Estimation of State-of-Charge and Capacity of Used Lithium-Ion Cells



Published Mar 26, 2021
Nenad G. Nenadic Howard E. Bussey Paul A. Ardis Michael G. Thurston


We describe an approach to estimate state-of-charge and faded capacity of cobalt-based lithium-ion cell based on timedomain analysis of a short-term transient. This approach requires a relatively short-duration test and is suitable for repurposing cells for less demanding applications. The successful estimation requires previous characterization of the cells for the given family because lithium ion chemistries differ significantly. Two algorithms were considered for estimation of unknown state-of-charge and capacity: Bayesian inference and boosted regression trees. The achieved accuracy was 95 % of capacity estimations; estimations were within 2 % of the nominal cell capacity from the true value.

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Amine, K., Chen, C., Liu, J., Hammond, M., Jansen, A., Dees, D., . . . Henriksen, G. (2001). Factors responsible for impedance rise in high power lithium ion batteries. Journal of power sources, 97, 684–687.
Bishop, C. M. (1995). Neural Networks for Pattern Recognition. In (p. 137-140). Oxford: Oxford University Press.
Bishop, C. M. (1st ed. 2006. Corr. 2nd printing). Pattern recognition and machine learning. New York: Springer.
Breiman, L. (1996). Bagging predictors. Machine learning, 24(2), 123–140.
Breiman, L. (2001a). Random forests. Machine learning, 45(1), 5–32.
Breiman, L. (2001b). Statistical modeling: The two cultures. Statistical Science, 16(3), 199–231.
Breiman, L., Friedman, J., Stone, C. J., & Olshen, R. A. (1984). Classification and regression trees. CRC press.
Broussely, M., Biensan, P., Bonhomme, F., Blanchard, P., Herreyre, S., Nechev, K., & Staniewicz, R. (2005). Main aging mechanisms in Li ion batteries. Journal of power sources, 146(1), 90–96.
Chen, M., & Rincon-Mora, G. (2006). Accurate electrical battery model capable of predicting runtime and IV performance. Energy Conversion, IEEE Transactions on, 21(2), 504–511.
Dees, D., Gunen, E., Abraham, D., Jansen, A., & Prakash, J. (2005). Alternating current impedance electrochemical modeling of lithium-ion positive electrodes. Journal of the Electrochemical Society, 152, A1409.
Duda, R., Hart, P., & Stork, D. (2000). Pattern classification. 2nd edn Wiley. In (p. 287-288).
Elith, J., Leathwick, J. R., & Hastie, T. (2008). A working guide to boosted regression trees. Journal of Animal Ecology, 77(4).
Freund, Y., & Schapire, R. E. (1995). A desicion-theoretic generalization of on-line learning and an application to boosting. In Computational learning theory (pp. 23–37).
Friedman, J., Hastie, T., Tibshirani, R., et al. (2000). Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors). The annals of statistics, 28(2), 337–407.
Goebel, K., Saha, B., Saxena, A., Celaya, J. R., & Christophersen, J. P. (2008). Prognostics in battery health management. IEEE instrumentation & measurement magazine, 11(4), 33.
Hawkins, J. (1994). Some field experience with battery impedance measurement as a useful maintenance tool. In Telecommunications Energy Conference, 1994. INTELEC’ 94., 16th International (pp. 263–269).
Hunter, J. (2007). Matplotlib: A 2D graphics environment. Computing in Science & Engineering, 90–95.
Jones, E., Oliphant, T., Peterson, P., et al. (2001–). SciPy: Open source scientific tools for Python. Retrieved from
Lasia, A. (1999). Electrochemical impedance spectroscopy and its applications. Modern aspects of electrochemistry, 32, 143–248.
Liu, D., Pang, J., Zhou, J., Peng, Y., & Pecht, M. (2013). Prognostics for state of health estimation of lithium-ion batteries based on combination Gaussian process functional regression. Microelectronics Reliability, 53(6), 832–839.
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., . . . Duchesnay, E. (2011). Scikit-learn: Machine Learning in Python . Journal of Machine Learning Research, 12, 2825–2830.
Plett, G. L. (2004). Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 3. State and parameter estimation. Journal of power sources, 134(2), 277–292.
Prettenhofer, P., & Louppe, G. (n.d.). Gradient Boosted Regression Trees in Scikit-Learn. In PyData, London 2014.
Saha, B., & Goebel, K. (2008). Uncertainty management for diagnostics and prognostics of batteries using Bayesian techniques. In Aerospace Conference, 2008 IEEE (pp. 1–8).
Saha, B., & Goebel, K. (2009). Modeling Li-ion battery capacity depletion in a particle filtering framework. In Proceedings of the annual conference of the prognostics and health management society (pp. 1–10).
Saha, B., Goebel, K., Poll, S., & Christophersen, J. (2009). Prognostics methods for battery health monitoring using a Bayesian framework. Instrumentation and Measurement, IEEE Transactions on, 58(2), 291–296.
Sankararaman, S., Daigle, M., Saxena, A., & Goebel, K. (2013). Analytical algorithms to quantify the uncertainty in remaining useful life prediction. In Aerospace Conference, 2013 IEEE (pp. 1–11).
Schaul, T., Bayer, J., Wierstra, D., Sun, Y., Felder, M., Sehnke, F., . . . Schmidhuber, J. (2010). PyBrain. Journal of Machine Learning Research, 11, 743–746.
Spotnitz, R. (2003). Simulation of capacity fade in lithiumion batteries. Journal of Power Sources, 113(1), 72–80.
Tr¨oltzsch, U., Kanoun, O., & Tr¨ankler, H. (2006). Characterizing aging effects of lithium ion batteries by impedance spectroscopy. Electrochimica acta, 51(8-9), 1664–1672.
Vetter, J., Novak, P., Wagner, M., Veit, C., M¨oller, K.-C., Besenhard, J., . . . Hammouche, A. (2005). Ageing mechanisms in lithium-ion batteries. Journal of power sources, 147(1), 269–281.
Wolpert, D. H. (1992). Stacked generalization. Neural networks, 5(2), 241–259.
Zhang, J., & Lee, J. (2011). A review on prognostics and health monitoring of Li-ion battery. Journal of Power Sources, 196(15), 6007–6014.
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