Modeling of synchronous machines with magnetic saturation

This paper deals with a method to derive multiple models of saturated round rotor synchronous machines, based on different selections of state-space variables. By considering the machine currents and fluxes as space vectors, possible d–q models are discussed and adequately numbered. As a result several novel models are found and presented. It is shown that the total number of d–q models for a synchronous machine, with basic dampers, is 64 and therefore much higher than known. Found models are classified into three families: current, flux and mixed models. These latter, the mixed ones, constitute the major part (52) and hence offer a large choice. Regarding magnetic saturation, the paper also presents a method to account for whatever the choice of state-space variables. The approach consists of just elaborating the saturation model with winding currents as main variables and deriving all the other models from it, by ordinary mathematical manipulations. The paper emphasizes the ability of the proposed approach to develop any existing model without exception. An application to prove the validity of the method and the equivalence between all developed models is reported.