Abstract：As the global energy system shifts from fossil fuels toward renewable sources, energy-storage technologies have become essential for maintaining flexibility and stability. Lithium-ion batteries are widely deployed in renewable energy systems, electric transportation, and power grids due to their high energy density, long cycle life, and environmental compatibility. However, long-term exposure to high-salinity and high-humidity conditions intensifies self-discharge and accelerates electrochemical degradation, thereby increasing the complexity and uncertainty of state estimation. Traditional state estimation methods often neglect the dynamic self-discharge behavior and the impact of environmental aging, resulting in reduced estimation accuracy and model adaptability under corrosive conditions. To address these limitations, this paper proposes a triple extended Kalman filter (TEKF)-based joint estimation framework for battery state of charge (SOC) and state of health (SOH). The TEKF algorithm introduces a multi-timescale recursive structure that performs parameter identification, SOC tracking, and capacity degradation estimation simultaneously, thus achieving both short-term accuracy and long-term adaptability. Firstly, a general nonlinear (GNL) equivalent circuit model is established by incorporating a parallel self-discharge resistance branch Rs into the conventional second-order RC structure. This addition allows the model to represent not only charge/discharge dynamics but also self-discharge behavior caused during open-circuit conditions. Secondly, a series of salt-fog corrosion experiments with durations of 4 h, 6 h, 8 h, and 10 h are designed to emulate environmental aging. After corrosion, the batteries undergo hybrid pulse power characterization (HPPC) tests to extract voltage-current responses under different states of charge. Based on these datasets, a parameter identification method considering both dynamic self-discharge features and environmental degradation effects is developed to update the model parameters (R0, R1, R2, C1, C2, Rs) in real time. The TEKF algorithm enables the updating and estimation of the state of charge, model parameters, and capacity across different time scales. At short time scales, it alternately performs SOC estimation, voltage correction, parameter identification, and model updating, while at long time scales, it conducts capacity and SOH estimation, thereby enhancing the estimation accuracy and stability under complex environmental conditions. Experimental results demonstrate that the proposed TEKF algorithm can accurately characterize the self-discharge process and perform precise state estimation across various corrosion conditions. The average model accuracy error is 0.12%, while the mean mean absolute error (MMAE) and mean root mean square error (MRMSE) for SOC estimation are 1.817 4% and 2.047 4%, respectively. For SOH estimation, the MAE and RMSE are 1.301 6% and 1.415 1%, respectively. Compared with conventional DEKF-based methods, the proposed algorithm improves SOC estimation accuracy by approximately 9% and SOH estimation accuracy by over 35%. Further analysis indicates that the self-discharge resistance Rs increases significantly with corrosion time and aging cycles, reflecting the cumulative effect of salt-induced degradation on the electrode surface. Moreover, the self-discharge rate is highest near full charge (SOC=100%) and lowest in the mid-SOC region, validating the GNL model’s capability to capture nonlinear electrochemical behaviors. The following conclusions can be drawn: (1) A parameter identification framework was established that simultaneously accounts for dynamic self-discharge characteristics and environmental aging effects, thereby providing a more realistic representation of the coupled evolution between self-discharge behavior and performance degradation of lithium-ion batteries under salt-fog conditions. (2) Based on the identified parameters, the evolution law of the self-discharge resistance Rs with respect to SOC and SOH was analyzed in depth, verifying the capability of the GNL model to characterize self-discharge features and revealing the underlying mechanism of how salt-fog corrosion accelerates battery aging. (3) A TEKF-based SOC-SOH joint estimation algorithm was proposed, which achieves dynamic parameter updating and high-accuracy estimation of SOC and SOH under various corrosion conditions. The results demonstrate that the proposed method effectively adapts to rapid performance degradation and changing self-discharge characteristics of batteries in high-salinity and high-humidity environments, exhibiting excellent estimation accuracy and robustness.
