锂离子电池快速充电策略设计研究进展

doi:10.3901/JME.2025.16.180

摘要/Abstract

摘要： 作为新型储能器件的代表，锂离子电池因其优异的性能表现与环保特性得到广泛应用。然而，无论是低速充电导致的漫长充电时间，还是快速充电导致的电池退化仍然是阻碍锂离子电池进一步推广与发展的关键问题。鉴于此，对锂离子电池的快速充电策略进行设计成了近年的一个研究热点。为了总结研究进展，从快速充电策略设计的核心内容充电问题描述、电池模型建立、充电方法设计三个方面对现有的研究进行了系统的综述。首先，介绍快速充电策略设计的研究背景，调查充电问题的优化目标、约束条件、设计变量的设置方式；然后，简述锂离子电池的内部机理与几种常用的电池模型，并归纳融合机器学习的建模方法；接着，重点分析现有的不同充电方法，并根据方法特点进行分类与讨论；最后，基于研究现状总结未来的可能研究方向，希望为学者提供研究思路以设计更高效、更易应用的快速充电策略。

关键词: 锂离子电池, 快速充电, 策略设计, 电池模型, 问题描述

Abstract: As a representative of innovative energy storage devices, lithium-ion batteries have been widely used due to their excellent performance and environmentally friendly properties. However, the long charging time caused by slow charging and the degradation caused by fast charging remain critical issues that hinder the further promotion and development of lithium-ion batteries. To this end, the design of the fast charging strategies of lithium-ion batteries has become a hot research topic recently. To summarize the research progress, a systematic review of current research on this topic is presented from three aspects： formulation of the charging problem, establishment of battery models, and design of charging methods, all core elements in the fast charging strategy design. First, the research background of the fast charging strategy design is introduced. Specifically, how to set the optimization objectives, constraints, and design variables of the design problem is investigated. Second, the internal mechanisms of lithium-ion batteries and some commonly used battery models are briefly described, and the modeling methods that incorporate machine learning are also summarized. Additionally, various existing charging methods are especially analyzed and classified based on their characteristics. Moreover, based on the current research status, some future directions are given, aiming to offer researchers a valuable opportunity to design more efficient and user-friendly fast charging strategies.

Key words: lithium-ion batteries, fast charging, strategy design, battery model, problem formulation

中图分类号:

TM912

毛阳阳, 邓海鹏, 王冰川, 王勇. 锂离子电池快速充电策略设计研究进展[J]. 机械工程学报, 2025, 61(16): 180-203.

MAO Yangyang, DENG Haipeng, WANG Bingchuan, WANG Yong. Review of Advances in Designing Fast Charging Strategies for Lithium-ion Batteries[J]. Journal of Mechanical Engineering, 2025, 61(16): 180-203.

参考文献

[1] XU C J, BEHRENS P, GASPER P, et al. Electric vehicle batteries alone could satisfy short-term grid storage demand by as early as 2030[J]. Nature Communications, 2023, 14: 119.
[2] ZHU J , WIERZBICKI T , LI W. A review of safety-focused mechanical modeling of commercial lithium-ion batteries[J]. Journal of Power Sources, 2018, 378: 153-168.
[3] GOURLEY S W D, OR T, CHEN Z. Breaking free from cobalt reliance in lithium-ion batteries[J]. iScience, 2020, 23(9): 153-168.
[4] WANG C Y, LIU T, YANG X G, et al. Fast charging of energy-dense lithium-ion batteries[J]. Nature, 2022, 611: 485-490.
[5] XIE W L, LIU X H, LI W, et al. Challenges and opportunities toward fast-charging of lithium-ion batteries[J]. Journal of Energy Storage, 2020, 32: 101837.
[6] DRESS R, LIENESCH F, KURRAT M. Fast charging lithium-ion battery formation based on simulations with an electrode equivalent circuit model[J]. Journal of Energy Storage, 2021, 36: 102345.
[7] MEI W X, LIU Z, WANG C D, et al. Monitoring of thermal runaway in commercial lithium-ion cells via advanced lab-on-fiber technologies[J]. Nature Communications, 2023, 14: 5251.
[8] HAN X B, LU L G, ZHENG Y J, et al. A review on the key issues of the lithiumion battery degradation among the whole life cycle[J]. eTtransportation, 2019(1): 100005.
[9] GAO Y Z, ZHANG X, CHENG Q Y, et al. Classification and review of the charging strategies for commercial lithium-ion batteries[J]. IEEE Access , 2019 , 7 : 43511-43524.
[10] YANG R , XIE Y , LI K N , et al. An enhanced electro-thermal coupled model with lithium plating detection for lithium-ion battery at low temperatures[J]. IEEE Transactions on Transportation Electrification , 2024, 10(1): 720-734.
