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.

I. Introduction

The lithium-ion battery (LIB) is playing a growing role in paving the way for reliable and low-carbon grids due to flexible deployment, rapid response, and energy-time-shifting capabilities. Through market participation, the battery is monetized and earns income for the owners, but its economics highly depends on dispatch strategies. Specifically, revenue-enhancing operations (e.g., deep cycles) risk severe aging costs since LIBs remain costly and degrade as the cycle progresses. On the other hand, price competition in liberalized markets has decreased the revenue potential. For instance, the reward price in Germany's frequency containment reserve market dropped about 50% in 2020 compared to the figure in 2015 [1]. Research into aging-aware battery operation is therefore essential against this backdrop.