[1] Kong Laiqiang, Luo Yingbing, Fang Sidun, et al.Electrochemical model based SoC-SoH estimation of lithium-ion batteries under shipboard swaying conditions[J]. Journal of Energy Storage, 2025, 124: 116827. [2] 王道剑. 锂离子电池SOC和SOH联合估算算法研究[D]. 长春: 吉林大学, 2022. Wang Daojian.Research on joint estimation algorithm of lithium-ion batteries SOC and SOH[D]. Changchun: Jilin University, 2022. [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] 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. [5] 于海洲. 锂离子电池自放电检测方法研究[D]. 长春: 长春工业大学, 2024. Yu Haizhou.Research on self-discharge detection method of lithium-ion battery[D]. Changchun: Changchun University of Technology, 2024. [6] 纪常伟, 潘帅, 汪硕峰, 等. 动力锂离子电池老化速率影响因素的实验研究[J]. 北京工业大学学报, 2020, 46(11): 1272-1282. Ji Changwei, Pan Shuai, Wang Shuofeng, et al.Experimental study on effect factors of aging rate for power lithium-ion batteries[J]. Journal of Beijing University of Technology, 2020, 46(11): 1272-1282. [7] 丁黎, 李帆, 蔡文嘉, 等. 锂离子电池的老化特性分析[J]. 电源技术, 2019, 43(1): 77-80. Ding Li, Li Fan, Cai Wenjia, et al.Analysis on aging characteristics of lithium-ion batteries[J]. Chinese Journal of Power Sources, 2019, 43(1): 77-80. [8] Zhang Dayu, Wang Zhenpo, Li Xue, et al.A battery degradation prediction framework considering differences in electric vehicle operating characteristics[J]. IEEE Transactions on Transportation Electrification, 2025, 11(2): 5223-5236. [9] Busà C, Belekoukia M, Loveridge M J.The effects of ambient storage conditions on the structural and electrochemical properties of NMC-811 cathodes for Li-ion batteries[J]. Electrochimica Acta, 2021, 366: 137358. [10] Chen Jiaying, Li Binqi, Li Jianping, et al.Exploring the electrochemical and mechanical properties of lithium-ion batteries in salt spray environments[J]. eTransportation, 2024, 20: 100324. [11] Grabow J, Klink J, Benger R, et al.Particle contamination in commercial lithium-ion cells: risk assessment with focus on internal short circuits and replication by currently discussed trigger methods[J]. Batteries, 2023, 9(1): 9. [12] Yi Pan, Xiao Kui, Dong Chaofang, et al.Effects of mould on electrochemical migration behaviour of immersion silver finished printed circuit board[J]. Bioelectrochemistry, 2018, 119: 203-210. [13] Byun S, Park J, Appiah W A, et al.The effects of humidity on the self-discharge properties of Li(Ni1/3Co1/3Mn1/3)O2/graphite and LiCoO2/graphite lithium-ion batteries during storage[J]. RSC Advances, 2017, 7(18): 10915-10921. [14] Kong Laiqiang, Fang Sidun, Niu Tao, et al.Exploring self-discharge characteristics of lithium-ion batteries corroded by salt spray condition[J]. Journal of Power Sources, 2025, 630: 236182. [15] Liu Jiahao, Shi Xinyuan, Yang Manjiang, et al.The electro-thermal behaviors of the lithium-ion batteries corroded by the salt spray environment[J]. Electrochimica Acta, 2024, 476: 143715. [16] Zhang Lin, Zhao Chunpeng, Liu Yujun, et al.Electrochemical performance and thermal stability of lithium ion batteries after immersion[J]. Corrosion Science, 2021, 184: 109384. [17] Kong Laiqiang, Luo Yingbing, Fang Sidun, et al.State estimation of lithium-ion battery for shipboard applications: key challenges and future trends[J]. Green Energy and Intelligent Transportation, 2025, 4(3): 100192. [18] 毛玲, 赵建辉, 林涛, 等. 