Modeling and State of Charge Estimation for Lithium-Ion Batteries Using Backpropagation Neural Network with Momentum
Tian Jiaqiang1, Zhang Zepei1, Pan Tianhong1, Huang Darong2, Liu Xinghua3
1. School of Electrical Engineering and Automation Anhui University Hefei 230039 China; 2. School of Artificial Intelligence Anhui University Hefei 230039 China; 3. School of Electrical Engineering Xi’an University of Technology Xi’an 710048 China;
Abstract：Boosting the adoption of new energy electric vehicles and energy storage technologies is pivotal in expediting the standardization of the “dual carbon” objectives. Lithium-ion batteries, serving as critical components in electric vehicles and energy storage systems, are indispensable for energy storage and buffering purposes. The precision of a battery model is vital for enhancing state estimation accuracy. Based on momentum back propagation neural networks, this paper introduces a fractional-order modeling and state- of-charge estimation technique for lithium-ion batteries, aiming to improve the interpretability of data-driven modeling. Firstly, a BPM neural network (BPMNN)-based battery model is constructed, which incorporates the physical information of a first-order fractional-order model. The weights of the BPMNN-based model represent the model parameters, including resistance, capacitance, and fractional order. With the hierarchical feature extraction capability of neural networks, the novel battery model enables the online optimization of fractional order. Secondly, the OCV-SOC relationship is linearized using a Taylor expansion, and the linearized OCV-SOC relationship is employed to reconstruct the BPMNN-based battery model. Thirdly, a momentum gradient descent algorithm is utilized. Historical data is introduced using momentum, which improves the stability of the estimation. Moreover, the convergence of the proposed method is analyzed. The loss function of the BPMNN-based battery model converges to a positive value with a suitable learning rate. Finally, the proposed method is verified with a 2.55 A·h LiFePO4 battery. The influence of temperature is compared with a UDDS profile at -5℃, 25℃, and 45℃. The result shows that the external temperature influences the ohmic resistance, model accuracy, and fractional order. However, it seems to have no relationship with the SOC estimation. The fractional order descends faster as the temperature decreases. Compared to the EKF-based and UKF-based methods, the proposed method improves the model accuracy by up to 64%, and the SOC estimation accuracy is improved by up to 36.5%. Compared to the GRU-RNN-based SOC estimation method, the BPMNN-based method yields a better result in SOC estimation because the combination of physical information enables online optimization of the BPMNN-based battery model. As the memory space increases, the computational burden also grows, and the battery model becomes more accurate. The model achieves a balance between accuracy and computational burden when the memory space includes 50~70 steps. The following conclusions can be drawn. (1) The BPMNN-based online estimation method converges with a suitable learning rate, significantly improving the accuracy of the battery model and SOC estimation. The BPMNN-based method estimates SOC more accurately than the GRU-RNN method. (2) The external temperature influences the variation of ohmic resistance and model accuracy, but the SOC estimation is not affected. The fractional order descends more rapidly as the temperature decreases. (3) The memory space influences the computational burden and model accuracy.
田佳强, 张泽培, 潘天红, 黄大荣, 刘兴华. 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, Huang Darong, Liu Xinghua. Modeling and State of Charge Estimation for Lithium-Ion Batteries Using Backpropagation Neural Network with Momentum. Transactions of China Electrotechnical Society, 2025, 40(24): 8156-8170.
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