State of Charge Estimation of EV Secondary Battery Pack Using Hybrid Hedge Feedforward Feedback-Based Gated Recurrent Unit to Extend Lifespan

Abstract

Accurate estimation of state of charge (SoC) and maintaining balanced charge levels across secondary battery cells are crucial in battery management systems (BMSs) to extend battery life while improving the performance and thermal stability of Li-ion batteries (LIBs) in electric vehicles (EVs). However, there are still underexplored challenges associated with circulating currents in electrochemical cells during continuous operation which can overheat battery packs, reducing their life span or result in dangerous thermal runaways. This paper investigates SoC estimation using various real-world charging and discharging profiles, along with charge-balancing strategies to enhance the longevity of parallel-connected Li-ion battery cells. A newly developed hedge feedforward feedback-based gated recurrent unit with H∞ controller (HFF-GRU-H∞) is introduced to improve the SoC estimation accuracy with comparisons to nine widely-applied deep-learning algorithms. Moreover, SoC balancing for three individual battery cells is achieved using a bidirectional DC/DC power converter controlled by an H∞ robust control system during charging-discharging cycles. The experimental results indicate that SoC capacity estimation error can be reduced to 0.043%. Also, the applied optimization algorithm minimized the determination time to 0.477 s when benchmarked with existing methods leading to better charge balance among the battery cells. As a result, the overall battery pack lifespan can be extended by 27.7%, offering substantial advantages for industrial applications.

Keywords

charge balancing / electric vehicle / gated recurrent unit / H_∞ control / optimization

References

[1] F. Yang, X. Song, F. Xu, and K.-L. Tsui, “State-of-Charge Estimation of Lithium-Ion Batteries Via Long Short-Term Memory Network,” IEEE Access 7 (2019): 53792-53799.

[2] M. Ohirul Qays, Y. Buswig, M. L. Hossain, and A. Abu-Siada, “Active Charge Balancing Strategy Using the State of Charge Estimation Technique for a PV-Battery Hybrid System,” Energies 13, no. 13 (2020): 1-17, https://doi.org/10.3390/en13133434.

[3] X. Li, H. Jiang, S. Guo, et al., “SOC Estimation of Lithium-Ion Battery for Electric Vehicle Based on Deep Multilayer Perceptron,” Computational Intelligence and Neuroscience 2022 (2022): 3920317, https://doi.org/10.1155/2022/3920317.

[4] M. J. Brand, M. H. Hofmann, M. Steinhardt, S. F. Schuster, and A. Jossen, “Current Distribution Within Parallel-Connected Battery Cells,” Journal of Power Sources 334 (2016): 202-212, https://doi.org/10.1016/j.jpowsour.2016.10.010.

[5] D. Zhang, S. Dey, H. E. Perez, and S. J. Moura, “Real-Time Capacity Estimation of Lithium-Ion Batteries Utilizing Thermal Dynamics,” IEEE Transactions on Control Systems Technology 28, no. 3 (2020): 992-1000, https://doi.org/10.1109/tcst.2018.2885681.

[6] V. Selvaraj and I. Vairavasundaram, “A Comprehensive Review of State of Charge Estimation in Lithium-Ion Batteries Used in Electric Vehicles,” Journal of Energy Storage 72 (2023): 108777, https://doi.org/10.1016/j.est.2023.108777.

[7] O. Qays, Y. Buswig, M. L. H. Hossain, and A. Abu-Siada, “Recent Progress and Future Trends on State of Charge Estimation Methods to Improve Battery-Storage Efficiency: A Review,” CSEE Journal of Power and Energy Systems 1, no. 1 (2020): 1-12, https://doi.org/10.17775/CSEEJPES.2019.03060.

[8] N. Li, Y. Zhang, F. He, et al., “Review of Lithium-Ion Battery State of Charge Estimation,” Global Energy Interconnection 4, no. 6 (2021): 619-630, https://doi.org/10.1016/j.gloei.2022.01.003.

[9] A. K. M. A. Habib and M. K. Hasan, “Lithium-Ion Battery State-of-Charge Balancing Circuit Using Single Resonant Converter for Electric Vehicle Applications,” Journal of Energy Storage 61 (2023): 106727, https://doi.org/10.1016/j.est.2023.106727.

[10] Z. Xia and J. A. Abu Qahouq, “State-Of-Charge Balancing of Lithium-Ion Batteries With State-of-Health Awareness Capability,” IEEE Transactions on Industry Applications 57, no. 1 (2021): 673-684.

[11] C. N. Van, T. N. Vinh, M.-D. Ngo, and S.-J. Ahn, “Optimal SoC Balancing Control for Lithium-Ion Battery Cells Connected in Series,” Energies 14, no. 10 (2021): 2875, https://www.mdpi.com/1996-1073/14/10/2875.

