Optimization by Means of Genetic Algorithm of the Equivalent Electrical Circuit Model of Different Order for Li-ion Battery Pack
The purpose of this article is to optimize the Equivalent Electric Circuit Model (EECM) of different orders to obtain greater precision in the modeling of Li-ion battery packs. Optimization includes considering circuits based on 1RC, 2RC and 3RC networks, with a dependent voltage source and a series resistor. The parameters are obtained experimentally using tests in the time domain and in the frequency domain. Due to the high non-linearity of the behavior of the battery pack, Genetic Algorithm (GA) was used to solve and optimize the parameters of each EECM considered (1RC, 2RC and 3RC). The objective of the estimation is to minimize the mean square error between the measured impedance in the real battery pack and those generated by the simulation of different proposed circuit models. The results have been verified by comparing the Nyquist graphs of the estimation of the complex impedance of the pack. As a result of the optimization, the 2RC and 3RC circuit alternatives are considered as viable to represent the battery behavior. These battery pack models are experimentally validated using a hardware-in-the-loop (HIL) simulation platform that reproduces the well-known New York City cycle (NYCC) and Federal Test Procedure (FTP) driving cycles for electric vehicles. The results show that using GA optimization allows obtaining EECs with 2RC or 3RC networks, with high precision to represent the dynamic behavior of a battery pack in vehicular applications.
[1] N. Baba, H. Yoshida, M. Nagaoka, C. Okuda and S. Kawauchi, “Numerical simulation of thermal behavior of lithium-ion secondary batteries using the enhanced single particle model”, Journal of Power Sources, vol. 252, pp. 214-228, April 2014.
[2] A. Jossen, “Fundamentals of battery dynamics” Journal of Power Source, vol. 154, No. 2, pp. 530-538, March 2016.
[3] A. Berrueta, A. Urtasun, A. Ursúa y P. Sanchis, “A comprehensive model for lithium-ion batteries: From the physical principles to an electrical model”, Energy, vol. 144, pp. 286-300, February2018.
[4] E. Samadani, S. Farhad, W. Scott, M. Mastali, L. Gimenez, M. Fowler y R. Fraser, “Empirical Modeling of Lithium-ion Batteries Based on Electrochemical Impedance Spectroscopy Tests”, Electrochimica Acta, vol. 160, pp. 169-177, 2015.
[5] V. Pizarro-Carmona, M. Cortés-Carmona, R. Palma-Behnke, W. Calderón-Muñoz, M. E. Orchard, P. A. Estévez, “An optimized Impedance Model for the Estimation of the State-of-Charge of a Li-Ion Cell: The Case LiFePO4 (ANR26650)”, Energies, vol. 12, pp. 1-16, February 2019.
[6] D. Andre, M. Meiler, K. Steiner, H. Walz, T. Soczka-Guth, D. Sauer, “Characterization of high-power lithium-ion batteries by electrochemical”, Journal of Power Source, vol. 196, pp. 5349-5356, June 2011.
[7] P. Attidekou, S. Lambert, S. Armstrong, J. Widmer , K. Scott y P. Christensen, “A study of 40 Ah lithium ion batteries at zero percent state of charge” Journal of Power Source, vol. 269, pp. 694-703, December 2014.
[8] E. Raszmann, K. Baker, Y. Shi, D. Christensen, “Modeling Stationary Lithium-Ion Batteries for optimization and predictive control” IEEE Power and Energy Conference at Illinois (PECI), Champaign, IL USA, June 2017.
[9] S. Castano-Solis, D. Serrano-Jimenez, J. Fraile-Ardanuy, J. Sanz-Feito, “Hybrid characterization procedure of Li-ion battery packs for wide frequency range dynamic applications”, Electric Power System Research, vol. 166, pp. 9-17, January 2019.
[10] R. Xiong, H. He, H. Guo, Y. Ding, “Modeling for Lithium-Ion Battery used in Electric Vehicles”, Procedia Engineering, vol. 15, pp. 2869-2874, 2011.
