Strong Tracking Method for State-of-Charge Estimation of Lithium Battery under Time Varying Non-Stationary Heavy-Tailed Measurement Noise
Shi Lin1, Wang Tianjing2, Huang Haidong1, Xiong Hao1, Zhang Qibing1
1. State Grid Jiangsu Electric Power Co. Ltd Nanjing 210024 China; 2. State Grid Electric Power Research Institute (NARI Group Corporation) Nanjing 211106 China
Abstract：Under the background of large-scale construction of new power energy storage system, lithium-ion battery (LIBs) has been widely used as the main electrochemical energy storage component of energy storage power station because of its excellent energy characteristics. However, in the complex environment of the new energy storage system, the data measurement noise of lithium batteries is no longer white Gaussian noise, and its amplitude shows two characteristics: Unknown statistical characteristics of distribution and ourliers. To estimate battery parameter and state of charge (SOC) with high precision and fast dynamic response under this condition is one of the main difficulties in the research field of lithium-ion battery measurement. Among the existing SOC estimation algorithms, ampere hour (AH) method and open circuit voltage (OCV) method are affected by the external environment and battery loss, which gravely effected the estimation accuracy. The method based on artificial neural network fitting is difficult to obtain reliable training data set under complex noise conditions, and the operation cost and space occupation are high. Methods based on conventional nonlinear filters are often unable to adapt to SOC estimation in non-Gaussian noise environments and cannot resist state model bias. To solve the problems above, a strong SOC tracking estimation method based on gereralized variable forgetting factor recursive least squares (GVFFRLS) online parameter identification and Gauss-G-Gamma mixed prior variational H-density robust cubature filter is proposed. Firstly, an online parameter identification method combining Sage-Husa adaptive weighting and generalized Gauss kernel forgetting factor was proposed to improve the stability and dynamic accuracy of battery online parameter identification. Then, a hierarchical Gaussian cubature Kalman filter was constructed based on the Gauss-G-Gamma mixed prior distribution noise modeling and variational parameter inference, achieving the adaptive update of variational parameters with the change of real noise distribution. Based on the QS-density function constructed by H-density theory, a new L2-1/2 norm-weighted robust loss function and status-measurement combination innovation was designed. The variational iterative calculation process was closely combined with the robust state posterior estimation constructed by H-density loss criterion, and a strong tracking filtering algorithm for SOC estimation was proposed. Finally, based on the INR 18650-20R lithium battery test data with non-stationary thick tail measurement noise under different temperatures and dynamic conditions, the proposed algorithm is simulated and compared with the common SOC estimation filtering algorithm. The results show that the voltage estimation accuracy is improved by 96.32% compared GVFFRLS with forgetting factor recursive least squares (FFRLS) method, and the average accuracy of SOC estimated by proposed algorithm under non-stationary thick tail measurement noise is improved by 78.94%, 80.80% and 75.05% compared with traditional Kalman filters including extended Kalman filter (EKF), unscented Kalman filter(UKF) and Sage-Husa unscented Kalman filter (SHUKF), respectively. The SOC initial value tracking convergence performance and measurement noise distribution registration performance are much stronger than the existing SOC estimation algorithms. The theoretical derivation process of the proposed algorithm is relatively complex, but the iterative calculation process is simple, and its operational efficiency is similar to that of the existing algorithms. Therefore, this method is easy to be applied to the engineering implementation of battery management system (BMS). This algorithm features adaptability to non-stationary measurement noise and strong adaptive correction performance for SOC state deviation tracking. It can be applied not only in complex noise environments but also in SOC estimation under normal conditions, thereby optimizing and enhancing the performance of the BMS algorithm, improving the utilization efficiency and safety of lithium battery modules. The safety and stability monitoring and maintenance measures for new energy storage power stations have been further enhanced.
