宽温度环境下基于改进电化学模型的锂电池荷电状态估计

doi:10.19799/j.cnki.2095-4239.2023.0342

摘要/Abstract

摘要：

为提升电化学模型的实用性以及复杂环境温度下的适用性，解决锂离子电池内部状态难以快速精确估计的难题，本文设计了一种基于改进电化学模型的荷电状态估计方法。首先，通过有限差分法和Galerkin法分别对P2D模型的固液相方程进行降阶求解以描述电池内部锂离子浓度的实时状态，同时进一步融合等效电路模型，采用2个RC网络结构表征电池内部极化过程，并包含了与温度相关的特性，形成了适合荷电状态估计的低阶常微分系统，实现了电化学模型的有效简化和降阶，节约计算成本。其次，为了处理由于模型简化导致的模型不确定性和降低噪声干扰，引入平方根容积卡尔曼滤波，设计了宽工作温度下的锂电池荷电状态估计算法。结果表明，本文提出的基于改进电化学模型的荷电状态估计方法可以在不同温度及复杂工况下实现荷电状态的精确估计，宽环境温度下的最大误差小于1.6%。

关键词: 锂电池, 改进电化学模型, 环境温度, 荷电状态, 平方根容积卡尔曼滤波

Abstract:

In order to improve the practicability of the electrochemical model and its applicability at complex temperature environments and solve the problem of difficulty in quickly and accurately estimating the internal state of lithium-ion batteries, a state-of-charge estimation method based on an improved electrochemical model is designed. First, the order reduction of the solid-liquid phase equation of the electrochemical model is solved using the finite difference method and Galerkin method to explain the real-time state of lithium-ion concentration in the battery. Simultaneously, the equivalent circuit model is integrated further, and two RC network structures are used to characterize the internal polarization process of the battery. The temperature-dependent characteristics are included to form a low-order ordinary differential system suitable for the state of charge estimation, realizing effective simplification and order reduction of the electrochemical model and saving the calculation cost. Then, to address the model uncertainty caused by model simplification and reduce noise interference, a square root volume Kalman filter was introduced to design a lithium battery state of charge estimation algorithm at full operating temperature. The results showed that the proposed state of charge estimation method based on the improved electrochemical model could accurately estimate the state of charge under different temperatures and complex working conditions, with a maximum error of less than 1.6% under diverse temperature settings.

Key words: lithium ion battery, electrochemical mode, ambient temperature, state of charge, square root cubature kalman filte

中图分类号:

TM 912

申江卫, 周灿彪, 舒星, 陈峥, 刘永刚. 宽温度环境下基于改进电化学模型的锂电池荷电状态估计[J]. 储能科学与技术, 2023, 12(9): 2904-2916.

Jiangwei SHEN, Canbiao ZHOU, Xing SHU, Zheng CHEN, Yonggang LIU. State of charge estimation for lithium batteries based on an improved electrochemical model at a wide temperature environment[J]. Energy Storage Science and Technology, 2023, 12(9): 2904-2916.

图/表 15

图1

表1

锂离子电池电化学模型方程"

名称	动力学方程
固相扩散方程	$∂ C s ∂ t = D s (2 r × ∂ C s ∂ r + ∂ C s 2 ∂ r 2)$
液相电势方程	$∂ ϕ e (x, t) ∂ x = - i e (x, t) k e f f ∂ i e (x, t) ∂ x = j$
固相电势方程	$∂ ϕ s (x, t) ∂ x = - i s (x, t) σ e f f ∂ i s (x, t) ∂ x = - j$
Bulter-Volme方程	$η (x, t) = ϕ s (x, t) - ϕ e (x, t) - U C s s C s, m a x - F R j j (x, t) j (x, t) = i 0 (x, t) F e x p ∂ F R T η (x, t) - e x p - ∂ F R T η (x, t)$
液相扩散方程	$ε e ∂ C e ∂ t = ∂ ∂ x D e ∂ C e ∂ t + a (1 - t c 0) j$
端电压方程	$V (t) = η p (t) - η n (t) + ϕ e, p (t) - ϕ e, n (t) + U O C V, p - U O C V, n - R f I$

表1

图2

图3

表2

图4

表3

辨识后的主要参数结果"

参数	$- 20 ℃$	$0 ℃$	$20 ℃$	$40 ℃$	$60 ℃$
$θ 0$	0.6574	0.467	0.3989	0.3629	0.3832
$θ 100$	0.9564	0.9576	0.9044	0.9481	0.9621
$C s_m a x$	15925	15910	16631	16058	15840

表3

表4

IEM参数列表"

符号	参数	负极	隔膜	正极
$D s$	固相扩散系数/( $m 2 / s$ )	5.6448×10^-13	—	7.4725×10^-13
$D s e f f$	液相扩散系数/( $m 2 / s$ )	4.97×10^-9	9.19×10^-9	4.93×10^-9
$t + 0$	锂离子液相转移数	0.363
$K e f f$	液相有效离子电导率/( $S / m$ )	0.104	0.224	0.104
$α a$	传递系数	0.5	—	0.5
$ε s$	固相体积分数	0.2718	—	0.3886
$ε e$	液相体积分数	0.5	—	0.55
$C s, m a x$	固相锂离子浓度最大值/( $m o l / m 3$ )	16600	—	17507
R_SEI	隔膜内阻/( $Ω ⋅ m 2$ )	0.004	—	0.001
T	电池工作温度/K	298
F	法拉第常数/( $C / m o l$ )	96485
R	摩尔气体常数/ $[J / (m o l ⋅ K)]$	8.314
$U O C V, p$	正极开路电压/V	$2.58 × θ p (6) - 11.5 × θ p (5) + 15.1 × θ p (4) - 7.926 × θ p (3) + 2.486 × θ p (2) - 1.683 × θ p + 4.399$
$U O C V, n$	负极开路电压/V	$0.72 + 0.1386 × θ n + 0.0019 × θ n (- 1.5) + 0.028 × θ n (0.5 - 0.0171 / θ n) + 0.2816 × e x p (0.9 - 15 × θ n) - 0.7896 × e x p (0.4598 × θ n - 0.4098)$

表4

图5

图6

图7

图8

表5

图9

表6

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参数	规格
额定容量/mAh	2000
电池材料	Li(NiCoMn)O₂/石墨
上限/下限截止电压/V	2.5/4.2
常温下最大电流/A	22

项目	0 ℃			25 ℃			45 ℃
项目	RMSE/%	MAE/%	MAXE/%	RMSE/%	MAE/%	MAXE/%	RMSE/%	MAE/%	MAXE/%
AEKF	1.577	1.453	2.747	1.041	0.738	2.520	1.475	1.263	3.317
SRCKF	0.766	0.442	1.563	0.606	0.432	1.522	0.661	0.480	1.564
减少量	51.41	69.54	43.10	41.79	41.46	39.60	55.186	61.995	52.85

项目	0 ℃			25 ℃			45 ℃
项目	RMSE/%	MAE/%	MAXE/%	RMSE/%	MAE/%	MAXE/%	RMSE/%	MAE/%	MAXE/%
ECM	1.601	1.063	3.873	2.045	0.450	3.073	1.738	1.410	2.642
IEM	0.549	0.259	1.047	0.860	0.289	1.434	0.782	0.512	1.430
减少量	1.052	75.635	72.97	57.946	35.778	53.34	55.006	63.688	45.87

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