A fast-specialized point estimate method for the probabilistic optimal power flow in distribution systems with renewable distributed generation

The increasing presence of renewable distributed generation (DG) units such as photovoltaic and wind power generation is a major challenge for the suitable operation of the electrical distribution systems (EDSs). Uncertainties of renewable DG units and loads, related to the stochastic nature of solar irradiation, wind speed, and consumer behavior, require efficient tools that help the distribution system operator to properly define a control plan of the EDS. Within this framework, the probabilistic optimal power flow (POPF) provides statistical information(e.g. voltage profile, power flows, and power losses) according to the variation of the stochastic variables (e.g. power demand and injection of generation units). Many available POPF methods have been designed for transmission systems and/or are based on Monte Carlo simulation (MCS), which requires a high computational effort. On the other hand, other approaches adopt analytical methods, which are not applied considering the characteristics of distribution systems. This paper proposes a fast-specialized point estimate method for the POPF in EDSs with the presence of renewable DG units, based on a linearization of the Branch Flow equations and Hong's point estimate method. Due to its convex nature, the advantage of the proposed method is to use wellestablished linear programming commercial solvers to solve the problem. Numerical results using the IEEE 69-bus and a real EDS demonstrate the efficiency in terms of computational burden and accuracy of the proposed method compared to MCS and Cumulant approaches.