基于AUKF的可穿戴式设备用锂离子电池SOE在线估计方法

doi:10.19799/j.cnki.2095-4239.2023.0721

储能科学与技术 ›› 2024, Vol. 13 ›› Issue (5): 1688-1698.doi: 10.19799/j.cnki.2095-4239.2023.0721

基于AUKF的可穿戴式设备用锂离子电池SOE在线估计方法

柳明贤¹(), 李继标¹, 唐炳南², 杨毅³, 肖仁鑫³()

^1.云南电网有限责任公司丽江供电局，云南丽江 674100
^2.云南电网有限责任公司丽江古城供电局，云南丽江 674199
^3.昆明理工大学交通工程学院，云南昆明 650500

收稿日期:2023-10-16 修回日期:2023-11-14 出版日期:2024-05-28 发布日期:2024-05-28
通讯作者: 肖仁鑫 E-mail:liumingxian@lj.csg.cn;xrx1127@foxmail.com
作者简介:柳明贤（1987—），男，学士，工程师，研究方向为配网运检、带电作业、人工智能，E-mail：liumingxian@lj.csg.cn；
基金资助:
中国南方电网有限责任公司科技项目(YNKJXM20220216)

Online state-of-energy estimation method for lithium-ion batteries used in wearable devices based on adaptive unscented Kalman filter

Mingxian LIU¹(), Jibiao LI¹, Bingnan TANG², Yi YANG³, Renxin XIAO³()

^1.Lijiang Power Supply Bureau of Yunnan Power Grid Co. Ltd, Lijiang 674100, Yunnan, China
^2.Lijiang Old Town Power Supply Bureau of Yunnan Power Grid Co. Ltd, Lijiang 674199, Yunnan, China
^3.Faculty of Transportation Engineering, Kunming University of Science and Technology, Kunming 650500, Yunnan, China

Received:2023-10-16 Revised:2023-11-14 Online:2024-05-28 Published:2024-05-28
Contact: Renxin XIAO E-mail:liumingxian@lj.csg.cn;xrx1127@foxmail.com

摘要/Abstract

摘要：

可穿戴式设备(wearable devices, WDs)体积小、工作时间长，在工业监测等领域应用越来越广泛。锂离子电池为WD上电子设备提供能量，其准确的能量状态(state of energy, SOE)在线估算对 WDs的电源实时管理与延长设备寿命有重要影响。传统的基于模型的估算方法需要离线获取SOE与开路电压(open circuit voltage, OCV)的关系，实验时间长，不能适应实际工况变化，难以在线实施，本工作提出一种基于开路电压(open-circuit voltage，OCV)在线辨识的可穿戴式设备用锂离子电池SOE在线估算方法。首先基于锂离子电池的一阶RC模型，采用带遗忘因子的递推最小二乘法(forgetting factor recursive least squares, FFRLS)在线辨识电池OCV等参数。分析了WDs运行负载变化特征，构建了WD运行工况和参数辨识工况，并开展锂离子电池实验。结合WDs工作负载特性，研究了开路电压和端电压的关系，在线获得OCV与SOE的关系曲线。采用无迹卡尔曼滤波(adaptive unscented Kalman filter, AUKF)算法实现SOE的在线估计，与传统通过离线实验获得OCV-SOE关系的方法进行了对比。研究结果表明，所提的SOE在线估算方法具有较好的精度，并在不同的SOE初始值时具有较好的鲁棒性。

关键词: 可穿戴式设备, SOE估算, OCV在线辨识, 自适应无迹卡尔曼滤波

Abstract:

Wearable devices (WDs) with small sizes and long working time are widely used in industrial monitoring and other fields. Lithium-ion batteries provide energy for electronics used in WDs, and their online accurate estimation of state of energy (SOE) critically impacts the real-time power management and life extension of WDs. Traditional model-based estimation methods must obtain the offline relationship between SOE and open circuit voltage (OCV). However, this requires a large amount of test time and is challenging to adapt to actual working conditions, thus hindering its online application. This paper proposes an SOE estimation method based on the online identification of OCV for lithium-ion batteries used in WDs. Based on the first-order RC model of the battery, the forgetting factor recursive least squares is used to identify the OCV online and other parameters of the lithium-ion battery. After analyzing the characteristics of load changes in the WD operation, the working condition and parameter identification condition are constructed, and the experiments are conducted on the test bench. Combined with the workload characteristics of WDs, the relationship between OCV and terminal voltage is discussed, and the relationship curves between OCV and SOE are obtained online. The adaptive unscented Kalman filter is used to estimate the SOE online and is compared with the traditional method based on the offline OCV-SOE relationship. The results show that the proposed SOE estimation method based on OCV online identification has good accuracy and robustness against different initial values.

