Skip to main content

Advertisement

Log in

Reduced order model-based observer design for online temperature distribution estimation in lithium-ion batteries

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Time/space separation-based modeling methods have been widely researched for estimating lithium-ion battery (LIB) thermal dynamics. However, these methods have been developed in an offline environment and may not perform well in real-time application since the battery systems in electric vehicles (EVs) are usually subject to external disturbances. Furthermore, the onboard measurements of temperature are often corrupted by significant error. To address these problems, we present a reduced model-based observer design for online temperature distribution estimation in LIBs. First, an extreme learning machine (ELM)-based offline spatiotemporal model is constructed to approximate the thermal dynamics of LIB. Second, an adaptive reduced order observer is designed based on the offline model developed in the previous step. The offline model is then updated with the estimation results of the observer. As the performance of the estimator is highly related to the placement of sensors, a genetic algorithm (GA)-based integrated optimization strategy is also developed to determine the optimal sensor location for online estimation. Finally, the whole temperature distribution is estimated in real time using the observer, the measured voltage, current and the limited available temperature data. Two experiments on different batteries with different input currents verify the effectiveness of this developed model.

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

Similar content being viewed by others

Data Availability

All data generated during the study are available from the corresponding author by request.

References

  1. Khaligh, A., Li, Z.: Battery, ultracapacitor, fuel cell, and hybrid energy storage systems for electric, hybrid electric, fuel cell, and plug-in hybrid electric vehicles: State of the art. IEEE Trans. Veh. Technol. 59(6), 2806–2814 (2010). https://doi.org/10.1109/TVT.2010.2047877

    Article  Google Scholar 

  2. Etacheri, V., Marom, R., Elazari, R., Salitra, G., Aurbach, D.: Challenges in the development of advanced Li-ion batteries: a review. Energy Environ. Sci. 4(9), 3243–3262 (2011). https://doi.org/10.1039/C1EE01598B

    Article  Google Scholar 

  3. Chen, Y., Chen, Y., Long, J.Y., Shi, D., Chen, X., Hou, M., Gao, J., Liu, H., He, Y., Fan, B., Wong, C.P., Zhao, N.: Achieving a sub-10 nm nanopore array in silicon by metal-assisted chemical etching and machine learning. Int. J. Extreme Manuf. 3(3), 35104 (2021). https://doi.org/10.1088/2631-7990/abff6a

    Article  Google Scholar 

  4. Shi, D., Chen, Y., Li, Z., Dong, S., Li, L., Hou, M., Liu, H., Zhao, S., Chen, X., Wong, C.P., Zhao, N.: Anisotropic charge transport enabling high-throughput and high-aspect-ratio wet etching of silicon carbide. Small Methods 6(8), 2200329 (2022). https://doi.org/10.1002/smtd.202200329

    Article  Google Scholar 

  5. Xiao, Y.: Model-based virtual thermal sensors for lithium-ion battery in EV applications. IEEE Trans. Ind. Electron. 62(5), 3112–3122 (2014). https://doi.org/10.1039/C1EE01598B

    Article  Google Scholar 

  6. Gholizadeh, M., Salmasi, F.R.: Estimation of state of charge, unknown nonlinearities, and state of health of a lithium-ion battery based on a comprehensive unobservable model. IEEE Trans. Ind. Electron. 61(3), 1335–1344 (2013). https://doi.org/10.1109/TIE.2013.2259779

    Article  Google Scholar 

  7. Abada, S., Marlair, G., Lecocq, A., Petit, M., Sauvant-Moynot, V., Huet, F.: Safety focused modeling of lithium-ion batteries: a review. J. Power Sources 306, 178–192 (2016). https://doi.org/10.1016/j.jpowsour.2015.11.100

    Article  Google Scholar 

  8. Jaguemont, J., Boulon, L., Dubé, Y.: A comprehensive review of lithium-ion batteries used in hybrid and electric vehicles at cold temperatures. Appl. Energy 164, 99–114 (2016). https://doi.org/10.1016/j.apenergy.2015.11.034

    Article  Google Scholar 

  9. Lu, X., Yin, F., Liu, C., Huang, M.: Online spatiotemporal extreme learning machine for complex time-varying distributed parameter systems. IEEE Trans. Ind. Inf. 13(4), 1753–1762 (2017). https://doi.org/10.1109/TII.2017.2666841

    Article  Google Scholar 

  10. Lu, X., Zou, W., Huang, M.: A novel spatiotemporal LS-SVM method for complex distributed parameter systems with applications to curing thermal process. IEEE Trans. Ind. Inf. 12(3), 1156–1165 (2016). https://doi.org/10.1109/TII.2016.2557805

