IFFRLS-IMMUKF-based estimation of the state of charge of lithium iron phosphate batteries for commercial vehicles

doi:10.19799/j.cnki.2095-4239.2025.0194

Abstract

Abstract:

State of charge (SOC) is a crucial parameter for characterizing the remaining capacities of electric vehicles (EVs). Accurate SOC estimation ensures EV safety and reliability. To facilitate accurate estimation of battery SOC in complex environments, the equivalent circuit model is constructed based on the characteristics of power batteries, and the equation of state (EOS) of the battery model is discretized. Further, to obtain the discretized EOS, the golden-jackal-optimization algorithm is combined with the forgetting factor recursive least square (FFRLS) algorithm to yield an improved FFRLS method for identifying the parameters of the battery model. Concurrently, the interacting multiple-model unscented Kalman filter (IMMUKF) algorithm is used to estimate the battery SOC, which is experimentally verified via dynamic stress tests (DST) and federal urban driving schedules (FUDS) at room and high temperatures. The experimental results indicate that the mean absolute error of the proposed improved IFFRLS-IMMUKF-based lithium-battery SOC-estimation method is within 0.8% and that the SOC-estimation accuracy for lithium iron phosphate batteries is high.

Key words: golden jackal optimization algorithm, forgetting factor recursive least square, interacting multiple model unscented Kalman filter, state of charge

CLC Number:

TM 912

Huawei WU, Chengze HE, Qiang HONG, Xiaogao ZHOU, Mingjin LI, Yajuan GU. IFFRLS-IMMUKF-based estimation of the state of charge of lithium iron phosphate batteries for commercial vehicles[J]. Energy Storage Science and Technology, 2025, 14(10): 3996-4008.

