Nonlinear theory of the switched reluctance motor for rapid computer-aided design

The nonlinear magnetisation characteristics of the switched reluctance motor are modelled analytically by piecewise first- or second-order functions of flux linkage against rotor position, with current as an undetermined parameter. This model is more efficient than previous models based on flux linkage against current (with rotor position as a parameter). It also avoids the concept of inductance, which is, perhaps, unnecessary and inappropriate in a machine with such pronounced magnetic nonlinearities. The model is suitable, and has been widely use, for CAD and performance analysis, particularly at the stage of ‘sizing’, or initial estimation, where accuracy can be traded for speed of computation. The model includes all the significant electromagnetic and dynamic characteristics of the SR motor. Its accuracy can be enhanced by means of correction factors derived from only two or three points on magnetisation curves that have been accurately measured or calculated by finite elements, permitting economy in the use of data that is expensive to generate. Because the magnetisation curves do not need to be precalculated, stored or curvefitted, the algorithms are extremely fast. The model is computationally linked with a very accurate companion based on cubic-spline models of externally generated magnetisation curves. A piecewise analytical formula for instantaneous torque is also included, permitting the rapid (though approximate) calculation of mathematically smooth torque waveforms. Because the magnetisation curves do not need to be precalculated, stored or curve-fitted, the algorithms are extremely fast. The paper also presents a new method for calculating the unaligned magnetisation curve, based on dual-energy principles. Results are compared with test data for a range of motors.