An efficient Differential Evolution algorithm for stochastic OPF based active–reactive power dispatch problem considering renewable generators

Optimal active–reactive power dispatch problems (OARPD) are non-convex and highly nonlinear complex optimization problems. Typically, such problems are expensive in terms of computational time and cost due to the load variations over the scheduling period. The conventional constraint-based solvers that are generally used to tackle such problems require a considerable high budget and may not provide high quality solutions. In the last decade, complexity of OARPD has further increased due to the incorporation of renewable energy sources such as: wind, solar and small-hydro generators. More specifically, the incorporation of renewable sources introduces uncertainty in generation on top of the load variations in conventional OARPD, making the problem more complicated. Recently, Differential Evolution (DE) is viewed as an excellent algorithm to solve OARPD problems, due to its effectiveness to optimize the objective function which is subject to many operational constraints. A new efficient Differential Evolution algorithm, denoted as DEa-AR, is propounded to solve the contemporary stochastic optimal power flow OARPD problems considering the renewable generators. DEa-AR uses arithmetic recombination crossover and adapts the scaling factor based on Laplace distribution. In addition, an efficient archive strategy that acts as a corresponding image of the population and stores the inferior individuals for later use, is also incorporated. The target behind using this strategy is to consider the information of inferior individuals as a direction toward finding new good solutions. The IEEE 57-bus system is used to evaluate the OARPD problems with different stochastic scenarios based on different probability distributions employed to model parameters of renewable energy sources. The performance of the proposed work is compared with other state-of-the-art algorithms. Simulation results indicate that the proposed technique can solve the OARPD problems with renewable sources effectively and can provide high quality solutions. The proposed algorithm is ranked the first with a Friedman rank equals to 1.8333 with a clear statistical significant difference compared with the most recent studies on the used problems.