Abstract：Aiming at the requirements of application scenarios for EV, this paper focused on the accurately expressing problem of the bidirectional mapping of the electro-thermal complex coupling relationship (E/T-CCR) within the battery, with the ultimate goal of improving the accuracy of battery state estimation. Taking 18650 lithium batteries as the research object, a multi-coupled states joint estimation algorithm for (including SOC, SOP, SOT, and capacity states) lithium batteries based on multi-domain hybrid model (MDHM) was proposed. The proposed MDHM had better accuracy and dynamic tracking performance under complex operating conditions. The proposed multi-coupled states joint estimation algorithm enabled high-accuracy joint estimation of 4 key battery states. The general execution process of the algorithm is as follows:Firstly, in the offline part, the coupling domain of MDHM based on long short-term memory (LSTM) was constructed to initially realize the bidirectional mapping expression of E/T-CCR for the batteries. Secondly, in the online part, the constructed LSTM, autoregressive equivalent circuit model (AR-ECM), and single state lumped thermal model (SSTM) together formed MDHM. They jointly describe the complex electro-thermal dynamic characteristics for batteries. Among them, the E/T-CCR of the electrical and thermal domains was determined by the coupling domain based on real-time battery operating data, and was corrected by the coupling domain corrector based on adaptive square root unscented Kalman filter (ASRUKF) before finally outputting to the state estimator. Finally, the state estimator achieved real-time joint estimation of SOC, SOT, and capacity based on the obtained dynamic E/T-CCR. SOP estimator implemented online estimation of SOP based on multi-constraints (Such as current I, terminal voltage Ud, SOC and SOT). By comparing with 2 typical multi-state joint estimation methods based on electro-thermal coupling model (ETCM) in 12 temperature scenarios under 3 dynamic operating conditions including aging for 2 types of batteries, the experimental results show that: Under 2 extreme temperatures of 50℃ and -10℃, the proposed MDHM has good accuracy when facing DST and mixed operating conditions. The MDHM can achieve an average improvement of 2.589 mV in electrical model accuracy and an average improvement of 0.027℃ in thermal model accuracy. The multi-coupled states joint estimation algorithm proposed has more stable RMSE over a wide temperature range of [10, 50]℃. It can improve the SOC, SOT and capacity accuracies by an average of 0.094%, 0.026℃, and 0.002 A·h, respectively. In addition, by comparing with MDHM without coupling domain corrector, the MDHM with coupled domain corrector can achieve an average improvement of 1.389 mV in electrical model accuracy and 0.019℃ in thermal model accuracy. This indicates that the stability of the coupling domain can be effectively compensated by the proposed coupling domain corrector based on ASRUKF. The following conclusions can be drawn from the experimental analysis: (1) The coupling domain in MDHM can more accurately express battery E/T-CCR in scenarios such as EV characterized by wide temperature, wide power, and wide discharge depth operating conditions. (2)The coupling domain corrector can enhance the stability, generalization ability, and reducing errors caused by differences in battery consistency and aging. (3) The proposed SOP estimation that considers SOT constraint is quite necessary. Firstly, the SOT constraint always plays a dominant role in the battery charging/discharging process. Secondly, as the continuous charging/discharging time increases, SOP estimation considering SOT constraint is more critical. In addition, in low-temperature scenarios, SOP estimation considering SOT constraint can avoid battery damage. Finally, in aging scenarios, due to the increase in battery internal resistance and faster temperature rise inside the battery, SOP estimation considering SOT constraint is more important for the battery safety.
刘芳, 刘佳一, 苏卫星, 孙连坤. 基于多域混合模型的锂电池多耦合状态联合估计算法[J]. 电工技术学报, 2026, 41(15): 5359-5374.
Liu Fang, Liu Jiayi, Su Weixing, Sun Liankun. Multi-Coupled States Joint Estimation Algorithm for Lithium Battery Based on Multi Domain Hybrid Model. Transactions of China Electrotechnical Society, 2026, 41(15): 5359-5374.
