Skip to main content
Log in

Robust state of charge and state of health estimation for batteries using a novel multi model approach

  • Research Article
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

Estimation of state-of-charge and state-of-health for batteries is one of the most important feature for modern battery management system (BMS). Robust or adaptive methods are the most investigated because a more intelligent BMS could lead to sensible cost reduction of the entire battery system. We propose a new robust method, called ERMES (extendible range multi-model estimator), for determining an estimated state-of-charge (SoC), an estimated state-of-health (SoH) and a prediction of uncertainty of the estimates (state-of-uncertainty—SoU), thanks to which it is possible to monitor the validity of the estimates and adjust it, extending the robustness against a wider range of uncertainty, if necessary. Specifically, a finite number of models in state-space form are considered starting from a modified Thevenin battery model. Each model is characterized by a hypothesis of SoH value. An iterated extended Kalman filter (EKF) is then applied to each model in parallel, estimating for each one the SoC state variable. Residual errors are then considered to fuse both the estimated SoC and SoH from the bank of EKF, yielding the overall SoC and SoH estimates, respectively. In addition, a figure of uncertainty of such estimates is also provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

References

  1. Chaturvedi, N. A., Klein, R., Christensen, J., Ahmed, J., & Kojic, A. (2010). Modeling, estimation, and control challenges for lithium-ion batteries. In Proceedings of the 2010 American Control Conference, pp. 1997–2002. Baltimore, MD, USA.

  2. Plett, G. L. (2004). Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 1. Background. Journal of Power Sources, 134(2), 252–261.

    Article  Google Scholar 

  3. Millner, A. (2010). Modeling Lithium Ion battery degradation in electric vehicles. In IEEE Conference on Innovative Technologies for an Efficient and Reliable Electricity Supply, pp. 349–356. Waltham, MA, USA.

  4. Ng, K., Huang, Y., Moo, C., & Hsieh, Y. (2009). An enhanced Coulomb counting method for estimating state-of-charge and state-of-health of lead-acid batteries. In INTELEC 2009 – 31st International Telecommunications Energy Conference, pp. 1–5. Incheon, South Korea.

  5. Murnane, M., & Ghazel, A. (2017). A closer look at state of charge (SoC) and state of health (SoH) estimation techniques for batteries. Technical article. https://www.mouser.mx/pdfDocs/SOC.pdf.

  6. Hannan, M. A., Lipu, M. S. H., Hussain, A., & Mohamed, A. (2017). A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: Challenges and recommendations. Renewable and Sustainable Energy Reviews, 78, 834–854.

    Article  Google Scholar 

  7. Berecibar, M., Gandiaga, I., Villarreal, I., Omar, N., Van Mierlo, J., & Van den Bossche, P. (2016). Critical review of state of health estimation methods of Li-ion batteries for real applications. Renewable and Sustainable Energy Reviews, 56, 572–587.

    Article  Google Scholar 

  8. Lavigne, L., Sabatier, J., Mbala Francisco, J., Guillemard, F., & Noury, A. (2016). Lithium-ion open circuit voltage (OCV) curve modelling and its ageing adjustment. Journal of Power Sources, 324, 694–703.

    Article  Google Scholar 

  9. Coleman, M., Lee, C. K., Zhu, C., & Hurley, W. (2007). State-of-charge determination from EMF voltage estimation: Using impedance, terminal voltage, and current for lead-acid and lithium-ion batteries. IEEE Transactions on Industrial Electronics, 54, 2550–2557.

  10. Marelli, S., & Corno, M. (2018). A mass-preserving sliding mode observer for Li-ion cells electrochemical model. In European Control Conference (ECC), pp. 2659–2664. Limassol, Cyprus.

  11. Marelli, S., & Corno, M. (2021). Model-based estimation of Lithium concentrations and temperature in batteries using soft-constrained dual unscented kalman filtering. IEEE Transactions on Control Systems Technology, 29(2), 926–933.

    Article  Google Scholar 

  12. Chaoui, H., & Ibe-Ekeocha, C. C. (2017). State of charge and state of health estimation for lithium batteries using recurrent neural networks. IEEE Transactions on Vehicular Technology, 66(10), 8773–8783.

