The increasing penetration of solar distributed generations (SDGs) and wind distributed generations (WDGs) together with plug-in electric vehicles (PEVs) will lead to a promising amount of reduction in greenhouse gas emissions. Nevertheless, they bring about adversities such as uncertainty in production-load sides, augmented power loss, and voltage instability in the power system, which should be carefully addressed to increase the reliability. In this concern, this paper proposes a multi-objective optimization methodology for sizing and siting of SDGs, WDGs, and capacitor banks (CBs) in the power system considering uncertainties stemmed from PEVs load demand, solar irradiance, wind speed, and the conventional load. The understudy objectives are the voltage stability index, green-house gas emissions, and the total cost. An unconventional point estimate method (PEM) is used to handle the related uncertainties, and chance-constrained programming method is deployed to deal with smooth constraints. The corresponding probability distribution functions of output variables are estimated by the maximum entropy method. Furthermore, robustness analysis is made by Monte Carlo simulation (MCS). The proposed methodology is applied to a typical radial distribution network. The results show that the presence of PEV’s significantly increases the load demand, which results in voltage collapse in the distribution system without the presence of distributed generations. However, the proposed probabilistic method ensures the safe operation of the distribution system with the optimal allocation of renewable distributed generations and CBs. Moreover, the results of deterministic and probabilistic cases are compared under different penetration levels of PEVs. The best tradeoff solution of the Pareto front is selected by the fuzzy satisfying method.

Introduction

The leading motivations in integrating distributed generations (DGs) in power systems are loss reduction, increasing reliability and voltage profile improvement [1]. However, the well-known defects of conventional DGs and the evident improvement in the competitiveness of renewable energy sources (RES) in terms of capital cost are encouraging investors to replace conventional DGs with solar distributed generations (SDGs) and wind distributed generations (WDGs) [2,3]. Optimal integration of these renewable DGs in power systems is crucial for their safe and economical operation [4]. Natural intermittencies of solar irradiation, wind speed, and plug-in electric vehicles (PEVs) load demand as a new aspect of power system should also be assimilated into sizing and siting problems, which is a mixed-integer nonlinear problem subjected to multiple objectives and constraints and many local optimums [5]. Additionally, the problem should handle these uncertainties with a reasonable tradeoff between computational burden and accuracy. Moreover, it might be in favor of the system operator to ignore the small probabilities of violation for soft constraints such as voltage and power limits [6]. According to the literature, DG planning can be generally categorized into single objective and multi-objective formulation [7]. They can also be categorized into subcategories such as deterministic, probabilistic, or in terms of the algorithm they apply, such as metaheuristic, analytical, etc. [5]. In the field of multi-objective DG allocation and sizing problems, some significant contributions have been made by [8–۱۳].