[11] KERMANI J R, TAHERI M M, SHAFⅡ M B, et al. Analytical solution, optimization and design of a phase change cooling pack for cylindrical lithium-ion batteries[J]. Applied Thermal Engineering, 2023, 232: 120963.
[12] 徐乐,邓忠伟, 谢翌,等. 锂离子电池高精度机理建模、参数辨识与寿命预测研究进展[J]. 机械工程学报, 2022, 58(22): 19-36. XU Le, DENG Zhongwei, XIE Yi, et al. Review on research progress in high-fidelity modeling, parameter identification and lifetime prognostics of lithium-ion battery[J]. Journal of Mechanical Engineering, 2022, 58(22): 19-36.
[13] NEJAD S, GLADWIN D T, STONE D A. A systematic review of lumped-parameter equivalent circuit models for real-time estimation of lithium-ion battery states[J]. Journal of Power Sources, 2016, 316: 183-196.
[14] KLEIN R, CHATURVEDI N A, CHRISTENSEN J, et al. Electrochemical model based observer design for a lithium-ion battery[J]. IEEE Transactions on Control Systems Technology, 2013, 21(2): 289-301.
[15] WANG H C, FU T F, DU Y Q, et al. Scientific discovery in the age of artificial intelligence[J]. Nature, 2023, 621: E33.
[16] TAGUCHI G C. Mahalanobis-Taguchi strategy a pattern technology system[M]. New York: John Wiley, 2002.
[17] ROY R K. Design of experiments using the Taguchi approach : 16 Steps to product and process improvement[M]. New York: John Wiley Sons, 2001.
[18] BELLMAN R E, DREYFUS S E. Applied dynamic programming[M]. Princeton: Princeton University Press 2015.
[19] 董昊轩,殷国栋,庄伟超,等. 基于迭代动态规划的网联电动汽车经济性巡航车速优化[J]. 机械工程学报, 2021, 57(6): 121-130. DONG Haoxuan, YIN Guodong, ZHUANG Weichao, et al. Economic cruising velocity optimization using iterative dynamic programming of connected electric vehicle[J]. Journal of Mechanical Engineering, 2021, 57(6): 121-130.
[20] MEI Y, CHEN Q, LENSEN A, et al. Explainable artificial intelligence by genetic programming: A survey[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(3): 621-641.
[21] 郑逸凡,钱斌,胡蓉,等. CE-GA 协同进化算法求解人机共同作业的 U 形装配线平衡问题[J]. 机械工程学报, 2020, 56(9): 199-214. ZHENG Yifan, QIAN Bin, HU Rong, et al. CE-GA Co-evolutionary algorithm for solving U-shaped assembly line balancing problem with man-robot cooperation[J]. Journal of Mechanical Engineering, 2020, 56(9): 199-214.
[22] GARNETT R. Bayesian optimization[M]. Cambridge: Cambridge University Press, 2023.
[23] 杨真真,李明富,张黎明,等. 基于模型预测控制的工业机器人曲面跟踪方法研究[J]. 机械工程学报, 2022, 58(19): 24-33. YANG Zhenzhen, LI Mingfu, ZHANG Liming, et al. Research on surface tracking method of industrial robot based on model predictive control[J]. Journal of Mechanical Engineering, 2022, 58(19): 24-33.
[24] 郭景华,李文昌,王班,等. 基于深度强化学习的网联混合动力汽车队列控制[J]. 机械工程学报, 2024, 60(2): 262-271. GUO Jinghua, LI Wenchang, WANG Ban, et al. Deep reinforcement learning-based control strategy of connected hybrid electric vehicles platooning[J]. Journal of Mechanical Engineering, 2024, 60(2): 262-271.
[25] YANG X G, WANG C Y. Understanding the trilemma of fast charging, energy density and cycle life of lithium-ion batteries[J]. Journal of Power Sources, 2018, 402: 489-498.
[26] LIU K L, HU X S, YANG Z L, et al. Lithium-ion battery charging management considering economic costs of electrical energy loss and battery degradation[J]. Energy Conversion and Management, 2019, 195: 167-179.
[27] OUYANG Q, FANG R Y, XU G T, et al. User-involved charging control for lithium-ion batteries with economic cost optimization[J]. Applied Energy, 2022, 314: 119978.
[28] LIU Y H, LUO Y F. Search for an optimal rapid-charging pattern for Li-ion batteries using the Taguchi approach[J]. IEEE Transactions on Industrial Electronics , 2010 , 57(12): 3963-3971.
[29] LEE C H, CHEN M Y, HSU S H, et al. Implementation of an SOC-based four-stage constant current charger for Li-ion batteries[J]. Journal of Energy Storage, 2018, 18: 528-537.
[30] JIANG L, LI Y, HUANG Y D, et al. Optimization of multi-stage constant current charging pattern based on Taguchi method for Li-ion battery[J]. Applied Energy, 2020, 259: 114148.
