﻿ 不同温度下磷酸铁锂电池的模型参数敏感性分析
 上海理工大学学报  2022, Vol. 44 Issue (5): 449-456 PDF

Sensitivity analysis of model parameters of LiFePO4 battery at different temperatures
WANG Mingzhu, XIAO Zhanlong, ZHENG Yuejiu
School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: In order to realize the high precision state estimation of battery, the basic performance experiments of LiFePO4 battery were carried out at four different temperatures. At the same time, an experimental method is designed to obtain the open circuit voltage of the full state of charge (SOC) range under variable temperature conditions, which provided data support for the establishment of the second-order RC battery model considering temperature factors and the parameter sensitivity analysis. In addition, using the test data of hybrid pulse power characterization at different temperatures, the accurate model parameters at different temperatures were identified based on the particle swarm optimization algorithm. Finally, the sensitivity analysis of each parameter in the established battery model was carried out based on the one factor of a time method. The analysis results can be used for reference for parameter identification and state estimation considering temperature.
Key words: different temperatures     LiFePO4battery     equivalent circuit model     parameter identification     sensitivity analysis

1 研究方法 1.1 温度特性实验 1.1.1 不同温度的基础性能实验

1.1.2 变温下开路电压实验

a.以1/3C恒流恒压充电将电池充满电；

b. 将电池搁置在 45 ℃ 温度条件下足够长的时间，此时测得的端电压可作为电池的开路电压。再由 45℃逐次降温至25，5，−15 ℃，分别都搁置一定时间，由此得到电池在该 SOC 点下各个温度点的开路电压；

c.搁置结束后，将温度调节至 25 ℃，搁置足够长的时间，以 1/3C 的电流对电池恒流放电至下一个 SOC 点，静置。再次执行步骤 b，得到电池在该 SOC 点下各个温度点的开路电压；

d.重复循环步骤b与步骤c，持续放电到截止电压。

 图 1 变温开路电压实验流程图 Fig. 1 Flow chart of variable temperature open circuit voltage experiment
1.2 电池模型及参数辨识方法

 图 2 考虑温度因素的二阶RC模型 Fig. 2 Second-order RC model considering temperature

 $\theta = [{R_{{\rm{c}}}},{R_{{\rm{d}}}},{R_1},{\tau _1},{R_2},{\tau _2}]$ (1)

 $\hat F({\hat \theta _{{k}}}) = \sqrt {\frac{1}{N}{\sum\limits_{k = 1}^N {({U_{{k}}} - {{\hat U}_{{k}}}({{\hat \theta }_{{k}}}))} ^2}}$ (2)

 图 3 电池模型参数辨识过程 Fig. 3 Battery model parameter identification process
1.3 敏感性分析方法

2 温度特性分析 2.1 容量特性分析

 图 4 不同温度下的容量和容量归一化 Fig. 4 Capacities and capacity normalization at different temperatures

2.2 内阻特性分析

 图 5 磷酸铁锂电池在不同温度下的总内阻 Fig. 5 Total internal resistance of LiFePO4 battery at different temperatures

2.3 开路电压特性分析

 图 6 不同温度下的开路电压与差值 Fig. 6 Open circuit voltages and difference at different temperatures
3 模型参数辨识结果分析

 图 7 不同温度下模型参数辨识结果 Fig. 7 Identification results of model parameters at different temperatures

 图 8 45 ℃时的模型端电压和电压误差 Fig. 8 Model terminal voltage and voltage error at 45 ℃

4 模型参数敏感性分析 4.1 整个SOC范围内的参数敏感性分析

 图 9 整个SOC范围内的参数敏感度变化率 Fig. 9 The rate of change of parameter sensitivity over the SOC range

4.2 不同温度下的参数敏感性分析

 图 10 磷酸铁锂电池在不同温度下的参数敏感度（50%SOC） Fig. 10 Parameter sensitivity of LiFePO4 battery at different temperatures （50%SOC）

5 结　论

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