To address the degradation of rechargeable batteries, this paper presents a two-phase gamma process model with a fixed change-point for modeling the voltage-discharge curves of battery cycle aging under a constant current. The model can be applied to estimate the state of charge (SOC) and the remaining useful discharge time (RUT) in a cycle with consideration of the effect of cycle aging, and can also be applied to estimate the state of life (SOL) and the remaining useful life (RUL) across cycles. The applications of the proposed model are demonstrated using the experimental cycle aging data of a lithium iron phosphate battery. A comparison shows that the proposed model generates a more accurate prediction than the conventional two-term exponential model with capacity data under a particle filter framework, and this reveals the superiority of modeling with voltage over modeling with capacity. The analytical expression of mean useful discharge time in a cycle (or mean time to failure) is developed with approximation by a Taylor expansion and the Birnbaum-Saunders distribution, and the result is shown to be in good agreement with the true mean of a gamma process.
Keywords: battery cycle aging; degradation modeling; gamma process; remaining useful life prediction; state of charge; state of life.