A joint estimation method for SOC/SOP of all vanadium redox batteries based on online parameter identification and ensemble Kalman filtering

doi:10.19799/j.cnki.2095-4239.2024.0534

Abstract

Abstract:

Accurate estimation of the state of charge (SOC) and state of peak power (SOP) is crucial for ensuring the safe and stable operation of vanadium redox batteries (VRBs). To address the high errors and poor robustness associated with traditional estimation algorithms, this paper proposes a joint estimation method for SOC and SOP of VRBs based on adaptive unscented Kalman filtering (AUKF) and economic model predictive control (EMPC). First, considering the coupling characteristics of the electrochemical and fluid dynamics fields of VRBs, a comprehensive equivalent circuit model is developed to accurately represent the VRB operation. The artificial bee colony (ABC) algorithm is employed for offline identification of model parameters. Subsequently, given the limitations of the traditional unscented Kalman filter (UKF) algorithm, such as sensitivity to system noise, poor convergence, and neglect of dynamic battery parameters, an online parameter identification and SOC estimation algorithm based on AUKF is proposed. This approach enhances the model's accuracy by adaptively adjusting UKF parameters. Building on the SOC estimation results, the EMPC algorithm is utilized to estimate SOP, considering constraints including voltage, current, SOC, and electrolyte flow rate. The proposed SOC/SOP joint estimation algorithm's accuracy is validated under multiple experimental conditions. The findings of this research provide a reliable basis for predicting the peak power of VRBs under various operating conditions and for the precise scheduling of energy storage stations.

Key words: vanadium redox flow battery, state of charge, state of peak power, online model identification, adaptive unscented Kalman filter, economic model predictive control

CLC Number:

TM 911

Yu ZHANG, Yao YAO, Rui LIU, Lei JIN, Fei XUE, Peng ZHOU, Binyu XIONG. A joint estimation method for SOC/SOP of all vanadium redox batteries based on online parameter identification and ensemble Kalman filtering[J]. Energy Storage Science and Technology, 2024, 13(11): 4089-4101.

Figures/Tables 14

Fig.1

Table 1

UKF algorithm process"

流程	UKF算法
系统初始化	$x ̂ 0 = E x 0 P 0 = E x 0 - x ̂ 0 x 0 - x ̂ 0 T$ (15)

时间更新(预测)	$χ k - 1 = x ̂ k - 1, x ̂ k - 1 + (n + λ) P k - 1 i, x ̂ k - 1 - (n + λ) P k - 1 i$ (16) $χ k \| k - 1 = f χ k - 1$ (17) $x ̂ k \| k - 1 = ∑ i = 0 2 n W i m χ i (k \| k - 1) P k \| k - 1 = ∑ i = 0 2 n W i c χ i (k \| k - 1) - x ̂ k \| k - 1 T χ i (k \| k - 1) - x ̂ k \| k - 1 + Q$ (18)

观测校正	$Y k \| k - 1 = h χ k \| k - 1$ (19) $z ̂ k \| k - 1 = ∑ i = 0 2 n W i (m) Y i (k \| k - 1) S k = ∑ i = 0 2 n W i (c) Y i (k \| k - 1) - z ̂ k \| k - 1 T Y i (k \| k - 1) - z ̂ k \| k - 1 + R P x z = ∑ i = 0 2 n W i (c) χ i (k \| k - 1) - x ̂ k \| k - 1 T Y i (k \| k - 1) - z ̂ k \| k - 1$ (20)

计算卡尔曼增益，更新状态估计和协方差	$K k = P x z S k - 1$ (21) $x ̂ k = x ̂ k \| k - 1 + K k z k - z ̂ k \| k - 1 P k = P k \| k - 1 - K k S k K k T$ (22)

