Modelling power systems with stochastic processes

Abstract

Any physical system and, thus, also power systems, contains randomness and uncertainty. For example, load power consumption is not fully deterministic. Moreover, in recent years, the massive installation of non-despatchable technologies, e.g., wind parks, has increased the degree of randomness in power systems. This chapter summarizes the state of the art of the modelling of stochastic perturbations in power systems by means of continuous stochastic differential equations (SDEs). The chapter begins with a brief theoretical introduction to SDEs and provides two designing methods of SDEs to represent perturbations with given statistical properties. Perturbation models derived from the application of the presented methods are illustrated through numerical examples. The chapter also describes a general procedure to define stochastic dynamic models for power system components. Practical issues related to the numerical integration of the resulting power system model are discussed. Finally, the dynamic behaviour of power systems subjected to stochastic phenomena is illustrated through simulations of the IEEE 145-bus 50-machine system.