[Paper Review] Factoring the Cycle Aging Cost of Batteries Participating in Electricity Markets

Bolun Xu, Jinye Zhao+3 more|arXiv (Cornell University)|Jul 14, 2017

Advanced Battery Technologies Research21 references17 citations

TL;DR

This paper proposes a piecewise linear cost function to accurately model battery cycle aging in electricity markets, enabling precise integration into economic dispatch and market clearing. The method closely approximates real battery degradation using rainflow cycle counting and achieves exact cost matching with benchmark models, maximizing battery profitability in ISO New England markets.

ABSTRACT

When participating in electricity markets, owners of battery energy storage systems must bid in such a way that their revenues will at least cover their true cost of operation. Since cycle aging of battery cells represents a substantial part of this operating cost, the cost of battery degradation must be factored in these bids. However, existing models of battery degradation either do not fit market clearing software or do not reflect the actual battery aging mechanism. In this paper we model battery cycle aging using a piecewise linear cost function, an approach that provides a close approximation of the cycle aging mechanism of electrochemical batteries and can be incorporated easily into existing market dispatch programs. By defining the marginal aging cost of each battery cycle, we can assess the actual operating profitability of batteries. A case study demonstrates the effectiveness of the proposed model in maximizing the operating profit of a battery energy storage system taking part in the ISO New England energy and reserve markets.

Motivation & Objective

• Address the lack of accurate, market-compatible battery degradation cost modeling in existing economic dispatch frameworks.
• Enable battery energy storage (BES) owners to bid profitably in electricity markets by accounting for cycle aging as an operating cost.
• Develop a computationally efficient model that integrates seamlessly into existing market clearing software.
• Ensure the model reflects actual battery aging mechanisms, particularly cycle depth dependence, through rigorous approximation of rainflow counting.
• Demonstrate the model's accuracy and effectiveness using real ISO New England market data and ex-post validation.

Proposed method

• Propose a piecewise linear cost function with 10 segments to approximate the quadratic cycle aging cost of electrochemical batteries.
• Use a vector-based state representation where each segment tracks energy levels from shallow to deep cycle depths (e.g., 0–10%, 10–20%, etc.).
• Apply Theorem 1 to determine discharge dispatch order: deeper segments are discharged first, ensuring correct cycle counting.
• Calculate marginal aging cost per time step as the dot product of the cost vector and discharge power vector: $ C_t = \mathbf{c}^T \mathbf{p}^{\text{dis}}_t $.
• Validate the model using rainflow counting as a benchmark, proving equivalence in cycle counting and cost calculation.
• Incorporate the model into economic dispatch by treating marginal aging cost as a dynamic, state-dependent cost component.

Experimental results

Research questions

• RQ1 How can battery cycle aging costs be modeled in a way that is both accurate and compatible with existing electricity market dispatch software?
• RQ2 To what extent does a piecewise linear approximation of the quadratic aging cost function match the results of the standard rainflow counting method?
• RQ3 Can the proposed model enable battery owners to design bids that fully recover the cost of cycle degradation in real-world markets?
• RQ4 How does the number of linearization segments affect the accuracy of the aging cost approximation?
• RQ5 What is the actual impact of cycle aging on the profitability of battery energy storage systems in real-time and reserve markets?

Key findings

• The proposed piecewise linear model achieves exact cost equivalence with the benchmark rainflow-based model when the number of linearization segments is sufficient, with error approaching zero.
• The model successfully replicates the cycle counting and cost calculation of the rainflow method, as proven by Theorem 2, ensuring physical accuracy.
• In a case study using one year of ISO New England market data, the model enabled accurate profit maximization by properly accounting for cycle aging costs.
• The marginal aging cost is dynamically calculated per time step based on discharge from specific depth segments, enabling precise cost recovery in bidding.
• The model’s accuracy improves with more linearization segments, and with 10 segments (10% depth intervals), it matches the benchmark model exactly in the numerical example.
• The model demonstrates practical feasibility for integration into existing market clearing systems, supporting profitable battery participation in energy and reserve markets.