    Article  Google Scholar 

  13. Bhangu, B. S., Bentley, P., Stone, D. A., & Bingham, C. M. (2005). Nonlinear observers for predicting state-of-charge and state-of-health of lead-acid batteries for hybrid-electric vehicles. IEEE Transactions on Vehicular Technology, 54(3), 783–794.

    Article  Google Scholar 

  14. Andre, D., Appel, C., SoCzka-Guth, T., & Uwe Sauer, D. (2013). Advanced mathematical methods of SoC and SoH estimation for lithium-ion batteries. Journal of Power Sources, 224(1), 20–27.

    Article  Google Scholar 

  15. 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.

    Article  Google Scholar 

  16. Wassiliadis, N., Adermann, J., Frericks, A., Pak, M., Reiterd, C., Lohmann, B., & Lienkamp, M. (2018). Revisiting the dual extended Kalman filter for battery state-of-charge and state-of-health estimation: A use-case life cycle analysis. Journal of Energy Storage, 19, 73–87.

    Article  Google Scholar 

  17. Zhao, X., Wang, Y., Sahinoglu, Z., Wada, T., Hara, S., & Callafon, R. A. (2014). Improved adaptive state-of-charge estimation for batteries using a multi-model approach. Journal of Power Sources, 254, 258–267.

    Article  Google Scholar 

  18. Maybeck, P. S., & Stevens, R. D. (1991). Reconfigurable flight control via multiple model adaptive control methods. IEEE Transactions on Aerospace and Electronic Systems, 27(3), 470–480.

    Article  Google Scholar 

  19. Hanlon, P. D., & Maybeck, P. S. (2000). Multiple-model adaptive estimation using a residual correlation Kalman filter bank. IEEE Transactions on Aerospace and Electronic Systems, 36(2), 393–406.

    Article  Google Scholar 

  20. Rodrigues, M., Theilliol, D., Adam-Medina, M., & Sauter, D. (2008). A fault detection and isolation scheme for industrial systems based on multiple operating models. Control Engineering Practice, 16(2), 225–239.

    Article  Google Scholar 

  21. Mu, H., Xiong, R., & Sun, F. (2016). A novel multi-model probability based battery state-of-charge fusion estimation approach. Energy Procedia, 88, 840–846.

    Article  Google Scholar 

  22. Wang, T., Dong, J., Xie, T., Diallo, D., & Benbouzid, M. (2019). A self-learning fault diagnosis strategy based on 2 multi-model fusion. Information, 10(3), 1–13.

    Google Scholar 

  23. Zhou, D., Zhang, K., Ravey, A., Gao, F., & Miraoui, A. (2016). Online estimation of lithium polymer batteries state-of-charge using particle filter-based data fusion with multimodels approach. IEEE Transactions on Industry Applications, 52(3), 2582–2595.

    Article  Google Scholar 

  24. Li, Y., Wang, C., & Gong, J. (2017). A multi-model probability SoC fusion estimation approach using an improved adaptive unscented Kalman filter technique. Energy, 141, 1402–1415.

    Article  Google Scholar 

  25. Alessandri, A., & Coletta, P. (2001). Switching observers for continuous-time and discrete-time linear systems. In Proceedings of the American Control Conference, pp. 2516–2521. Arlington, VA, USA.

  26. Liu, Y. (1997). Switching observer design for uncertain nonlinear systems. IEEE Transactions on Automatic Control, 42(12), 1699–1703.

    Article  MathSciNet  Google Scholar 

  27. Paesa, D., Llorente, S., Sagues, C., & Aldana, O. (2009). Adaptive observers applied to pan temperature control of induction hobs. IEEE Transactions on Industry Applications, 45(3), 1116–1125.

    Article  Google Scholar 

  28. Lamloumi, L., & Chaari, A. (2012). Switching control design based on multi-observer for nonlinear systems. In: Proceedings of the Mediterranean Electrotechnical Conference—MELECON, Yasmine Hammamet, Tunisia. https://doi.org/10.1109/MELCON.2012.6196525.

