Multi-objective optimization for microgrid sizing, electric vehicle scheduling and vehicle-to-grid integration

This paper presents a multi-objective mixed integer linear programming (MILP) framework for the sizing of a microgrid that integrates distributed energy resource (DER), such as thermal generator (TG), photovoltaic system (PV) systems, and battery energy storage system (BESS), alongside electric vehicle (EV) scheduling and the procurement of electric vehicle charging station (EVCS). The proposed formulation incorporates uncertainty in generation and demand profiles, as well as contingencies that model off-grid scenarios, by means of a scenario-based stochastic programming approach. By employing a linearization approach that eliminates the need for additional binary variables for charging and discharging decisions, the optimization simultaneously minimizes total cost, greenhouse gas (GHG) emissions, and EV idle time. The model also determines an optimal vehicle-to-grid (V2G) price through a Nash equilibrium, which balances the interests of both the system operator and EV owners. Numerical results indicate that allowing moderate EV idle time can reduce the required number of EVCS, thus lowering capital investment without substantially affecting emissions. Furthermore, scenarios with stringent GHG constraints lead to a higher share of PV and BESS, increasing overall cost but reducing emissions. A case study demonstrates that the optimized microgrid can effectively handle off-grid conditions, with BESS and EV contributions maintaining supply reliability.