[31] KUMAR K, PAREEK K. Fast charging of lithium-ion battery using multistage charging and optimization with grey relational analysis[J]. Journal of Energy Storage, 2023, 68: 107704.
[32] WU X G, SHI W W, DU J Y. Multi-objective optimal charging method for lithium-ion batteries[J]. Energies, 2010, 10(9): 1271.
[33] LIN X K, HAO X G, LIN Z Y, et al. Health conscious fast charging of Li-ion batteries via a single particle model with aging mechanisms[J]. Journal of Power Sources, 2018, 400: 305-316.
[34] LIN X K, WANG S, KIM Y K. A framework for charging strategy optimization using a physics-based battery model[J]. Journal of Applied Electrochemistry, 2019, 49(8): 779-793.
[35] XU M, WANG R, ZHAO P, et al. Fast charging optimization for lithium-ion batteries based on dynamic programming algorithm and electrochemical thermal capacity fade coupled model[J]. Journal of Power Sources, 2019, 438: 227015.
[36] WANG S C, LIU Y H. A PSO-based fuzzy-controlled searching for the optimal charge pattern of Li-ion batteries[J]. IEEE Transactions on Industrial Electronics, 2015, 62(5): 2983-2993.
[37] ZHANG C P, JIANG J C, GAO Y, et al. Charging optimization in lithium-ion batteries based on temperature rise and charge time[J]. Applied Energy, 2017, 194: 569-577.
[38] LIU K L, ZOU C F, LI K, et al. Charging pattern optimization for lithium-ion batteries with an electrothermal aging model[J]. IEEE Transactions on Industrial Informatics, 2018, 14(12): 5463-5474.
[39] HU X S, ZHENG Y S, LIN X K, et al. Optimal multistage charging of NCA/graphite lithium-ion batteries based on electrothermal-aging dynamics[J]. IEEE Transactions on Transportation Electrification, 2020, 6(2): 427-438.
[40] YOU H Z, DAI H F, LI L Z, et al. Charging strategy optimization at low temperatures for Li-ion batteries based on multi-factor coupling aging model[J]. IEEE Transactions on Vehicular Technology, 2021, 70(11): 11433-11445.
[41] LI Y J, LI K N, XIE Y, et al. Optimization of charging strategy for lithium-ion battery packs based on complete battery pack model[J]. Journal of Energy Storage, 2021, 37: 102466.
[42] WU X G, ZHANG K, CHEN Y, et al. Multistage fast charging optimization protocol for lithium-ion batteries based on the biogeography-based algorithm[J]. Journal of Energy Storage, 2022, 52: 104679.
[43] TIAN J Q, LI S Q, LIU X H, et al. Lithium-ion battery charging optimization based on electrical, thermal and aging mechanism models[J]. Energy Reports, 2022, 8: 13723-13734.
[44] WANG B C, MAO Y Y, LI H X, et al. Gaussian process-accelerated multi-objective evolutionary design of charging process considering multiple user preferences[J]. IEEE Transactions on Industrial Informatics, 2024, 20(8): 10123-10133.
[45] ATTIA P M, GROVER A, JIN N, et al. Closed-loop optimization of fast-charging protocols for batteries with machine learning[J]. Nature, 2020, 578(7795): 397-402.
[46] JIANG B B , WANG X Z. Constrained bayesian optimization for minimum-time charging of lithium-ion batteries[J]. IEEE Control Systems Letters, 2022, 6: 1682-1687.
[47] JIANG B B, BERLINER M D, LAI K, et al. Fast charging design for lithium-ion batteries via Bayesian optimization[J]. Applied Energy, 2022, 307: 118244.
[48] WANG X Z, JIANG B B. Multi-objective optimization for fast charging design of lithium-ion batteries using constrained Bayesian optimization[J]. Journal of Power Sources, 2023, 584: 233602.
[49] ZOU C F, HU X S, WEI Z B, et al. Electrothermal dynamics-conscious lithium-ion battery cell-level charging management via state-monitored predictive control[J]. Energy, 2017, 141: 250-259.
[50] ZOU C F, HU X S, WEI Z B, et al. Electrochemical estimation and control for lithium-ion battery health-aware fast charging[J]. IEEE Transactions on Industrial Electronics, 2018, 65(8): 6635-6645.
[51] YIN Y L, BI Y L, HU Y, et al. Optimal fast charging method for a large-format lithium-ion battery based on nonlinear model predictive control and reduced order electrochemical model[J]. Journal of the Electrochemical Society, 2020, 167(16): 160559.
[52] ALOISIO K S, GREGORY P, SCOTT T. Lithium-ion battery charging control using a coupled electro-thermal model and model predictive control[C]//Applied Power Electronics Conference and Exposition (APEC). New Orleans, LA, USA, New York: IEEE. 2020: 3534-3539.
