Abstract In the lithium-battery charge state prediction, the Kalman filter algorithm is independent of a large number of dataset training. It can predict the state quantities with the observed data to obtain the optimal estimation of the system in the form of extended Kalman (extended Kalman filter (EKF)), untraceable Kalman filter (UKF), and other extended forms. However, the Kalman filtering algorithm and its extended forms for lithium battery nonlinear time-varying system obtain a fixed noise covariance, easily leading to the prediction error. Therefore, this paper proposes a variable-window adaptive untraceable Kalman (VAUKF) to determine the adaptive untraceable Kalman time window length, avoiding the prediction error caused by improper window length selection. The adaptive genetic algorithm (AGA) has been proven to achieve good parameter computation ability in avoiding local optimization and convergence speed problems. Thus, AGA calculates the optimal time window length, the overlapping grouped Allan ANOVA identifies the error sequence fluctuation, and the iterative process adjusts the window length appropriately. The VAUKF improves the SOC’s prediction accuracy and robustness compared to the AUKF. First, based on the second-order RC lithium-ion battery equivalent circuit model, simulation modeling is carried out under the Federal Urban Driving Schedule (FUDS) and US06 high-speed cycling condition (US06) data. The noise level of the prediction process is obtained through the Allan variance, the variable window adjustment rule is determined, and the impact of noise fluctuations on prediction performance is analyzed. Then, the SOC prediction performance of VAUKF under different multiplicities is explored for the noise-matching window update rule, which provides more reasonable parameter conditions for VAUKF. Finally, the tracking ability and convergence speed of VAUKF and AUFK under different working conditions are analyzed, and the simulation results are discussed. Compared with AUKF, the VAUKF decreases MAE by 25.3% and RMSE by 24.4% in RMSE under the FUDS condition. MAE and RMSE are decreased by 21.4% and 20.2% under the US06 condition. When the VAUKF takes different variance multiplicities, the FDUS condition still obtains better prediction results than AUKF, with the best performance when the multiplier is 10. The proposed VAUKF has better prediction performance than the AUKF with a fixed noise covariance matching time window. It can improve the anti-interference ability against time-varying noise the accuracy and robustness of SOC predictions.
Fan Xingming,Wu Runwei,Feng Hao等. Lithium-Ion Battery State of Charge Estimation Based on Variable-Window Adaptive Untraceable Kalman Filtering Algorithm[J]. Transactions of China Electrotechnical Society, 2025, 40(6): 1974-1983.
[1] How D N T, Hannan M A, Hossain Lipu M S, et al. State of charge estimation for lithium-ion batteries using model-based and data-driven methods: a review[J]. IEEE Access, 2019, 7: 136116-136136. [2] Hannan M A, Wali S B, Ker P J, et al.Battery energy-storage system: a review of technologies, optimization objectives, constraints, approaches, and outstanding issues[J]. Journal of Energy Storage, 2021, 42: 103023. [3] 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. [4] Chen Kui, Zhou Shuyuan, Liu Kai, et al.State of charge estimation for lithium-ion battery based on whale optimization algorithm and multi-kernel relevance vector machine[J]. The Journal of Chemical Physics, 2023, DOI:10.1063/5.0139376. [5] 黄凯, 孙恺, 郭永芳, 等. 基于观测方程重构滤波算法的锂离子电池荷电状态估计[J]. 