A Basis Function Approach to the Nonlinear Average Value Modeling of Switched Reluctance Machines

Abstract

This work sets forth a nonlinear average value model (NLAM) of a switched reluctance machine. NLAMs are characterized by state variables that are constant in the steady-state facilitating high-speed simulation and control analysis and design. The main difficulties in deriving such a model for the switched reluctance machine arise from nonlinearities due to magnetic saturation, absence of mutual inductance, and a nonsinusoidal self-inductance profile which prevents the use of a rotational transformation in arriving at a rotor position-invariant machine description. Herein, these difficulties are overcome by introducing a variable representation that approximates machine variables by the inner product of a vector of basis functions and a time-varying coefficient vector. A set of nonlinear differential equations is derived which governs the behavior of the coefficient vectors. These equations are rotor position invariant and feature state variables which are constant in the steady-state. The resulting model is experimentally validated.