A conditional value at risk based stochastic allocation of SOP in distribution networks

Soft open points (SOPs) have been noticed to enhance the operation efficiency of distribution networks due to their capability of exchanging power between feeders as well as reactive power compensation. The uncertainty of distributed renewable energy sources (DRESs) and load demands make its optimal allocation and active power flow settings difficult. Uncertainties should be modeled through appropriate techniques to give more reliable schemes for SOPs allocation and regulation. However, in the probabilistic environment, decreasing the risk of violations from objectives and constraints is also important to guarantee confident solutions. This paper finds the optimal location of an SOP and its power flow setpoints, considering the uncertainty of DRESs and load demands. The mentioned uncertainties are handled by the efficient K-medoids data clustering technique. In addition to considering the expected value of losses and voltage deviation as objective functions, the conditional value at risk (CVaR) of voltage deviation is considered, too. This ensures that in the final solution, the probability of voltage deviation in most worst scenarios will not be considerable. The proposed optimization model is implemented in a multi-objective optimization frame and solved by the multi-objective particle swarm optimization (MOPSO) algorithm and tested on the modified IEEE 33-bus test distribution system and the effect of considering the CVaR index on results is comprehensively discussed.