Research on fractional modeling and SOC estimation strategy for lithium batteries

doi:10.19799/j.cnki.2095-4239.2022.0551

Abstract

Abstract:

To improve the accuracy of the lithium battery model and realize an accurate estimation of the lithium battery state, a second-order fractional electrical model is established for the lithium battery based on the second-order RC equivalent circuit. In this study, the adaptive genetic algorithm is used to realize the parameter identification of the fractional order model, which can increase the convergence speed, reduce the identification time, avoid falling into the local optimal solution, overcome the parameter dispersion, and improve the accuracy of the model parameters. Based on the fractional order electrical model, a state estimation method is proposed for the unscented particle filter by adopting the Schmidt orthogonal transformation. Instead of using traditional unscented particle filters, a method that combines standard sampling with the Schmidt orthogonal transformation is adopted in the selection of sampling points to screen the symmetrically sampled particles, which leads to a reduced number of sampling points and an improved calculation efficiency. In addition, it can also limit the divergence of the estimated value caused by the nonlinearity of the system or the particle shortage caused by a small particle number for the particle filter algorithm. The simulation results show that the established fractional order electrical model can more accurately account for the dynamic characteristics of charging and discharging for lithium batteries, and the proposed state estimation strategy demonstrates higher accuracy than the conventional control strategy. In general, the system robustness is improved, and the SOC of lithium batteries can be estimated with an error of within 1%. Moreover, the overall calculation efficiency is improved, which makes it easy to realize the algorithm in real-time.

Key words: lithium battery, fractional order, state of charge, schmidt orthogonal transformation, unscented particle filter algorithm

CLC Number:

TM 911

Lulu LI, Zhengshun TAO, Tinglong PAN, Weilin YANG, Guanyang HU. Research on fractional modeling and SOC estimation strategy for lithium batteries[J]. Energy Storage Science and Technology, 2023, 12(2): 544-551.

Figures/Tables 8

Fig. 1

Fig. 2

Table 1

Comparison table of calculated quantities of FOUPF and FOSOUPF"

计算复杂度	FOUPF	FOSOUPF
采样点数	$2 L + 1$	$L + 1$
协方差阵Cholesky分解	$o (L 3 / 6)$	$o [(L / 2) 3 / 6)]$
确定采样点	$o [m (L 3 / 6)]$	$o [m (L / 2) 3 / 6]$
时间更新	$o [m (L 3 / 6)]$	$o [m (L / 2) 3]$
量测更新	$o (m M 2)$	$o (m M 2)$

Table 1

Table 2

Parameter identification results"

R₀/Ω	R₁/Ω	R₂/Ω	$C c p e 1$ /kF	$C c p e 2$ /kF	m	n
0.0036	0.0025	0.0093	1.624	3.11	0.9759	0.9947

