# A Convex Cycle-based Degradation Model for Battery Energy Storage Planning and Operation

arXiv: https://arxiv.org/abs/1703.07968 · HTML: https://mlsanity.com/paper/1703.07968/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2017.

## Built on by (most cited first, 2 of 2)

- [Microgrid Optimal Energy Scheduling Considering Neural Network based Battery Degradation](https://mlsanity.com/paper/2202.12416/) (2022)
- [Degradation-Aware Frequency Regulation of a Heterogeneous Battery Fleet via Reinforcement Learning](https://mlsanity.com/paper/2601.22865/) (2026)

## Abstract (arXiv)

A vital aspect in energy storage planning and operation is to accurately model its operational cost, which mainly comes from the battery cell degradation. Battery degradation can be viewed as a complex material fatigue process that based on stress cycles. Rainflow algorithm is a popular way for cycle identification in material fatigue process, and has been extensively used in battery degradation assessment. However, the rainflow algorithm does not have a closed form, which makes the major difficulty to include it in optimization. In this paper, we prove the rainflow cycle-based cost is convex. Convexity enables the proposed degradation model to be incorporated in different battery optimization problems and guarantees the solution quality. We provide a subgradient algorithm to solve the problem. A case study on PJM regulation market demonstrates the effectiveness of the proposed degradation model in maximizing the battery operating profits as well as extending its lifetime.