On the Application of the Lyapunov Method to Synchronous Machine Stability†

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Abstract
The Lyapunov stability method is applied to two problems in the dynamic behaviour of round-rotor synchronous machines. In one case analytical results of a sufficient nature are obtained from an approximate mathematical model which explain the dependence of the self-oscillation of a machine on the stator impedance and the rotor excitation, and good agreement is found with experimental results. The other case is the ‘two-machine’ problem of two synchronous machines connected by a transmission line subject to a fault. Using the complete set of Park's equations an analytical expression is obtained for the transient stability surface. In general this is of a fairly weak sufficient nature but in a restricted region of the state-Space it gives a close agreement with the computed region of stability. The dynamic equations of the machines involve trigonometrieal functions of the state variables, and in this study the variable gradient method of Schultz and Gibson has been found useful for generating Lyapunov functions for this typo of equation.

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