An iterative MILP-based model for optimal V2G scheduling considering battery degradation and thermal dynamics

This paper presents an optimal charge and discharge scheduling (OCDS) framework for an electric vehicle (EV) with vehicle-to-grid (V2G) capability. The objective is to minimize total costs during the charging period by balancing electricity costs, battery degradation costs, and V2G revenues. The core of the approach is a mixed-integer linear programming (MILP) model that determines optimal hourly power exchange between the EV and the grid. A semi-empirical, nonlinear cycle aging model is adopted to quantify the EV's Lithium-ion battery degradation as a function of temperature, C-rate, and energy throughput. This model is linearized using piecewise-linear approximation, enabling its integration into the MILP structure. To capture the critical effect of temperature on battery aging, an electro-thermal battery model is developed based on physical and circuit principles. It dynamically estimates battery temperature during operation, enhancing degradation prediction accuracy. Additionally, a novel metric called “Aging Price” quantifies battery degradation costs. Due to the interdependency between battery temperature, Aging Price, and the charging/discharging pattern (CDP), an iterative algorithm is also proposed to refine the optimization outputs. Finally, the proposed model is implemented in MATLAB and solved using MOSEK. Different case studies confirm the effectiveness of the developed framework.