[12] Q. Ouyang, N. Ghaeminezhad, Y. Li, T. Wik, and C. Zou, “A Unified Model for Active Battery Equalization Systems,” IEEE Transactions on Control Systems Technology 33, no. 2 (2025): 685-699, https://doi.org/10.1109/tcst.2024.3496439.

[13] K. Liu, Z. Wei, C. Zhang, Y. Shang, R. Teodorescu, and Q. L. Han, “Towards Long Lifetime Battery: AI-Based Manufacturing and Management,” IEEE/CAA Journal of Automatica Sinica 9, no. 7 (2022): 1139-1165, https://doi.org/10.1109/JAS.2022.105599.

[14] M. S. Hosen, J. Jaguemont, J. Van Mierlo, and M. Berecibar, “Battery Lifetime Prediction and Performance Assessment of Different Modeling Approaches,” iScience 24, no. 2 (2021): 102060, https://doi.org/10.1016/j.isci.2021.102060.

[15] J. Schulte, J. Figgener, P. Woerner, H. Broering, and D. Uwe Sauer, “Forecast-Based Charging Strategy to Prolong the Lifetime of Lithium-Ion Batteries in Standalone PV Battery Systems in Sub-Saharan Africa,” Solar Energy 258 (2023): 130-142, https://doi.org/10.1016/j.solener.2023.03.029.

[16] O. Qays, Y. Buswig, H. Basri, et al., “An Intelligent Controlling Method for Battery Lifetime Increment Using State of Charge Estimation in PV-Battery Hybrid System,” Applied Sciences 10, no. 24 (2020): 1-13, https://doi.org/10.3390/app10248799.

[17] O. Qays, Y. Buswig, and M. Anyi, “Active Cell Balancing Control Method for Series-Connected Lithium-Ion Battery,” International Journal of Innovative Technology and Exploring Engineering 8, no. 9 (2019): 2424-2430, https://doi.org/10.35940/ijitee.i8905.078919.

[18] M. Etxandi-Santolaya, L. Canals Casals, and C. Corchero, “Extending the Electric Vehicle Battery First Life: Performance Beyond the Current End of Life Threshold,” Heliyon 10, no. 4 (2024): e26066, https://doi.org/10.1016/j.heliyon.2024.e26066.

[19] Y. Liu, Y. Tian, D. Liu, et al., “A Novel Dual Gated Recurrent Unit Neural Network Based on Error Compensation Integrated With Kalman Filter for the State of Charge Estimation of Parallel Battery Modules,” Journal of Power Sources 635 (2025): 236508, https://doi.org/10.1016/j.jpowsour.2025.236508.

[20] S. Fan, Z. Shao, D. Wen, et al., “Low Pass Filter Based Lithium-Ion Battery Equivalent Circuit Model With High Accuracy,” ChemistrySelect 9, no. 47 (2024): 1-8, https://doi.org/10.1002/slct.202402844.

[21] X. Ding, D. Zhang, J. Cheng, B. Wang, and P. C. K. Luk, “An Improved Thevenin Model of Lithium-Ion Battery With High Accuracy for Electric Vehicles,” Applied Energy 254 (2019): 113615, https://doi.org/10.1016/j.apenergy.2019.113615.

[22] I. Ranaweera and O.-M. Midtgård, “Optimization of Operational Cost for a Grid-Supporting PV System With Battery Storage,” Renewable Energy 88 (2016): 262-272, /04/01/2016, https://doi.org/10.1016/j.renene.2015.11.044.

[23] E. Martinez-Laserna, V. Herrera, I. Gandiaga, A. Milo, E. Sarasketa-Zabala, and H. Gaztañaga, “Li-Ion Battery Lifetime Model's Influence on the Economic Assessment of a Hybrid Electric Bus's Operation,” World Electric Vehicle Journal 9, no. 2 (2018): 28, https://doi.org/10.3390/wevj9020028.

[24] H. de Vries, T. T. Nguyen, and B. Op het Veld, “Increasing the Cycle Life of Lithium Ion Cells by Partial State of Charge Cycling,” Microelectronics Reliability 55, no. 11 (2015): 2247-2253, https://doi.org/10.1016/j.microrel.2015.08.014.

[25] R. Cahuantzi, X. Chen, and S. Güttel, “A Comparison of LSTM and GRU Networks for Learning Symbolic Sequences,” in Lecture Notes in Networks and Systems 739 LNNS (2023): 771-785.

[26] M. O. Qays, I. Ahmad, D. Habibi, and M. A. S. Masoum, “System Strength Forecasting Using Hedge Feedforward Feedback-Based Gated Recurrent Unit Algorithm in Renewable Energy-Based Grid System,” CSEE Journal of Power and Energy Systems 1 (2024): 1-10, https://doi.org/10.17775/CSEEJPES.2024.01820.

