A semi-empirical model of the calendar ageing of lithium-ion batteries aimed at automotive and deep-space applications

Lithium-ion batteries are highly affected by calendar ageing effects, which can lead to capacity loss even when the battery is not used at all. The current literature proposes plenty of semi-empirical models to predict the calendar ageing of the lithium-ion batteries, which are mostly based on Arrhenius functions for temperature dependency, exponential models for state of charge dependency and power laws for time dependency. Those models are easy to calibrate, and they provide a sufficiently precise prediction of capacity loss over time. However, it might be difficult to find a physical meaning to the parameters determined in these models, due to their lumped nature and the optimization process used. Therefore, in this work a semi-empirical model able to predict the capacity degradation over time with physically meaningful parameters is proposed. The dependency on temperature is considered by a pre-exponential factor whereas the dependency on state of charge is considered by a power law coefficient. A two-step constrained optimization process is considered to calibrate the model parameters. The model allows to predict the capacity loss over a wide range of different temperature and state of charge conditions, and it is calibrated for 4 different cell chemistries: LMO-NMC, LFP, NCA, and NMC. It was found that the worst storing condition is given by the highest temperature and state of charge conditions. The capacity degradation is provided over a period of 50 years. Two end-of-life conditions were analyzed: a loss of capacity of 20 % as representative of an end-of-life condition for automotive applications, and a loss of capacity of 50 % as an end-of-life condition for deep-space applications. In both cases, it was observed that NMC provided the best performance (the slowest ageing over time) for storing temperatures below 15 degrees C and storing state of charge below 10 %, whereas for temperatures higher than 15 degrees C and state of charge higher than 10 %, the LFP chemistry resulted to be the most longevous.