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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.
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Keywords:
- Li-ion battery /
- single particle model /
- distributed parameter system /
- partial difference equation
[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 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 61 180201]
[4] Hong L, Xu J X 2000 Acta Phys. Sin. 49 1228 (in Chinese) [洪灵, 徐健学 2000 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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[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 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 61 180201]
[4] Hong L, Xu J X 2000 Acta Phys. Sin. 49 1228 (in Chinese) [洪灵, 徐健学 2000 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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