Mathematical modeling for economic evaluation of electric vehicle to smart grid interaction

The objective of this work is to develop a mathematical model for the integration of electric vehicle (EVs) to the grid. Integrating the EV with the grid would help in simultaneous charging of numerous EVs and provide peak hour energy to the grid (from EV). This bi-directional exchange of energy between the grid and EV results in a complex financial calculations. So a simple model has been proposed. The energy provided by the EV to the grid depends on the battery capacity. Battery capacity is affected by capacity losses (CL). The model includes the possible cases of CL, such as CL due to battery usage (discharge during vehicle transportation) and CL due to the grid interaction. The main cause for a higher per kilometer (Km) transportation cost in EV, when compared to conventional vehicle, is the high cost of the battery and its maintenance. In this model, the economic analysis has been done in such a way that the battery related liabilities do not become a financial burden to EV owners. The above scenario has been evaluated for different combinations of charge rate (C _r) and discharge rate (D_r) ranging from 1C_r - 1D_r to 3C_r - 3D_r. Finally the optimal cost of electricity is determined such that the grid, EV owners, and consumers (EV users) are benefitted.