  29. Orjuela, R., Marx, B., Ragot, J., & Maquin, D. (2008). Proportional-integral observer design for nonlinear uncertain systems modelled by a multiple model approach. In The 47th IEEE Conference on Decision and Control, pp. 3577–3582. Cancun, Mexico.

  30. Nagy, A. M., Mourot, G., Marx, B., Schutz, G., & Ragot, J. (2009). State estimation of the three-tank system using a multiple model. In Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with the 28th Chinese Control Conference, pp. 7795–7800. Shanghai, China.

  31. Ishii, H., & Francis, B. A. (2002). Stabilizing a linear system by switching control with dwell time. IEEE Transactions on Automatic Control, 47(12), 1962–1973.

    Article  MathSciNet  Google Scholar 

  32. Battistelli, G., Hespanha, J. P., Mosca, E., & Tesi, P. (2013). Model-free adaptive switching control of time-varying plants. IEEE Transactions on Automatic Control, 58(5), 1208–1220.

    Article  MathSciNet  Google Scholar 

  33. Mousavi, G., Mohammad, S., & Nikdel, M. (2014). Various battery models for various simulation studies and applications. Renewable and Sustainable Energy Reviews, 32, 477–485.

    Article  Google Scholar 

  34. He, H., Xiong, R., Zhang, X., Sun, F., & Fan, J. (2011). State-of-charge estimation of the lithium-ion battery using an adaptive extended Kalman filter based on an improved Thevenin model. IEEE Transactions on Vehicular Technology, 60(4), 1461–1469.

    Article  Google Scholar 

  35. Salameh, Z. M., Casacca, M. A., & Lynch, W. A. (1992). A mathematical model for lead-acid batteries. IEEE Transactions on Energy Conversion, 7(1), 93–98.

    Article  Google Scholar 

  36. Rahimi-Eichi, H., Baronti, F., & Chow, M. (2012). Modeling and online parameter identification of Li-Polymer battery cells for SoC estimation. In IEEE International Symposium on Industrial Electronics, pp. 1336–1341. Hangzhou, China.

  37. Plett, G. L. (2004). Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification. Journal of Power Sources, 134(2), 262–276.

    Article  Google Scholar 

  38. Lee, P., & Kim, J. (2019). Impact analysis of deterioration and SoH estimation based on multiple regression analysis. In IEEE Transportation Electrification Conference and Expo, Seogwipo, South Korea. https://doi.org/10.1109/ITEC-AP.2019.8903656.

  39. Haeffner, J., & Wetzel, G. (2008). Sensor array for detecting the state of a battery. Patent USA No.: US20090153143A1.

  40. Haifeng, D., Xuezhe, W., & Zechang, S. (2009). A new SoH prediction concept for the power lithium-ion battery used on HEVs. In IEEE Vehicle Power and Propulsion Conference, pp. 1649–1653. Dearborn, MI, USA.

  41. Liu, Z., & He, H. (2017). Sensor fault detection and isolation for a lithium-ion battery pack in electric vehicles using adaptive extended Kalman filter. Applied Energy, 185, 2033–2044.

    Article  Google Scholar 

  42. Song, Z., Wu, X., Li, X., Sun, J., Hofmann, H. F., & Hou, J. (2019). Current profile optimization for combined state of charge and state of health estimation of lithium ion battery based on Cramer-Rao bound analysis. IEEE Transactions on Power Electronics, 34(7), 7067–7078.

    Article  Google Scholar 

Download references

Acknowledgements

Prof. Eros Pasero, DET department, director of Neuronic Laboratory of polytechnic School of engineering of Turin, for huge support about testing procedures and HW design. Prof. Alessandro Rizzo, DAUIN department of Polytechnic School of Engineering of Turin, for methodological support and advices profused in development of this work. Innovation Cluster Mechatronics of Regione Piemonte, MESAP and Regione Piemonte for supporting this work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Giovanni Guida.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guida, G., Faverato, D., Colabella, M. et al. Robust state of charge and state of health estimation for batteries using a novel multi model approach. Control Theory Technol. 20, 418–438 (2022). https://doi.org/10.1007/s11768-022-00103-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-022-00103-0

Keywords

Navigation