电动汽车用锂离子电池SOC估算方法综述

doi:10.19799/j.cnki.2095-4239.2021.0013

储能科学与技术 ›› 2021, Vol. 10 ›› Issue (3): 1127-1136.doi: 10.19799/j.cnki.2095-4239.2021.0013

电动汽车用锂离子电池SOC估算方法综述

付诗意^1,²(), 吕桃林^1,², 闵凡奇^2,^3,⁴, 罗伟林^1,^2,³, 罗承东^1,², 吴磊^1,², 解晶莹^1,²()

^1.空间电源国家重点实验室，上海空间电源研究所
^2.上海动力与储能电池系统工程技术研究中心，上海 200245
^3.上海动力储能电池系统工程技术有限公司，上海 200241
^4.哈尔滨工业大学化工与化学学院，黑龙江哈尔滨 150001

收稿日期:2021-01-11 修回日期:2021-01-23 出版日期:2021-05-05 发布日期:2021-04-30
通讯作者: 解晶莹 E-mail:syFu1996@126.com;jyxie@hit.edu.cn
作者简介:付诗意（1996—），男，硕士研究生，研究方向为锂离子电池状态预测诊断及管理、电池大数据分析等，E-mail：syFu1996@126.com
基金资助:
国家重点研发计划项目(2018YFB0104400);上海市科委项目(18DZ2284000)

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

Shiyi FU^1,²(), Taolin LYU^1,², Fanqi MIN^2,^3,⁴, Weilin LUO^1,^2,³, Chengdong LUO^1,², Lei WU^1,², Jingying XIE^1,²()

^1.Space Power Technology State Key Laboratory, Shanghai Institute of Space Power-Sources, Shanghai 200245, China
^2.Shanghai Engineering Center of Power and Energy Storage Battery Systems, Shanghai 200245, China
^3.Shanghai Power & Energy Storage Battery System Engineering Technology Co. Ltd. , Shanghai 200241, China
^4.School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China

Received:2021-01-11 Revised:2021-01-23 Online:2021-05-05 Published:2021-04-30
Contact: Jingying XIE E-mail:syFu1996@126.com;jyxie@hit.edu.cn

摘要/Abstract

摘要：

综述了锂离子电池荷电状态(state of charge，SOC)估算方法的研究进展。作为电动汽车电池管理中的重要指标，SOC表征了电池在当前循环中剩余的电量。准确的SOC估算可有效地避免电池工作于过低电量等不良工况，保证电池始终运行在安全的状态中，从而有效提高电池使用的效率和延长使用寿命。介绍并比较了几种常用的SOC估算方法：安时积分法最为简单，但由于其是开环估算系统，无法对估计误差进行修正；开路电压法可以根据开路电压与SOC之间的对应关系实现查表式估算，然而由于需要长时间静置来获取稳定的电压值，不适用于在线估算；卡尔曼滤波族方法是前两种方法的结合，可依靠系统观测值的误差对状态估计值进行及时修正，搭配适合的电池模型可获得较高的估算精度且适用于在线估算；数据驱动的方法则需要长期性的历史数据进行数据库的建立。本文总结了每种SOC估算方法的优缺点以及改进的方案。基于以上分析，结合SOC估算算法在工程实际中应用的局限与面对的挑战，对锂离子电池SOC在线估算的发展做出了展望。

关键词: 锂离子电池, SOC, 在线估算

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

中图分类号:

TM 912.6

付诗意, 吕桃林, 闵凡奇, 罗伟林, 罗承东, 吴磊, 解晶莹. 电动汽车用锂离子电池SOC估算方法综述[J]. 储能科学与技术, 2021, 10(3): 1127-1136.

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.

图/表 5

图1

图2

图3

表1

EKF、UKF和CKF的递推过程"

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： $x ? k = x k - + K k z k - z ? k$ ； $P k = P k - - K k P z z, k K k T$

表1

图4

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电动汽车用锂离子电池SOC估算方法综述

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

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