张涛, 陈东明, 侯鹏鹏,等.基于变遗忘因子的改进卡尔曼滤波锂电池荷电状态估算研究[J].河南理工大学学报（自然科学版）,2024,43(4):126-132.

ZHANG T, CHEN D M, HOU P P, et al.Estimation the state of charge of lithium battery based on variable forgetting factor and improved extend Kalman filter[J].Journal of Henan Polytechnic University(Natural Science) ,2024,43(4):126-132.

基于变遗忘因子的改进卡尔曼滤波锂电池荷电状态估算研究

张涛, 陈东明, 侯鹏鹏, 王尧彬

河南理工大学 电气工程与自动化学院，河南 焦作 454000

摘要: 目的 为了解决锂电池在不同放电阶段和噪声干扰下荷电状态（SOC）估算结果发散问题， 方法 通过分析锂电池机理特性，查找影响估算结果的因素和原因。选取适当的数学模型并得到开路电压特性-荷电状态（OCV-SOC）试验曲线后，针对传统算法估算误差波动较大的问题，提出变遗忘因子递推最小二乘（VFF-RLS）与自适应平方根无迹卡尔曼滤波（ASRUKF）算法联合估算SOC。 结果 以动态应力测试（DST）为例，遗忘因子最小二乘（FFRLS）算法的开路电压初期误差最大值为0.02 V，稳定后端电压误差为0.004~0.010 V，误差收敛时间约45 s；UKF算法的SOC估算初期最大误差为0.03，在400 s左右逐渐收敛到理论值附近，稳定后的波动误差为0.83%；VFF-RLS算法在相同的条件下，开路电压实验初期误差最大值为0.04 V，稳定后端电压误差为0.003~0.007 V，误差收敛时间约10 s；ASRUKF的SOC估算初期最大误差为0.1，随着算法迭代，200 s内收敛到理论值附近，稳定后最大波动误差0.413%。 结论 为了保证算法适用的普遍性，在不同初值下观察算法的收敛性，结果表明，在复杂的试验工况下，与传统算法比较，改进算法的参数辨识速度明显加快，精度提高，在估算SOC阶段，波动范围明显变小；在实际值误差较大的情况下，依然能够迅速收敛，证明本文方法的改进切实可行，可用于实际电池研究。

关键词:锂电池;变遗忘因子;荷电状态;自适应滤波;平方根滤波

doi:10.16186/j.cnki.1673-9787.2022030035

基金项目:国家自然科学基金资助项目（U1804143）；河南省科技攻关项目（202102210295）；河南省高校基本科研业务费专项项目（NSFRF210424）；河南省科技创新团队基金资助项目（CXTD2017085）；河南理工大学青年骨干教师资助项目（2019XQG-17）

收稿日期:2022/03/14

修回日期:2022/09/14

出版日期:2024/07/15

Estimation the state of charge of lithium battery based on variable forgetting factor and improved extend Kalman filter

ZHANG Tao, CHEN Dongming, HOU Pengpeng, WANG Yaobin

School of Electrical Engineering and Automation，Henan Polytechnic University，Jiaozuo 454000，Henan，China

Abstract: Objectives To solve the problem of divergence of state-of-charge（SOC） estimation results of lithium batteries under different discharge stages and noise interference，  Methods the factors and reasons affecting the estimation results were analyzed by studying and analyzing the mechanism characteristics of lithium batteries，and then， for the problem of large fluctuations in the estimation error of traditional algorithms，the variable forgetting factor recursive least squares （VFF-RLS） in conjunction with the adaptive squareroot unscented Kalman filter （ASRUKF） algorithm was proposed to estimate the SOC.  Results Taking the dynamic stress test （DST） as an example，the maximum initial error of the opencircuit voltage of the forgetting factor recursive least squares（FFRLS） algorithm was 0.02 V，the terminal voltage error after stabilization was in the range of 0.004 ~0.010 V，the error convergence time was about 45 s，the maximum initial error of the SOC estimation was 0.3，and it gradually converged to around the theoretical value at about 400 s，and the fluctuation error after stabilization was 0.83%.Under the same conditions，the maximum initial error of the VFF-RLS algorithm in the open circuit voltage experiment was 0.04 V，the terminal voltage error after stabilization was in the range of 0.003~0.007 V，the error convergence time was about 10 s，the maximum initial error of SOC estimation was 0.1，and with the iteration of the algorithm，it converged to around the theoretical value within 200 s，and the maximum fluctuation error after stabilization was 0.413%.Finally，in order to ensure the universality of the application of the algorithm，the convergence of the algorithm was observed under different initial values.  Conclusions The results showed that under complex test conditions， compared with the traditional algorithm，the parameter identification speed of the improved algorithm was significantly accelerated，the accuracy was improved，the fluctuation range was significantly smaller in the SOC estimation stage，and it could still converge quickly in the case of large error of the actual value，which proved that the improvement of the algorithm was feasible and could be used for actual battery research.

Key words:lithium battery;variable forgetting factor;state of charge;adaptive filtering;square root filtering