Solving the Optimal Control Strategy Problem for Electric Vehicles in V2G Using Quadratic Programming Algorithms

Vehicle-to-Grid (V2G) technology provides flexible energy storage and load regulation capabilities for power systems, but efficiently coordinating the charging/discharging behaviors of large-scale electric vehicles remains a critical challenge. Quadratic Programming (QP), as a major branch of convex optimization, is particularly suitable for solving such problems due to its computational efficiency and guaranteed global optimal solutions.

The core modeling approach transforms objectives like charging cost minimization, battery degradation reduction, and grid load balancing into quadratic objective functions, while converting constraints such as battery State-of-Charge (SOC) limits and charging power boundaries into linear inequalities. For instance, the objective function can be designed to minimize the weighted sum of grid peak-valley differences and user charging costs, with constraints ensuring batteries reach preset energy levels before disconnection.

Two key implementation considerations require attention: first, approximating nonlinear battery degradation models into quadratic terms through Taylor expansion; second, employing sparse matrix storage for Jacobian matrices to enhance computational speed during large-scale vehicle scheduling. In practice, this can be combined with rolling horizon optimization using forecast data to dynamically adjust control strategies. Code implementation typically involves constructing the Hessian matrix for quadratic objectives and using solvers like MATLAB's quadprog or Python's CVXOPT with proper constraint handling.

This method balances computational complexity with solution accuracy, making it especially suitable for minute-level scheduling scenarios. Future enhancements could integrate machine learning for user behavior prediction to further improve strategy adaptability. Algorithm implementation would benefit from parallel computing techniques for real-time optimization of thousands of vehicles simultaneously.