Abstract：Offline and online methods are used to identify model parameters, but the model dynamic characteristic obtained by the online method is better. The recursive least squares method is simple and often used for online parameter identification of lithium-ion battery models. However, the least square method(RLS) has a low identification accuracy. Thus, the forgetting factor recursive least square method was proposed to improve the accuracy of parameter identification. To improve the dynamic identification ability, the variable forgetting factor least square (VFFRLS) method and adaptive forgetting factor recursive least square (AFFRLS) method appear. Yet the current adaptive methods tend to ignore the stability of model parameters, and the undetermined coefficient range of this method is large and difficult to confirm. The model parameter changes drastically, and it is easy to cause the divergence of the algorithm. This paper proposes a simpler AFFRLS method without an undetermined coefficient to address these issues. And it takes into account the accuracy and stability of the model. Firstly, based on dynamic stress testing (DST) and Federal City Operating Conditions (FUDS) data, the FFRLS method with fixed forgetting factor value is simulated and analyzed, and the influence trend of different forgetting factors on the accuracy and stability of model parameters is obtained. Secondly, the proposed AFFRLS method is compared with other AFFRLS and VFFRLS, and the stability and accuracy of the identification parameters are analyzed. Finally, the error tracking ability and convergence speed of the three adaptive methods are analyzed, and the adaptive performance of the proposed AFFRLS to DST and FUDS conditions are analyzed. The FFRLS simulation results with fixed forgetting factor(λ) value show that when λ value decreases, the algorithm has better tracking ability for time-varying parameters, the convergence speed is accelerated, and the identification accuracy is effectively improved. However, when the λ value decreases, the parameter changes drastically, and the stability decreases. It can be seen that obtaining the appropriate λ value is important for the identification ability of the adaptive methods. The results of the three adaptive methods simulations show that the improved AFFRLS in this paper has better tracking ability for time-varying parameters and high model accuracy. And it has better stability of the parameter obtained by FFRLS with fixed λ values of 0.980 and 0.985. It can be seen that the proposed AFFRLS can achieve a better balance between accuracy and stability.The relationship between the λ value and the error of the adaptive methods shows that the improved AFFRLS can track the error variation better. By comparing the operation time with the three methods, the results show that the proposed AFFRLS has a faster convergence rate. According to the relationship between λ value and time in DST and FUDS conditions, the improved AFFRLS method has the majority of λ value near 0.980 in the FUDS condition, and the majority of λ value is 1 in the DST condition. The simulation analysis shows that: (1) The proposed AFFRLS method can improve the accuracy of thealgorithm and take the stability of model parameters into consideration, and it has a good balance between algorithm accuracy and parameter stability. Applying the proposed AFFRLS method and Kalman filter to predict the state of charge can improve the prediction accuracy. (2) The proposed AFFRLS method has better tracking ability for error variation and faster convergence speed. (3) The proposed method can improve the algorithm's accuracy under both slow and drastic conditions, so it's suitable for different online conditions.
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. Transactions of China Electrotechnical Society, 2024, 39(5): 1577-1588.
