Power flow optimization in the presence of microgrids

Power flow optimization problems consist in generating electricity from di↵erent types of power plants in order to attend the demand of the electrical network. Many di↵erent types of such problems exist, depending on the type of electrical network (transmission, distribution, ...) and the types of power plants considered (thermic, nuclear, solar, wind, hydro, ...). Even when the context is well specified (type of network and power plants), the true resulting mathematical optimization problems are often intractable due the presence of discrete decisions variables and non-convexities in the functions describing the technical constraints. As a result, one should also decide of the level of simplification used to model the electrical power flows (AC model, DC model, or bus model) and the technical constraints faced by the power plants. We can mention, among other, the following three types of power flow optimization problems that have heavily been studied in the literature, each of them resulting in a large scale multi-stage stochastic mixed-integer non-linear program: