Optimal V2G Scheduling of an EV with Calendar and Cycle Aging of Battery: An MILP Approach

Since battery cost represents a substantial part of an electric vehicle’s (EV) total cost, the degradation of EV battery and how it is affected by being used in vehicle-to-grid (V2G) applications is a concern and the main argument against implementing V2G. Battery degradation is too complex in terms of non-linearity for practical optimization of V2G scheduling. This paper develops a mixed-integer linear programming (MILP) model to optimize the V2G scheduling of an EV, considering a detailed battery degradation model for calendar aging and cycle aging. In the developed model, calendar aging is affected by the state of charge, battery age, and temperature. The cycle aging is affected by temperature, C-rate, and the energy throughput of the battery. A case study is performed to minimize the annual operational cost of an EV with V2G capability for two different years of electricity cost and ambient temperature data. The results of the developed model are compared with four different cases: immediate charging, smart charging algorithms without V2G, V2G without degradation cost, and V2G with degradation cost as the objective function. It is shown that the developed V2G model achieves a slightly increased cycle aging due to usage in V2G. However, it reduces the overall scheduling cost of the EV by 48-88% compared to the immediate charging and by 10-73% compared to the smart charging. Furthermore, neglecting battery degradation in optimal V2G could lead to a 28% increase in scheduling cost.