    Article  Google Scholar 

  11. Zhou. Y., Deng. H., Li. H.-X., Xie. S. L.: Dual separation-based spatio-temporal modeling methodology for battery thermal process under non-homogeneous boundary conditions. IEEE Trans. Transp. Electrif. https://doi.org/10.1109/TTE.2021.3061426 (2021). https://ieeexplore.ieee.org/document/9360789

  12. Feng, Y., Li, H.-X.: Detection and spatial identification of fault for parabolic distributed parameter systems. IEEE Trans. Ind. Electron. 66(9), 7300–7309 (2019)

    Article  Google Scholar 

  13. Li, H.X., Qi, C.: Modeling of distributed parameter systems for applications—a synthesized review from time-space separation. J. Process Control 20(8), 891–901 (2010). https://doi.org/10.1016/j.jprocont.2010.06.016

    Article  Google Scholar 

  14. Wang, J.W., Wu, H.N.: Exponential pointwise stabilization of semilinear parabolic distributed parameter systems via the Takagi-Sugeno fuzzy PDE model. IEEE Trans. Fuzzy Syst. 26(1), 155–173 (2016). https://doi.org/10.1109/TFUZZ.2016.2646745

    Article  Google Scholar 

  15. Forgez, C., Do, D.V., Friedrich, G., Morcrette, M., Delacourt, C.: Thermal modeling of a cylindrical LiFePO4/graphite lithium-ion battery. J. Power Sources 195(9), 2961–2968 (2010). https://doi.org/10.1016/j.jpowsour.2009.10.105

    Article  Google Scholar 

  16. Hariharan, K.S.: A coupled nonlinear equivalent circuit–Thermal model for lithium ion cells. J. Power Sources 227, 171–176 (2013). https://doi.org/10.1016/j.jpowsour.2012.11.044

    Article  Google Scholar 

  17. Jiang, J., Ruan, H., Sun, B., Zhang, W., Gao, W., Zhang, L.: A reduced low-temperature electro-thermal coupled model for lithium-ion batteries. Appl. Energy 177, 804–816 (2016). https://doi.org/10.1016/j.apenergy.2016.05.153

    Article  Google Scholar 

  18. Lin, X., Perez, H.E., Mohan, S., Siegel, J.B., Stefanopoulou, A.G., Ding, Y., Castanier, M.P.: A lumped-parameter electro-thermal model for cylindrical batteries. J. Power Sources 257, 1–11 (2014). https://doi.org/10.1016/j.jpowsour.2014.01.097

    Article  Google Scholar 

  19. Fang, W., Kwon, O.J., Wang, C.Y.: Electrochemical–thermal modeling of automotive Li-ion batteries and experimental validation using a three-electrode cell. Int. J. Energy Res. 34(2), 107–115 (2010). https://doi.org/10.1002/er.1652

    Article  Google Scholar 

  20. Zhang, X., Lu, J., Yuan, S., Yang, J., Zhou, X.: A novel method for identification of lithium-ion battery equivalent circuit model parameters considering electrochemical properties. J. Power Sources 345, 21–29 (2017). https://doi.org/10.1016/j.jpowsour.2017.01.126

    Article  Google Scholar 

  21. Anwar, S., Zou, C., Manzie, C.: Distributed thermal-electrochemical modeling of a lithium-ion battery to study the effect of high charging rates. IFAC Proc. Volumes. 47(3), 6258–6263 (2014). https://doi.org/10.3182/20140824-6-ZA-1003.00919

    Article  Google Scholar 

  22. Yazdanpour, M., Taheri, P., Mansouri, A., Bahrami, M.: A distributed analytical electro-thermal model for pouch-type lithium-ion batteries. J. Electrochem. Soc. 161(14), A1953 (2014)

    Article  Google Scholar 

  23. Kim, U.S., Shin, C.B., Kim, C.S.: Modeling for the scale-up of a lithium-ion polymer battery. J. Power Sources 189(1), 841–846 (2009). https://doi.org/10.1016/j.jpowsour.2008.10.019

    Article  Google Scholar 

  24. Northrop, P.W., Pathak, M., Rife, D., De, S., Santhanagopalan, S., Subramanian, V.R.: Efficient simulation and model reformulation of two-dimensional electrochemical thermal behavior of lithium-ion batteries. J. Electrochem. Soc. 162(6), A940 (2015)

    Article  Google Scholar 

  25. Xu, K., Fan, B., Yang, H., Hu, L., Shen, W.: Locally weighted principal component analysis-based multimode modeling for complex distributed parameter systems. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2021.3061741