[1] Hu Xiaosong, Feng Fei, Liu Kailong, et al.State estimation for advanced battery management: key challenges and future trends[J]. Renewable and Sustainable Energy Reviews, 2019, 114: 109334. [2] 刘旖琦, 雷万钧, 刘茜, 等. 基于双自适应扩展粒子滤波器的锂离子电池状态联合估计[J]. 电工技术学报, 2024, 39(2): 607-616. Liu Yiqi, Lei Wanjun, Liu Qian, et al.Joint state estimation of lithium-ion battery based on dual adaptive extended particle filter[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 607-616. [3] 梁继业, 袁至, 王维庆, 等. 基于电池储能系统的综合自适应一次调频策略[J]. 电工技术学报, 2025, 40(7): 2322-2334. Liang Jiye, Yuan Zhi, Wang Weiqing, et al.Comprehensive adaptive primary frequency control strategy based on battery energy storage system[J]. Transactions of China Electrotechnical Society, 2025, 40(7): 2322-2334. [4] Liu Fang, Shao Chen, Su Weixing, et al.Online joint estimator of key states for battery based on a new equivalent circuit model[J]. Journal of Energy Storage, 2022, 52: 104780. [5] Liu Fang, Liu Xinhui, Su Weixing, et al.Multi-state online joint estimation method for lithium battery based on a new electro-thermal coupling model[J]. Applied Thermal Engineering, 2025, 264: 125430. [6] 张帅涛, 蒋品群, 宋树祥, 等. 基于注意力机制和CNN-LSTM融合模型的锂电池SOC预测[J]. 电源学报, 2024, 22(5): 269-277. Zhang Shuaitao, Jiang Pinqun, Song Shuxiang, et al.SOC prediction for lithium battery based on fusion model of attention mechanism and CNN-LSTM[J]. Journal of Power Supply, 2024, 22(5): 269-277. [7] Zhu Jiangong, Knapp M, Darma M S D, et al. An improved electro-thermal battery model complemented by current dependent parameters for vehicular low temperature application[J]. Applied Energy, 2019, 248: 149-161. [8] Zhang Cheng, Li Kang, Deng Jing, et al.Improved realtime state-of-charge estimation of LiFePO4 battery based on a novel thermoelectric model[J]. IEEE Transactions on Industrial Electronics, 2017, 64(1): 654-663. [9] Zheng Yusheng, Che Yunhong, Hu Xiaosong, et al.Online sensorless temperature estimation of lithium-ion batteries through electro-thermal coupling[J]. IEEE/ASME Transactions on Mechatronics, 2024, 29(6): 4156-4167. [10] Zhang Xingchen, Wang Yujie, Chen Zonghai.SoC-modified core temperature estimation of lithium-ion battery based on control-oriented electro-thermal model[J]. IEEE Transactions on Power Electronics, 2023, 38(9): 11642-11651. [11] Wang Yujie, Zhou Caijie, Zhao Guanghui, et al.A framework for battery internal temperature and state-of-charge estimation based on fractional-order thermoelectric model[J]. Transactions of the Institute of Measurement and Control, 2022: 01423312211067293. [12] Dang Zhaoshuai.Online joint estimation of lithium electronic main states based on WGAN-informer hybrid model[J]. Journal of Energy Storage, 2024, 97: 112627. [13] Li Yichao, Ma Chen, Liu Kailong, et al.A novel joint estimation for core temperature and state of charge of lithium-ion battery based on classification approach and convolutional neural network[J]. Energy, 2024, 308: 132721. [14] Shi Qin, Jiang Zhengxin, Wang Zhi, et al.State of charge estimation by joint approach with model-based and data-driven algorithm for lithium-ion battery[J]. IEEE Transactions on Instrumentation and Measurement, 2022, 71: 3000610. [15] Odungat A, Chanda S.Data-driven model for predicting the electro-thermal behavior of lithium-ion pouch cell under varying ambient temperature conditions[J]. Applied Thermal Engineering, 2025, 265: 125367. [16] Yu Hanqing, Zhang Hongcai, Zhang Zhengjie, et al.State estimation