Review of estimation methods on SOC of lithium-ion batteries in electric vehicles

doi:10.19799/j.cnki.2095-4239.2021.0013

Abstract

Abstract:

The estimation methods of state-of-charge (SOC) for lithium-ion batteries are reviewed. SOC is used to characterize the remaining capacity of the battery in the current cycle, which is also an important indicator of battery management in electric vehicles. When an accurate estimation of SOC is obtained, batteries would avoid bad working conditions, such as a run with low capacity, ensure that the battery always runs in a safe-state. Thus, the battery efficiency was improved and the life-time was prolonged. The common estimation methods of SOC are introduced and compared. The ampere-hour integration method is the simplest. However, it is an open-loop estimation system; thus, the estimation error is unable to correct itself. The open-circuit voltage method is used to estimate SOC based on the corresponding relationship between the open-circuit voltage and SOC. The need for long-standing time to obtain stable voltage values makes this method unsuitable for on-line estimation. The Kalman filter family method is a combination of ampere-hour integration and open-circuit voltage, which is suitable for on-line estimation. The system observation value error is used to correct the state estimation. When an appropriate battery model is established, high estimation accuracy can be obtained. The data-driven method needs long-term historical data to build a database. The advantages and disadvantages of these methods and the improvement scheme are summarized. Based on the above analyses, combined with the limitations and challenges of the SOC estimation algorithm in practice, the future research direction of on-line SOC estimation for lithium-ion batteries is presented.

Key words: lithium-ion battery, SOC, on-line estimation

CLC Number:

TM 912.6

Shiyi FU, Taolin LYU, Fanqi MIN, Weilin LUO, Chengdong LUO, Lei WU, Jingying XIE. Review of estimation methods on SOC of lithium-ion batteries in electric vehicles[J]. Energy Storage Science and Technology, 2021, 10(3): 1127-1136.

Figures/Tables 5

Fig. 1

Fig. 2

Fig. 3

Table 1

Recursive process of EKF、UKF and CKF"

对非线性系统

x k = f x k - 1, u k + w k z k = g x k, u k + v k

给定初始值

x 0

、

P 0

、

Q

、

R

。

EKF：

计算雅克比矩阵： $A k = ? f x k, u k x k x k = x ? k$ ； $C k = ? g x k, u k x k x k = x ? k$

计算状态变量的一部预测及协方差矩阵： $x ? k - = f x ? k - 1, u k$ ； $P k - = A k P k - 1 A k T + Q$

计算卡尔曼增益： $K k = P k - C k T C k P k - C k T + R - 1$

计算观测值： $z ? k = g x k - 1, u k$

状态和协方差矩阵更新： $x ? k = x ? k - + K k z k - z ? k$ ； $P k = I - K k C k P k -$

UKF：

构造sigma点集与权值，对于n维状态向量，一共有2n+1个sigma点

$x k - 1 i = x ? k - 1 ??? i = 0 x ? k - 1 + λ + n P x i ??? i = 1, ?, n x ? k - 1 - λ + n P x i ??? i = n + 1, ?, 2 n$ ；

$ω m 0 = λ λ + n ω c 0 = λ λ + n + 1 - α 2 + β ω m i = ω c i = 1 2 λ + n ??? i = 1, ?, 2 n$

计算sigma数据点集的一步预测值： $x k -, i = f x k - 1 i, u k ??? i = 0, ?, 2 n$

计算状态变量的一步预测及协方差矩阵： $x k - = ∑ i = 0 2 n ω m i x k -, i$ ； $P k - = ∑ i = 0 2 n ω m i x k - - x k -, i x k - - x k -, i T + Q$

计算新sigma点集： $X k -, i = x k - ??? i = 0 x k - + λ + n P k - i ??? i = 1, ?, n x k - - λ + n P k - i ??? i = n + 1, ?, 2 n$ 其中 $P i$ 表示矩阵 $P$ 的第i列

利用新sigma点集代入观测方程： $z ? k i = g X k -, i, u k ??? i = 0, ?, 2 n$

计算观测估计值的均值： $z ? k = ∑ i = 0 2 n ω m i z ? k i$

计算自相关矩阵： $P z z, k = ∑ i = 0 2 n ω c i z ? k - z ? k i z ? k - z ? k i T + R$

计算互相关矩阵： $P x z, k = ∑ i = 0 2 n ω c i x k - - X k -, i z ? k - z ? k i T$

计算卡尔曼增益： $K k = P x z, k P z z, k - 1$

状态和协方差矩阵更新： $x ? k = x k - + K k z k - z ? k$ ； $P k = P k - - K k P z z, k K k T$

CKF：

构造容积点集，对于n维状态向量，一共有m=2n个容积点： $x k - 1 -, i = S k - 1 - ξ i + x ? k - 1$

其中 $S k - 1$ 通过对协方差矩阵进行cholesky分解获取，如式： $P k - 1 = S k - 1 S k - 1 T$

$ξ i = m 2 10 ? 0 01 ? 0 ? 00 ? 1 - 1 0 ? 0 0 - 1 ? 0 ? 00 ? - 1$

传播容积点： $x k -, i = f x k - 1 -, i, u k$

计算状态一步预测值： $x k - = 1 m ∑ i = 1 m x k -, i$

计算状态预测方差矩阵： $P k - = 1 m ∑ i = 1 m x k -, i x k -, i T - x k - x k - T + Q$

计算方差矩阵平方根 $S k -$ ： $P k - = S k - S k - T$

构造新容积点集： $X k - 1 -, i = S k - ξ i + x k -$

传播新容积点： $z k -, i = h X k - 1 -, i, u k$

计算观测估计值： $z ? k = 1 m ∑ i = 1 m z k -, i$

计算自相关矩阵： $P z z, k = 1 m ∑ i = 1 m z k -, i z k -, i T - z ? k z ? k T + R$

计算互相关矩阵： $P x z, k = 1 m ∑ i = 1 m X k - 1 -, i z k -, i T - x k - z ? k T$

计算卡尔曼增益： $K k = P x z, k P z z, k - - 1$

状态和协方差矩阵更新： $x ? k = x k - + K k z k - z ? k$ ； $P k = P k - - K k P z z, k K k T$

Table 1

Fig. 4

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