  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.
