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 dqθ mapping approach to fully include space harmonics. A central discovery of this study is that the presence of high frequency noise in simulation results is influenced by the choice of the state variables: models implemented with dq 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 dqθ motor simulation and more in general in circuital simulators.