[11] S. Lee, J. Kim, J. Lee, B. Cho, “State-of-charge and capacity estimation of lithium-ion battery”, Journal of Power Source, vol. 185, pp. 1367-1373, December 2008.
[12] C. Zhang, W. Allafi, Q. Dinh, P. Ascencio, J. Marco, “Online estimation of battery equivalent circuit model parameters and state of charge using decoupled least squares technique”, Energy, vol. 142, pp. 678-688, January 2018.
[13] P. Baudry, M. Neri, M. Gueguen, G. Lonchampt, “Electro-thermal modelling of polymer lithium batteries”, Journal of Power Source, vol. 54, pp. 393-395, April 1995.
[14] J. Xu, C. Chir, B. Cao, J. Cao, “A new method to estimate the state of charge of lithium-ion batteries based on the battery impedance model” Journal of Power Source, vol. 233, pp. 277-284, July 2013.
[15] Y. Hu, S. Yurkovich, Y. Guezennec, B. Yurkovich, “A technique for dynamic battery model identification in automotive applications using linear parameter varying structures”, Control Engineering Practice, vol. 17, pp. 1190-1201, October 2009.
[16] K. Khan, M. Jafari, L. Gauchia, “Comparison of Li-ion battery equivalent circuit modelling using impedance analyzer and Bayesian Networks” IET Electr. Syst. Trans., vol. 8, pp. 197-204, April 2018.
[17] R. Li, J. Wu, H. Wang, G. Li, “Prediction of state of charge of lithium-ion rechargeable battery with electrochemical impedance spectroscopy theory”, Proceedings of the 5th IEEE Conference on Industrial Electronics and Applications, Taichung, Taiwan, 2010, pp. 684-688.
[18] P.M. Gomadan, J.W. Weidner, “Analysis of electrochemical impedance spectroscopy in proton exchange membrane fuel cells”, Int. J. Energy Res., vol. 29, pp.1133–1151, September 2015.
[19] S. Castano-Solis, D. Serrano-Jimenez, L. Gauchia, J. Sanz-Feito, “The Influence of BMSs on the Characterization and Modeling of Series and Parallel Li-Ion Packs”, Energies, vol. 10, pp. 273, February 2017.
[20] E. Ferg, C. Rossouw, P. Loyson, “The testing of batteries linked to supercapacitors with electrochemical impedance spectroscopy: A comparison between Li-ion and valve regulated lead acid batteries” Journal Power of Source, vol. 226, pp. 299-305, March 2013.
[21] S. Rodrigues, N. Munichandrajah, K. Shukla, “A review of state of charge indication of batteries by means AC impedance measurements”, Journal of Power Source, vol. 87, pp. 59-69, April 2000.
[22] A. Hammouchen, E. Karden, W. Rik, “Monitoring state of charge of Ni-MH and Ni-Cd batteries using impedance spectroscopy”, Journal of Power Source, vol. 127, pp. 105-111, March 2004.
[23] H. Rahimi-Eichi, U. Ojha, F. Baronti, M. Chow, “Battery Management System: an overview of its applications in the smart grid and electric vehicles”, IEEE Ind. Electron. Mag., vol. 7, pp. 4-16, June 2013.
[24] B. Xia, C. Chen, Y. Tian, W. Sun, Z. Xu, W. Zheng, “A novel method for state of charge estimation of lithium-ion batteries using a nonlinear observer”, Journal of Power Sources, vol. 270, pp. 359-366, December 2014.
[25] S. Castano-Solis, L. Gauchia, D. Serrano Jimenez, and J. Sanz Feito, “Off-the-Shelf and Flexible Hybrid Frequency and Time Domain Experimental Architecture Setup for Electrochemical Energy Modules Testing under Realistic Operating Conditions”, IEEE Trans. On Energy Conversion, vol. 32, pp. 620- 627, June 2017.
[1] N. Baba, H. Yoshida, M. Nagaoka, C. Okuda and S. Kawauchi, “Numerical simulation of thermal behavior of lithium-ion secondary batteries using the enhanced single particle model”, Journal of Power Sources, vol. 252, pp. 214-228, April 2014.