[53] KOLLURI S, ADURU S V, PATHAK M, et al. Real-time nonlinear model predictive control (NMPC) strategies using physics-based models for advanced lithium-ion battery management system (BMS)[J]. Electrochemical Society Interface, 2020, 29(3): 160559.
[54] TIAN N, FANG H Z, WANG Y B. Real-time optimal lithium-ion battery charging based on explicit model predictive control[J]. IEEE Transactions on Industrial Informatics, 2021, 17(2): 1318-1330.
[55] HWANG G, SITAPURE N, MOON J, et al. Model predictive control of lithium-ion batteries: Development of optimal charging profile for reduced intracycle capacity fade using an enhanced single particle model (SPM) with first-principled chemical/mechanical degradation mechanisms[J]. Chemical Engineering Journal, 2022, 435(1): 134768.
[56] PARK S , POZZI A , WHITMEYER M , et al. Reinforcement learning-based fast charging control strategy for Li-ion batteries[C]//Conference on Control Technology and Applications (CCTA). Montreal, QC, Canada, New York: IEEE. 2020: 100-107.
[57] PARK S, POZZI A, WHITMEYER M, et al. A deep reinforcement learning framework for fast charging of Li-ion batteries[J]. IEEE Transactions on Transportation Electrification, 2022, 8(2): 2770-2784.
[58] WEI Z B, QUAN Z Y, WU J D, et al. Deep deterministic policy gradient-DRL enabled multiphysics-constrained fast charging of lithium-ion battery[J]. IEEE Transactions on Industrial Electronics, 2022, 69(3): 2588-2598.
[59] HAO Y H, LU Q G, WANG X Z, et al. Adaptive model-based reinforcement learning for fast charging optimization of lithium-ion batteries[J]. IEEE Transactions on Industrial Informatics, 2024, 20(1): 127-137.
[60] WEI Z B, YANG X F, LI Y, et al. Machine learning-based fast charging of lithium-ion battery by perceiving and regulating internal microscopic states[J]. Energy Storage Materials, 2023, 56: 62-75.
[61] WILJAN V , GAUTHAM R C M , PAVOL B. A comprehensive review on the characteristics and modeling of lithium-ion battery aging[J]. IEEE Transactions on Transportation Electrification, 2022, 8(2): 2205-2232.
[62] ZHANG Y M, SHEN Z W, PAN W B, et al. Constant current and constant voltage charging of wireless power transfer system based on three-coil structure[J]. IEEE Transactions on Industrial Electronics, 2023, 70(1): 1066-1070.
[63] WU X G, XIA Y L, DU J Y, et al. Multi-stage constant current charging strategy based on multi-objective current optimization[J]. IEEE Transactions on Transportation Electrification, 2023, 9(4): 4990-5001.
[64] TAHIR M U, SANGWONGWANICH A, STROE D I, et al. Overview of multi-stage charging strategies for Li-ion batteries[J]. Journal of Energy Chemistry, 2023, 84: 228-241.
[65] HUANG X R, LIU W J, ACHARYA A B, et al. Effect of pulsed current on charging performance of lithium-ion batteries[J]. IEEE Transactions on Industrial Electronics, 2022, 69(10): 10144-10153.
[66] PURUSHOTTHAMAN B K , MORRISON P W , LANDAU U. Reducing mass-transport limitations by application of special pulsed current modes[J]. Journal of the Electrochemical Society, 2005, 152(4): J33-J39.
[67] PATNAIK L, PRANEETH A V J S, WILLIAMSON S S. A closed-loop constant-temperature constant-voltage charging technique to reduce charge time of lithium-ion batteries[J]. IEEE Transactions on Industrial Electronics, 2019, 66(2): 1059-1067.
[68] GUO Z, LIAW B Y, QIU X P, et al. Optimal charging method for lithium ion batteries using a universal voltage protocol accommodating aging[J]. Journal of Power Sources, 2015, 274: 957-964.
[69] CHU Z Y, FENG X N, LU L G, et al. Non-destructive fast charging algorithm of lithium-ion batteries based on the control-oriented electrochemical model[J]. Applied Energy, 2017, 204: 1240-1250.
[70] WANG Lulu , ZHENG Kun , LI Yijing , et al. A multitime-scale deep learning model for lithium-ion battery health assessment using soft parameter-sharing mechanism[J]. Chinese Journal of Electrical Engineering, 2024, 10(3): 1-11.
[71] TIAN Y, LIU C, CHEN X, et al. Reversible lithium plating on working anodes enhances fast charging capability in low-temperature lithium-ion batteries[J]. Energy Storage Materials, 2023, 56: 412-423.
[72] ZHANG S S, XU K, JOW T R. The low temperature performance of Li-ion batteries[J]. Journal of Power Sources, 2003, 115(1): 137-140.