Table 2

Fig. 3

Fig. 4

Fig. 5

Table 3

References 19

1	LU L G, HAN X B, LI J Q, et al. A review on the key issues for lithium-ion battery management in electric vehicles[J]. Journal of Power Sources, 2013, 226: 272-288.
2	COLEMAN M, HURLEY W G, LEE C K. An improved battery characterization method using a two-pulse load test[J]. IEEE Transactions on Energy Conversion, 2008, 23(2): 708-713.
3	袁世斐, 吴红杰, 殷承良. 锂离子电池简化电化学模型: 浓度分布估计[J]. 浙江大学学报(工学版), 2017, 51(3): 478-486.
	YUAN S F, WU H J, YIN C L. Simplified electrochemical model for Li-ion battery: Lithium concentration estimation[J]. Journal of Zhejiang University (Engineering Science), 2017, 51(3): 478-486.
4	TAMANWE P, SOROUSH R, KIRAN K, et al. Detailed electrochemical model of microphotosynthetic power cells[J]. IEEE Transactions on Industry Applications, 2021, 57(2).
5	TROVÒ A, SACCARDO A, GIOMO M, et al. Thermal modeling of industrial-scale vanadium redox flow batteries in high-current operations[J]. Journal of Power Sources, 2019, 424: 204-214.
6	朱磊, 刘子博, 李路路, 等. 基于RLS-DLUKF算法的锂电池SOC预测方法研究[J]. 储能科学与技术, 2021, 10(3): 1137-1144.
	ZHU L, LIU Z B, LI L L, et al. Research on a battery SOC prediction method based on the RLS-DLUKF algorithm[J]. Energy Storage Science and Technology, 2021, 10(3): 1137-1144.
7	HU X S, LI S E, YANG Y L. Advanced machine learning approach for lithium-ion battery state estimation in electric vehicles[J]. IEEE Transactions on Transportation Electrification, 2016, 2(2): 140-149.
8	刘树林, 崔纳新, 李岩, 等. 基于分数阶理论的车用锂离子电池建模及荷电状态估计[J]. 电工技术学报, 2017, 32(4): 189-195.
	LIU S L, CUI N X, LI Y, et al. Modeling and state of charge estimation of lithium-ion battery based on theory of fractional order for electric vehicle[J]. Transactions of China Electrotechnical Society, 2017, 32(4): 189-195.
9	WANG B J, LI S E, PENG H E, et al. Fractional-order modeling and parameter identification for lithium-ion batteries[J]. Journal of Power Sources, 2015, 293: 151-161.
10	罗勇, 祁朋伟, 黄欢, 等. 基于容量修正的安时积分SOC估算方法研究[J]. 汽车工程, 2020, 42(5): 681-687.
	LUO Y, QI P W, HUANG H, et al. Study on battery SOC estimation by ampere-hour integral method with capacity correction[J]. Automotive Engineering, 2020, 42(5): 681-687.
11	徐文华, 王顺利, 于春梅, 等. 基于Thevenin模型和UKF的锂电池SOC估算方法研究[J]. 自动化仪表, 2020, 41(5): 31-36.
	XU W H, WANG S L, YU C M, et al. Research on the estimation method of lithium battery SOC based on thevenin model and UKF[J]. Process Automation Instrumentation, 2020, 41(5): 31-36.
12	谢长君, 费亚龙, 曾春年, 等. 基于无迹粒子滤波的车载锂离子电池状态估计[J]. 电工技术学报, 2018, 33(17): 3958-3964.
	XIE C J, FEI Y L, ZENG C N, et al. State-of-charge estimation of lithium-ion battery using unscented particle filter in vehicle[J]. Transactions of China Electrotechnical Society, 2018, 33(17): 3958-3964.
13	刘新天, 李贺, 何耀, 等. 基于IUPF算法与可变参数电池模型的SOC估计方法[J]. 东南大学学报(自然科学版), 2018, 48(1): 54-62.
	LIU X T, LI H, HE Y, et al. SOC estimation method based on IUPF algorithm and variable parameter battery model[J]. Journal of Southeast University (Natural Science Edition), 2018, 48(1): 54-62.
14	谢滟馨, 王顺利, 史卫豪, 等. 一种用于高保真锂电池SOC估计的无迹粒子滤波新方法[J]. 储能科学与技术, 2021, 10(2): 722-731.
	XIE Y X, WANG S L, SHI W H, et al. A new method of unscented particle filter for high-fidelity lithium-ion battery SOC estimation[J]. Energy Storage Science and Technology, 2021, 10(2): 722-731.
15	黄耀光, 高博, 李建新, 等. 基于施密特正交变换UKF的单站无源定位算法[J]. 电光与控制, 2013, 20(2): 37-40.
	HUANG Y G, GAO B, LI J X, et al. Single-observer passive location based on Schmidt orthogonal transform UKF algorithm[J]. Electronics Optics & Control, 2013, 20(2): 37-40.
16	吴铁洲, 刘康丽, 杜炘宇. 基于UKPF算法的锂离子电池SOC估算[J]. 电源技术, 2021, 45(5): 602-605, 625.
	WU T Z, LIU K L, DU X Y. SOC estimation of lithium ion battery based on UKPF algorithm[J]. Chinese Journal of Power Sources, 2021, 45(5): 602-605, 625.
17	何耀, 秦少勋, 刘新天, 等. 基于分数阶无迹粒子滤波的动力电池SOC估计[J]. 汽车技术, 2018(5): 6-11.
	HE Y, QIN S X, LIU X T, et al. Power battery SOC estimation based on fractional unscented particle filter[J]. Automobile Technology, 2018(5): 6-11.
18	KONATOWSKI S, KANIEWSKI P, MATUSZEWSKI J. Comparison of estimation accuracy of EKF, UKF and PF filters[J]. Annual of Navigation, 2016, 23: 69-87.
19	李嘉波, 魏孟, 李忠玉, 等. 基于自适应扩展卡尔曼滤波的锂离子电池荷电状态估计[J]. 储能科学与技术, 2020, 9(4): 1147-1152.
	LI J B, WEI M, LI Z Y, et al. State of charge estimation of Li-ion battery based on adaptive extended Kalman filter[J]. Energy Storage Science and Technology, 2020, 9(4): 1147-1152.

状态估计方法	SOC初始值为1		SOC初始值为0.8
状态估计方法	SOC误差	电压误差	SOC误差	电压误差
FOSOUPF	0.0036	0.0048	0.0037	0.0053
FOUPF	0.0042	0.0065	0.0051	0.0067
FOUKF	0.0062	0.0072	0.0063	0.0075

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