锂电池分数阶建模及SOC估计策略

doi:10.19799/j.cnki.2095-4239.2022.0551

摘要/Abstract

摘要：

为了提高锂电池模型的精度，实现锂电池状态的精确估计，本工作在二阶RC等效电路的基础上建立了锂电池的二阶分数阶电气模型，并采用自适应遗传算法实现分数阶模型的参数辨识，加快了算法收敛速度，缩短了辨识时间，避免陷入局部最优解，提高了模型参数精度；在分数阶电气模型的基础上，采用了一种基于施密特正交变换思想的无迹粒子滤波的状态估计方法，与传统的无迹粒子滤波算法相比，在采样点选取过程中，采用一种标准采样与施密特正交变换相结合的办法，对对称采样的粒子进行筛选，减少了采样点的数量，提高了计算效率，并能有效避免由于系统的非线性引起的估算结果发散或单一使用粒子滤波而引起的粒子数短缺。仿真结果表明所建立的锂电池分数阶电气模型能更精确描述锂电池的充放电动态特性，所提出的状态估计策略精度相比于常规控制策略具有更高的精度，系统鲁棒性提高，可以在误差仅为1%的范围内估计锂电池的SOC，并提高了计算效率，易于算法的实时实现。

关键词: 锂电池, 分数阶, 荷电状态, 施密特正交变换, 无迹粒子滤波算法

Abstract:

To improve the accuracy of the lithium battery model and realize an accurate estimation of the lithium battery state, a second-order fractional electrical model is established for the lithium battery based on the second-order RC equivalent circuit. In this study, the adaptive genetic algorithm is used to realize the parameter identification of the fractional order model, which can increase the convergence speed, reduce the identification time, avoid falling into the local optimal solution, overcome the parameter dispersion, and improve the accuracy of the model parameters. Based on the fractional order electrical model, a state estimation method is proposed for the unscented particle filter by adopting the Schmidt orthogonal transformation. Instead of using traditional unscented particle filters, a method that combines standard sampling with the Schmidt orthogonal transformation is adopted in the selection of sampling points to screen the symmetrically sampled particles, which leads to a reduced number of sampling points and an improved calculation efficiency. In addition, it can also limit the divergence of the estimated value caused by the nonlinearity of the system or the particle shortage caused by a small particle number for the particle filter algorithm. The simulation results show that the established fractional order electrical model can more accurately account for the dynamic characteristics of charging and discharging for lithium batteries, and the proposed state estimation strategy demonstrates higher accuracy than the conventional control strategy. In general, the system robustness is improved, and the SOC of lithium batteries can be estimated with an error of within 1%. Moreover, the overall calculation efficiency is improved, which makes it easy to realize the algorithm in real-time.

Key words: lithium battery, fractional order, state of charge, schmidt orthogonal transformation, unscented particle filter algorithm

中图分类号:

TM 911

李路路, 陶正顺, 潘庭龙, 杨玮林, 胡官洋. 锂电池分数阶建模及SOC估计策略[J]. 储能科学与技术, 2023, 12(2): 544-551.

Lulu LI, Zhengshun TAO, Tinglong PAN, Weilin YANG, Guanyang HU. Research on fractional modeling and SOC estimation strategy for lithium batteries[J]. Energy Storage Science and Technology, 2023, 12(2): 544-551.

图/表 8

图1

图2

表1

FOUPF与FOSOUPF计算量的对比"

计算复杂度	FOUPF	FOSOUPF
采样点数	$2 L + 1$	$L + 1$
协方差阵Cholesky分解	$o (L 3 / 6)$	$o [(L / 2) 3 / 6)]$
确定采样点	$o [m (L 3 / 6)]$	$o [m (L / 2) 3 / 6]$
时间更新	$o [m (L 3 / 6)]$	$o [m (L / 2) 3]$
量测更新	$o (m M 2)$	$o (m M 2)$

表1

表2

参数辨识结果"

R₀/Ω	R₁/Ω	R₂/Ω	$C c p e 1$ /kF	$C c p e 2$ /kF	m	n
0.0036	0.0025	0.0093	1.624	3.11	0.9759	0.9947

表2

图3

图4

图5

表3

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状态估计方法	SOC初始值为1		SOC初始值为0.8
状态估计方法	SOC误差	电压误差	SOC误差	电压误差
FOSOUPF	0.0036	0.0048	0.0037	0.0053
FOUPF	0.0042	0.0065	0.0051	0.0067
FOUKF	0.0062	0.0072	0.0063	0.0075

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