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Online Co-Estimation of State of Charge and Voltage Dynamics of Li-ion Batteries via Physics-Inspired Modeling
Ahmadzadeh, Omidreza
Ahmadzadeh, Omidreza
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2025-05
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Mechanical Engineering
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Ahmadzadeh_temple_0225E_15984.pdf
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https://doi.org/10.34944/j06j-2d02
Abstract
This study presents an interpretable physics-inspired, data-driven approach to discovering governing equations of Li-ion batteries for state-of-charge (SOC) and voltage dynamics. A key parameter for the safe and efficient utilization of these batteries is SOC, which represents the remaining charge in the battery. SOC is not directly measurable and has to be estimated based on other measurements. Despite significant efforts by the industry and academia, the state-of-the-art SOC estimation algorithms have significant errors in low and high SOC regions, leading to original equipment manufacturers (OEMs) limiting the range of charge and discharge of the batteries, hence limiting the endurance and range in high-demand applications such as electric vehicles. Here, we propose a novel approach to SOC estimation. This research introduces an interpretable physics-inspired, data-driven technique that estimates SOC and discovers the governing equations of battery voltage and SOC. The algorithm employs a sparse identification method designed to uncover governing equations suitable for such nonlinear systems from a library of potential functions. We selected these functions based on the battery’s electrochemistry rather than generic terms. This process results in a model with connections to physics. A key to this modeling process is a sparsification step. Here, we proposed a novel formulation for sparsifying the library terms instead of the common approach of using maximum likelihood analysis of training data. We formulated the problem as a regularization with hyperparameters. The new formulation allows for the use of multiple datasets to address the shortcomings of the previous approaches while balancing the model’s accuracy and complexity. The previous parsimonious modeling techniques were sensitive to noisy measurements. To address this issue, we augment the modeling technique with a joint un- scented Kalman filter (JUKF), enabling more accurate estimates of SOC and voltage. The JUKF mitigates the effects of noisy voltage measurements. The experimental data demonstrate that the identified model with JUKF achieves a root mean square error (RMSE) of 1% for SOC prediction, which is a significant improvement over the common approach of equivalent circuit model augmented by extended Kalman filters (RMSE: 6%). Additionally, the model achieves an RMSE of 0.6 mV for voltage correction. Finally, we address one of the most important and complex issues in the battery management systems of high-demand applications: SOC estimation. We developed a co-estimation framework that utilizes JUKF to update model parameters, account for noise effects, and estimate the SOC. This framework eliminates the need for initial SOC values and ensures convergence by using voltage dynamics as an online SOC-voltage map, making it suitable for real-time applications with uncertain SOC values. In an unseen standard city driving cycle, the model is initialized with a 20% initial SOC error and voltage measurement noise. The SOC values converge to the true values with an RMSE of 1% (Voltage RMSE = 4 mV). The model also performs robustly across temperatures (10°C and 40°C), achieving a SOC RMSE of less than 3%. In conclusion, this dissertation offers a novel control-oriented data-driven frame- work for discovering governing equations and state estimation of complex systems. We applied the method to the critical task of accurate and reliable SOC estimation in battery management systems, focusing particularly on low SOC levels where battery behavior is highly nonlinear. By integrating physical insights with data-driven techniques and enhancing robustness with JUKF, this approach advances battery reliability and operational range for electric vehicles and energy storage systems.
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