Universal Simulation Model of Battery Degradation with Optimization of Parameters by Genetic Algorithm

Modeling of batteries is necessary to control their operating mode and diagnose their condition. It is important to model the life cycle, i. e. degradation of basic parameters over a long service life. This is due to the fact that the cost of buffering electricity by batteries is associated with their cycling resource, which can be increased by optimizing the mode of operation of the drive in the energy system. The existing models of battery degradation are characterized by specificity, limited work on standardized charge-discharge cycles, and mathematical cumbersomeness. The article proposes a universal approach devoid of the above disadvantages. The concept of continuous battery wear during the service life is used. A simple empirical model is presented that does not consider in detail the characteristics of the state of batteries during a separate charge-discharge cycle, and does not include voltaic variables. The model considers the intensity of the current wear of the battery as a function of the state of its charge, temperature, the current of the external circuit and the current of self-discharge, the full charge that has flowed through the battery since the beginning of its operation. In this case, the amount of wear (degradation) is determined by the integral of the function of the intensity of current wear over the battery life. To optimize the parameters of the model, a random search method is used in combination with a genetic selection algorithm. The corresponding model of degradation of parameters for the Delta GEL-12-55 lead-acid battery has been constructed, in which the data on degradation of capacity given in the technical description from the manufacturer are used. The efficiency of the parameter optimization algorithm and the adequacy of the resulting model are shown. The model developed by the authors can be used for technical and economic calculations of generator – storage –consumer systems, hybrid power storage systems, and compact representation of large volumes of experimental data on the degradation of specific batteries.

1. The World Market of Energy Storage Devices. Available at: https://nangs.org/news/renewables/eksperty-mirovoy-rynok-nakopiteley-energii-do-2030-goda-budet-rasti-na-23-v-god (accessed 20 May 2022) (in Russian).

2. Manwell J. F., McGowan J. G. (1993) Lead Acid Battery Storage Model for Hybrid Energy Systems. Solar Energy, 50 (5), 399–405. https://doi.org/10.1016/0038-092X(93)90060-2.

3. Borisevich A. V. (2014) Modeling of Lithium-Ion Batteries for Battery Management Systems: the Survey of Current State. Sovremennaya Tekhnika i Tekhnologii = Modern Technics and technologies, (5). Available at: https://technology.snauka.ru/2014/05/3542 (accessed 13 September 2022) (in Russian).

4. Ceraolo M., Lutzemberger G., Huria T. (2011) Experimentally Determined Models for High-Power Lithium Batteries. SAE International. https://doi.org/10.4271/2011-01-1365.

5. Huria T., Ceraolo M., Gazzarri J., Jackey R. (2013) Simplified Extended Kalman Filter Observer for SOC Estimation of Commercial Power-Oriented LFP Lithium Battery Cells.SAE 2013 World Congress & Exhibition. https://doi.org/10.4271/2013-01-1544.

6. Barsali T., Ceraolo M. (2002) Dynamic Models of Lead Acid Batteries: Implementation Issues. IEEE Transactions on Energy Conversion, 17 (1), 16–23. https://doi.org/10.1109/60.986432.

7. Bindner H., Cronin T., Lundsager P., Manwell J. F., Abdulwahid U., Baring-Gould I. (2005). Lifetime Modelling of Lead Acid Batteries. Denmark. Forskningscenter Risoe. Risoe-R No 1515 (EN).

8. Mkahl R., Nait Sidi Moh A. (2013) Modeling Charging Stations Batteries for Electric Vehicles. Journal of Aisan Electric Vehicles, 11 (2), 1667–1675. https://doi.org/10.4130/jaev.11.1667.

9. Dobrego K. V., Bladyko V. V. (2021) Modeling of Batteries and their Assemblies Taking into Account the Degradation of Parameters. Enеrgеtika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 64 (1), 27–39. https://doi.org/10.21122/10297448-2021-64-1-27-39 (in Russian).

10. Dobrego K. V., Bladyko Y. V. (2021) Modeling Battery Connections in the Electronic Lab. Enеrgеtika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 64 (5), 381–392. https://doi.org/10.21122/1029-7448-2021-64-5-381-392 (in Russian).

11. Klein R., Chaturvedi N. A., Christensen J., Ahmed J., Findeisen R., Kojic A. (2010) State Estimation of a Reduced Electrochemical Model of a Lithium-Ion Battery. Proceedings of the 2010 American Control Conference, 6618–6623. https://doi.org/10.1109/ACC.2010.5531378.

12. Chen M., Rincon-Mora G. A. (2006) Accurate Electrical Battery Model Capable of Predicting Runtime and IV Performance. IEEE Transactions on Energy Conversion, 21 (2), 504–511. https://doi.org/10.1109/TEC.2006.874229.

13. Nonlinear State Estimation of a Degrading Battery System. Available at: https://www.math works.com/help/control/ug/nonlinear-state-estimation-of-a-degrading-battery-system.html (accessed 10 March 2022).

