Probabilistic-Optimal Power Flow for Radial Distribution Systems with Wind Generators

Radial Distribution Systems (RDS) connect a large number of renewable generators that are inherently uncertain. From being unidirectional power flow systems, RDS now enable bi-directional power flow. Depending upon availability of power from renewables, they receive or feed power to the connected transmission system. RDS optimal power flow (OPF), is an important tool in this new era for utilities, to minimize losses and operate efficiently. With large scale integration of wind generators to distribution systems, they must be appropriately represented using probabilistic models capturing their intermittent nature in these OPF algorithms. This paper proposes characterizing the solution of a Probabilistic Optimal Power Flow (P-OPF) for RDS using the Cumulant Method. This method makes it possible to linearly relate the probabilistic parameters of renewables at the optimal solution point to the state of the RDS. To assess the accuracy of the proposed P-OPF Cumulant Method, wind generators and system probabilistic data are incorporated in a 33-bus and 129-bus test system. The results are compared with those of Monte Carlo simulations (MCS). It is shown that the proposed method possesses high degree of accuracy, is significantly faster and more practical than an MCS approach.