Table 1

Fig.2

Fig.3

Fig.4

Table 2

Table 3

Fig.5

Fig.6

Table 4

Fig.7

Fig.8

Fig.9

Fig.10

References 26

1	张爱芳, 魏邦达, 李卓昊, 等. 全钒液流电池建模及SOC在线估计研究进展[J]. 储能科学与技术, 2024, 13(3): 1036-1049. DOI: 10.19799/j.cnki.2095-4239.2023.0734.
	ZHANG A F, WEI B D, LI Z H, et al. Research progress on modeling and SOC online estimation of vanadium redox-flow batteries[J]. Energy Storage Science and Technology, 2024, 13(3): 1036-1049. DOI: 10.19799/j.cnki.2095-4239.2023.0734.
2	徐冉, 王宝冬, 王绍亮, 等.杂原子掺杂电极用于全钒液流电池中的研究进展[J].储能科学与技术, 2024, 13(6): 1849-1860. DOI: 10.19799/j.cnki.2095-4239.2023.0929.
	XU R, WANG B D, WANG S L, et al. Research progress on heteroatom doped electrodes used in all vanadium flow batteries [J]. Energy Storage Science and Technology, 2024, 13(06): 1849-1860. DOI: 10.19799/j.cnki.2095-4239.2023.0929.
3	LI Z Y, WANG M R, YANG J W, et al. A quantitative analysis method of complex sulfide components for understanding initial capacity degradation mechanism in lithium-sulfur batteries[J]. Journal of Colloid and Interface Science, 2024, 662: 1086-1095. DOI: 10.1016/j.jcis.2024.02.017.
4	ROSCHER V, RIEMSCHNEIDER K R. Method and measurement setup for battery state determination using optical effects in the electrode material[J]. IEEE Transactions on Instrumentation and Measurement, 2018, 67(4): 735-744. DOI: 10.1109/TIM. 2017. 2782018.
5	JIN S, WANG C, ZHEN Z Z, et al. Estimation of temperature for premixed flame by relative permittivity and conductivity[J]. IEEE Transactions on Instrumentation and Measurement, 2024, 73: 4502810. DOI: 10.1109/TIM.2024.3366578.
6	XIONG B Y, ZHAO J Y, WEI Z B, et al. Extended Kalman filter method for state of charge estimation of vanadium redox flow battery using thermal-dependent electrical model[J]. Journal of Power Sources, 2014, 262: 50-61. DOI: 10.1016/j.jpowsour. 2014.03.110.
7	WEI Z B, TSENG K J, WAI N, et al. Adaptive estimation of state of charge and capacity with online identified battery model for vanadium redox flow battery[J]. Journal of Power Sources, 2016, 332: 389-398. DOI: 10.1016/j.jpowsour.2016.09.123.
8	郭向伟, 李璐颖, 王晨, 等. 自适应渐消无迹卡尔曼滤波锂电池SoC估计[J]. 电子测量与仪器学报, 2024, 38(3): 167-175. DOI: 10.13382/j.jemi.B2306921.
	GUO X W, LI L Y, WANG C, et al. SoC estimation of lithium battery based on adaptive fading unscented Kalman filter[J]. Journal of Electronic Measurement and Instrumentation, 2024, 38(3): 167-175. DOI: 10.13382/j.jemi.B2306921.
9	邓丹, 刘胜永, 王顺利, 等. 基于FFRLS和ASR-UKF滤波算法的锂电池SOC估计[J]. 电源技术, 2024, 48(2): 299-305.
	DENG D, LIU S Y, WANG S L, et al. Lithium battery SOC estimation based on FFRLS and ASR-UKF filtering algorithm[J]. Chinese Journal of Power Sources, 2024, 48(2): 299-305.
10	FENG X, CHEN J X, ZHANG Z W, et al. State-of-charge estimation of lithium-ion battery based on clockwork recurrent neural network[J]. Energy, 2021, 236: 121360. DOI: 10.1016/j.energy.2021.121360.
11	ZHANG X S, LIU X J, LI J H. A novel method for battery SOC estimation based on slime mould algorithm optimizing neural network under the condition of low battery SOC value[J]. Electronics, 2023, 12(18): 3924. DOI: 10.3390/electronics 12183924.
12	陈清炀, 何映晖, 余官定, 等. 模型与数据双驱动的锂电池状态精准估计[J]. 储能科学与技术, 2023, 12(1): 209-217. DOI: 10.19799/j.cnki.2095-4239.2022.0508.
	CHEN Q Y, HE Y H, YU G D, et al. Integrating model-and data-driven methods for accurate state estimation of lithium-ion batteries[J]. Energy Storage Science and Technology, 2023, 12(1): 209-217. DOI: 10.19799/j.cnki.2095-4239.2022.0508.
13	XIONG R, HE H W, SUN F C, et al. Model-based state of charge and peak power capability joint estimation of lithium-ion battery in plug-in hybrid electric vehicles[J]. Journal of Power Sources, 2013, 229: 159-169. DOI: 10.1016/j.jpowsour.2012.12.003.
