Extending an Empirical Degradation Model for Li-Ion Batteries into Second-Life Applications
Authors: Hua Jinsong , Vie Preben J. S. , Wind Julia 
Published: August 2024

Lithium-ion batteries have been used increasingly in recent years for a wide range of applications, e.g., electric vehicles and large-scale power grids. Lithium-ion batteries suffer from degradation caused by their operation and their exposure to environmental conditions and thus have a limited lifetime within their first application. These batteries might be available for re-use in a different application, commonly under more moderate usage conditions. The influence of such a change in operating conditions on battery degradation within a second life application is not very well understood. Here we present the extension of an empirical degradation model that formulates the degradation process as a function of battery operations for both, first- and second life applications.
Our extended semi-empirical model for battery degradation is based on work of Xu et al. [1] and combines the degradation mechanism due to the growth of the SEI layer and the degradation depth obtained in dedicated ageing tests. Within this work we focus on a commercial 64 Ah NMC-graphite pouch cell. The model parametrization is based on a large dataset containing both calendar and cycle life data of more than 100 cells, covering a large window of temperatures (5-45 °C), C-rates (0.2-1.5 C), SoC windows, and average SoC.
Figure 1(a) shows the variations of state of health (SoH) with the number of the full equivalent cycle (FEC) for four cells cycling at the same constant ageing conditions (0.75C, 25°C, and 0-100% SoC). Figure 1(b) shows the fitting results of the empirical degradation model using the data from the ageing tests. It is assumed that the SEI layer model parameters are constant for this specific cell. The degradation depth increases linearly with cycle number, where the degradation rate varies with the battery operation condition. The degradation of the battery cell depends not only on external stress factors such as temperature, SoC, DoD, C-rate, but also its previous ageing history. The formation of the SEI film contributes non-linearly to the battery degradation, while the contribution of the degradation rate of different stress factors can be accounted for linearly. The degradation rate depends on the ageing modes: calendar or cycle ageing. Calendar ageing reflects the inherent degradation over time and the rate is affected by temperature and SoC. The calendar degradation rate per time unit can be obtained as a function of temperature and SoC [2, 3]. The cycle SoC window can be interpreted using DoD and mean SoC. The cycle degradation rate per FEC can be estimated as a function of temperature, mean SoC, and DoD [3]. Data-driven models and empirical correlations are applied to obtain battery degradation rate functions. The total degradation depth can be estimated by summarizing the degradation caused by the calendar ageing and the degradation resulting from all cycles.
To verify the performance of the empirical degradation model, a dynamic ageing test was designed, including both calendar and cycle ageing. The historical data of SoC and temperature are shown in Figures 2 (a) and 2(b), respectively. Through analyzing the time series data of cell SoC, all cycle information can be obtained to calculate the cycle ageing. The calendar ageing was calculated based on time duration for each cycle, and the average temperature and SoC. Using the correlations for the degradation rates, the degradation depth during for each cycle can be evaluated. The accumulated degradation depth can be used to estimate the change of remaining capacity with time. Figure 2(c) shows the comparison of the prediction of SoH with the experimental data.
When moving into the 2nd life regime, degradation mechanisms and their interplay become more complex, leading to a larger statistical variation in ageing rates between individual cells (i.e., see time offset in Fig 2c). This can be accounted for by readjustment of the model’s initial 2nd life SoH to the last SoH from the first life application data, as well as including statistical variation into the model’s parameters.

References

[1] B. Xu, A. Oudalov, A. Ulbig, G. Andersson, D.S. Kirschen, Modelling of Lithium-Ion Battery Degradation for Cell Life Assessment, IEEE Transactions on Smart Grid 9 (2018) 1131-1140. https://doi.org/10.1109/TSG.2016.2578950
[2] J. Nájera, J.R. Arribas, R.M. de Castro, C.S. Núñez, Semi-empirical ageing model for LFP and NMC Li-ion battery chemistries, Journal of Energy Storage 72 (2023) 108016. https://doi.org/10.1016/j.est.2023.108016
[3] I. Horstkötter, B. Bäker, An application-oriented lithium-ion battery degradation modelling framework for ageing prediction, Journal of Energy Storage 60 (2023) 106640. https://doi.org/10.1016/j.est.2023.106640

Figure 1