Multi-objective optimal planning of wind distributed generation considering uncertainty and different penetration level of plug-in electric vehicles

•Computationally light and accurate point estimate method is used.•Chance-constrained programming method is assimilated using the maximum entropy method.•The necessity of using a different kind of point estimate method is proved.•Obtained results are evaluated with Monte-Carlo simulation Method. Despite the many challenges related to the simultaneous surge in wind-based distributed generation (WDGs) and plug-in electric vehicles (PEVs) in modern power systems, they will be a great help in reducing greenhouse gas emissions. Nonetheless, the associated problems such as uncertainty in production-load sides, voltage instability, and power loss augmentation should be reanalyzed. These predicaments can be dealt to some extent with proper siting and sizing of WDGs together with capacitor banks (CBs) as a conventional voltage regulator and reactive power compensator. However, the sizing and siting problem consists of various objectives, such as voltage stability improvement, emission reduction, and cost reduction. It is a great challenge to optimize these contradictory objectives altogether. Hence, to overcome all these struggles, this paper proposes a tri-objective optimization formulation for optimal planning of WDGs and CBs in the power system, considering uncertainties derived from PEVs’ load demand, wind speed, and conventional load. The objectives to be optimized are, namely, voltage stability index, total cost, and greenhouse gas emissions. Moreover, this study assimilates an unaccustomed type of point estimate method (PEM) into strength Pareto multi-objective differential evolution algorithm, which is not only computationally light but also reasonably accurate. Moreover, chance-constrained programming is integrated into the PEM using a maximum entropy method to deal with smooth constraints. The accuracy of the proposed method is evaluated by the Monte-Carlo simulation. Eventually, the proposed algorithm is compared with other standard multi-objective metaheuristic optimization algorithms.