[73] 王军,阮琳,邱彦靓. 锂离子电池低温快速加热方法研究进展[J]. 储能科学与技术, 2022, 11(5): 1563-1574. WANG Jun, RUAN Lin, QIU Yanliang. Research progress on rapid heating methods for lithium-ion battery in low-temperature[J]. Energy Storage Science and Technology, 2022, 11(5): 1563-1574.
[74] LI W, XIE Y, HU X S, et al. An internal heating strategy for lithium-ion batteries without lithium plating based on self-adaptive alternating current pulse[J]. IEEE Transactions on Vehicular Technology, 2023, 72(5): 5809-5823.
[75] LIU X J, HONG X H, JIANG X H, et al. Novel approach for liquid-heating lithium-ion battery pack to shorten low temperature charge time[J]. Journal of Energy Storage, 2023, 68: 107507.
[76] LIU J H , WANG X. Investigating effects of pulse charging on performance of Li-ion batteries at low temperature[J]. Journal of Power Sources, 2023, 574: 233177.
[77] GUAN K F, HUANG Z W, LIU Y J, et al. A state of charge-aware internal preheating strategy for Li-ion batteries at low temperatures[J]. Journal of Energy Storage, 2023, 72: 108585.
[78] 吴晓刚,李凌任,高鑫家,等. 锂离子电池脉冲频率优化的低温预热[J]. 电机与控制学报, 2021, 25(11): 56-65. WU Xiaogang, LI Lingren, GAO Xinjia, et al. Preheating the lithium-ion battery with real-time optimized pulse frequency under low temperature[J]. Electric Machines and Control, 2021, 25(11): 56-65.
[79] CHEN Z G, ZHANG F. Numerical study of the phase change material and heating plates coupled battery thermal management in low temperature environment[J]. Journal of Energy Storage, 2024, 84: 110935.
[80] HU X S, ZHENG Y S, HOWEY D A, et al. Battery warm-up methodologies at subzero temperatures for automotive applications : Recent advances and perspectives[J]. Progress in Energy and Combustion Science, 2020, 77: 100806.
[81] SHENGXIN E, LIU Y X, CUI Y X, et al. Effects of composite cooling strategy including phase change material and cooling air on the heat dissipation performance improvement of lithium ion power batteries pack in hot climate and its catastrophe evaluation[J]. Energy, 2023, 283: 129074.
[82] SUN H G, DIXON R. Development of cooling strategy for an air cooled lithium-ion battery pack[J]. Journal of Power Sources, 2014, 272: 404-414.
[83] XIE Y, LI B, HU X S, et al. Improving the air-cooling performance for battery packs via electrothermal modeling and particle swarm optimization[J]. IEEE Transactions on Transportation Electrification, 2021, 7(3): 1285-1302.
[84] LI Kuijie, LI Yalun, RUI Xinyu, et al. Experimental study on the effect of state of charge on failure propagation characteristics within battery modules[J]. Chinese Journal of Electrical Engineering, 2023, 9(3): 3-14.
[85] GUO Z C, XU J, XU Z M, et al. A lightweight multichannel direct contact liquid-cooling system and its optimization for lithium-ion batteries[J]. IEEE Transactions on Transportation Electrification, 2022, 8(2): 2334-2345.
[86] KIM D Y, LEE B Y, KIM M G, et al. Thermal assessment of lithium-ion battery pack system with heat pipe assisted passive cooling using Simulink[J]. Thermal Science and Engineering Progress, 2023, 46: 102230.
[87] ADENIRAN A, PARK S. Optimized cooling and thermal analysis of lithium-ion pouch cell under fast charging cycles for electric vehicles[J]. Journal of Energy Storage, 2023, 68: 107580.
[88] JIN L W, LEE P S, KONG X X, et al. Ultra-thin minichannel LCP for EV battery thermal management[J]. Applied Energy, 2014, 113: 1786-1794.
[89] ADAIKKAPPAN M , SATHIYAMOORTHY N. Modeling, state of charge estimation, and charging of lithium-ion battery in electric vehicle : A review[J]. International Journal of Energy Research, 2022, 46(3): 2141-2165.
[90] ROUHOLAMINI M, WANG C S, NEHRIR H, et al. A review of modeling, management, and applications of grid-connected Li-ion battery storage systems[J]. IEEE Transactions on Smart Grid, 2022, 13(6): 4505-4524.
[91] MENG J H, STROE D I, RICCO M, et al. A simplified mode based state-of-charge estimation approach for lithium-ion battery with dynamic linear model[J]. IEEE Transactions on Industrial Electronics, 2019, 66(10): 7717-7727.
[92] KIRAD K, CHAUDHARI M. Design of cell spacing in lithium-ion battery module for improvement in cooling performance of the battery thermal management system[J]. Journal of Power Sources, 2021, 481: 229016.