[1] 庞辉, 郭龙, 武龙星, 等. 考虑环境温度影响的锂离子电池改进双极化模型及其荷电状态估算[J]. 电工技术学报, 2021, 36(10): 2178-2189. Pang Hui, Guo Long, Wu Longxing, et al.An improved dual polarization model of Li-ion battery and its state of charge estimation considering ambient temperature[J]. Transactions of China Electrotechnical Society, 2021, 36(10): 2178-2189. [2] 郭向伟, 邢程, 司阳, 等. RLS锂电池全工况自适应等效电路模型[J]. 电工技术学报, 2022, 37(16): 4029-4037. Guo Xiangwei, Xing Cheng, Si Yang, et al.RLS adaptive equivalent circuit model of lithium battery under full working condition[J]. Transactions of China Electrotechnical Society, 2022, 37(16): 4029-4037. [3] You H W, Bae J I, Cho S J, et al.Analysis of equivalent circuit models in lithium-ion batteries[J]. AIP Advances, 2018, 8(12): 125101. [4] Han Xuebing, Ouyang Minggao, Lu Languang, et al.Simplification of physics-based electrochemical model for lithium ion battery on electric vehicle. Part I: Diffusion simplification and single particle model[J]. Journal of Power Sources, 2015, 278: 802-813. [5] Xu Jun, Mi C C, Cao Binggang, et al.A new method to estimate the state of charge of lithium-ion batteries based on the battery impedance model[J]. Journal of Power Sources, 2013, 233: 277-284. [6] Ettihir K, Boulon L, Agbossou K.Optimization-based energy management strategy for a fuel cellbattery hybrid power system[J]. Applied Energy, 2016, 163: 142-153. [7] He Lin, Wang Yangyang, Wei Yujiang, et al.An adaptive central difference Kalman filter approach for state of charge estimation by fractional order model of lithium-ion battery[J]. Energy, 2022, 244: 122627. [8] 谷苗, 夏超英, 田聪颖. 基于综合型卡尔曼滤波的锂离子电池荷电状态估算[J]. 电工技术学报, 2019, 34(2): 419-426. Gu Miao, Xia Chaoying, Tian Congying.Li-ion battery state of charge estimation based on comprehensive Kalman filter[J]. Transactions of China Electrotechnical Society, 2019, 34(2): 419-426. [9] 黄凯, 郭永芳, 李志刚. 基于信息反馈粒子群的高精度锂离子电池模型参数辨识[J]. 电工技术学报, 2019, 34(增刊1): 378-387. Huang Kai, Guo Yongfang, Li Zhigang.High precision parameter identification of lithium-ion battery model based on feedback particle swarm optimization algorithm[J]. Transactions of China Electrotechnical Society, 2019, 34(S1): 378-387. [10] 张彩萍, 姜久春. 用基于遗传优化的扩展卡尔曼滤波算法辨识电池模型参数[J]. 吉林大学学报(工学版), 2012, 42(3): 732-737. Zhang Caiping, Jiang Jiuchun.Identification of battery model parameters by extended Kalman filter algorithm based on genetic optimization[J]. Journal of Jilin University (Engineering and Technology Edition), 2012, 42(3): 732-737. [11] Zhang Shuzhi, Zhang Xiongwen.A comparative study of different online model parameters identification methods for lithium-ion battery[J].Science China Technological Sciences, 2021, 64(10): 2312-2327. [12] 陈玉珊, 秦琳琳, 吴刚, 等. 基于渐消记忆递推最小二乘法的电动汽车电池荷电状态在线估计[J]. 上海交通大学学报, 2020, 54(12): 1340-1346. Chen Yushan, Qin Linlin, Wu Gang, et al.Online state of charge estimation for battery in electric vehicles based on forgetting factor recursive least squares[J]. Journal of Shanghai Jiao Tong University, 2020, 54(12): 1340-1346. [13] Wei Zhongbao, Meng Shujuan, Xiong Binyu, et al.Enhanced online model identification and state of charge estimation for lithium-ion battery with a FBCRLS based observer[J]. Applied Energy, 2016, 181: 332-341. [14] Sun Xiangdong, Ji Jingrun, Ren Biying, et al.A novel online identification algorithm of lithium-ion battery parameters and model order based on a fractional order model[J]. IET Renewable Power Generation, 2021, 15(11): 2396-2408. [15] Zhang Cheng, Allafi W, Dinh Q, et al.Online estimation of battery equivalent circuit model parameters and state of charge using decoupled least squares technique[J]. Energy, 2018, 142: 678-688. [16] Feng Tianheng, Yang Lin, Zhao Xiaowei, et al.Online identification of lithium-ion battery parameters based on an improved equivalent-circuit model and its implementation on battery state-of-power prediction[J]. Journal of Power Sources, 2015, 281: 192-203. [17] 谢文超, 赵延明, 方紫微, 等. 带可变遗忘因子递推最小二乘法的超级电容模组等效模型参数辨识方法[J]. 电工技术学报, 2021, 36(5): 996-1005. Xie Wenchao, Zhao Yanming, Fang Ziwei, et al.Variable forgetting factor recursive least squales based parameter identification method for the equivalent circuit model of the supercapacitor cell module[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 996-1005. [18] Lao Zizhou, Xia Bizhong, Wang Wei, et al.A novel method for lithium-ion battery online parameter identification based on variable forgetting factor recursive least squares[J]. Energies, 2018, 11(6): 1358. [19] Wang Hao, Zheng Yanping, Yu Yang.Lithium-ion battery SOC estimation based on adaptive forgetting factor least squares online identification and unscented Kalman filter[J]. Mathematics, 2021, 9(15): 1733. [20] Sun Xiangdong, Ji Jingrun, Ren Biying, et al.Adaptive forgetting factor recursive least square algorithm for online identification of equivalent circuit model parameters of a lithium-ion battery[J]. Energies, 2019, 12(12): 2242. [21] Zheng Fangdan, Xing Yinjiao, Jiang Jiuchun, et al.Influence of different open circuit voltage tests on state of charge online estimation for lithium-ion batteries[J]. Applied Energy, 2016, 183: 513-525.
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