A Stable and Computationally Efficient Spatial Harmonic Model for Predicting the DC Winding Induced Voltage in WFSF Machine

Abstract

In order to predict the DC winding induced voltage under pulse width modulation excitation in the wound field switched flux (WFSF) machine with consideration of the impact of magnetic coupling among <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis and the DC winding, lamination magnetic saturation and current harmonics in both AC and DC windings, the field-circuit coupling method based on the high-fidelity spatial harmonic (SH) model is applied in this paper, including the inductance-based SH model and flux-linkage-based SH model. However, it is found that the inductance-based SH model of the WFSF machine suffers from numerical instability in dynamic operation due to the high condition number of the inductance matrix caused by the magnetic coupling among <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis and the DC winding, resulting in prediction errors of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis flux-linkages, and that of the DC winding. To solve this problem, a flux-linkage-based SH model is proposed for the WFSF machine in this paper, and it shows that the proposed flux-linkage-based SH model is numerically stable during the dynamic operation. In addition, the calculation speed of the flux-linkage-based SH model is 147 times faster than the inductance-based one, due to the exemption of the calculation of the partial derivation equations. Finally, the analyzed 24-stator-slot/10-rotor-pole WFSF machine is built and tested to validate the flux-linkage-based SH model, and the experimental results agree well with those of the SH model.