基于SOC⁃OCV优化曲线与EKF的锂离子电池荷电状态全局估计

doi:10.19562/j.chinasae.qcgc.2021.01.003

Abstract

Abstract:

The SOC?OCV curve is the basis of the state estimation for lithium?ion battery. To solve the problems of failure of the traditional HPPC test method to describe the nonlinear characteristics of the battery at non?test points and the low accuracy of the OCV curve by the small?constant?current discharge method， an OCV curve optimization method based on the particle swarm optimization algorithm is proposed. In this method， the OCV curve by the small?constant?current discharge method is translated， and the OCV curve is optimized by minimizing the sum of error between the translation curve at the test point and the OCV value obtained by HPPC test. Then， the model parameters of the second?order RC model are identified and the model terminal voltage is estimated based on the optimized OCV curve. The experimental results show that the overall model accuracy based on the optimized OCV curve is higher than that based on HPPC， and the former is twice the accuracy of the latter in the low SOC region. Finally， based on the optimized OCV curve and identified model parameters， an EKF algorithm is designed to estimate the SOC in the whole SOC region. The test results show that the SOC estimation error based on the optimized OCV curve and EKF algorithm can keep within 2% over the whole SOC region.

Key words: lithium?ion battery, second?order RC model, SOC?OCV curve optimization, SOC estimation, extended Kalman filter

Xin Lai,Yunfei Li,Yuejiu Zheng,Jingjing Wang,Tao Zhou Long Sun. An Overall Estimation of State⁃of⁃Charge Based on SOC⁃OCV Optimization Curve and EKF for Lithium⁃ion Battery[J].Automotive Engineering, 2021, 43(1): 19-26.

Figures/Tables 14

SOC/%	$R 0_c h a / m Ω$	$R 0_d c h / m Ω$	$R 1 / m Ω$	$R 2 / m Ω$	$τ 1$	$τ 2$	RMSE/mV
100	1.245 0	1.337 6	1.7×10^-7	1.146 7	0.001 1	42.750 0	1.309 5
90	1.211 1	1.326 5	0.929 1	0.810 7	943.500 0	41.002 0	1.908 8
80	1.213 9	1.323 3	1.056 8	1.027 5	912.760 0	45.375 0	1.679 8
70	1.262 0	1.303 4	1.345 7	1.552 8	62.213 0	0.001 4	1.034 6
60	1.326 2	1.238 6	1.679 0	4.9×10^-6	74.322 0	799.700 0	3.473 0
50	1.196 1	1.282 1	0.848 5	0.936 0	41.082 0	0.001 2	1.140 0
40	1.215 2	1.293 0	0.883 2	1.647 3	46.919 0	0.001 9	1.346 0
30	1.281 9	1.244 1	0.558 2	1.204 5	34.330 0	214.340 0	1.618 8
20	1.290 7	1.389 6	1.054 3	1.770 7	49.662 0	0.001 2	1.122 3
10	1.444 5	1.574 5	8.258 5	0.664 1	0.001 2	14.902 0	3.585 7
0	0.500 0	3.000 0	1.720 0	11.407 3	1.924 0	106.660 0	50.431 0

定义
$A ? k = ? f (x k, u k) ? x k x k = x ? k +$ ， $C ? k = ? g (x k, u k) ? x k x k = x ? k -$
初始化：
当k=0时，设定
$x ? 0 + = E [x 0]$
$P 0 + = E [(x - x ? 0 +) (x - x ? 0 +) T]$
迭代计算：
当k=1,2,…
状态向量更新： $x ? k - = f (x ? k - 1 +, u k - 1)$
误差协方差矩阵更新： $P k - = A ? k - 1 P k - 1 + A ? k - 1 T + Σ w$
计算卡尔曼增益： $L k = P k - C ? k T [C ? k P k - C ? k T + Σ v] - 1$
状态向量测量更新： $x ? k + = x ? k - + L k [y k - g (x ? k -, u k)]$
误差协方差矩阵测量更新： $P k + = (I - L k C ? k) P k -$

References 15

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项目	参数值
标准容量/（A · h）	72.8
尺寸/mm³	342×102×11.5
质量/g	921
负极材料	NCM
正极材料	石墨
截止电压/V	4.2/2.5
开路电压/V	3.64
能量密度/(W·h·kg^-1)	287.6

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An Overall Estimation of State⁃of⁃Charge Based on SOC⁃OCV Optimization Curve and EKF for Lithium⁃ion Battery

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步骤 1: 变量初始化，随机产生一个种群，粒子的适应度计算。
步骤 2: 重复以下步骤直到满足终止条件(误差足够小或到达最大循环次数)。
2.1 对每个个体做如下操作：
2.1.1 速度与位置状态更新(根据式(9)与式(10)); 2.1.2 更新个体最优位置变量。
步骤 3: 输出优化结果。