[1] 孟国栋, 李雨珮, 唐佳, 等. 锂离子电池储能电站的热失控状态检测与安全防控技术研究进展[J]. 高电压技术, 2024, 50(7): 3105-3127. Meng Guodong, Li Yupei, Tang Jia, et al.Research progress of thermal runaway detection and safety control technology for lithium-ion battery energy storage power stations[J]. High Voltage Engineering, 2024, 50(7): 3105-3127. [2] 程林, 索克兰, 许鹤麟. 新能源侧电池储能系统运行评价: 现状与展望[J]. 电力系统自动化, 2025, 49(15): 1-19. Cheng Lin, Suo Kelan, Xu Helin.Operation evaluation of battery energy storage systems on renewable energy side: current status and prospects[J]. Automation of Electric Power Systems, 2025, 49(15): 1-19. [3] Shang Yunlong, Cui Naxin, Duan Bin, et al.Analysis and optimization of star-structured switched-capacitor equalizers for series-connected battery strings[J]. IEEE Transactions on Power Electronics, 2018, 33(11): 9631-9646. [4] Cui Xiangbo, Xu Bowen.State of charge estimation of lithium-ion battery using robust kernel fuzzy model and multi-innovation UKF algorithm under noise[J]. IEEE Transactions on Industrial Electronics, 2022, 69(11): 11121-11131. [5] 李斌, 李博睿, 李超, 等. 考虑过充/过放的电化学储能电站建模及故障特性分析[J]. 电力系统自动化, 2024, 48(14): 119-128. Li Bin, Li Borui, Li Chao, et al.Modeling and fault characteristic analysis of electrochemical energy storage station considering overcharging/overdisch-arging[J]. Automation of Electric Power Systems, 2024, 48(14): 119-128. [6] Li Xiaoyu, Wang Zhenpo, Zhang Lei.Co-estimation of capacity and state-of-charge for lithium-ion batteries in electric vehicles[J]. Energy, 2019, 174: 33-44. [7] 胡明辉, 朱广曜, 刘长贺, 等. 考虑迟滞特性的卡尔曼滤波和门控循环单元神经网络的锂离子电池SOC联合估计[J]. 汽车工程, 2023, 45(9): 1688-1701. Hu Minghui, Zhu Guangyao, Liu Changhe, et al.Joint estimation of state of charge for lithium-ion battery with Kalman filtering and gated recurrent unit neural networks considering hysteresis characteristics[J]. Automotive Engineering, 2023, 45(9): 1688-1701. [8] 朱元富, 贺文武, 李建兴, 等. 基于Bi-LSTM/Bi-GRU循环神经网络的锂电池SOC估计[J]. 储能科学与技术, 2021, 10(3): 1163-1176. Zhu Yuanfu, He Wenwu, Li Jianxing, et al.SOC estimation for Li-ion batteries based on Bi-LSTM and Bi-GRU[J]. Energy Storage Science and Technology, 2021, 10(3): 1163-1176. [9] How D N T, Hannan M A, Lipu M S H, et al. State-of-charge estimation of Li-ion battery in electric vehicles: a deep neural network approach[J]. IEEE Transactions on Industry Applications, 2020, 56(5): 5565-5574. [10] 陈治铭, 刘建华, 柯添赐, 等. 基于对抗性的权重注意力机制序列到序列模型的锂离子电池SOC估计方法[J]. 电工技术学报, 2024, 39(19): 6244-6256. Chen Zhiming, Liu Jianhua, Ke Tianci, et al.SOC prediction of lithium-ion batteries based on sequence-to-sequence model with adversarial weighted attention mechanism[J]. Transactions of China Electrotechnical Society, 2024, 39(19): 6244-6256. [11] Zhu Rui, Duan Bin, Zhang Junming, et al.Co-estimation of model parameters and state-of-charge for lithium-ion batteries with recursive restricted total least squares and unscented Kalman filter[J]. Applied Energy, 2020, 277: 115494. [12] 费亚龙, 谢长君, 汤泽波, 等. 基于平方根无迹卡尔曼滤波的锂电池状态估计[J]. 中国电机工程学报, 2017, 37(15): 4514-4520, 4593. Fei Yalong, Xie Changjun, Tang Zebo, et al.State-of-charge estimation based on square root unscented Kalman filter algorithm for Li-ion batteries[J]. Proceedings of the CSEE, 2017, 37(15): 4514-4520, 4593. [13] 范兴明, 吴润玮, 封浩, 等. 基于变窗口自适应无迹卡尔曼滤波的锂离子电池荷电状态预测[J]. 电工技术学报, 2025, 40(6): 1974-1983. Fan Xingming, Wu Runwei, Feng Hao, et al.Lithium-ion battery state of charge estimation based on variable-window adaptive untraceable Kalman filtering algorithm[J]. Transactions of China Electro-technical Society, 2025, 40(6): 1974-1983. [14] 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. [15] Wang Shunli, Stroe D I, Fernandez C, et al.A novel energy management strategy for the ternary lithium batteries based on the dynamic equivalent circuit modeling and differential Kalman filtering under time-varying conditions[J]. Journal of Power Sources, 2020, 450: 227652. [16] 胡劲, 赵靖英, 姚帅亮, 等. 