Optimal charge scheduling of electric vehicles in solar energy integrated power systems considering the uncertainties

Nowadays, vehicle to grid (V2G) capability of the electric vehicle (EV) is used in the smart distribution network (SDN). The main reasons for using the EVs, are improving air quality by reducing greenhouse gas emissions, peak demand shaving and applying ancillary service, and etc. So, in this chapter, a non-linear bi-level model for optimal operation of the SDN is proposed where one or more solar based-electric vehicle parking lots (PLs) with private owners exist. The SDN operator (SDNO) and the PL owners are the decision-makers of the upper-level and lower-level of this model, respectively. The objective functions at two levels are the SDNO’s profit maximization and the PL owners’ cost minimization. For transforming this model into the single-level model that is named mathematical program with equilibrium constraints (MPEC), firstly, Karush–Kuhn–Tucker (KKT) conditions are used. Furthermore, due to the complementary constraints and non-linear term in the upper-level objective function, this model is linearized by the dual theory and Fortuny-Amat and McCarl linearization method. In the following, it is assumed that the SDNO is the owner of the solar-based EV PLs. In this case, the proposed model is a single-level model. The uncertainty of the EVs and the solar system, as well as two programs, are considered for the EVs, i.e., controlled charging (CC) and charging/discharging schedule (CDS). Because of the uncertainties, a risk-based model is defined by introducing a Conditional Value-at-Risk (CVaR) index. Finally, the bi-level model and the single-level model are tested on an IEEE 33-bus distribution system in three modes; i.e., without the EVs and the solar system, with the EVs by controlled charging and with/ without the solar system, and with the EVs by charging/discharging schedule and with/without the solar system. The main results are reported and discussed.