Analytical model of the cross-magnetizing effect in saturated synchronous machines

An analytical model of the cross-magnetizing effect in saturated synchronous machines is proposed in which a second-order polynomial function is used to approximate the magnetization curve. The d- and q-axis magnetizing flux linkages are found as closed-form nonlinear functions of the d- and q-axis magnetizing currents. The magnetic reciprocity appears in this analytical model and can be applied to the simulation of saturated synchronous machines. The machine equations can be linearized to give the small-signal model around an operating point, whose associated eigenvalues can be computed. The discrepancy between machine performances with and without cross-magnetization is manifest at heavy loads due to increased saturation.