State Variable Selection in dqθ Models of Saturated Synchronous Machines: Impact on Accuracy and Simulation Quality in PLECS

This work develops and compares custom models for 3-phase saturated Permanent-Magnet and Synchronous Reluctance Machines, capturing both space harmonic and saturation effects. Both Voltage-Behind-Reactance (VBR) and Rotor-Reference-Frame (RRF) circuital models are extended using the $\mathrm{dq} \theta$ mapping approach to fully include space harmonics. A central discovery of this study is that the presence of highfrequency noise in simulation results is influenced by the choice of the state variables: models implemented with $d q$ currents as state variables consistently deliver smooth and accurate waveforms, whereas those based on dq flux linkage integration and using the inverse flux maps suffer from high-frequency noise. Critically, this behavior is independent of the underlying circuital architecture, applying to both VBR and RRF formulations. The work establishes the use of current-based state variables as a key enabler for high-fidelity, harmonics-inclusive $\mathrm{dq} \theta$ motor simulation and more in general in circuital simulators.