[93] YANG Y K, HE J R, CHEN C L, et al. Balancing awareness fast charging control for lithium-ion battery pack using deep reinforcement learning[J]. IEEE Transactions on Industrial Electronics, 2024, 71(4): 3528-3543.
[94] TOMASZEWSKA A, CHU Z Y, FENG X N, et al. Lithium-ion battery fast charging : A review[J]. eTransportation, 2020(1): 100011.
[95] SARKAR S, HALIM S Z, EL-HALWAGI M M, et al. Electrochemical models: Methods and applications for safer lithium-ion battery operation[J]. Journal of the Electrochemical Society, 2022, 169(10): 100501.
[96] DOYLE M, FULLER T F, NEWMAN J. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell[J]. Journal of the Electrochemical Society, 1993, 140: 6.
[97] ANDERSSON M , STREB M , KO J Y , et al. Parametrization of physics-based battery models from input-output data: A review of methodology and current research[J]. Journal of Power Sources, 2022, 521: 230859.
[98] MOURA S J, ARGOMEDO F B, KLEIN R, et al. Battery state estimation for a single particle model with electrolyte dynamics[J]. IEEE Transactions on Control Systems Technology, 2017, 25(2): 453-468.
[99] RINGBECK F , GARBADE M , SAUER D U. Uncertainty-aware state estimation for electrochemical model-based fast charging control of lithium-ion batteries[J]. Journal of Power Sources, 2020, 470: 228221.
[100] ZHANG D, POPOV B N, WHITE R E. Modeling lithium intercalation of a single spinel particle under potentiodynamic control[J]. Journal of the Electrochemical Society, 2000, 147(3): 831-838.
[101] HAN X B, OUYANG M G, LU L G, et al. Simplification of physics-based electrochemical model for lithium ion battery on electric vehicle. Part I : Diffusion simplification and single particle model[J]. Journal of Power Sources, 2015, 278: 802-813.
[102] HAN X B, OUYANG M G, LU L G, et al. Simplification of physics-based electrochemical model for lithium ion battery on electric vehicle. Part Ⅱ : Pseudo two dimensional model simplification and state of charge estimation[J]. Journal of Power Sources, 2015, 278: 814-825.
[103] LI W H, FAN Y, RINGBECK F, et al. Electrochemical model-based state estimation for lithium-ion batteries with adaptive unscented Kalman filter[J]. Journal of Power Sources, 2020, 476: 228534.
[104] WANG B C , LI H X , YANG H D. Spatial correlation-based incremental learning for spatiotemporal modeling of battery thermal process[J]. IEEE Transactions on Industrial Electronics, 2020, 67(4): 2885-2893.
[105] LI J, LOTFI N, LANDERS R G, et al. A single particle model for lithium-ion batteries with electrolyte and stress-enhanced diffusion physics[J]. Journal of the Electrochemical Society, 2017, 164(4): A874-A883.
[106] ZENG Y Q, CHALISE D, LUBNER S D, et al. A review of thermal physics and management inside lithium-ion batteries for high energy density and fast charging[J]. Energy Storage Materials, 2021, 41: 264-288.
[107] JEON C H, LEE Y, KIM R, et al. Development of equivalent circuit model for thermal runaway in lithium-ion batteries[J]. Journal of Energy Storage, 2023, 74: 109318.
[108] SHI H T, WANG L P, WANG S L, et al. A novel lumped thermal characteristic modeling strategy for the online adaptive temperature and parameter co-estimation of vehicle lithium-ion batteries[J]. Journal of Energy Storage, 2023, 50: 104309.
[109] JAGUEMENT J, NIKOLIAN A, OMAR N, et al. Development of a two-dimensional-thermal model of three battery chemistries[J]. IEEE Transactions on Energy Conversion, 2017, 32(4): 1447-1455.
[110] JAGUEMENT J, OMAR N, ABDEL-MONEM M, et al. Fast-charging investigation on high-power and high-energy density pouch cells with 3D-thermal model development[J]. Applied Thermal Engineering, 2018, 128: 1282-1296.
[111] AYKOL M, GOPAL C B, ANAPOLSKY A, et al. Perspective-combining physics and machine learning to predict battery lifetime[J]. Journal of the Electrochemical Society, 2021, 168(3): 030525.
[112] PINSON M B, BAZANT M Z. Theory of SEI formation in rechargeable batteries: Capacity fade, accelerated aging and lifetime prediction[J]. Journal of the Electrochemical Society, 2013, 160(2): A243-A250.
[113] EKSTROM H, LINDBERGH G. A model for predicting capacity fade due to SEI formation in a commercial Graphite/LiFePO4 cell[J]. Journal of the Electrochemical Society, 2015(162): A1003.
[114] JANAKIRAMAN U, GARRICCK T R, FORTIER M E. Review-lithium plating detection methods in Li-ion batteries[J]. Journal of the Electrochemical Society, 2020, 167(16): 160552.
