Describing function analysis of the electric nonlinear model of a SRM autonomous AC generator

This paper focuses on the Switched Reluctance Motor (SRM) used as self-excited generator. The phase inductance resonates autonomously with an external capacitor parallel connected producing an AC voltage almost sinusoidal. Although the voltage quality is not good enough to be directly connected the network utility it is able to be used as a battery charger in isolated locations. As the machine shows a nonlinear relationship among current, flux and angular position, the system equations are nonlinear therefore, analytical solutions describing its behaviour can not be found. However, it is shown that the system follows a known nonlinear second order equation describing mechanical systems. This experience is transferred to gain insight in this application. It is shown that the steady state can be identified as a limit cycle whose main variables are derived. The analysis procedure followed is known as the describing function method. It is an extended version of the frequency response method, and can be used to approximately analyze and predict nonlinear behaviour. The main use of describing function method is for the prediction of limit cycles in nonlinear systems. A simulated example is developed to illustrate the method and to derive the relationship among the electrical variables, useful for design purposes.