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

## TL;DR

This paper introduces a convex degradation model for batteries based on rainflow cycle analysis, enabling its integration into optimization problems to improve planning and operation.

## Contribution

It proves the convexity of rainflow cycle-based costs and develops a subgradient algorithm for optimization, facilitating better battery management strategies.

## Key findings

- Convexity of rainflow cycle-based degradation cost established
- Model effectively maximizes battery profits in PJM regulation market
- Extends battery lifetime through optimized operation

## Abstract

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.