Numerical and Analytical Solution of Probabilistic Optimal Power Flow Problems Considering Renewable Energy Resources Uncertainty

With the Penetration of renewable energies into power system, the influence of uncertainties in solving various problems in the field of power system operation has increased. One of the most important concepts in this field is optimal power flow, which, with the presence of uncertainties, cannot be modeled by definite methods, and should be revised based on applying the probabilistic approaches. In this paper, numerical methods including the Monte Carlo Simulation method and analytical methods including point estimation methods, internal point method and unscented transformation method are used to solve the POPF in an IEEE-118 bus system. The obtained results indicate that the methods based on point estimation are able to find the optimal points in less computational time than other techniques. This is mainly due to the limited points, which these methods need as the starting points. From another perspective, the magnitude changes in the voltage profile of the generation units are also more stable in the internal point method. Furthermore, in terms of the convergence rate, the internal point method is much faster than the Monte Carlo Simulation method.