数据缺失下基于构建可靠电池模型的荷电状态估计[J]. 电工技术学报, 2025, 40(20): 6733-6743. Mao Ling, Zhao Jianhui, Lin Tao, et al.State of charge estimation based on constructing a reliable battery model with data missing[J]. Transactions of China Electrotechnical Society, 2025, 40(20): 6733-6743. [19] 田佳强, 张泽培, 潘天红, 等. 基于动量反向传播神经网络的锂离子电池建模与荷电状态估计[J]. 电工技术学报, 2025, 40(24): 8156-8170. Tian Jiaqiang, Zhang Zepei, Pan Tianhong, et al.Modeling and state of charge estimation for lithium-ion batteries using backpropagation neural network with momentum[J]. Transactions of China Electro-technical Society, 2025, 40(24): 8156-8170. [20] 方斯顿, 刘龙真, 孔赖强, 等. 基于双向长短期记忆网络含间接健康指标的锂电池SOH估计[J]. 电力系统自动化, 2024, 48(4): 160-168. Fang Sidun, Liu Longzhen, Kong Laiqiang, et al.State-of-health estimation for lithium-ion batteries incorporating indirect health indicators based on bi-directional long short-term memory networks[J]. Automation of Electric Power Systems, 2024, 48(4): 160-168. [21] Ramsey D, German R, Bouscayrol A, et al.Comparison of equivalent circuit battery models for energetic studies on electric vehicles[C]//2020 IEEE Vehicle Power and Propulsion Conference (VPPC), Gijon, Spain, 2020: 1-5. [22] Hidalgo-Leon R, Urquizo J, Jacome-Ruiz P, et al.Modeling battery under discharge using improved thevenin-shepherd electrical battery model[C]//2018 IEEE Vehicle Power and Propulsion Conference (VPPC), Chicago, IL, USA, 2018: 1-5. [23] Madani S S, Schaltz E, Kær S K.A review of different electric equivalent circuit models and parameter identification methods of lithium-ion batteries[J]. ECS Transactions, 2018, 87(1): 23-37. [24] Yan Xiangwu, Guo Yuwei, Cui Yang, et al.Electric vehicle battery SOC estimation based on GNL model adaptive Kalman filter[J]. Journal of Physics: Conference Series, 2018, 1087: 052027. [25] 郭玉威. 基于GNL模型自适应无迹卡尔曼滤波的电池荷电状态估计[D]. 北京: 华北电力大学, 2019. Guo Yuwei.Battery SOC estimation based on GNL model adaptive Kalman filter[D]. Beijing: North China Electric Power University, 2019. [26] Kalman R E.A new approach to linear filtering and prediction problems[J]. Journal of Basic Engineering, 1960, 82(1): 35-45. [27] 赵月荷. 基于自适应无迹卡尔曼滤波的动力电池健康状态估计研究[D]. 南京: 南京邮电大学, 2023. Zhao Yuehe.Research on the state of health estimation of power batteries based on adaptive unscented Kalman filter[D]. Nanjing: Nanjing University of Posts and Telecommunications, 2023. [28] Tao Zhen, Zhao Zhenyu, Wang Changdong, et al.State of charge estimation of lithium batteries: review for equivalent circuit model methods[J]. Measurement, 2024, 236: 115148. [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. [30] 张禹轩. 电动汽车动力电池模型参数在线辨识及SOC估计[D]. 长春: 吉林大学, 2014. Zhang Yuxuan.Parameter identification and SOC estimation of power battery for electric vehicle[D]. Changchun: Jilin University, 2014. [31] 苏晓峰. 锂离子电池荷电状态与健康估计方法研究[D]. 大连: 大连交通大学, 2025. Su Xiaofeng.Research on estimation methods of the state of charge and state of health for lithium-ion batteries[D]. Dalian: Dalian Jiaotong University, 2025. [32] 卢路. 基于多尺度DEKF的串联锂电池组SOC估计研究[D]. 淮南: 安徽理工大学, 2022. Lu Lu.Study on the estimation of charge state of series lithium-ion battery packs based on multi-time scale DEKF[D]. Huainan: Anhui University of Science & Technology, 2022.
2026, Vol. 41 