of lithium-ion batteries via physics-machine learning combined methods: a methodological review and future perspectives[J]. eTransportation, 2025, 24: 100420. [17] Fahmy H M, Hasanien H M, Alharbi M, et al.Hybrid extended Kalman filter with Newton Raphson method for lifetime prediction of lithium-ion batteries[J]. Scientific Reports, 2025, 15: 14592. [18] Tao Junjie, Wang Shunli, Cao Wen, et al.A comprehensive review of multiple physical and data-driven model fusion methods for accurate lithium-ion battery inner state factor estimation[J]. Batteries, 2024, 10(12): 442. [19] Fan Tiane, Liu Songming, Tang Xin, et al.Simultaneously estimating two battery states by combining a long short-term memory network with an adaptive unscented Kalman filter[J]. Journal of Energy Storage, 2022, 50: 104553. [20] Xu Yidan, Hu Minghui, Zhou Anjian, et al.State of charge estimation for lithium-ion batteries based on adaptive dual Kalman filter[J]. Applied Mathematical Modelling, 2020, 77: 1255-1272. [21] Wang Chunyu, Li Changlong, Wang Guangfeng, et al.Fast identification method for thermal model parameters of lithium-ion battery based on discharge temperature rise[J]. Journal of Energy Storage, 2021, 44: 103362. [22] Li Xichao, Chang Xiuliang, Feng Yan, et al.Investigation on the heat generation and heat sources of cylindrical NCM811 lithium-ion batteries[J]. Applied Thermal Engineering, 2024, 241: 122403. [23] Hariharan K S.A coupled nonlinear equivalent circuit-Thermal model for lithium ion cells[J]. Journal of Power Sources, 2013, 227: 171-176. [24] 王新栋, 董政, 王书华, 等. 基于改进开路电压模型和自适应平方根无迹卡尔曼滤波的锂离子电池宽温度多工况 SOC 估计[J]. 电工技术学报, 2024, 39(24): 7950-7964. Wang Xindong, Dong Zheng, Wang Shuhua, et al.State-of-charge estimation for lithium-ion batteries across wide temperature range and multiple working conditions based on improved open-circuit voltage model and adaptive square root unscented Kalman filter algorithm[J]. Transactions of China Electro-technical Society, 2024, 39(24): 7950-7964. [25] 李强, 张凯旋, 袁文文, 等. 基于多时间尺度双扩展卡尔曼滤波的电池峰值功率估计方法[J]. 电工技术学报, 2024, 39(7): 2225-2235. Li Qiang, Zhang Kaixuan, Yuan Wenwen, et al.Lithium-ion battery peak power estimation based on multi-time scale double extended Kalman filter[J]. Transactions of China Electrotechnical Society, 2024, 39(7): 2225-2235. [26] Qin Peijun, Che Yanbo, Li Hongfeng, et al.Joint SOC-SOP estimation method for lithium-ion batteries based on electro-thermal model and multi-parameter constraints[J]. Journal of Power Electronics, 2022, 22(3): 490-502. [27] 杜伟, 王圣, 李健, 等. 基于CNN-LSTM-AM模型的储能锂离子电池荷电状态预测[J]. 电工技术学报, 2025, 40(9): 2982-2995. Du Wei, Wang Sheng, Li Jian, et al.Prediction of state of charge for energy storage lithium-ion batteries based on CNN-LSTM-AM model[J]. Transactions of China Electrotechnical Society, 2025, 40(9): 2982-2995. [28] Kollmeyer P, Hackl A, Emadi A.Li-ion battery model performance for automotive drive cycles with current pulse and EIS parameterization[C]//2017 IEEE Transportation Electrification Conference and Expo (ITEC), Chicago, IL, USA, 2017: 486-492. [29] Xu Zhicheng, Zhang Chuang, Sun Bo, et al.The electric-thermal coupling simulation and state estimation of lithium-ion battery[J]. Journal of Energy Storage, 2023, 58: 106431. [30] Liu Fang, Yu Dan, Su Weixing, et al.Adaptive multitimescale joint estimation method for SOC and capacity of series battery pack[J]. IEEE Transactions on Transportation Electrification, 2024, 10(2): 4484-4502.
2026, Vol. 41 
