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一种求解锂离子电池单粒子模型液相扩散方程的新方法

谢奕展 程夕明

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一种求解锂离子电池单粒子模型液相扩散方程的新方法

谢奕展, 程夕明

A new method to solve electrolyte diffusion equations for single particle model of lithium-ion batteries

Xie Yi-Zhan, Cheng Xi-Ming
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  • 电解液中的锂离子浓度表达是锂离子电池电化学模型求解的基本任务之一. 为了平衡单粒子模型的液相动态性能和计算效率, 假设反应仅发生在集电极和电解质界面上, 为此, 提出一种基于液相扩散方程无穷级数解析解的界面浓度求解新方法. 在恒流工况下, 利用数列单调收敛准则将解析解转化为一个收敛和函数. 在动态工况下, 将该解析解简化为输入与和函数的无限离散卷积. 利用和函数随时间单调衰减并收敛至零的特性对其进行截断, 从而得到有限离散卷积求解算法. 对比专业有限元分析软件, 该方法在恒流工况和动态工况下均能以较少的计算时间获得相当好的精度. 而且, 该方法仅有一个配置参数. 因此, 所提方法将有效减小应用于实时电池管理系统上的电化学模型计算负担.
    It is one of basic tasks to solve the electrochemical model of lithium-ion batteries for obtaining the lithium-ion concentration in the electrolyte. In order to balance the computational efficiency and electrolyte dynamic property, it is assumed that reactions occur only at interfaces between the collector and the electrolyte. Based on the analytical solution to the liquid diffusion equations, which is in the form of infinite series, a new method is proposed to solve it. Under galvanostatic profiles, the analytic solution is an infinite time series transformed into a converged sum function by using the monotone convergence theorem. Under the dynamic profiles, the infinite series solution is simplified into an infinite discrete convolution of both the input and the sum function. The sum function is truncated by its characteristic of monotonic decay approaching to zero over time, thus obtaining a finite discrete convolution algorithm. Reference to the results from a professional finite element analysis software, the proposed algorithm can produce high accuracy with less computation time under both galvanostatic profiles and dynamic profiles. Also, there is only one parameter to be configured. Therefore, our algorithm will reduce the computation burden of the electrochemical model applied to a real-time battery management system.
      通信作者: 程夕明, cxm2004@bit.edu.cn
    • 基金项目: 国家重点研发计划(批准号: 2018YFB0106104)和国家自然科学基金(批准号: 51677006)资助的课题.
      Corresponding author: Cheng Xi-Ming, cxm2004@bit.edu.cn
    • Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2018YFB0106104) and the National Natural Science Foundation of China (Grant No. 51677006).
    [1]

    Tarascon J M, Armand M 2001 Nature 414 359Google Scholar

    [2]

    Lu L, Han X, Li J, Hua J, Ouyang M 2013 J. Power Sources 226 272Google Scholar

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    Khumprom P, Yodo N 2019 Energies 12 660Google Scholar

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    Richardson R R, Birkl C R, Osborne M A, Howey D A 2019 IEEE Trans. Ind. Inf. 15 127Google Scholar

    [5]

    Shen S, Sadoughi M, Chen X, Hong M, Hu C 2019 J. Energy Storage 25 100817Google Scholar

    [6]

    Zhao L, Wang Y P, Cheng J H 2019 Appl. Sci. 9 1890Google Scholar

    [7]

    Lai X, Zheng Y, Sun T 2018 Electrochim. Acta 259 566Google Scholar

    [8]

    Hu X, Li S, Peng H 2012 J. Power Sources 198 359Google Scholar

    [9]

    Cheng X M, Yao L G, Pecht M 2017 J. Zhejiang Univ. -Sci. A 18 256

    [10]

    李涛, 程夕明, 胡晨华 2021 物理学报 70 138801Google Scholar

    Li T, Cheng X M, Hu C H 2021 Acta Phys. Sin. 70 138801Google Scholar

    [11]

    Chaturvedi N A, Klein R, Christensen J, Ahmed J, Kojic A 2010 IEEE Control Syst. Mag. 30 49Google Scholar

    [12]

    Gu R, Malysz P, Yang H, Emadi A 2016 IEEE Trans. Transp. Electrification 2 417Google Scholar

    [13]

    Meng J H, Luo G Z, Ricco M, Swierczynski M, Stroe D I, Teodorescu R 2018 Appl. Sci. 8 659Google Scholar

    [14]

    Han X, Ouyang M, Lu L, Li J 2015 J. Power Sources 278 802Google Scholar

    [15]

    Mehta R, Gupta A 2021 Electrochim. Acta 389 138623Google Scholar

    [16]

    Xie Y, Cheng X 2021 Electrochim. Acta 399 139391Google Scholar

    [17]

    Guduru A, Northrop P W C, Jain S, Crothers A C, Marchant T R, Subramanian V R 2012 J. Appl. Electrochem. 42 189Google Scholar

    [18]

    Yuan S, Jiang L, Yin C, Wu H, Zhang X 2017 J. Power Sources 352 245Google Scholar

    [19]

    Tanim T R, Rahn C D, Wang C Y 2014 American Control Conference (ACC) Portland, OR, December 4–6, 2014 pp141–146

    [20]

    Khaleghi Rahimian S, Rayman S, White R E 2013 J. Power Sources 224 180Google Scholar

    [21]

    Luo W, Lyu C, Wang L, Zhang L 2013 Microelectron. Reliab. 53 797Google Scholar

  • 图 1  液相模型

    Fig. 1.  The electrolyte model.

    图 2  h(t)函数曲线

    Fig. 2.  The curve of h(t).