电工技术学报, 2024, 39(7): 2214-2224. Huang Kai, Sun Kai, Guo Yongfang, et al.State of charge estimation of lithium-ion battery based on observation equation reconstruction filtering algo- rithm[J]. Transactions of China Electrotechnical Society, 2024, 39(7): 2214-2224. [6] 颜湘武, 邓浩然, 郭琪, 等. 基于自适应无迹卡尔曼滤波的动力电池健康状态检测及梯次利用研究[J]. 电工技术学报, 2019, 34(18): 3937-3948. Yan Xiangwu, Deng Haoran, Guo Qi, et al.Study on the state of health detection of power batteries based on adaptive unscented Kalman filters and the battery echelon utilization[J]. Transactions of China Elec- trotechnical Society, 2019, 34(18): 3937-3948. [7] 孙金磊, 唐传雨, 李磊, 等. 基于状态与模型参数联合估计的老化电池可充入电量估计方法[J]. 电工技术学报, 2022, 37(22): 5886-5898. Sun Jinlei, Tang Chuanyu, Li Lei, et al.An estimation method of rechargeable electric quantity for aging battery based on joint estimation of state and model parameters[J]. Transactions of China Electrotechnical Society, 2022, 37(22): 5886-5898. [8] Chen Zewang, Yang Liwen, Zhao Xiaobing, et al.Online state of charge estimation of Li-ion battery based on an improved unscented Kalman filter approach[J]. Applied Mathematical Modelling, 2019, 70: 532-544. [9] Zhang Shuzhi, Zhang Chen, Jiang Shiyong, et al.A comparative study of different adaptive extended/ unscented Kalman filters for lithium-ion battery state- of-charge estimation[J]. Energy, 2022, 246: 123423. [10] Sun Daoming, Yu Xiaoli, Wang Chongming, et al.State of charge estimation for lithium-ion battery based on an Intelligent Adaptive Extended Kalman Filter with improved noise estimator[J]. Energy, 2021, 214: 119025. [11] 李岩松, 欧阳进, 刘君, 等. 基于Allan方差的磁光玻璃型光学电流互感器噪声分析[J]. 电力系统自动化, 2015, 39(12): 126-129, 137. Li Yansong, Ouyang Jin, Liu Jun, et al.Analysis on noise of magneto-optical glass type optical current transformer based on Allan variance[J]. Automation of Electric Power Systems, 2015, 39(12): 126-129, 137. [12] 胡杰, 程向红, 朱倚娴. 基于Allan方差解耦自适应滤波的旋转SINS精对准方法[J]. 中国惯性技术学报, 2017, 25(2): 156-160, 165. Hu Jie, Cheng Xianghong, Zhu Yixian.Refined alignment in rotary SINS based on Allan variance decoupling adaptive filter[J]. Journal of Chinese Inertial Technology, 2017, 25(2): 156-160, 165. [13] 李醒飞, 韩佳辰, 刘帆. 基于Allan方差解耦自适应滤波的MHD/MEMS信号融合方法[J]. 中国惯性技术学报, 2020, 28(2): 237-241. Li Xingfei, Han Jiachen, Liu Fan.Signal fusion method of MHD-MEMS based on Allan variance decoupling adaptive filter[J]. Journal of Chinese Inertial Technology, 2020, 28(2): 237-241. [14] 欧阳晓凤, 曾芳玲, 吕大千, 等. 升空平台相对测量误差对定位精度的影响及定位算法[J]. 北京航空航天大学学报, 2024, 50(1): 187-197. Ouyang Xiaofeng, Zeng Fangling, Lü Daqian, et al.Positioning accuracy and localization algorithm with relative measurement errors in blast-off platforms[J]. Journal of Beijing University of Aeronautics and Astronautics, 2024, 50(1): 187-197. [15] 苏玉刚, 陈龙, 吴学颖, 等. 基于遗传算法的SS型磁耦合WPT系统负载与互感识别方法[J]. 电工技术学报, 2018, 33(18): 4199-4206. Su Yugang, Chen Long, Wu Xueying, et al.Load and mutual inductance identification method of SS-type magnetically-coupled WPT system based on genetic algorithm[J]. Transactions of China Electrotechnical Society, 2018, 33(18): 4199-4206. [16] Zhang Shumei, Qiang Jiaxi, Yang Lin, et al.Prior- knowledge-independent equalization to improve battery uniformity with energy efficiency and time efficiency for lithium-ion battery[J]. Energy, 2016, 94: 1-12. [17] He Lin, Wang Yangyang, Wei Yujiang, et al.An adaptive central difference Kalman filter approach for state of charge estimation by fractional order model of lithium-ion battery[J]. Energy, 2022, 244: 122627. [18] 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]. Transa- ctions of China Electrotechnical Society, 2024, 39(5): 1577-1588.
2025, Vol. 40 
