Mathematical Models of Synchronous Reluctance Motor Considering Iron Loss and Cross-Magnetic Saturation with Reciprocity Relation of Mutual Inductance

Abstract

A unique approximation function for the d- and q-axes inductances for a synchronous reluctance motor (SynRM) is shown. This inductance approximation function has excellent features, such as continuous and differentiable over the entire current range when taking into account cross-magnetic saturation and satisfactory reciprocity relation of the mutual inductance. It is also possible to derive an equivalent inverse inductance function that can estimate the d- and q-axes currents from d- and q-axes stator flux linkages. Using the proposed inductance approximation function, the authors derive two mathematical models. The first is a strict model in which the state and input variables are the respectively load current and stator voltage. The second is a simple model in which the state and input variables are respectively the flux linkage and stator voltage, which are derived using the equivalent inverse inductance function. These models are applied to simulate the transient performances considering the iron loss and cross-magnetic saturation. The experimental and simulated results with a flux-barrier SynRM validate the proposed method.