Abstract: To improve the accuracy of battery SOC estimation， a higher order EKF algorithm was used to estimate SOC. Firstly， the first-order Thevenin equivalent circuit model（ECM） of lithium-ion battery was established， and the function relationship between open circuit voltage（OCV） and SOC was expressed by spline function. In order to more accurately identify the ECM parameters， a new kind of with VFFRLS algorithm was proposed for on-line identification of model parameters. Since the accuracy of the VFFRLS solution depended on the setting of the initial values of the algorithm， the improved particle swarm optimization algorithm was used to obtain the initial parameters of ECM， which helped to obtain more accurate initial values of VFFRLS. Finally， the second-order EKF was employed to estimate the SOC of the batterys to improve the estimation accuracy. Two different datasets were used to demonstrate the universality of second-order EKF estimation SOC. The experimental results indicate that the mean absolute error（MAE） of second-order EKF is within 1% when estimating SOC under different working conditions， which proves the effectiveness of the proposed method. 

Key words:  , state of charge（SOC）, second-order extended Kalman filter（EKF）, variable forgetting factor recursive least square（VFFRLS）, improved particle swarm optimization, parameter identification

摘要： 为提高电池荷电状态（SOC）估计的准确性，更高阶的扩展卡尔曼滤波（EKF）算法被用来估计SOC值。首先建立锂离子电池一阶Thevenin等效电路模型，采用样条函数来表述开路电压（OCV）和SOC值的函数关系。为更加精确地识别等效电路模型参数，提出一种新的带有可变遗忘因子最小二乘法（VFFRLS）的算法来在线识别模型参数。由于VFFRLS解的精度依赖于算法初始值的设定，为此采用改进粒子群算法求得模型初始参数值，进而得到更加精确的VFFRLS初始值。最后采用二阶EKF来估计电池的SOC值，以此提高估计精度。两组不同的数据集用来证明二阶EKF估计SOC值具有普适性。实验结果表明，二阶EKF在估计不同工况条件下的SOC值时，平均绝对误差（MAE）都保持在1%以内，由此证明了所提方法的有效性。

关键词: 电池荷电状态, 二阶扩展卡尔曼滤波, 可变遗忘因子最小二乘法, 改进粒子群算法, 参数识别