Online SOC estimation of a lithium-ion battery based on FFRLS and AEKF

doi:10.19799/j.cnki.2095-4239.2020.0296

Abstract

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

CLC Number:

TM 911

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.

Figures/Tables 12

Fig.1

Fig.2

Table 1

Detailed flow of FFRLS online parameter identification method[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

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

Table 1

Table 2

Detailed flow of EKF algorithm[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

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

Table 2

Fig.3

Table 3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.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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