Analytical Model of Rainflow-Based Cyclic Aging for Economic Battery Dispatch Optimization

Integrating more accurate models for battery aging into dispatch optimization can help enhance the economic performance of battery systems. To this end, this paper proposes an analytical Rainflow-based cyclic aging model that accounts for the cycle depth and average state of charge (SoC) stress factors, particularly crucial for batteries that experience irregular cycling patterns under complex market conditions. As a function of the battery SoC time series, the aging model is compatible with a mixed integer linear programming (MILP) formulation, enabling the dispatch problem to be solvable by commercial solvers. The flexibility of the model enables decision-makers to fine-tune its specific expressions, creating variants that balance model accuracy with solution efficiency. A lightweight dispatch optimization framework and a convex variant of the aging model are developed for batteries participating in a pay-for-performance frequency regulation market to reduce problem-solving time significantly. Validated on two batteries with different aging characteristics, the proposed model shows high prediction accuracy, with an average error of less than 5%. Case studies employing full-year historical market data from ISO New England (ISO-NE) and PJM validate the effectiveness and reliability of the proposed methods in enhancing battery economics for price arbitrage and frequency regulation tasks.