Expansion of the homogeneous electrochemical model for lithium-ion batteries to incorporate electrode particle radius distribution

doi:10.19799/j.cnki.2095-4239.2024.0318

Abstract

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

CLC Number:

O 411.3

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.

Figures/Tables 6

Fig. 1

Table 1

Common electrode PRD function and corresponding specific surface area correction"

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	$Γ x = ∫ 0 ∞ t x - 1 e - t d t$	$e r f x = 2 π ∫ 0 x e - t 2 d t$	$Γ x = ∫ 0 ∞ t x - 1 e - t d t$

Table 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

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