    图 3  恒流工况仿真结果 (a) 0.25 C浓度; (b) 0.25 C误差; (c) 1.0 C浓度; (d) 1.0 C误差; (e) 3.0 C浓度; (f) 3.0 C误差

    Fig. 3.  Simulation results of the galvanostatic profiles: (a) 0.25 C concentration; (b) 0.25 C error; (c) 1.0 C concentration; (d) 1.0 C error; (e) 3.0 C concentration; (f) 3.0 C error.

    图 4  DST工况仿真结果 (a) 放电倍率; (b) 浓度; (c) 误差

    Fig. 4.  Simulation results for the DST profile: (a) Profile; (b) concentration; (c) error.

    图 5  NEDC工况仿真结果 (a) 放电倍率; (b) 浓度; (c) 误差

    Fig. 5.  Simulation results for the NEDC profile: (a) Profile; (b) concentration; (c) error.

    图 6  WLTC工况仿真结果 (a) 放电倍率; (b) 浓度; (c) 误差

    Fig. 6.  Simulation results for the WLTC profile: (a) Profile, (b) concentration, (c) error.

    表 1  模型参数*

    Table 1.  Model Parameters*.

    参数单位
    扩散系数D7.5 × 10–11m2/s
    液相总厚度R3.35 × 10–4m
    初始浓度c02000mol/m3
    1 C放电时液相两侧界面通量 j1C1.74 × 10–4mol·m–2·s–1
    *ComSol
    下载: 导出CSV

    表 2  动态工况误差

    Table 2.  Errors under dynamic profiles.

    参数RRMSE(%)RMAE(%)
    AnaN0(200)DST0.99552.8533
    AnaN0(∞)DST0.08800.6093
    AnaN0(200)NEDC1.87874.882
    AnaN0(600)NEDC0.09910.3123
    AnaN0(1000)NEDC0.03730.1635
    AnaN0(∞)NEDC0.03830.1779
    AnaN0(200)WLTC2.67676.0554
    AnaN0(600)WLTC0.14050.3221
    AnaN0(1000)WLTC0.04720.1425
    AnaN0(∞)WLTC0.04630.1565
    下载: 导出CSV

    表 3  WLTC工况下卷积算法与Comsol比较

    Table 3.  The comparison between the convolution algorithm and COMSOL under the WLTC.

    参数RRMSE(%)RT(%)
    eT(1 × 10–3)WLTC0.121835.14
    AnaN0(200)WLTC2.67670.06166
    AnaN0(600)WLTC0.14050.06765
    AnaN0(1000)WLTC0.04720.09490
    AnaN0($\infty $)WLTC0.04630.09573
    下载: 导出CSV
  • [1]

    Tarascon J M, Armand M 2001 Nature 414 359Google Scholar

    [2]

    Lu L, Han X, Li J, Hua J, Ouyang M 2013 J. Power Sources 226 272Google Scholar

    [3]

    Khumprom P, Yodo N 2019 Energies 12 660Google Scholar

    [4]

    Richardson R R, Birkl C R, Osborne M A, Howey D A 2019 IEEE Trans. Ind. Inf. 15 127Google Scholar

    [5]

    Shen S, Sadoughi M, Chen X, Hong M, Hu C 2019 J. Energy Storage 25 100817Google Scholar

    [6]

    Zhao L, Wang Y P, Cheng J H 2019 Appl. Sci. 9 1890Google Scholar

    [7]

    Lai X, Zheng Y, Sun T 2018 Electrochim. Acta 259 566Google Scholar

    [8]

    Hu X, Li S, Peng H 2012 J. Power Sources 198 359Google Scholar

    [9]

    Cheng X M, Yao L G, Pecht M 2017 J. Zhejiang Univ. -Sci. A 18 256

    [10]

    李涛, 程夕明, 胡晨华 2021 物理学报 70 138801Google Scholar

    Li T, Cheng X M, Hu C H 2021 Acta Phys. Sin. 70 138801Google Scholar

    [11]

    Chaturvedi N A, Klein R, Christensen J, Ahmed J, Kojic A 2010 IEEE Control Syst. Mag. 30 49Google Scholar

    [12]

    Gu R, Malysz P, Yang H, Emadi A 2016 IEEE Trans. Transp. Electrification 2 417Google Scholar

    [13]

    Meng J H, Luo G Z, Ricco M, Swierczynski M, Stroe D I, Teodorescu R 2018 Appl. Sci. 8 659Google Scholar

    [14]

    Han X, Ouyang M, Lu L, Li J 2015 J. Power Sources 278 802Google Scholar

    [15]

    Mehta R, Gupta A 2021 Electrochim. Acta 389 138623Google Scholar

    [16]

    Xie Y, Cheng X 2021 Electrochim. Acta 399 139391Google Scholar

    [17]

    Guduru A, Northrop P W C, Jain S, Crothers A C, Marchant T R, Subramanian V R 2012 J. Appl. Electrochem. 42 189Google Scholar

    [18]

    Yuan S, Jiang L, Yin C, Wu H, Zhang X 2017 J. Power Sources 352 245Google Scholar

    [19]

    Tanim T R, Rahn C D, Wang C Y 2014 American Control Conference (ACC) Portland, OR, December 4–6, 2014 pp141–146

    [20]

    Khaleghi Rahimian S, Rayman S, White R E 2013 J. Power Sources 224 180Google Scholar

    [21]

    Luo W, Lyu C, Wang L, Zhang L 2013 Microelectron. Reliab. 53 797Google Scholar

计量
  • 文章访问数:  3867
  • PDF下载量:  115
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-09-01
  • 修回日期:  2021-10-20
  • 上网日期:  2022-02-13
  • 刊出日期:  2022-02-20

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