Key words: wearable device, SOE estimation, OCV online identification, adaptive unscented Kalman filter

中图分类号:

TM 912

柳明贤, 李继标, 唐炳南, 杨毅, 肖仁鑫. 基于AUKF的可穿戴式设备用锂离子电池SOE在线估计方法[J]. 储能科学与技术, 2024, 13(5): 1688-1698.

Mingxian LIU, Jibiao LI, Bingnan TANG, Yi YANG, Renxin XIAO. Online state-of-energy estimation method for lithium-ion batteries used in wearable devices based on adaptive unscented Kalman filter[J]. Energy Storage Science and Technology, 2024, 13(5): 1688-1698.

图/表 13

图1

表1

基于AUKF的SOE估算流程"

针对电池等效电路模型中，非线性离散系统状态空间方程：

$x k = f (x k - 1, u k - 1) + w k y k = g (x k, u k) + v k$

式中，x是状态变量，y是可测量输出，u是输入电流I，f是非线性状态函数对应公式(16)，g是非线性性测量函数对应公式(17)，w是过程噪声，v是测量噪声。

采样时间k = 0时SOE 初始化如下：

步骤(1)：状态初始化

$x ¯ 0 = E (x 0) P 0 = E (x 0 - x ¯ 0) (x 0 - x ¯ 0) T$

式中， $x ¯ 0$ 是状态初始值x₀ 的均值, P₀是误差协方差矩阵初始值。

k ≥ 1时每个采样时刻k估算SOE，迭代执行步骤(2) ~(7)：

步骤(2)：计算采样点Sigma及加权系数

①产生Sigma点

$x ⌢ k - 1 = x ¯ 0 x i, k - 1 = x ⌢ k - 1 + (N + s) P k - 1 i i = 1,2, ⋯, N x i, k 1 = x ⌢ k - 1 - (N + s) P k - 1 i - N i = N + 1, N + 2, ⋯, 2 N$

式中， $x ⌢ k - 1$ 表示为k-1时刻状态变量的最优估计值，2N为样本个数，本工作N=2；s为尺度系数，可以表示为 $s = α 2 (N + κ) - N$ ，其中，κ为缩放参数，状态估计时通常设置为0，α为Sigma点在 $x ⌢$ 周围扩展的比例参数，用于控制采样点分布状态，取值范围为0~1，本工作α=0.01；

②计算加权系数

$w m (0) = r N + s w c (0) = r N + s + (1 - α 2 + ξ) w m (i) = w c (i) = 1 2 (N + s), i = 1,2, ⋯, 2 N$

式中，w_m, w_c为权重因子，ξ为合并高阶项中的误差的参数，本工作ξ=2。

步骤(3)：k|k-1时刻的系统状态变量均值与协方差更新，生成新的sigma点：

$x i, k k - 1 = f (x i, k - 1, u k) + q k - 1 x ¯ ̑ k k - 1 = ∑ i = 0 2 n w m (i) f (x i, k k - 1, u k) P ¯ k k - 1 = ∑ i = 0 2 n w c (i) (x i, k k - 1 - x ¯ ̑ k k - 1) • (x i, k k - 1 - x ¯ ̑ k k - 1) T + Q k - 1$

式中，q为系统过程噪声均值，Q为过程噪声的协方差。

生成新的sigma点：

$x ⌢ i, k = x ⌢ k | k - 1 x i, k = x ⌢ k | k - 1 + (N + r) P k i i = 1,2 ⋯ N x i, k = x ⌢ k | k - 1 - (N + r) P k i - N i = N + 1, N + 2 ⋯ 2 N$

步骤(4)：测量更新

$y i, k k - 1 = g (x ¯ ̑ k k - 1, u k) + r k y ¯ ̑ k k - 1 = ∑ i = 0 2 n w m (i) y i, k k - 1$

式中，r为测量噪声的平均值。

步骤(5)：误差协方差与增益矩阵 K 的更新

$P y y, k = ∑ i = 0 2 N w c (i) (y i, k k - 1 - y ¯ ̑ k k - 1) (y i, k k - 1 - y ¯ ̑ k k - 1) T + R k P x y, k = ∑ i = 0 2 N w c (i) (x i, k k - 1 - x ¯ ̑ k k - 1) (y i, k k - 1 - y ¯ ̑ k k - 1) T K k = P x y, k P y y, k$

