Sensitivity Analysis in Power System Dynamic Stability Studies

In this paper, the second method of Liapunov is used to investigate the dynamic stability problem of power systems using the perturbed system dynamics in state variable form. Defining stability measure in terms of Liapunov functions and their time derivatives, the paper formulates a method for the calculation of the sensitivity of the dynamic stability measure to variations in various machine and control system parameters. The method provides a basis for optimal dynamic stability design of power systems, the criterion of optimality being that the sensitivity of the dynamic stability measure to parameter variations be zero. For simplicity, the case of a synchronous machine connected to an infinite bus is considered. The effect of various voltage regulator parameters on the sensitivity of the dynamic stability measure is investigated. A numerical example is used to demonstrate the superiority of the time response resulting from the choice of parameter settings corresponding to zero sensitivity of the dynamic stability measure. The method is readily generalized to the case of multi- machine power systems.