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Stochastic optimization for reactive power planning problems

In this paper, a stochastic optimal power flow is developed to solve the reactive power planning (RPP) problem while dealing with uncertainties such as intermittent power generation and loads. The RPP problem is formulated as a mixed integer non-linear problem (MINLP) which is a hard problem to solve. Therefore, Benders decomposition is used in order to get feasible solutions. The uncertainty sources are characterized by probability density functions from which samples are generated. If rare events are considered, conventional Monte Carlo method gives rise to a too large number of samples. The main objective of this paper is to identify the most critical samples leading to possible voltage limits violations due to a lack of reactive power supply and find the required optimal reactive power compensation. An iterative procedure is developed and aims to concentrate the samples in the zones having the highest influence on the RPP. First, both MINLP and Benders formulations are compared on a 9-node system to show the validity of the Benders decomposition. Then the iterative sampling process is assessed on the same test case and allows finding the optimal robust reactive power compensation with a reduced number of samples compared to direct Monte Carlo Simulation (MCS).