Development of stability charts for double salience reluctance machine modeled using hill’s equation

Abstract

The paper presents a novel algorithm for the development of stability charts. The second-order differential homogeneous equation describing a double salient reluctance machine with a capacitance connected to its stator winding is transformed into hill’s equation. The circuit components are the stator coil time-varying inductance of a double salient reluctance machine, capacitance and resistance. All these are modeled by hill’s equation. The double salient reluctance machine acts as an energy conversion system. The maximum and minimum inductance of the energy conversion system is measured in laboratory by inductance, capacitance, and resistance (LCR) meter. These values help to determine the inductance modulation index. The inductance modulation indetx, the characteristic constant and the characteristic parameter obtained from modeling equations are used in the MATLAB/Simulink model. The MATLAB/Simulink simulations generate stable and unstable oscillations to form stability charts. The proposed stability charts are in good agreement with the Ince-Stritt stability chart, which is widely applied in physics, mechanics and in electrical engineering, especially where the state of stability of a system or an electric oscillatory circuit is to be determined.