Liapunov Stability Analysis of Reluctance Motors

The application of a relatively simple Liapunov theorem to the stability analysis of a reluctance synchronous motor is described. The analysis proceeds as follows: 1) The differential equations representing the reluctance motor are written with the machine regarded as a group of coupled windings including time-varying self and mutual inductances. In developing these equations, it is assumed that balanced 3-phase sinusoidal voltages are applied to the stator windings and the effects of saturation, iron loss, and space harmonics in machine flux are neglected. 2) The well-known d-q transformation is used to transform the motor equations to simpler relations involving d-q variables in place of the phase voltages, currents, and flux linkages. 3) The resulting set of equations is replaced by an equivalent first-order vector system of differential equations. 4) One of the simpler theorems of Liapunov is used to predict the conditions for which asymptotic stability will occur.