Determination of Saturated Values of Rotating Machinery Incremental and Apparent Inductances by an Energy Perturbation Method

Energy and winding current perturbations form the basis of a method for calculation of the saturated apparent and incremental inductances of rotating machinery as functions of rotor position and machine winding excitation currents. The method is totally general and utilizes numerical field calculation techniques in obtaining stored energy in the magnetic circuits of such machines. Thus, it can be applied to a wide class of machinery with practically any cross-sectional contours and number of windings. It can be used at any given set of excitations (any loads). This method was applied to the calculation of the apparent and incremental inductances of a 15 hp samarium cobalt permanent magnet synchronous machine. The necessary-numerical field soluitions were obtained by finite elements at both rated and no load conditions. The calculated inductances, at various rotor positions, were compared with those obtained during laboratory measurements and the agreement between calculated and measured values was consistently very good. The advantage of this method over the more traditional calculations of only the direct and quadrature axes inductances (or reactances, including transient and subtransient components) is that the entire n > n matrix of incremental inductances that truely govern the dynamic performance of an n winding machine can be determined regardless of the validity of a rotating d-q-o frame of reference.