基于单粒子模型与偏微分方程的锂离子电池建模与故障监测

黄亮; 李建远

doi:10.7498/aps.64.108202

摘要

锂离子电池内部结构是一种复杂的分布参数系统, 如果为了降低计算难度而使用常微分方程描述锂离子电池, 可能会引入系统误差, 降低系统模型的可信度, 需要使用偏微分方程建立分布参数系统的精确模型. 本文提出了一种基于单粒子模型和抛物型偏微分方程的锂离子电池系统建模与故障监测系统设计方法, 当锂离子浓度实测值与理想值的残差大于预设门槛时判定分布参数系统处于故障状态. 通过一个仿真实例进行了锂离子电池系统建模和故障诊断实验, 实验证明基于单粒子模型和偏微分方程的锂离子电池故障监测系统具有更高的精确度和可信度.

关键词:

Abstract

Li-ion battery is a complicated distributed parameter system that can be described precisely by field theory and partial differential equations. In order to reduce the calculation amount and the solution difficulty, a distributed parameter system is often described by ordinary differential equation model during the design and the analysis. As a result, systemic error is caused, and the reliability of the system model is reduced. The rechargeable Li-ion batteries are widely used in many fields because of their excellent properties. The research on the modeling and failure monitor of Li-ion battery can evaluate its working state, and improve the security during its servicing. Li-ion battery system is regarded as a distributed parameter system in this paper. Single particle model is a simplification of a Li-ion battery under a few assumptions. According to the measured data, single particle model can be used for estimating the parameter at a fast simulation speed. Li-ion battery model based on partial difference equations and single particle model is proposed to detect the failure and evaluate the working state of Li-ion battery system. Lithium ion concentration is an unmeasurable distributed variable in the anode of Li-ion battery. The failure monitor system can track the real-time Li ion concentration in the anode of Li-ion battery, calculate the residual which is the difference between the measured value and the ideal value. A failure can be judged when the residual is beyond a predefined failure threshold. A simulation example verifies that the accuracy and the effectiveness of Li-ion battery failure monitor system based on parabolic partial difference equations and single particle model is reliable.

Keywords:

作者及机构信息

黄亮¹,
李建远²

1.
北京交通大学电子信息工程学院, 北京 100044;

2.
北京大学物理学院, 北京 100871

基金项目: 中央高校基本科研业务费专项资金(批准号: 2013JBM016)、国家自然科学基金(批准号: 61201363, 61172130)和国家留学基金(批准号: 201307095030)资助的课题.

Authors and contacts

Huang Liang¹,
Li Jian-Yuan²

1.
School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China;

2.
School of Physics, Peking University, Beijing 100871, China

Funds: Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2013JBM016), the National Natural Science Foundation of China (Grant Nos. 61201363, 61172130) and the Studying Abroad Funding of China Scholarship Council, China (Grant No. 201307095030).