[115] ADAM A, WANDT J, KNOBBE E, et al. Fast-charging of automotive lithium-ion cells: In-situ lithium-plating detection and comparison of different cell designs[J]. Journal of the Electrochemical Society, 2020, 167(13): 130503.
[116] YANG X G, LENG Y J, ZHANG G S, et al. Modeling of lithium plating induced aging of lithium-ion batteries: Transition from linear to nonlinear aging[J]. Journal of Power Sources, 2017, 360: 28-40.
[117] SARKAR A , NLEBEDIM I C , SHROTRIYA P. Performance degradation due to anodic failure mechanisms in lithium-ion batteries[J]. Journal of Power Sources, 2021, 502: 229145.
[118] HANNAN M A, LIPU M S H, HUSSAINN A, et al. Toward enhanced state of charge estimation of lithium-ion batteries using optimized machine learning techniques[J]. Scientific Reports, 2020, 10(1): 4687.
[119] REN Z , DU C Q. A review of machine learning state-of-charge and state-of-health estimation algorithms for lithium-ion batteries[J]. Energy Reports, 2023(9): 2993-3021.
[120] CHEN L P, XIE S Q, LOPES A M, et al. A new SOH estimation method for Lithium-ion batteries based on model-data-fusion[J]. Energy, 2024, 286: 129597.
[121] HE N, WANG Q Q, LU Z F, et al. Early prediction of battery lifetime based on graphical features and convolutional neural networks[J]. Applied Energy , 2024, 353: 122048.
[122] SEVERSON K A, ATTIA P A, JIN N, et al. Data-driven prediction of battery cycle life before capacity degradation[J]. Nature Energy, 2019, 4(5): 383-391.
[123] ZHU J G, WANG Y X, HUANG Y, et al. Data-driven capacity estimation of commercial lithium-ion batteries from voltage relaxation[J]. Nature Communications, 2022, 13: 2261.
[124] REN L, DONG J B, WANG X K, et al. A data-driven auto-CNN-LSTM prediction model for lithium-ion battery remaining useful life[J]. IEEE Transactions on Industrial Informatics, 2021, 17(5): 3478-3487.
[125] CHEMALI E, KOLLMEYER P J, PREINDL M, et al. Long short-term memory networks for accurate state-of-charge estimation of Li-ion batteries[J]. IEEE Transactions on Industrial Electronics, 2018, 65(8): 6730-6739.
[126] ZHANG Z Z , SONG W , LI Q Q. Dual-aspect self-attention based on transformer for remaining useful life prediction[J]. IEEE Transactions on Instrumentation and Measurement, 2022, 71: 2505711.
[127] WANG Y X, ZHU J G, CAO L, et al. Long short-term memory network with transfer learning for lithium-ion battery capacity fade and cycle life prediction[J]. Applied Energy, 2023, 350: 121660.
[128] HE Y B , WANG B C , DENG H P , et al. Physics-reserved spatiotemporal modeling of battery thermal process : Temperature prediction , parameter identification, and heat generation rate estimation[J]. Journal of Energy Storage, 2024, 75: 109604.
[129] PANG H, WU L X, LIU J H, et al. Physics-informed neural network approach for heat generation rate estimation of lithium-ion battery under various driving conditions[J]. IEEE Transactions on Industrial Electronics, 2023, 78: 1-12.
[130] LI W H , ZHANG J W , RINGBECK F , et al. Physics-informed neural networks for electrode-level state estimation in lithium-ion batteries[J]. Journal of Power Sources, 2021, 506: 230034.
[131] WANG B C, LI H X. A sliding window based dynamic spatiotemporal modeling for distributed parameter systems with time-dependent boundary conditions[J]. IEEE Transactions on Industrial Informatics, 2019, 15(4): 2044-2053.
[132] DENG H P, HE Y B, WANG B C, et al. Physics-dominated neural network for spatiotemporal modeling of battery thermal process[J]. IEEE Transactions on Industrial Informatics, 2023, 20(1): 452-460.
[133] 胡天中,余建波. 基于多尺度分解和深度学习的锂电池寿命预测[J]. 浙江大学学报(工学版), 2019, 53(10): 1852-1864. HU Tianzhong , YU Jianbo. Life prediction of lithium-ion batteries based on multiscale decomposition and deep learning[J]. Journal of Zhejiang University (Engineering Science), 2019, 53(10): 1852-1864.
[134] 李龙,燕旭朦,张钰声,等. 小样本锂电池数据 SOC 估算方法[J]. 西安交通大学学报, 2023, 20(1):452-460. LI Long, YAN Xumeng, ZHANG Yusheng, et al. Lithium battery SOC estimation method based on transfer learning and deep learning[J]. Journal of Xi’an Jiaotong University, 2023, 20(1): 452-460.
