State of charge estimation for lithium batteries based on an improved electrochemical model at a wide temperature environment

doi:10.19799/j.cnki.2095-4239.2023.0342

Abstract

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

CLC Number:

TM 912

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.

Figures/Tables 15

Fig. 1

Table 1

Electrochemical model equations for lithium-ion batteries"

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	$V (t) = η p (t) - η n (t) + ϕ e, p (t) - ϕ e, n (t) + U O C V, p - U O C V, n - R f I$

Table 1

Fig. 2

Fig. 3

Table 2

Fig. 4

Table 3

The main result parameters after identification"

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

Table 3

Table 4

List of parameters for the IEM"

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	$0.72 + 0.1386 × θ n + 0.0019 × θ n (- 1.5) + 0.028 × θ n (0.5 - 0.0171 / θ n) + 0.2816 × e x p (0.9 - 15 × θ n) - 0.7896 × e x p (0.4598 × θ n - 0.4098)$

Table 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 5

Fig. 9

Table 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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