锂离子电池均质化电化学模型的电极颗粒半径分布拓展

doi:10.19799/j.cnki.2095-4239.2024.0318

摘要/Abstract

摘要：

锂离子电池的仿真对电池研发和评估具有重要作用。当前锂离子电池仿真所使用的经典伪二维模型采用恒定电极颗粒半径假设，无法满足对仿真精度的需求。本工作通过对电极颗粒半径分布的累积分布函数进行逆变换采样，并开展电极颗粒活性比表面积校正，在维持伪二维模型均质化特性的基础上成功引入了电极颗粒半径分布，从而提升了仿真精度。首先，从数学上推导了在伪二维模型中引入电极颗粒半径分布的理论方法，将由伪随机函数生成的关联电极空间坐标的均匀分布数代入电极颗粒半径分布的累积分布函数中，以逆变换采样获得不同电极空间坐标的电极颗粒半径。然后，推导和论证了在引入电极颗粒半径分布后电极颗粒活性比表面积的校正方式，并给出了常见电极颗粒半径分布在伪二维模型中的拓展方程。最后，通过对正极和负极是否进行电极颗粒半径分布拓展的四种组合建立的伪二维模型进行了相同条件的仿真对比，并基于实验数据对无拓展的和含电极颗粒半径分布拓展的伪二维模型开展仿真验证，结果表明本工作提出的电极颗粒半径分布拓展方法能够更准确地仿真电池内部的极化变化，尤其是对弛豫过程的仿真结果更接近实际电池表现，因而具有更高的仿真精度。

关键词: 锂离子电池, 电化学模型, 电极颗粒半径分布, 仿真

Abstract:

Simulation of lithium-ion batteries plays an important role in battery research and evaluation. The classical pseudo-two-dimensional model used in battery simulations typically assumes a constant electrode particle radius, which limits simulation accuracy. In this study, we enhance the pseudo-two-dimensional model by integrating the cumulative distribution function of electrode particle radius distribution through inverse transformation sampling. This process corrects the active specific surface area of the electrode particles, effectively incorporating the electrode particle radius distribution while maintaining the homogeneity characteristics of the pseudo-two-dimensional model, thereby improving simulation accuracy. Firstly, we derive a theoretical method to incorporate the electrode particle radius distribution into the pseudo-two-dimensional model. We use a pseudo-random function to generate uniform distribution numbers based on electrode spatial coordinates, which are then substituted into the cumulative distribution function to determine the electrode particle radius at different electrode spatial coordinates through inverse transformation sampling. Then, we present a method for correcting the active specific surface area of the electrode particles after introducing the radius distribution, along with expansion equations for common electrode particle radius distributions within the pseudo-two-dimensional model, each with different combinations of expanded radius distribution for the positive and negative electrodes, under the same conditions. Simulations comparing the pseudo-two-dimensional model with and without the expanded radius distribution are conducted and validated against experimental data. The results show that incorporating the radius distribution significantly improves the simulation of polarization changes inside the battery, especially during the relaxation process, leading to enhanced simulation accuracy.

Key words: lithium-ion batteries, electrochemical model, electrode particle radius distribution, simulation

中图分类号:

O 411.3

曹昕, 李棉刚, 侯宇程, 贡晓旭, 李香龙, 周奎, 梁惠施, 杨清华. 锂离子电池均质化电化学模型的电极颗粒半径分布拓展[J]. 储能科学与技术, 2024, 13(10): 3622-3629.

Xin CAO, Miangang LI, Yucheng HOU, Xiaoxu GONE, Xianglong LI, Kui ZHOU, Huishi LIANG, Qinghua YANG. Expansion of the homogeneous electrochemical model for lithium-ion batteries to incorporate electrode particle radius distribution[J]. Energy Storage Science and Technology, 2024, 13(10): 3622-3629.

图/表 6

图1

表1

常见电极颗粒半径分布函数及对应的比表面积校正"

项目	Weibull分布	对数Gauss分布	Rosin-Rammler分布
PDF	$f x = k λ x λ k - 1 e x p - x λ k$	$f x = 1 x 2 π σ e x p - l n x - μ 2 2 σ 2$	$f x = m n x n m - 1 e x p - x n m$
参数条件	$k > 0, λ > 0$	$σ ≥ 0$	$m > 0, n > 0$
CDF	$F x = 1 - e x p - x λ k$	$F x = - 12 e r f μ - l n x 2 σ - 1$	$F x = 1 - e x p - x n m$
ITS函数	$F - 1 x = λ - l n 1 - x 1 k$	$F - 1 x = e x p μ - 2 σ ⋅ e r f - 1 1 - 2 x$	$F - 1 x = n - l n 1 - x m$
ASSA校正	$a v R = 3 ε s R 2 λ 3 Γ 1 + 3 k$	$a v R = 3 ε s R 2 e x p 3 μ + 92 σ 2$	$a v R = 3 ε s R 2 n 3 Γ 1 + 3 m$
辅助函数	$Γ x = ∫ 0 ∞ t x - 1 e - t d t$	$e r f x = 2 π ∫ 0 x e - t 2 d t$	$Γ x = ∫ 0 ∞ t x - 1 e - t d t$

表1

图2

图3

图4

图5

参考文献 21

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