[2] A. Jossen, “Fundamentals of battery dynamics” Journal of Power Source, vol. 154, No. 2, pp. 530-538, March 2016.
[3] A. Berrueta, A. Urtasun, A. Ursúa y P. Sanchis, “A comprehensive model for lithium-ion batteries: From the physical principles to an electrical model”, Energy, vol. 144, pp. 286-300, February2018.
[4] E. Samadani, S. Farhad, W. Scott, M. Mastali, L. Gimenez, M. Fowler y R. Fraser, “Empirical Modeling of Lithium-ion Batteries Based on Electrochemical Impedance Spectroscopy Tests”, Electrochimica Acta, vol. 160, pp. 169-177, 2015.
[5] V. Pizarro-Carmona, M. Cortés-Carmona, R. Palma-Behnke, W. Calderón-Muñoz, M. E. Orchard, P. A. Estévez, “An optimized Impedance Model for the Estimation of the State-of-Charge of a Li-Ion Cell: The Case LiFePO4 (ANR26650)”, Energies, vol. 12, pp. 1-16, February 2019.
[6] D. Andre, M. Meiler, K. Steiner, H. Walz, T. Soczka-Guth, D. Sauer, “Characterization of high-power lithium-ion batteries by electrochemical”, Journal of Power Source, vol. 196, pp. 5349-5356, June 2011.
[7] P. Attidekou, S. Lambert, S. Armstrong, J. Widmer , K. Scott y P. Christensen, “A study of 40 Ah lithium ion batteries at zero percent state of charge” Journal of Power Source, vol. 269, pp. 694-703, December 2014.
[8] E. Raszmann, K. Baker, Y. Shi, D. Christensen, “Modeling Stationary Lithium-Ion Batteries for optimization and predictive control” IEEE Power and Energy Conference at Illinois (PECI), Champaign, IL USA, June 2017.
[9] S. Castano-Solis, D. Serrano-Jimenez, J. Fraile-Ardanuy, J. Sanz-Feito, “Hybrid characterization procedure of Li-ion battery packs for wide frequency range dynamic applications”, Electric Power System Research, vol. 166, pp. 9-17, January 2019.
[10] R. Xiong, H. He, H. Guo, Y. Ding, “Modeling for Lithium-Ion Battery used in Electric Vehicles”, Procedia Engineering, vol. 15, pp. 2869-2874, 2011.
[11] S. Lee, J. Kim, J. Lee, B. Cho, “State-of-charge and capacity estimation of lithium-ion battery”, Journal of Power Source, vol. 185, pp. 1367-1373, December 2008.
[12] C. Zhang, W. Allafi, Q. Dinh, P. Ascencio, J. Marco, “Online estimation of battery equivalent circuit model parameters and state of charge using decoupled least squares technique”, Energy, vol. 142, pp. 678-688, January 2018.
[13] P. Baudry, M. Neri, M. Gueguen, G. Lonchampt, “Electro-thermal modelling of polymer lithium batteries”, Journal of Power Source, vol. 54, pp. 393-395, April 1995.
[14] J. Xu, C. Chir, B. Cao, J. Cao, “A new method to estimate the state of charge of lithium-ion batteries based on the battery impedance model” Journal of Power Source, vol. 233, pp. 277-284, July 2013.
[15] Y. Hu, S. Yurkovich, Y. Guezennec, B. Yurkovich, “A technique for dynamic battery model identification in automotive applications using linear parameter varying structures”, Control Engineering Practice, vol. 17, pp. 1190-1201, October 2009.
[16] K. Khan, M. Jafari, L. Gauchia, “Comparison of Li-ion battery equivalent circuit modelling using impedance analyzer and Bayesian Networks” IET Electr. Syst. Trans., vol. 8, pp. 197-204, April 2018.
[17] R. Li, J. Wu, H. Wang, G. Li, “Prediction of state of charge of lithium-ion rechargeable battery with electrochemical impedance spectroscopy theory”, Proceedings of the 5th IEEE Conference on Industrial Electronics and Applications, Taichung, Taiwan, 2010, pp. 684-688.