[27] D. Sahoo, Q. Pham, J. Lu, and S. C. Hoi, “Online Deep Learning: Learning Deep Neural Networks on the Fly,” in Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, California, (2017), vol. 2660-2666, https://doi.org/10.24963/ijcai.2018/369.

[28] C. Pan, S. Wen, M. Zhu, H. Ye, J. Ma, and S. Jiang, “Hedge Backpropagation Based Online LSTM Architecture for Ultra-Short-Term Wind Power Forecasting,” IEEE Transactions on Power Systems, vol. PP (2023): 1-14, https://doi.org/10.1109/TPWRS.2023.3304898.

[29] S. Mohsen, “Recognition of Human Activity Using GRU Deep Learning Algorithm,” Multimedia Tools and Applications 82, no. 30 (2023): 47733-47749, https://doi.org/10.1007/s11042-023-15571-y.

[30] M. O. Qays, I. Ahmad, D. Habibi, and M. A. S. Masoum, “H∞ Control System for Synchronous Condensers in Renewable Energy-Integrated Weak Grids,” CSEE Journal of Power and Energy Systems 1 (2024): 1-13, https://doi.org/10.17775/CSEEJPES.2024.01090.

[31] L. Z. Sunshine Energy Technology Co.. “Tesla Powerwall Deep Cycle 100ah 12V Lithium LiFePO4 Li Ion Battery Pack.” accessed, https://zhsunshineenergy.en.made-in-china.com/product/CXMmbejDQqUw/China-Tesla-Powerwall-Deep-Cycle-100ah-12V-Lithium-LiFePO4-Li-Ion-Battery-Pack-with-BMS-for-Solar-Storage.html.

[32] M. V. Micea, L. Ungurean, G. N. Cârstoiu, and V. Groza, “Online State-of-Health Assessment for Battery Management Systems,” IEEE Transactions on Instrumentation and Measurement 60, no. 6 (2011): 1997-2006, https://doi.org/10.1109/TIM.2011.2115630.

[33] P. Kergus, Control System Synthesis - Robust Control (Lund University, 2020, https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2020/Control_System_Synthesis___Robust_control.pdf.

[34] B. Xiao, Y. Liu, and B. Xiao, “Accurate State-of-Charge Estimation Approach for Lithium-Ion Batteries by Gated Recurrent Unit With Ensemble Optimizer,” IEEE Access 7 (2019): 54192-54202, https://doi.org/10.1109/ACCESS.2019.2913078.

[35] O. Demirci, S. Taskin, E. Schaltz, and B. Acar Demirci, “Review of Battery State Estimation Methods for Electric Vehicles—Part I: SOC Estimation,” Journal of Energy Storage 87 (2024): 111435, https://doi.org/10.1016/j.est.2024.111435.

[36] C. S. Han, H. Kim, and K. M. Lee, “Reevaluating the Potential of a Vanilla Transformer Encoder for Unsupervised Time Series Anomaly Detection in Sensor Applications,” Sensors (Basel) 25, no. 8, (April 2025): 1-22, https://doi.org/10.3390/s25082510.

[37] T. Wang, S. Chen, H. Ren, and Y. Zhao, “Model-Based Unscented Kalman Filter Observer Design for Lithium-Ion Battery State of Charge Estimation,” International Journal of Energy Research 42, no. 4 (2018): 1603-1614, https://doi.org/10.1002/er.3954.

[38] H. M. Hussein, A. Aghmadi, M. S. Abdelrahman, S. M. S. H. Rafin, and O. Mohammed, “A Review of Battery State of Charge Estimation and Management Systems: Models and Future Prospective,” WIREs Energy and Environment 13, no. 1 (2024): 1-37, https://doi.org/10.1002/wene.507.

[39] M. O. Qays, I. Ahmad, D. Habibi, and M. A. S. Masoum, “Forecasting Data-Driven System Strength Level for Inverter-Based Resources-Integrated Weak Grid Systems Using Multi-Objective Machine Learning Algorithms,” Electric Power Systems Research 238 (2025): 111112, https://doi.org/10.1016/j.epsr.2024.111112.

[40] X. Yang, S. Wang, W. Xu, J. Qiao, C. Yu, and C. Fernandez, “Fuzzy Adaptive Singular Value Decomposition Cubature Kalman Filtering Algorithm for Lithium-Ion Battery State-of-Charge Estimation,” International Journal of Circuit Theory and Applications 50, no. 2 (2021): 614-632, https://doi.org/10.1002/cta.3166.

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2026 The Author(s). Battery Energy published by Xijing University and John Wiley & Sons Australia, Ltd.