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.
Fan Xingming,Feng Hao,Zhang Xin. Optimization of Least Squares Method and Its Application in Parameter Identification of Lithium-Ion Battery Model[J]. Transactions of China Electrotechnical Society, 2024, 39(5): 1577-1588.
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2024, Vol. 39 
