confidence-interval based multi-objective constrained probabilistic optimal capacitor placement in distribution systems

this paper presents a probabilistic confidence-interval based method for optimal placement of shunt capacitors in distribution networks by considering probabilistic characteristics of loads. the main objective function are reducing loss and improving the voltage profile. backward forward sweep method has been employed to obtain the power flow results in distribution system. in addition, integer harmony search algorithm has been used to solve the optimization problem. the probabilistic aspects of problem have been solved using point estimation (pe) method. the novelty of this paper is introducing a confidence interval index using gram-charlier expansion. this index shows the risk of system to violate its security constraints when loads are considered as stochastic random variables. using this index, planners can find the optimal sitting and sizing of capacitors in distribution systems based on their desired level of risk. verification of the proposed method has been tested on 33-bus radial distribution system. results demonstrate the effectiveness and merits of the proposed method.