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References 26

[1]	沈佳妮, 贺益君, 马紫峰. 基于模型的锂离子电池SOC及SOH估计方法研究进展[J]. 化工学报, 2018, 69(1): 309-316. DOI: 10.11949/j.issn.0438-1157.20171097.
	SHEN J N, HE Y J, MA Z F. Progress of model based SOC and SOH estimation methods for lithium-ion battery[J]. CIESC Journal, 2018, 69(1): 309-316. DOI: 10.11949/j.issn.0438-1157. 20171097.
[2]	宋磊, 陆春光, 刘琳, 等. 基于修正安时积分法的磷酸铁锂电池荷电状态估计[J]. 郑州大学学报(工学版), 2023, 44(6): 84-90. DOI: 10. 13705/j.issn.1671-6833.2023.06.003.
	SONG L, LU C G, LIU L, et al. State of charge estimation of LiFePO₄ battery based on modified amper-hour integral method[J]. Journal of Zhengzhou University (Engineering Science), 2023, 44(6): 84-90. DOI: 10.13705/j.issn.1671-6833.2023.06.003.
[3]	王少华. 电动汽车动力锂电池模型参数辨识和状态估计方法研究[D]. 长春: 吉林大学, 2021. DOI: 10.27162/d.cnki.gjlin.2021. 007576.
	WANG S H. Research on model parameter identification and state estimation method of power lithium battery for electric vehicle[D]. Changchun: Jilin University, 2021. DOI: 10.27162/d.cnki.gjlin.2021.007576.
[4]	田从丰, 汪文浦, 张风奇, 等. 电动车辆动力电池SOC估计方法研究进展及展望[J]. 中国公路学报, 2025, 38(5): 224-247. DOI: 10.19721/j.cnki.1001-7372.2025.05.019.
	TIAN C F, WANG W P, ZHANG F Q, et al. Research progress and prospects of state of charge estimation methods for electric vehicle power batteries[J]. China Journal of Highway and Transport, 2025, 38(5): 224-247. DOI: 10.19721/j.cnki.1001-7372.2025.05.019.
[5]	凌六一, 吴贤圆, 王星凯, 等. 基于FFRLS-AUKF的锂电池参数在线辨识及SOC估计[J]. 安徽理工大学学报(自然科学版), 2023, 43(1): 1-7.
	LING L Y, WU X Y, WANG X K, et al. Online parameter identification and SOC estimation of lithium battery based on FFRLS-AUKF[J]. Journal of Anhui University of Science and Technology (Natural Science), 2023, 43(1): 1-7.
[6]	LIANG Y W, WANG S L, FAN Y C, et al. An error covariance correction-adaptive extended Kalman filter based on piecewise forgetting factor recursive least squares method for the state-of-charge estimation of lithium-ion batteries[J]. Journal of Energy Storage, 2023, 68: 107629. DOI: 10.1016/j.est.2023.107629.
[7]	PENG J K, LUO J Y, HE H W, et al. An improved state of charge estimation method based on cubature Kalman filter for lithium-ion batteries[J]. Applied Energy, 2019, 253: 113520. DOI: 10.1016/j.apenergy.2019.113520.
[8]	RESHMA P, MANOHAR V J. Collaborative evaluation of SoC, SoP and SoH of lithium-ion battery in an electric bus through improved remora optimization algorithm and dual adaptive Kalman filtering algorithm[J]. Journal of Energy Storage, 2023, 68: 107573. DOI: 10.1016/j.est.2023.107573.
[9]	SUN C, LIU S L, SUN B. Joint estimation of SOC and SOH of lithium battery based on multi-time scale EKF-ASRCKF algorithm[J]. Journal of Physics: Conference Series, 2023, 2477(1): 012015. DOI: 10.1088/1742-6596/2477/1/012015.
[10]	LI Z X, SHEN S Y, ZHOU Z, et al. Novel method for modelling and adaptive estimation for SOC and SOH of lithium-ion batteries[J]. Journal of Energy Storage, 2023, 62: 106927. DOI: 10.1016/j.est.2023.106927.
[11]	XIA B Z, LAO Z Z, ZHANG R F, et al. Online parameter identification and state of charge estimation of lithium-ion batteries based on forgetting factor recursive least squares and nonlinear Kalman filter[J]. Energies, 2018, 11(1): 3. DOI: 10.3390/en11010003.
[12]	XIAO W J, WANG S L, YU C M, et al. Online parameter identification and state of charge estimation of lithium-ion batteries based on improved artificial fish swarms forgetting factor least squares and differential evolution extended Kalman filter[J]. Journal of the Electrochemical Society, 2022, 169(12): 120534. DOI: 10.1149/1945-7111/acaa5b.
[13]	徐伟杰. 基于模型法的锂电池SOC估计及均衡控制研究[D]. 秦皇岛: 燕山大学, 2023. DOI: 10.27440/d.cnki.gysdu.2023.000237.
[14]	李堂, 黄康, 毛行奎, 等. 基于EKF算法的动力锂离子电池SOC估计[J]. 电器与能效管理技术, 2023(9): 62-68, 75. DOI: 10.16628/j.cnki.2095-8188.2023.09.010.
	LI T, HUANG K, MAO X K, et al. SOC estimation of power lithium-ion battery based on EKF algorithm[J]. Electrical & Energy Management Technology, 2023(9): 62-68, 75. DOI: 10.16628/j.cnki.2095-8188.2023.09.010.
