drive model, with data connections in both directions between the physical drive and its virtual representation, and validates it experimentally. The virtual representation includes the machine, six-phase inverter, mechanical dynamics, and field-oriented control (FOC), while preserving physical interpretability. The proposed identification procedure extracts the PM flux linkage, reciprocity-constrained flux maps, absolute and incremental inductances, including the cross-coupling inductances Ldq and Lqd, and the stator resistance with temperature correction directly from steady-state voltage and current measurements, without requiring manufacturer or FEA data. A closed-form, non-iterative methodology based on motoring and braking tests is developed to account for magnetic saturation and cross-coupling, while removing the resistive and iron-loss effects from the flux maps. The identified parameters update the virtual model periodically from new measurements and are returned to the physical drive through retuned current controllers. Experimental validation using an 8 kW six-phase PMSM shows back-EMF errors of at most 0.21%, while the closed-loop RMS current errors remain below 0.18%. For voltage estimation, the identified parameters reduce the maximum estimation errors from approximately 25.6% and 8.0% with datasheet parameters to 3.65% and 0.70% for the d- and q-axis voltages, respectively. The proposed method is also benchmarked against particle swarm optimisation (PSO) and a multilayer perceptron artificial neural network (MLP-ANN), trained on the same data. At the 500 rpm identification condition, the proposed method and PSO achieve comparable accuracy, while the proposed method identifies physically meaningful parameters without iterative optimisation, compared with approximately 26 s for PSO and 44 s for the MLP-ANN. On the withheld operating points above the identification current range and at the unseen 700 rpm condition, the proposed method remains accurate, with R2 above 0.996, whereas the PSO error increases, particularly for the q-axis voltage, and the MLP-ANN does not generalise beyond its training range. The results demonstrate a fast, experimentally grounded, and physically interpretable DT suitable for controller tuning, virtual testing, and periodic model updating from experimental measurements, providing a practical alternative to computationally intensive optimisation and purely data-driven models for multiphase machine drives.