A generalized probabilistic multi-objective method for optimal allocation of soft open point (SOP) in distribution networks

Soft open point (SOP) as a novel power electronics-based device has been introduced to control active power flow, compensate reactive power, and regulate voltage for flexible operation of distribution networks. The increasing penetration of renewable energy resources (RESs) such as wind turbine (WT) and photovoltaic (PV) units with uncertain outputs in distribution networks increases the importance of optimal and robust allocation of SOP against multiple uncertainties to improve the performance of these networks. In this paper, a probabilistic multi-objective framework is proposed for optimal allocation of SOP in RESs included distribution networks. A novel SOP modeling in the forward-backward load flow method without any simplification is introduced. In addition, this study investigates the impact of various correlation levels between uncertain input variables in the problem. The multi-objective particle swarm optimization (MOPSO) method is used to extract Pareto-based solutions set considering the expected value of active power losses, feeder load balancing index (LBI), and investment cost of SOP as objective functions. Also, the Latin hypercube sampling (LHS) and Cholesky decomposition methods are implemented to uncertainties modeling and handling the correlations, respectively. The results of the proposed study framework are argued on the IEEE 33-node and the IEEE 118-node distribution networks.