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We introduce a new method to model permanent-magnet synchronous machines (PMSMs) with saliencies due to the salient structure and magnetic saturation. We define two parameters to indicate these saliencies, i.e., the structural saliency ratio and the saturation saliency ratio . To verify the nonlinear model, we tested a real PMSM and numerically simulated it. The nonlinear inductance matrix is deduced and expressed by a nonlinear function regressed from the experimental data. The simulation and experimental results agree well with each other.