14	ZHENG F D, JIANG J C, SUN B X, et al. Temperature dependent power capability estimation of lithium-ion batteries for hybrid electric vehicles[J]. Energy, 2016, 113: 64-75. DOI: 10.1016/j.energy.2016.06.010.
15	金鑫娜, 顾启蒙, 潘宇巍, 等. 锂离子动力电池SOP在线估计方法研究[J]. 电源技术, 2019, 43(9): 1448-1452. DOI: 10.3969/j.issn.1002-087X.2019.09.011.
	JIN X N, GU Q M, PAN Y W, et al. Online state of power estimation methods for lithium-ion batteries in EV[J]. Chinese Journal of Power Sources, 2019, 43(9): 1448-1452. DOI: 10.3969/j.issn.1002-087X.2019.09.011.
16	SUN F C, XIONG R, HE H W. Estimation of state-of-charge and state-of-power capability of lithium-ion battery considering varying health conditions[J]. Journal of Power Sources, 2014, 259: 166-176. DOI: 10.1016/j.jpowsour.2014.02.095.
17	ZOU C F, KLINTBERG A, WEI Z B, et al. Power capability prediction for lithium-ion batteries using economic nonlinear model predictive control[J]. Journal of Power Sources, 2018, 396: 580-589. DOI: 10.1016/j.jpowsour.2018.06.034.
18	FARMANN A, SAUER D U. A comprehensive review of on-board state-of-available-power prediction techniques for lithium-ion batteries in electric vehicles[J]. Journal of Power Sources, 2016, 329: 123-137. DOI: 10.1016/j.jpowsour.2016.08.031.
19	WEI Z B, MENG S J, TSENG K J, et al. An adaptive model for vanadium redox flow battery and its application for online peak power estimation[J]. Journal of Power Sources, 2017, 344: 195-207. DOI: 10.1016/j.jpowsour.2017.01.102.
20	XIONG B Y, DONG S D, LI Y, et al. Peak power estimation of vanadium redox flow batteries based on receding horizon control[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2023, 11(1): 154-165. DOI: 10.1109/JESTPE. 2022. 3152588.
21	安治国, 田茂飞, 赵琳, 等. 基于自适应无迹卡尔曼滤波的锂电池SOC估计[J]. 储能科学与技术, 2019, 8(5): 856-861. DOI: 10.12028/j.issn.2095-4239.2019.0113.
	AN Z G, TIAN M F, ZHAO L, et al. SOC estimation of lithium battery based on adaptive untracked Kalman filter[J]. Energy Storage Science and Technology, 2019, 8(5): 856-861. DOI: 10.12028/j.issn.2095-4239.2019.0113.
22	HOU J, LIU J W, CHEN F W, et al. Robust lithium-ion state-of-charge and battery parameters joint estimation based on an enhanced adaptive unscented Kalman filter[J]. Energy, 2023, 271: 126998. DOI: 10.1016/j.energy.2023.126998.
23	孙乐平, 韩帅, 吴宛潞, 等. 基于经济模型预测控制的多虚拟电厂两阶段协调优化调度[J]. 储能科学与技术, 2021, 10(5): 1845-1853. DOI: 10.19799/j.cnki.2095-4239.2021.0195.
	SUN L P, HAN S, WU W L, et al. Coordinated optimal scheduling of multiple virtual power plants in multiple time scales based on economic model predictive control[J]. Energy Storage Science and Technology, 2021, 10(5): 1845-1853. DOI: 10.19799/j.cnki.2095-4239.2021.0195.
24	HU M J, LI C K, BIAN Y G, et al. Fuel economy-oriented vehicle platoon control using economic model predictive control[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(11): 20836-20849. DOI: 10.1109/TITS.2022.3183090.
25	赵安军, 米璐, 于军琪, 等. 多区域建筑灰箱建模及参数辨识方法[J]. 建筑科学, 2023, 39(12): 222-231, 254. DOI: 10.13614/j.cnki.11-1962/tu.2023.12.25.
	ZHAO A J, MI L, YU J Q, et al. Multi-zone building grey-box modeling and parameter identification method[J]. Building Science, 2023, 39(12): 222-231, 254. DOI: 10.13614/j.cnki.11-1962/tu.2023.12.25.
26	ESFANDYARI M J, HAIRI YAZDI M R, ESFAHANIAN V, et al. A hybrid model predictive and fuzzy logic based control method for state of power estimation of series-connected lithium-ion batteries in HEVs[J]. Journal of Energy Storage, 2019, 24: 100758. DOI: 10.1016/j.est.2019.100758.

