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| Lithium-Ion Battery State Estimation Accounting for Dynamic Self-Discharge |
| Fang Sidun, Xu Nuo, Kong Laiqiang, Niu Tao, Liao Ruijin |
| State Key Laboratory of Power Transmission Equipment Technology School of Electrical Engineering Chongqing University Chongqing 400044 China |
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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.
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Received: 16 September 2025
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2026, Vol. 41 