式中，R为测量噪声协方差。

步骤(6)：状态变量测量校正及其协方差的更新

$x ⌢ k = x ¯ ̑ k k - 1 + K k (y k - y ¯ ̑ k k - 1) P k = P ¯ k k - 1 - K k P ¯ y y, k K k T$

步骤(7)：过程噪声以及测量噪声的更新

$r k + 1 = (1 - d k) r k + d k v k - ∑ i = 0 2 n y i, k k - 1 - r k R k + 1 = (1 - d k) R k + d k (v k - y ¯ ̑ k k - 1) (v k - y ¯ ̑ k k - 1) T q k + 1 = (1 - d k) q k + d k (x ⌢ k - x ¯ ̑ k - q k) Q k + 1 = (1 - d k) Q k + d k (K k (v k - y ¯ ̑ k k - 1) (v k - y ¯ ̑ k k - 1) T K k T + P k) d k = (1 - b) (1 - b k)$

式中，d是估计的残值，b是[0~ 1]范围内的遗忘因子，通常取0.95。

表1

表2

图2

图3

图4

图5

图6

图7

图8

表3

图9

图10

参考文献 30

1	ILYAS M. Wireless sensor networks for smart healthcare[C]//2018 1st International Conference on Computer Applications & Information Security (ICCAIS). Riyadh, Saudi Arabia. IEEE, 2018: 1-5.
2	ZHANG Z R, GLASER S, WATTEYNE T, et al. Long-term monitoring of the sierra Nevada snowpack using wireless sensor networks[J]. IEEE Internet of Things Journal, 2022, 9(18): 17185-17193.
3	DENG F, YUE X H, FAN X Y, et al. Multisource energy harvesting system for a wireless sensor network node in the field environment[J]. IEEE Internet of Things Journal, 2019, 6(1): 918-927.
4	PUTRA S A, TRILAKSONO B R, RIYANSYAH M, et al. Multiagent architecture for bridge capacity measurement system using wireless sensor network and weight in motion[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 2502714.
5	HUANG P, XIAO L, SOLTANI S, et al. The evolution of MAC protocols in wireless sensor networks: A survey[J]. IEEE Communications Surveys & Tutorials, 2013, 15(1): 101-120.
6	张志杰, 李茂德. 锂离子动力电池温升特性的研究[J]. 汽车工程, 2010, 32(4): 320-323.
	ZHANG Z J, LI M D. A study on the temperature rise characteristic of lithium-ion power battery[J]. Automotive Engineering, 2010, 32(4): 320-323.
7	RADFAR M, NAKHLESTANI A, LE VIET H, et al. Battery management technique to reduce standby energy consumption in ultra-low power IoT and sensory applications[J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2020, 67(1): 336-345.
8	EMAMI S. Modulation/coding options for coin cell battery operated transmitters[J]. IEEE Communications Letters, 2015, 19(8): 1319-1322.
9	王海峰. 纯电动汽车锂动力电池能量状态估算算法研究[D]. 长春: 吉林大学, 2012.
	WANG H F. Study on state of energy estimation algorithm for lithium power battery used on pure electric vehicle[D]. Changchun: Jilin University, 2012.
10	STOCKAR S, MARANO V, CANOVA M, et al. Energy-optimal control of plug-in hybrid electric vehicles for real-world driving cycles[J]. IEEE Transactions on Vehicular Technology, 2011, 60(7): 2949-2962.
11	李超然, 肖飞, 樊亚翔, 等. 基于卷积神经网络的锂离子电池SOH估算[J]. 电工技术学报, 2020, 35(19): 4106-4119.
	LI C R, XIAO F, FAN Y X, et al. An approach to lithium-ion battery SOH estimation based on convolutional neural network[J]. Transactions of China Electrotechnical Society, 2020, 35(19): 4106-4119.
12	ÁLVAREZ ANTÓN J C, GARCÍA NIETO P J, BLANCO VIEJO C, et al. Support vector machines used to estimate the battery state of charge[J]. IEEE Transactions on Power Electronics, 2013, 28(12): 5919-5926.
13	SAHINOGLU G O, PAJOVIC M, SAHINOGLU Z, et al. Battery state-of-charge estimation based on regular/recurrent Gaussian process regression[J]. IEEE Transactions on Industrial Electronics, 2018, 65(5): 4311-4321.
14	KIM I S. The novel state of charge estimation method for lithium battery using sliding mode observer[J]. Journal of Power Sources, 2006, 163(1): 584-590.
15	XIONG R, YU Q Q, WANG L Y. Open circuit voltage and state of charge online estimation for lithium ion batteries[J]. Energy Procedia, 2017, 142: 1902-1907.
16	LIU X T, CHEN Z H, ZHANG C B, et al. A novel temperature-compensated model for power Li-ion batteries with dual-particle-filter state of charge estimation[J]. Applied Energy, 2014, 123: 263-272.