[18] P.M. Gomadan, J.W. Weidner, “Analysis of electrochemical impedance spectroscopy in proton exchange membrane fuel cells”, Int. J. Energy Res., vol. 29, pp.1133–1151, September 2015.
[19] S. Castano-Solis, D. Serrano-Jimenez, L. Gauchia, J. Sanz-Feito, “The Influence of BMSs on the Characterization and Modeling of Series and Parallel Li-Ion Packs”, Energies, vol. 10, pp. 273, February 2017.
[20] E. Ferg, C. Rossouw, P. Loyson, “The testing of batteries linked to supercapacitors with electrochemical impedance spectroscopy: A comparison between Li-ion and valve regulated lead acid batteries” Journal Power of Source, vol. 226, pp. 299-305, March 2013.
[21] S. Rodrigues, N. Munichandrajah, K. Shukla, “A review of state of charge indication of batteries by means AC impedance measurements”, Journal of Power Source, vol. 87, pp. 59-69, April 2000.
[22] A. Hammouchen, E. Karden, W. Rik, “Monitoring state of charge of Ni-MH and Ni-Cd batteries using impedance spectroscopy”, Journal of Power Source, vol. 127, pp. 105-111, March 2004.
[23] H. Rahimi-Eichi, U. Ojha, F. Baronti, M. Chow, “Battery Management System: an overview of its applications in the smart grid and electric vehicles”, IEEE Ind. Electron. Mag., vol. 7, pp. 4-16, June 2013.
[24] B. Xia, C. Chen, Y. Tian, W. Sun, Z. Xu, W. Zheng, “A novel method for state of charge estimation of lithium-ion batteries using a nonlinear observer”, Journal of Power Sources, vol. 270, pp. 359-366, December 2014.
[25] S. Castano-Solis, L. Gauchia, D. Serrano Jimenez, and J. Sanz Feito, “Off-the-Shelf and Flexible Hybrid Frequency and Time Domain Experimental Architecture Setup for Electrochemical Energy Modules Testing under Realistic Operating Conditions”, IEEE Trans. On Energy Conversion, vol. 32, pp. 620- 627, June 2017.
@article{"International Journal of Electrical, Electronic and Communication Sciences:79984", author = "V. Pizarro-Carmona and S. Castano-Solis and M. Cortés-Carmona and J. Fraile-Ardanuy and D. Jimenez-Bermejo", title = "Optimization by Means of Genetic Algorithm of the Equivalent Electrical Circuit Model of Different Order for Li-ion Battery Pack ", abstract = "The purpose of this article is to optimize the Equivalent Electric Circuit Model (EECM) of different orders to obtain greater precision in the modeling of Li-ion battery packs. Optimization includes considering circuits based on 1RC, 2RC and 3RC networks, with a dependent voltage source and a series resistor. The parameters are obtained experimentally using tests in the time domain and in the frequency domain. Due to the high non-linearity of the behavior of the battery pack, Genetic Algorithm (GA) was used to solve and optimize the parameters of each EECM considered (1RC, 2RC and 3RC). The objective of the estimation is to minimize the mean square error between the measured impedance in the real battery pack and those generated by the simulation of different proposed circuit models. The results have been verified by comparing the Nyquist graphs of the estimation of the complex impedance of the pack. As a result of the optimization, the 2RC and 3RC circuit alternatives are considered as viable to represent the battery behavior. These battery pack models are experimentally validated using a hardware-in-the-loop (HIL) simulation platform that reproduces the well-known New York City cycle (NYCC) and Federal Test Procedure (FTP) driving cycles for electric vehicles. The results show that using GA optimization allows obtaining EECs with 2RC or 3RC networks, with high precision to represent the dynamic behavior of a battery pack in vehicular applications.
", keywords = "Li-ion battery packs modeling optimized, EECM, GA, electric vehicle applications. ", volume = "14", number = "11", pages = "343-6", }