基于阻容参数滤波优化UKF的锂电池SOC估计[J]. 电源学报, 2025, 23(2): 247-255. Hu Jin, Zhao Jingying, Yao Shuailiang, et al.SOC estimation of lithium battery based on resistance-capacitance parameters filtering optimization UKF[J]. Journal of Power Supply, 2025, 23(2): 247-255. [17] Wu Muyao, Wang Li, Wang Yuqing, et al.State of charge estimation of the lithium-ion power battery based on a multi-time-scale improved adaptive unscented Kalman filter[J]. IEEE Transactions on Instrumentation and Measurement, 2024, 73: 9003212. [18] 董祥祥, 武鹏, 葛传久, 等. 基于自适应无迹卡尔曼滤波的锂电池荷电状态估计[J]. 电工电能新技术, 2021, 40(2): 58-65. Dong Xiangxiang, Wu Peng, Ge Chuanjiu, et al.State of charge estimation of Li-ion battery based on adaptive unscented Kalman filter[J]. Advanced Technology of Electrical Engineering and Energy, 2021, 40(2): 58-65. [19] 巫春玲, 赵玉冰, 耿莉敏, 等. 采用广义混合最大相关熵准则扩展卡尔曼滤波算法的锂离子电池荷电状态估计[J]. 西安交通大学学报, 2025, 59(7): 159-169. Wu Chunling, Zhao Yubing, Geng Limin, et al.State of charge estimation for lithium-ion batteries using a generalized mixture maximum correlation-entropy criterion-based extended Kalman filter algorithm[J]. Journal of Xi’an Jiaotong University, 2025, 59(7): 159-169. [20] Ma Wentao, Guo Peng, Wang Xiaofei, et al.Robust state of charge estimation for Li-ion batteries based on cubature Kalman filter with generalized maximum correntropy criterion[J]. Energy, 2022, 260: 125083. [21] 刘萍, 李泽文, 蔡雨思, 等. 基于等效电路模型和数据驱动模型融合的SOC和SOH联合估计方法[J]. 电工技术学报, 2024, 39(10): 3232-3243. Liu Ping, Li Zewen, Cai Yusi, et al.Joint estimation method of SOC and SOH based on fusion of equivalent circuit model and data-driven model[J]. Transactions of China Electrotechnical Society, 2024, 39(10): 3232-3243. [22] Liu Xingtao, Li Qiule, Wang Li, et al.Data-driven state of charge estimation for power battery with improved extended Kalman filter[J]. IEEE Transactions on Instrumentation and Measurement, 2023, 72: 1500910. [23] 李超然, 肖飞, 樊亚翔, 等. 基于门控循环单元神经网络和Huber-M估计鲁棒卡尔曼滤波融合方法的锂离子电池荷电状态估算方法[J]. 电工技术学报, 2020, 35(9): 2051-2062. Li Chaoran, Xiao Fei, Fan Yaxiang, et al.A hybrid approach to lithium-ion battery SOC estimation based on recurrent neural network with gated recurrent unit and Huber-M robust Kalman filter[J]. Transactions of China Electrotechnical Society, 2020, 35(9): 2051-2062. [24] 李建林, 彭禹宸, 王茜, 等. 锂离子电池建模研究现状与展望[J]. 发电技术, 2025, 46(5): 857-871. Li Jianlin, Peng Yuchen, Wang Qian, et al.Research status and prospect of lithium-ion battery modelling[J]. Power Generation Technology, 2025, 46(5): 857-871. [25] 封居强, 伍龙, 黄凯峰, 等. 基于FFRLS和AEKF的锂离子电池SOC在线估计研究[J]. 储能科学与技术, 2021, 10(1): 242-249. Feng Juqiang, Wu Long, Huang Kaifeng, et al.Online SOC estimation of a lithium-ion battery based on FFRLS and AEKF[J]. Energy Storage Science and Technology, 2021, 10(1): 242-249. [26] Huang Yulong, Zhang Yonggang, Shi Peng, et al.Variational adaptive Kalman filter with Gaussian-inverse-wishart mixture distribution[J]. IEEE Transactions on Automatic Control, 2021, 66(4): 1786-1793. [27] Aleksandr Y Aravkin, James V Burke, Gianluigi Pillonetto.Sparse/robust estimation and Kalman smoothing with nonsmooth log-concave densities: modeling, computation, and theory[J]. The Journal of Machine Learning Research, 2013, 14(1): 2689-2728. [28] Wang Guoqing, Li Ning, Zhang Yonggang.Maximum correntropy unscented Kalman and information filters for non-Gaussian measurement noise[J]. Journal of the Franklin Institute, 2017, 354(18): 8659-8677. [29] 范兴明, 封浩, 张鑫. 最小二乘算法优化及其在锂离子电池参数辨识中的应用[J]. 电工技术学报, 2024, 39(5): 1577-1588. Fan Xingming, Feng Hao, Zhang Xin.Optimization of least squares method and its application in parameter identification of lithium-ion battery model[J]. Transactions of China Electrotechnical Society, 2024, 39(5): 1577-1588.
2026, Vol. 41 
