Stochastic Second-Order Conic Programming for Optimal Sizing of Distributed Generator Units and Electric Vehicle Charging Stations

The increased penetration of electric vehicles (EVs) and distributed generator (DG) units has led to uncertainty in distribution systems. These uncertainties—which have not been adequately considered in the literature—can entail risks in the optimal sizing of EV charging stations (EVCSs) and DG units in active distribution network planning. This paper proposes a method for obtaining the optimal sizing of DG units and EVCSs (considering uncertainty), to achieve exact power system analysis and ensure EV driver satisfaction. To model uncertainties in optimal sizing planning, this study first generates scenarios for each system asset using a probability distribution that considers the asset characteristics. In this step, the wind-turbine (WT), PV, and EVCS are modeled applying the Weibull, exponential, and kernel density estimation (KDE), and scenarios for each asset are gen-erated using random sampling. Then, the k-means clustering is carried out for scenario reduction and the representative scenario abstract. The probability of occurrence for each representative scenario is assigned depending on the number of observations within each cluster. The representative scenarios for each asset are integrated into the scenario for all assets through the joint probability. The integrated scenarios are applied in the optimization problem for optimal sizing of the system asset framework. The optimal sizing of the system assets problem is proposed (to minimize the line loss and voltage deviation) and formulated via stochastic second-order conic programming, to re-flect the uncertainty under an AC power flow; this is a convex problem that can be solved in poly-nomial time. The proposed method is tested on a modified IEEE 15 bus system, and the simulation is performed with various objective functions. The simulation results demonstrate the effectiveness of the proposed method.