    Article  Google Scholar 

  26. Gambhire, P., Ganesan, N., Basu, S., Hariharan, K.S., Kolake, S.M., Song, T., Doo, S.: A reduced order electrochemical thermal model for lithium ion cells. J. Power Sources 290, 87–101 (2015). https://doi.org/10.1016/j.jpowsour.2015.04.179

    Article  Google Scholar 

  27. Cai, L., White, R.E.: An efficient electrochemical–thermal model for a lithium-ion cell by using the proper orthogonal decomposition method. J. Electrochem. Soc. 157(11), A1188 (2010)

    Article  Google Scholar 

  28. Muratori, M., Canova, M., Guezennec, Y.: A spatially-reduced dynamic model for the thermal characterisation of Li-ion battery cells. Int. J. Veh. Des. 58(2–4), 134–158 (2012). https://doi.org/10.1504/IJVD.2012.047402

    Article  Google Scholar 

  29. Liu, Z., Li, H.X.: Extreme learning machine based spatiotemporal modeling of lithium-ion battery thermal dynamics. J. Power Sources 277, 228–238 (2015). https://doi.org/10.1016/j.jpowsour.2014.12.013

    Article  Google Scholar 

  30. Xu, K.K., Li, H.X., Liu, Z.: Isomap based spatiotemporal modeling for lithium-ion battery thermal process. IEEE Trans. Industr. Inf. 99, 1–1 (2017). https://doi.org/10.1109/TII.2017.2743260

    Article  Google Scholar 

  31. Xu, K.K., Li, H.X., Yang, H.D.: Local-properties-embedding-based nonlinear spatiotemporal modeling for lithium-ion battery thermal process. IEEE Trans. Ind. Electron. (2018). https://doi.org/10.1109/TIE.2018.2818645

    Article  Google Scholar 

  32. Hu, X., Xiong, R., Egardt, B.: Model-based dynamic power assessment of lithium-ion batteries considering different operating conditions. IEEE Trans. Ind. Inf. 10(3), 1948–1959 (2013). https://doi.org/10.1109/TII.2013.2284713

    Article  Google Scholar 

  33. Sun, J., Wei, G., Pei, L., Lu, R., Zhu, C.: Online internal temperature estimation for lithium-ion batteries based on kalman filter. Energies 8(5), 4400–4415 (2015). https://doi.org/10.3390/en8054400

    Article  Google Scholar 

  34. Dai, H., Zhu, L., Zhu, J., Wei, X., Sun, Z.: Adaptive kalman filtering based internal temperature estimation with an equivalent electrical network thermal model for hard-cased batteries. J. Power Sources 293(oct20), 351–365 (2015). https://doi.org/10.1016/j.jpowsour.2015.05.087

    Article  Google Scholar 

  35. Deshpande, V.M., Bhattacharya, R., Subbarao, K.: Sensor placement with optimal precision for temperature estimation of battery systems. IEEE Control Syst. Lett. (2021). https://doi.org/10.1109/LCSYS.2021.3089564

    Article  Google Scholar 

  36. Hoo, K.A., Zheng, D.: Low-order control-relevant models for a class of distributed parameter systems. Chem. Eng. Sci. 56(23), 6683–6710 (2001). https://doi.org/10.1016/S0009-2509(01)00357-8

    Article  Google Scholar 

  37. Huang, G.B., Zhu, Q.Y., Siew, C.K.: Extreme learning machine: theory and applications. Neurocomputing 70(1–3), 489–501 (2006). https://doi.org/10.1016/j.neucom.2005.12.126

    Article  Google Scholar 

  38. Lu, X.J., Li, H.X., Yuan, X.: PSO-based intelligent integration of design and control for one kind of curing process. J. Process Control 20(10), 1116–1125 (2010). https://doi.org/10.1016/j.jprocont.2010.06.019

    Article  Google Scholar 

  39. Hu, Y., Yurkovich, S., Guezennec, Y., Yurkovich, B.J.: A technique for dynamic battery model identification in automotive applications using linear parameter varying structures. Control. Eng. Pract. 17, 1190–1201 (2009). https://doi.org/10.1016/j.conengprac.2009.05.002

    Article  Google Scholar 

Download references

Funding

This project was supported by the National Natural Science Foundation of China (Grant Nos. 51905109, 71701136), and by the Natural Science Foundation of Guangdong Province (Grant Nos. 2021A1515011971, 2022A1515011009).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kangkang Xu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, B., Zhuang, Y., Liu, Z. et al. Reduced order model-based observer design for online temperature distribution estimation in lithium-ion batteries. Nonlinear Dyn 111, 3327–3344 (2023). https://doi.org/10.1007/s11071-022-08025-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-08025-x

Keywords

Navigation