Modelling uncertainties in electrical power systems with stochastic differential equations

The presence of uncertainties in electrical power systems is a critical issue due to the effects that those perturbations can induce in the quality, safety and economy of the electrical supply. An accurate representation of these phenomena is needed in order to understand and predict possible damage scenarios, which allows the improvement of system operation. In this context, the method of stochastic differential equations provides a dynamic representation of power systems under continuous time uncertainties. Thus, this paper presents the application of stochastic differential equation in power system analysis and explain a systematic methodology to get a representative model of a perturbation, including estimation methods and a validation procedure. Three real examples are given, two of them related to non-conventional energy resources and the third related to energy consumption.