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Some uncertainties, such as the uncertain output power of a plug-in electric vehicle (PEV) due to its stochastic charging and discharging schedule, that of a wind generation unit due to the stochastic wind speed, and that of a solar generating source due to the stochastic illumination intensity, volatile fuel prices, and future uncertain load growth could lead to some risks in determining the optimal siting and sizing of distributed generators (DGs) in distribution system planning. Given this background, under the chance constrained programming (CCP) framework, a new method is presented to handle these uncertainties in the optimal siting and sizing of DGs. First, a mathematical model of CCP is developed with the minimization of the DGs' investment cost, operating cost, maintenance cost, network loss cost, as well as the capacity adequacy cost as the objective, security limitations as constraints, and the siting and sizing of DGs as optimization variables. Then, a Monte Carlo simulation-embedded genetic-algorithm-based approach is employed to solve the developed CCP model. Finally, the IEEE 37-node test feeder is used to verify the feasibility and effectiveness of the developed model and method, and the test results have demonstrated that the voltage profile and power-supply reliability for customers can be significantly improved and the network loss substantially reduced.
Liu et al. (Wed,) studied this question.