[15]	张远进, 吴华伟, 叶从进. 基于AUKF-BP神经网络的锂电池SOC估算[J]. 储能科学与技术, 2021, 10(1): 237-241. DOI: 10.19799/j.cnki.2095-4239.2020.0285.
	ZHANG Y J, WU H W, YE C J. Estimation of the SOC of a battery based on the AUKF-BP algorithm[J]. Energy Storage Science and Technology, 2021, 10(1): 237-241. DOI: 10.19799/j.cnki. 2095-4239.2020.0285.
[16]	王建锋, 张照震, 李平. 基于加权自适应递推最小二乘法与EKF的锂离子电池SOC估计[J]. 汽车技术, 2021(10): 16-22. DOI: 10.19620/j.cnki.1000-3703.20200990.
	WANG J F, ZHANG Z Z, LI P. State of charge estimation for lithium-ion battery based on adaptive recursive weighted least squares and extended Kalman filter algorithm[J]. Automobile Technology, 2021(10): 16-22. DOI: 10.19620/j.cnki.1000-3703.20200990.
[17]	SUN X D, JI J R, REN B Y, et al. Adaptive forgetting factor recursive least square algorithm for online identification of equivalent circuit model parameters of a lithium-ion battery[J]. Energies, 2019, 12(12): 2242. DOI: 10.3390/en12122242.
[18]	夏小虎, 刘明. 基于交互式多模型卡尔曼滤波的电池荷电状态估计[J]. 信息与控制, 2017, 46(5): 519-524. DOI: 10.13976/j.cnki.xk. 2017.0519.
	XIA X H, LIU M. Battery state-of-charge estimation using interactive multiple-model Kalman filter[J]. Information and Control, 2017, 46(5): 519-524. DOI: 10.13976/j.cnki.xk.2017. 0519.
[19]	谭霁宬, 颜学龙. 基于交互式多模型无迹卡尔曼滤波的锂电池荷电状态估计[J]. 科学技术与工程, 2019, 19(12): 170-175.
	TAN J C, YAN X L. Estimation of state-of-charge for lithium-ion battery by interactive multiple model unscented Kalman filter[J]. Science Technology and Engineering, 2019, 19(12): 170-175.
[20]	李锦满, 李儒欢, 李浩南, 等. 基于无迹卡尔曼滤波的动力电池状态估计[J]. 电池, 2024, 54(3): 340-343. DOI:10.19535/j.1001-1579. 2024.03.010.
	LI J M, LI R H, LI H N, et al. State estimation for power battery based on unscented Kalman filter[J]. Dianchi(Battery Bimonthly), 2024, 54(3): 340-343. DOI:10.19535/j.1001-1579.2024.03.010.
[21]	吴华伟, 洪强, 陈运星, 等. 基于CSO-AUKF的锂电池SOC估算方法[J]. 重庆交通大学学报(自然科学版), 2024, 43(9): 118-126.
	WU H W, HONG Q, CHEN Y X, et al. Lithium battery SOC estimation method based on CSO-AUKF[J]. Journal of Chongqing Jiaotong University (Natural Science), 2024, 43(9): 118-126.
[22]	高铭琨, 徐海亮, 吴明铂. 基于等效电路模型的动力电池SOC估计方法综述[J]. 电气工程学报, 2021, 16(1): 90-102.
	GAO M K, XU H L, WU M B. Review of SOC estimation methods for power battery based on equivalent circuit model[J]. Journal of Electrical Engineering, 2021, 16(1): 90-102.
[23]	CHOPRA N, MOHSIN ANSARI M. Golden jackal optimization: A novel nature-inspired optimizer for engineering applications[J]. Expert Systems with Applications, 2022, 198: 116924. DOI: 10. 1016/j.eswa.2022.116924.
[24]	黄锐. 基于可变遗忘因子递推最小二乘法的三元锂电池荷电状态估计[D]. 重庆: 重庆大学, 2022. DOI: 10.27670/d.cnki.gcqdu.2022. 002239.
[25]	赵可沦, 江境宏, 邓进, 等. 基于遗忘因子递推最小二乘法的锂电池等效电路模型参数辨识方法[J]. 电子测量技术, 2022, 45(16): 87-92. DOI: 10.19651/j.cnki.emt.2209936.
	ZHAO K L, JIANG J H, DENG J, et al. Parameter identification method of lithium battery equivalent circuit model based on forgetting factor recursive least squares[J]. Electronic Measurement Technology, 2022, 45(16): 87-92. DOI: 10.19651/j.cnki.emt.2209936.
[26]	张武, 孙士山, 张家福. 基于自适应无迹卡尔曼滤波的动力电池SOC估计[J]. 电源技术, 2021, 45(1): 14-17. DOI: 10.3969/j.issn.1002-087X.2021.01.004.
	ZHANG W, SUN S S, ZHANG J F. SOC estimation of power batteries based on adaptive unscented Kalman filter[J]. Chinese Journal of Power Sources, 2021, 45(1): 14-17. DOI: 10.3969/j.issn.1002-087X.2021.01.004.

FFRLS	MAE/mV	RMSE/mV	IFFRLS	MAE/mV	RMSE/mV
DST	0.48295	2.50754	DST	0.40793	1.77810
FUDS	0.58532	3.03267	FUDS	0.51131	2.45441

FFRLS	MAE/mV	RMSE/mV	IFFRLS	MAE/mV	RMSE/mV
DST	0.42090	2.00484	DST	0.36123	1.35677
FUDS	0.38668	1.90763	FUDS	0.28619	0.40209

FFRLS	最大误差/%	MAE/%	RMSE/%	IFFRLS	最大误差/%	MAE/%	RMSE/%
DST	4.326	1.470	1.658	DST	2.205	0.702	0.865
FUDS	5.008	1.472	1.722	FUDS	2.468	0.741	0.854

FFRLS	最大误差/%	MAE/%	RMSE/%	IFFRLS	最大误差/%	MAE/%	RMSE/%
DST	5.015	1.304	1.561	DST	2.170	0.573	0.634
FUDS	4.172	1.275	1.514	FUDS	2.435	0.506	0.628