基于FFRLS和AEKF的锂离子电池SOC在线估计研究

doi:10.19799/j.cnki.2095-4239.2020.0296

摘要/Abstract

摘要：

本文基于Thevenin等效电路模型，结合遗忘因子最小二乘法(FFRLS)和自适应扩展卡尔曼滤波算法(AEKF)提出联合估计荷电状态(SOC)算法。FFRLS对模型进行参数辨识，为SOC估计提供时变的模型参数；AEKF对SOC进行在线估计，为模型参数辨识提供准确的开路电压。以北京公交的纯电动客车用动力动态测试工况(BBDST)进行仿真实验，并与FFRLS在线辨识及安时积分法的SOC估计进行对比。该算法实现端电压的快速跟踪，精度较FFRLS提高了85%；SOC估计结果能够快速收敛，精度在1.5%～2%范围。研究结果表明，本文算法能够对模型系统进行闭环修正，从而具有更高的精度和更好的适应性。

关键词: 荷电状态估计, FFRLS, AEKF, BBDST

Abstract:

Based on the Thevenin equivalent circuit model, this paper proposes a joint estimation SOC algorithm combining the forgetting factor least squares (FFRLS) and adaptive extended Kalman filter (AEKF) methods. FFRLS identifies and provides the model parameters for the SOC estimation. AEKF estimates the SOC online and provides an accurate open circuit voltage for the model parameter identification. The Beijing bus dynamic stress test (BBDST) was used to simulate and compare with the FFRLS online identification and the SOC estimation based on ampere-hour integration. The algorithm realizes the fast tracking of terminal voltage, and the accuracy is improved by 85% compared with FFRLS. The SOC estimation results can be rapidly converged with an accuracy up to 1.5%～2%. The results show that the algorithm in this paper can modify the model system in a closed-loop manner, thus achieving higher accuracy and better adaptability.

Key words: SOC estimation, FFRLS, AEKF, BBDST

中图分类号:

TM 911

封居强, 伍龙, 黄凯峰, 卢俊, 张星. 基于FFRLS和AEKF的锂离子电池SOC在线估计研究[J]. 储能科学与技术, 2021, 10(1): 242-249.

Juqiang FENG, Long WU, Kaifeng HUANG, Jun LU, Xing ZHANG. Online SOC estimation of a lithium-ion battery based on FFRLS and AEKF[J]. Energy Storage Science and Technology, 2021, 10(1): 242-249.

图/表 12

图1

图2

表1

FFRLS在线参数辨识方法详细流程[11-15]"

输入：估计向量 $θ ∧ (k)$ ，输入向量 $h (k + 1)$

遗忘因子 $λ$ ，增益向量 $K (k)$ 、协方差矩阵 $P (k)$

输出：滤波输出 $y ∧ (k + 1)$ 、更新估计向量 $θ ∧ (k + 1)$

协方差矩阵 $P (k + 1)$

（1）初始化： $θ ∧ (k)$ 、协方差矩阵 $P (k)$ 、误差 $e (k + 1)$

$y (k) = h T (k) θ (k) h (k) = [U (k - 1), ? I (k), ? I (k - 1)] T θ (k) = [α 1 α 2 α 3] T$

（2）计算增益矩阵

$K (k + 1) = P (k + 1) h (k + 1) [λ (k) + h T (K + 1) P (K) h (k + 1)] - 1$

（3）计算估计变量

$y ∧ (k + 1) = h T (k + 1) θ (k)$

（4）计算误差估计

$e (k + 1) = y (k + 1) - y ∧ (k + 1)$

（5）更新估计向量

$θ ∧ (k + 1) = θ ∧ (k) + K (k + 1) e (k + 1)$

（6）更新协方差矩阵

$P (k + 1) = T r i {λ - 1 [(I + K (k + 1)] h T (k + 1) P (k)}$

（7）解析辨识参数

$R 0 = a 3 - a 2 1 + a 1 R p = 2 (a 3 + a 1 a 2) a 12 - 1 C p = - T (1 + a 1) 4 (a 3 + a 1 a 2)$

表1

表2

EKF算法详细流程[12-14]"

输入：输入向量

u k - 1

，状态向量

x ∧ 0 +

、均方差矩阵

P 0 +

输出：状态变量最优估计

x ∧ k +

、均方差最优估计

P k +

（1）初始化： $x 0$ 、 $P 0$ 、 $Q 0$ 、 $R 0$

$x ∧ 0 + = E (x 0) P 0 + = E [(x 0 - x ∧ 0 +) (x 0 - x ∧ 0 +) T]$

（2）更新状态变量

$x ∧ k - = f (x ∧ k - 1 +, u k - 1)$

（3）更新均方估计误差

$P k - = A k - 1 P k - 1 + A k - 1 T + Q k$

（4）计算增益

$L k = P k - C k T (C k P k - C k T + R k) - 1$

（5）状态最优估计

$x ∧ k + = x ∧ k - + L [k y k - h (x ∧ k -, u k)]$

（6）均方差最优估计

$P k + = (I - L k C k) P k -$

表2

图3

表3

图4

图5

图6

图7

图8

图9

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工步	电流/A	时间/s	累计时间/s	工况
1	-26	21	21	起步
2	-47	12	33	加速
3	-7	16	49	滑行
4	8.5	6	55	制动
5	-26	21	76	加速
6	-7	16	92	滑行
7	8.5	6	98	制动
8	-47	9	107	加速
9	-60	6	113	急加速
10	-26	21	134	均速
11	-7	16	150	滑行
12	8.5	6	156	制动
13	-47	9	165	加速
14	-60	6	171	急加速
15	-26	21	192	均速
16	-7	16	208	滑行
17	20	9	217	制动
18	8.6	12	229	制动
19	-7	71	300	停车

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