[135] 杨淞元,田勇,田劲东. 基于 iCEEMDAN 和迁移学习的锂离子电池 SOH 估计[J]. 电气工程学报, 2022, 17(4): 2-10. YANG Songyuan, TIAN Yong, TIAN Jindong. State of health estimation of lithium-ion batteries based on iCEEMDAN and transfer learning[J]. Archives of Computational Methods in Engineering, 2022, 17(4): 2-10.
[136] PENG G C Y, ALBER M, TEPOLE A B, et al. Multiscale modeling meets machine learning: What can we learn?[J] Archives of Computational Methods in Engineering, 2020, 28(3): 1017-1037.
[137] LI Y, KARUNATHILAKE D, VILATHGAMUWA D M , et al. Model order reduction techniques for physics-based lithium-ion battery management : A survey[J]. IEEE Industrial Electronics Magazine, 2021, 16(3): 36-51.
[138] LU Y F, HAN X B, LI Y L, et al. Health-aware fast charging for lithium-ion batteries : Model predictive control, lithium plating detection, and lifelong parameter updates[J]. IEEE Transactions on Industry Applications, 2024, 60(5): 7389-7398.
[139] POWELL W B. Approximate dynamic programming: Solving the curses of dimensionality[M]. New York: Wiley Interscience, 2007.
[140] GAD A G. Particle swarm optimization algorithm and its applications : A systematic review[J]. Archives of Computational Methods in Engineering, 2022, 29: 2531-2561.
[141] MA H P, SIMON D, SIARRY P, et al. Biogeography based optimization : A 10-year review[J]. IEEE Transactions on Emerging Topics in Computational Intelligence, 2017, 1(5): 391-407.
[142] DAS S, SUGANTHAN P N. Differential evolution: A survey of the state-of-the-art[J]. IEEE Transactions on Evolutionary Computation, 2011, 15(1): 4-31.
[143] MA H P , SU S F, SIMON D , et al. Ensemble multi-objective biogeography-based optimization with application to automated warehouse scheduling[J]. Engineering Applications of Artificial Intelligence , 2015, 44: 79-90.
[144] DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm : NSGA-Ⅱ[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.
[145] LI J Y , ZHAN Z H , ZHANG J. Evolutionary computation for expensive optimization: A Survey[J]. Machine Intelligence Research, 2022, 19(1): 3-23.
[146] WANG Y J, ZHOU C J, CHEN Z H. Optimization of battery charging strategy based on nonlinear model predictive control[J]. Energy, 2022, 241: 122877.
[147] DONG G Z, ZHU Z P, LOU Y J, et al. Optimal charging of lithium-ion battery using distributionally robust model predictive control with wasserstein metric[J]. IEEE Transactions on Industrial Informatics, 2024, 20(5): 7630-7640.
[148] BERTSEKAS D P. Reinforcement learning and optimal control[M]. Wassem: Athena Scientific, 2020.
[149] ANDRYCHOWICZ M, RAICHUK A, STANCZYK P, et al. What matters for on-policy deep actor-critic methods? A large-scale study[C]//International Conference on Learning Representations (ICLR). Vienna, Austria, 2021.
[150] WASSILIADIS N, SCHNEIDER J, FRANK A, et al. Review of fast charging strategies for lithium-ion battery systems and their applicability for battery electric vehicles[J]. Journal of Energy Storage, 2021, 44: 103306.
[151] CHEN C L , WEI Z B , KNOLL A C. Charging optimization for li-ion battery in electric vehicles: A review[J]. IEEE Transactions on Transportation Electrification, 2022, 8(3): 3068-3089.
[152] WU Q C, HUANG R, YU X L. Measurement of thermophysical parameters and thermal modeling of 21, 700 cylindrical battery[J]. Journal of Energy Storage, 2021, 65: 107338.
[153] GAO Y Z, ZHANG X, GUO B J, et al. Health-aware multiobjective optimal charging strategy with coupled electrochemical-thermal-aging model for lithium-ion battery[J]. IEEE Transactions on Industrial Informatics, 2020, 16(5): 3417-3429.
[154] PATNAIK L, PRANEETH A V J S, WILLIAMSON S S. A closed-loop constant-temperature constant-voltage charging technique to reduce charge time of lithium-ion batteries[J]. IEEE Transactions on Industrial Electronics, 2018, 66(2): 1059-1067.
[155] RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks : A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational Physics , 2019 , 378(1) : 686-707.
[156] 查文舒,李道伦,沈路航,等. 基于神经网络的偏微分方程求解方法研究综述[J]. 力学学报, 2022, 54(3): 543-556. ZHA Wenshu, LI Daolun, SHEN Luhang, et al. Review of neural network-based methods for solving partial differential equations[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 543-556.
[157] YE Z, YU J B. State-of-health estimation for lithium-ion batteries using domain adversarial transfer learning[J]. IEEE Transactions on Power Electronics, 2022, 37(3): 3718-3727.