参考文献

[1]	Ucinski D 2004 Optimal Measurement Methods for Distributed Parameter System Identification (Boca Raton: CRC Press Inc.) p1
[2]	Ma X K, Yang M, Zou J L, Wang L T 2006 Acta Phys. Sin. 55 5648 (in Chinese) [马西奎, 杨梅, 邹建龙, 王玲桃 2006 物理学报 55 5648]
[3]	Hou X L, Zheng X J, Zhang L, Liu T L 2012 Acta Phys. Sin. 61 180201 (in Chinese) [侯祥林, 郑夕健, 张良, 刘铁林 2012 物理学报 61 180201]
[4]	Hong L, Xu J X 2000 Acta Phys. Sin. 49 1228 (in Chinese) [洪灵, 徐健学 2000 物理学报 49 1228]
[5]	Wang C, Zhou Y Q, Shen G W, Wu W W, Ding W 2013 Chin. Phys. B 22 124601
[6]	Huang L, Hou J J, Liu Y, Guo Y 2013 Chin. J. Electron. 22 615
[7]	Oh M, Pantelides C C 1996 Comput. Chem. Eng. 20 611
[8]	Ghantasala S, El-Farra N H 2011 Int. J. Robust Nonlin. 22 24
[9]	Ghantasala S, El-Farra N H 2009 Automatica 45 2368
[10]	Demetriou M A 2002 ESAIM. COCV 7 43
[11]	Armaou A, Demetriou M A 2008 AIChE J. 54 2651
[12]	Chen M, Rincon-Mora G A 2006 IEEE Trans. Energy Conver. 21 504
[13]	Santhanagopalan S, Guo Q Z, Ramadass P, White R E 2006 J. Pow. Sour. 156 620
[14]	Moura S J, Chaturvedi N A, Krstic M E 2013 J. Dyn. Sys., Meas., Control 136 011015
[15]	Schmidt A P, Bitzer M, Imre A W, Guzzella L 2010 J. Pow. Sour. 195 5071
[16]	Andrieu V, Praly L 2006 SIAM J. Control Optim. 45 432
[17]	Smyshlyaev A, Orlov Y, Krstic M 2009 Int. J. Adapt. Control Process. 23 131
[18]	Osler T J 1972 Math. Comput. 26 903
[19]	De Las Casas C, Li W Z 2012 J. Pow. Sour. 208 74
[20]	Zhang W J 2011 J. Pow. Sour. 196 13
[21]	Wouwer A V, Saucez P, Schiesser W E 2004 Ind. Eng. Chem. Res. 43 3469

施引文献

[1]	Ucinski D 2004 Optimal Measurement Methods for Distributed Parameter System Identification (Boca Raton: CRC Press Inc.) p1
[2]	Ma X K, Yang M, Zou J L, Wang L T 2006 Acta Phys. Sin. 55 5648 (in Chinese) [马西奎, 杨梅, 邹建龙, 王玲桃 2006 物理学报 55 5648]
[3]	Hou X L, Zheng X J, Zhang L, Liu T L 2012 Acta Phys. Sin. 61 180201 (in Chinese) [侯祥林, 郑夕健, 张良, 刘铁林 2012 物理学报 61 180201]
[4]	Hong L, Xu J X 2000 Acta Phys. Sin. 49 1228 (in Chinese) [洪灵, 徐健学 2000 物理学报 49 1228]
[5]	Wang C, Zhou Y Q, Shen G W, Wu W W, Ding W 2013 Chin. Phys. B 22 124601
[6]	Huang L, Hou J J, Liu Y, Guo Y 2013 Chin. J. Electron. 22 615
[7]	Oh M, Pantelides C C 1996 Comput. Chem. Eng. 20 611
[8]	Ghantasala S, El-Farra N H 2011 Int. J. Robust Nonlin. 22 24
[9]	Ghantasala S, El-Farra N H 2009 Automatica 45 2368
[10]	Demetriou M A 2002 ESAIM. COCV 7 43
[11]	Armaou A, Demetriou M A 2008 AIChE J. 54 2651
[12]	Chen M, Rincon-Mora G A 2006 IEEE Trans. Energy Conver. 21 504
[13]	Santhanagopalan S, Guo Q Z, Ramadass P, White R E 2006 J. Pow. Sour. 156 620
[14]	Moura S J, Chaturvedi N A, Krstic M E 2013 J. Dyn. Sys., Meas., Control 136 011015
[15]	Schmidt A P, Bitzer M, Imre A W, Guzzella L 2010 J. Pow. Sour. 195 5071
[16]	Andrieu V, Praly L 2006 SIAM J. Control Optim. 45 432
[17]	Smyshlyaev A, Orlov Y, Krstic M 2009 Int. J. Adapt. Control Process. 23 131
[18]	Osler T J 1972 Math. Comput. 26 903
[19]	De Las Casas C, Li W Z 2012 J. Pow. Sour. 208 74
[20]	Zhang W J 2011 J. Pow. Sour. 196 13
[21]	Wouwer A V, Saucez P, Schiesser W E 2004 Ind. Eng. Chem. Res. 43 3469

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