Estimation of Reduced Order Equivalent Circuit Model Parameters of Batteries from Noisy Current and Voltage Measurements

Öz

Identification of reduced order equivalent circuit battery model from current and voltage measurements allows modeling, classification and monitoring of batteries, and these tasks are very essential for battery management systems. This study presents a theoretical study to investigate performance of computer-aided identification of the reduced order equivalent circuit battery model from noisy current and voltage measurement data. The battery model is expressed by fractional order differential equation and time domain solution of this model is numerically calculated according to Grünwald-Letnikov definition of fractional-order derivative. Paper demonstrates an application of this numerical solution in order to fit noisy current and voltage measurement data by using particle swarm optimization (PSO) method. Then, parameters of the equivalent circuit battery model are estimated. Performance of the parameter estimation method is investigated for various noise levels of the synthetically generated current and voltage profiles.

Anahtar Kelimeler

• Battery model,fractional order system model,Grünwald-Letnikov definition,,PSO

Kaynakça

1. [1] J.X. Chuntin,g C. Mi, B. Cao, J. Cao, "New method to estimate the state of charge of lithium-ion batteries based on the battery impedance model", Journal of Power Sources, Vol.233, 2013, pp.277-284.
2. [2] W. Waag, S. Käbitz, D.U. Sauer, "Application-specific parameterization of reduced order equivalent circuit battery models for improved accuracy at dynamic load", Measurement, Vol.46, 2013, pp. 4085–4093.
3. [3] C.B. Shin, BATTERIES: modeling, in: Encyclopedia of Electrochemical Power Sources, vol. I, Elsevier, 2009. pp.510–521.
4. [4] X. Hu, S. Li, H. Peng, "A comparative study of equivalent circuit models for Li-ion batteries", Journal of Power Sources, Vol.198, 2012, pp.359–367.
5. [5] S. Buller, "Impedance-Based Simulation Models for Energy Storage Devices in Advanced Automotive Power Systems", Institue for Power Electronics and Electrical Drives, RWTH Aachen University, Ph.D. Thesis, 2003.
6. [6] T.J. Freeborn, B. Maundy, A.S. Elwakil, "Fractional-order models of supercapacitors, batteries and fuel cells: a survey", Mater Renew Sustain Energy Vol.4, No.2, 2015, pp.1-7
7. [7] Y.Q. Chen, Ivo Petras, D. Xue, "Fractional order control-a tutorial", In: American Control Conference, 2009. ACC'09. IEEE, 2009. p. 1397-1411.
8. [8] R. Scherer, S.L. Kalla, Y. Tang, J. Huang, "The Grünwald–Letnikov method for fractional differential equations", Computers and Mathematics with Applications Vol.62, 2011, pp.902–917.

9. [9] C. Zhao, L. Luo, Y. Zhao, "Fractional Modeling Approach with Mittag-Leffler Functions for Linear Fractional-order System", 2012 Fifth International Conference on Intelligent Computation Technology and Automation, pp. 386- 389.
10. [10] R.S. Awski, K.J. Latawiec, M. Lukaniszyn, W. Czuczwara, and R. Kopka, "Modeling and identification of fractional first-order systems with Laguerre-Grunwald-Letnikov fractional-order differences", 2016 21st International Conference on Methods and Models in Automation and Robotics (MMAR),2016,pp.174-177.
11. [11] P. Sopasakisy, S. Ntouskas, H. Sarimveis, "Robust Model Predictive Control for Discrete-time Fractional-order Systems", 2015 23rd Mediterranean Conference on Control and Automation (MED), Torremolinos, Spain, 2015, pp. 384-389.
12. [12] E Dorcák, J. Valsa, J. Terpák, E. Gonzalez, "Comparison of the methods for the calculation of fractional-order differential equations", In Carpathian Control Conference (ICCC), 2011, pp. 80-84.
13. [13] S.E. Li, B. Wang, H. Peng, and X. Hu, “An electrochemistry-based impedance model for lithium-ion batteries,” J. Power Sour., Vol. 258, 2014, pp.9–18.
14. [14] B. Wang, Z. Liu, S.E. Li, , S.J. Moura, H. Peng, "State-of-charge estimation for lithium-ion batteries based on a nonlinear fractional model", IEEE Transactions on Control Systems Technology, Vol.25, No.1, 2017, pp. 3-11.
15. [15] D. Zhou, K. Zhang, A. Ravey, F. Gao, A. Miraoui, "Parameter sensitivity analysis for fractional-order modeling of lithium-ion batteries", Energies, Vol.9, No.3, 2016, pp.123.
16. [16] E. Barsukov, J.R. Macdonald, Impedance Spectroscopy: Theory, Experiment and Applications, second ed., Wiley-Interscience, 2005.
17. [17] M.E. Orazem, P. Shukla, M.A. Membrino, "Extension of the measurement model approach for deconvolution of underlying distributions for impedance measurements", Electrochimica Acta, Vol.47, 2002, pp.2027-2034.