17	ZHANG S W, SUN H, LYU C. A method of SOC estimation for power Li-ion batteries based on equivalent circuit model and extended Kalman filter[C]//2018 13th IEEE Conference on Industrial Electronics and Applications (ICIEA). Wuhan, China. IEEE, 2018: 2683-2687.
18	HOU E G, QIAO X, LIU G M. SOC estimation for Power Lithium-ion Battery Based on AUKF[C]//Proceedings of the 2016 International Conference on Artificial Intelligence and Engineering Applications. November 12-13, 2016. Hong Kong, China. Paris, France: Atlantis Press, 2016: 14-8.
19	DUAN W X, SONG C X, CHEN Y, et al. Online parameter identification and state of charge estimation of battery based on multitimescale adaptive double Kalman filter algorithm[J]. Mathematical Problems in Engineering, 2020, 2020: 9502605.
20	ZHENG Y J, GAO W K, OUYANG M G, et al. State-of-charge inconsistency estimation of lithium-ion battery pack using mean-difference model and extended Kalman filter[J]. Journal of Power Sources, 2018, 383: 50-58.
21	ZHU Q, XU M G, LIU W Q, et al. A state of charge estimation method for lithium-ion batteries based on fractional order adaptive extended Kalman filter[J]. Energy, 2019, 187: 115880.
22	FENG T H, YANG L, ZHAO X W, et al. Online identification of lithium-ion battery parameters based on an improved equivalent-circuit model and its implementation on battery state-of-power prediction[J]. Journal of Power Sources, 2015, 281: 192-203.
23	YU Q Q, XIONG R, WANG L Y, et al. A comparative study on open circuit voltage models for lithium-ion batteries[J]. Chinese Journal of Mechanical Engineering, 2018, 31(1): 65.
24	ZHENG F D, XING Y J, JIANG J C, et al. Influence of different open circuit voltage tests on state of charge online estimation for lithium-ion batteries[J]. Applied Energy, 2016, 183: 513-525.
25	LIN C, YU Q Q, XIONG R, et al. A study on the impact of open circuit voltage tests on state of charge estimation for lithium-ion batteries[J]. Applied Energy, 2017, 205: 892-902.
26	HUANG C, WANG L. Gaussian process regression-based modelling of lithium-ion battery temperature-dependent open-circuit-voltage[J]. Electronics Letters, 2017, 53(17): 1214-1216.
27	SONG Y, PARK M, SEO M, et al. Improved SOC estimation of lithium-ion batteries with novel SOC-OCV curve estimation method using equivalent circuit model[C]//2019 4th International Conference on Smart and Sustainable Technologies (SpliTech). Split, Croatia. IEEE, 2019: 1-6.
28	HE H W, XIONG R, GUO H Q. Online estimation of model parameters and state-of-charge of LiFePO₄ batteries in electric vehicles[J]. Applied Energy, 2012, 89(1): 413-420.
29	FENG F, LU R G, WEI G, et al. Online estimation of model parameters and state of charge of LiFePO₄ batteries using a novel open-circuit voltage at various ambient temperatures[J]. Energies, 2015, 8(4): 2950-2976.
30	WANG J, XIONG R, LI L L, et al. A comparative analysis and validation for double-filters-based state of charge estimators using battery-in-the-loop approach[J]. Applied Energy, 2018, 229: 648-659.

估算方法	MAE/%	RMSE/%
端电压法	0.52	0.72
FFRLS-OCV	0.54	0.78
查表法OCV	1.00	1.36

[1]	李青, 张劭玮, 罗斯伦, 李炬晨, 成海超, 卢丞一. 不同温度下的基于BPNN-AUKF的新型自动水下航行器SOC估计器[J]. 储能科学与技术, 2024, 13(4): 1205-1215.
[2]	黄鹏超, 鄂加强. 基于双自适应卡尔曼滤波的锂电池状态估算[J]. 储能科学与技术, 2022, 11(2): 660-666.

基于AUKF的可穿戴式设备用锂离子电池SOE在线估计方法

Online state-of-energy estimation method for lithium-ion batteries used in wearable devices based on adaptive unscented Kalman filter

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 13

参考文献 30

相关文章 2

编辑推荐

Metrics

本文评价