参数	值
k₁	0.0042
k₂	1.3118
k₃	1.6930
E₀^T⁰/V	1.2887
R₀/Ω	0.1027
A_ed/m²	0.6363
R_act	0.0904
C_act	10000

模型参数	数值	模型参数	数值
η_pump	85%	μ	7×10^-3 Pa·s
ρ	1400 kg/m³	L_ed	0.24 m
A_p	1.28×10^-4 m²	d_f	3×10^-15 m
f_p	0.005	ε	0.54
L_p	0.48 m	K_ck	2
D_p	0.003 m	D_mc	8×10^-3 m
K_form	2.1

SOC₀	AUKF			UKF
SOC₀	MAE	RMSE	跟随系数	MAE	RMSE	跟随系数
0.8(恒流工况)	0.0018	0.0017	0.0216	0.01	0.023	0.0407
0.8(变流工况)	0.0083	0.0085	0.0074	0.0149	0.0167	0.0756

[1]	Xuefeng HU, Xianlei CHANG, Xiaoxiao LIU, Wei XU, Wenbin ZHANG. SOC estimation of lithium-ion batteries under multiple temperatures conditions based on MIARUKF algorithm [J]. Energy Storage Science and Technology, 2024, 13(9): 2983-2994.
[2]	Qingbo LI, Maohui ZHANG, Ying LUO, Taolin LYU, Jingying XIE. Lithium-ion battery state of charge estimation based on equivalent circuit model [J]. Energy Storage Science and Technology, 2024, 13(9): 3072-3083.
[3]	Zheng CHEN, Bo YANG, Zhigang ZHAO, Jiangwei SHEN, Renxin XIAO, Xuelei XIA. State of charge estimation considering lithium battery temperature and aging [J]. Energy Storage Science and Technology, 2024, 13(8): 2813-2822.
[4]	Ran XU, Baodong WANG, Shaoliang WANG, Qi ZHANG, Lei ZHANG, Ziyang FENG. Research progress on heteroatom-doped electrodes used in all vanadium redox flow batteries [J]. Energy Storage Science and Technology, 2024, 13(6): 1849-1860.
[5]	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.
[6]	Gaoqi LIAN, Min YE, Qiao WANG, Yan LI, Yuchuan MA, Yiding SUN, Penghui DU. State-of-charge estimation of lithium-ion batteries in rapid temperature-varying environments based on improved battery model and optimized adaptive cubature Kalman filter [J]. Energy Storage Science and Technology, 2024, 13(5): 1667-1676.
[7]	Lin HE, Jiangyan LIU, Bin LIU, Kuining LI, Shuai DAI. Generalized impact of data distribution diversity on SOC prediction of lithium battery [J]. Energy Storage Science and Technology, 2024, 13(5): 1677-1687.
[8]	Qing LI, Shaowei ZHANG, Silun LUO, Juchen LI, Haichao CHENG, Chenyi LU. A novel automatic underwater vehicle SOC estimator based on BPNN-AUKF at different temperatures [J]. Energy Storage Science and Technology, 2024, 13(4): 1205-1215.
[9]	Aifang ZHANG, Bangda WEI, Zhuohao LI, Yang YANG, Tianqiang YANG, Jun YAO, Jie ZHANG, Fei LIU, Haomiao LI, Kangli WANG, Kai JIANG. Research progress on modeling and SOC online estimation of vanadium redox-flow batteries [J]. Energy Storage Science and Technology, 2024, 13(3): 1036-1049.
[10]	Kangyong YIN, Lei SUN, Haomiao LI, Dongliang GUO, Peng XIAO, Kangli WANG, Kai JIANG. SOC estimation of lithium-ion batteries based on DN-AUKF [J]. Energy Storage Science and Technology, 2024, 13(11): 4065-4077.
[11]	Jiangwei SHEN, Canbiao ZHOU, Xing SHU, Zheng CHEN, Yonggang LIU. State of charge estimation for lithium batteries based on an improved electrochemical model at a wide temperature environment [J]. Energy Storage Science and Technology, 2023, 12(9): 2904-2916.
[12]	Honghui WANG, Yifan LIU, Deren CHU. Calendar aging of lithium titanate battery with different state of charge [J]. Energy Storage Science and Technology, 2023, 12(8): 2606-2614.
[13]	Hongsheng GUAN, Cheng QIAN, Binghui XU, Bo SUN, Yi REN. SAM-GRU-based fusion neural network for SOC estimation in lithium-ion batteries under a wide range of operating conditions [J]. Energy Storage Science and Technology, 2023, 12(7): 2229-2237.
[14]	Birong TAN, Jianhua DU, Xianghu YE, Xin CAO, Chang QU. Overview of SOC estimation methods for lithium-ion batteries based on model [J]. Energy Storage Science and Technology, 2023, 12(6): 1995-2010.
[15]	Feng LIU, Haizhong CHEN. Lithium-ion battery state prediction based on CEEMDAN and ISOA-ELM [J]. Energy Storage Science and Technology, 2023, 12(4): 1244-1256.