14. Huria T., Ceraolo M., Gazzarri J., Jackey R. (2012) High Fidelity Electrical Model with Thermal Dependence for Characterization and Simulation of High Power Lithium Battery Cells. 2012 IEEE International Electric Vehicle Conference. 4–8 March 2012, Greenville, 1–8. https://doi.org/10.1109/IEVC.2012.6183271.

15. Cordoba-Arenas A., Onori S., Guezennec Y., Rizzoni G. (2015) Capacity and Power Fade Cycle-Life Model for Plug-in Hybrid Electric Vehicle Lithium-Ion Battery Cells Containing Blended Spinel and Layered-Oxide Positive Electrodes. Journal of Power Sources, 278, 473–483. https://doi.org/10.1016/j.jpowsour.2014.12.047.

16. Li L., Saldivar A. A., Bai Y., Li Y. (2019) Battery Remaining Useful Life Prediction with Inheritance Particle Filtering. Energies, 12 (14), 2784. https://doi.org/10.3390/en12142784.

17. Unagar A., Tian Y., Chao M. A., Fink O. (2021) Learning to Calibrate Battery Models in Real-Time with Deep Reinforcement Learning. Energies, 14 (5), 1361. https://doi.org/10.3390/en14051361.

18. Simulink. Available at: https://www.mathworks.com/products/simulink.html (accessed 10 June 2022).

19. Wan E. A., Van Der Merwe R. (2000) The Unscented Kalman Filter for Nonlinear Estimation. Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No 00EX373). 4 October 2000, Lake Louise, 153–158. https://doi.org/10.1109/ASSPCC.2000.882463.

20. Lithium-Ion Battery Aging Model. Available at: https://www.mathworks.com/help/physmod/sps/ug/12-8-v-40-ah-lithium-ion-lifepo4-battery-aging-model-1000-h-simulation.html (accessed 10 June 2022).

21. Xu B., Oudalov A., Ublig A., Anderrson G., Kirschen D. S. (2016) Modeling of Lithium-Ion Battery Degradation for Cell Life Assessment. IEEE Transactions on Smart Grid, 9 (2), 1131–1140. https://doi.org/10.1109/TSG.2016.2578950.

22. Thingvad M., Calearo L., Thingvad A., Viskinde R., Marinell M. (2020) Characterization of NMC Lithium-Ion Battery Degradation for Improved Online State Estimation. Proceedings of 55th International Universities Power Engineering Conference. 1–4 September 2020, Turin, 1–6. https://doi.org/10.1109/UPEC49904.2020.9209879.

23. Guo J., Li Y., Pedersen K., Stroe D.-I. (2021) Lithium-Ion Battery Operation, Degradation, and Aging Mechanism in Electric Vehicles: An Overview. Energies, 14 (17), 5220. https://doi.org/ 10.3390/en14175220.

24. Delta GEL 12-55 Rechargeable Battery (12V/55Ah). Available at: https://www.delta-battery.ru/catalog/delta-gel/delta-gel-12-55/ (accessed 10 Juny 2022) (in Russian).

25. Gladkov L. A., Kureichik V. V., Kureichik V. M. (2010) Genetic Algorithms. Moscow, Fizmatlit Publ. 368 (in Russian).

26. Dobrego K. V., Shevel' A. A., Koznacheev I. A. (2013) Determination of Kinetics Parameters of Thermal Decomposition of Solid Fuels from Thermogravimetric Analysis Data. Teplo- i Massoperenos – 2012 [Heat and Mass Transfer – 2012]. Minsk, ITMT named after A.V. Lykov of the National Academy of Sciences of Belarus, 296–299 (in Russian).

27. Oxford Battery Degradation Dataset. Available at: https://ora.ox.ac.uk/objects/uuid:03ba 4b01-cfed-46d3-9b1a-7d4a7bdf6fac (accessed 15 March 2022).

28. Battery Research Group. University of Maryland. A. James Clark School of Engineering. Center for Advanced Life Cycle Engineering. Available at: https://calce.umd.edu/battery-research-group (accessed 15 March 2022).

29. Yu H., Li J., Ji Y., Pecht M. (2022) Life-Cycle Parameter Identification Method of an Electrochemical Model for Lithium-Ion Battery Pack. Journal of Energy Storage, 47, 103591. https://doi.org/10.1016/j.est.2021.103591.

30. Saha B., Goebel K. (2007) Battery Data Set. NASA Ames Prognostics Data Repository, NASA Ames Research Centre, Moffett Field, CA, USA. Available at: https://www.nasa.gov/content/prognostics-center-of-excellence-data-set-repository (accessed 10 Juny 2022).

31. Saxena A., Bole B., Daigle M., Goebel K. (2012) Prognostics for Batteries. Aging Experiments and Modeling. Presented at NASA Battery Workshop 2012. Available at: https://www. nasa.gov/sites/default/files/atoms/files/prog_batt_aging_exp_model_asaxena.pdf (accessed 10 June 2022).

32. BatteryArchive.org. Available at: https://www.batteryarchive.org/study_summaries.html (accessed 11 May 2022).

33. Birkl C. (2017) Diagnosis and Prognosis of Degradation in Lithium-Ion Batteries. University of Oxford.