Modeling of a High Speed High Inertia Outrunner Reluctance Synchronous Machine Using Trivariate Polynomial Approximation of Flux Surfaces

Achieving a good performance of a field oriented encoderless control of a synchronous machine requires an accurate model of the electromechanical behavior of the machine. Modern reluctance synchronous machines show strongly self- and cross-saturation dependent nonlinearities of the flux linkages related to the d- and q-currents. Reluctance machine presented in this paper is used as a motor-generator unit in a flywheel energy storage system and is integrated in its rotor. Because of an outrunner design and a high inertia and rotational speed of the machine, a high centrifugal force acts on the rotor. This force causes the rotational speed dependent air gap variation between stator and rotor. This leads to an additional nonlinear effect on flux linkage surfaces. This paper presents a model of the reluctance synchronous machine with rotational speed dependent flux linkage and inductance surfaces. These surfaces are therefore trivariate functions and depend both on direct- and quadrature-axis currents and on a rotational speed. A simple trivariate polynomial approximation of the flux linkages and inductances is proposed, which can be efficiently implemented on a FPGA or DSP.