The effect of the linear method on electrochemical impedance spectroscopy calculation in the time domain under the noise condition

Document Type : Research Paper


1 Mechanical Engineering Faculty, K. N. Toosi University of Technology, Tehran, Iran

2 Analytical Chemistry Department, Chemistry Faculty, School of Sciences, University of Tehran, Tehran, Iran



Electrochemical impedance spectroscopy is a powerful tool for determining the behavior of electrochemical systems. Despite being costly and time-consuming, the time-domain impedance calculation of electrochemical systems is advantageous. However, this method exhibits a high error rate under noise conditions. In this study, the linear technique is developed to minimize noise effects when calculating the impedance of electrochemical systems in the time domain. Multiple equivalent circuit samples are simulated, and the linear technique versus the standard fast Fourier transform method for a noisy input is compared. The results indicate that its error rate is considerably less than that of the fast Fourier transform. The error rate in the Li-ion battery equivalent circuit was reduced from 273.5446 using the fast Fourier transform to 0.0049 using the linear method. Notably, this reduction is significant and on the order of . Additionally, the decline in the real and imaginary parts of mean relative error is in the order of 10. It is concluded that the linear method results in less error in the presence of noise and is faster than traditional electrochemical impedance spectroscopy in the frequency domain. Thus, the linear method outperforms the fast Fourier transform method in time-domain electrochemical impedance spectroscopy.


[1] L. A. Middlemiss, A. J. Rennie, R. Sayers, and A. R. West, “Characterization of batteries by electrochemical impedance spectroscopy,” Energy Reports, vol. 6, pp. 232–241, 2020.
[2] G. Krikis, “Diagnostic of lithium-ion batteries,” Master’s thesis, Aalborg University, Denmark, 2018.
[3] P. Vyroubal and T. Kazda, “Equivalent circuit model parameters ex- traction for lithium-ion batteries using electrochemical impedance spectroscopy,” Journal of Energy Storage, vol. 15, pp. 23–31, 2018.
[4] B. Jiang, J. Zhu, X. Wang, X. Wei, W. Shang, and H. Dai, “A compara­tive study of different features extracted from electrochemical impedance spectroscopy in state of health estimation for lithium-ion batteries,” Ap­plied Energy, vol. 322, p. 119502, 2022.
[5] R. Scipioni, P. S. Jørgensen, C. Graves, J. Hjelm, and S. H. Jensen, “A physically-based equivalent circuit model for the impedance of a lifepo4/graphite 26650 cylindrical cell,” Journal of The Electrochemical Society, vol. 164, no. 9, p. A2017, 2017.
[6] R. Ma, J. He, and Y. Deng, “Investigation and comparison of the elec­trochemical impedance spectroscopy and internal resistance indicators for early-stage internal short circuit detection through battery aging,” Journal of Energy Storage, vol. 54, p. 105346, 2022.
[7] F. Amano and S. Koga, “Electrochemical impedance spectroscopy of wo3 photoanodes on different conductive substrates: the interfacial charge transport between semiconductor particles and ti surface,” Jour­nal of Electroanalytical Chemistry, p. 116685, 2022.
[8] L. Yao, Q. Cheng, Z. Long, Z. Chen, Z. Lin, Y. Li, Y. Tian, and Y. Liao, “Characterizing phenol mass transfer coefficients of composite extractive membranes with different pdms thicknesses by electrochem­ical impedance spectroscopy,” Journal of Water Process Engineering, vol. 49, p. 103057, 2022.
[9] J. Jiang, Z. Lin, Q. Ju, Z. Ma, C. Zheng, and Z. Wang, “Electrochemical impedance spectra for lithium-ion battery aging considering the rate of discharge ability,” Energy Procedia, vol. 105, pp. 844–849, 2017.
[10] J. Schmitt, A. Maheshwari, M. Heck, S. Lux, and M. Vetter, “Impedance change and capacity fade of lithium nickel manganese cobalt oxide-based batteries during calendar aging,” Journal of Power Sources, vol. 353, pp. 183–194, 2017.
[11] E. Teliz, C. F. Zinola, and V. D´ıaz, “Identification and quantification of aging mechanisms in li-ion batteries by electrochemical impedance spectroscopy.” Electrochimica Acta, vol. 426, p. 140801, 2022.
[12]M.Koseoglou, E. Tsioumas, D. Ferentinou, N. Jabbour, D. Papagian- nis, and C. Mademlis, “Lithium plating detection using dynamic electrochemical impedance spectroscopy in lithium-ion batteries,” Journal of Power Sources, vol. 512, p. 230508, 2021.
[13] I.Ezpeleta,  L.Freire,  C.  Mateo-Mateo, X.  R.  No´voa, A.  Pintos, and S.Valverde-P´erez, “Characterization of commercial li-ion batteries using electrochemical impedance spectroscopy,” ChemistrySelect, vol. 7, no. 10, p. e202104464, 2022.
[14] D. Capkova, V. Knap, A. S. Fedorkova, and D.-I. Stroe, “Analysis of 3.4 ah lithium-sulfur pouch cells by electrochemical impedance spectroscopy,” Journal of Energy Chemistry, 2022.
[15] M. Mohsin, A. Picot, and P. Maussion, “A new lead-acid battery state- of-health evaluation method using electrochemical impedance spectroscopy for second life in rural electrification systems,” Journal of Energy Storage, vol. 52, p. 104647, 2022.
[16] N. Lohmann, P. Weßkamp, P. Haußmann, J. Melbert, and T. Musch, “Electrochemical impedance spectroscopy for lithium-ion cells: Test equipment and procedures for aging and fast characterization in time and frequency domain,” Journal of Power Sources, vol. 273, pp. 613–623, 2015.
[17] D. Klotz, “Characterization and modeling of electrochemical energy conversion systems by impedance techniques,” Ph.D. dissertation, Universit¨at Karlsruhe, 2012.
[18] N. Hallemans, W. D. Widanage, X. Zhu, S. Moharana, M. Rashid, A. Hubin, and J. Lataire, “Operando electrochemical impedance spec­troscopy and its application to commercial li-ion batteries,” Journal of Power Sources, vol. 547, p. 232005, 2022.
[19] M. Kuipers, P. Schr¨oer, T. Nemeth, H. Zappen, A. Bl¨omeke, and D. U. Sauer, “An algorithm for an online electrochemical impedance spec­troscopy and battery parameter estimation: Development, verification and validation,” Journal of Energy Storage, vol. 30, p. 101517, 2020.
[20] S. R. Islam and S.-Y. Park, “Precise online electrochemical impedance spectroscopy strategies for Li-ion batteries,” IEEE Transactions on In­dustry Applications, vol. 56, no. 2, pp. 1661–1669, 2019.
[21] M. Messing, T. Shoa, and S. Habibi, “Estimating battery state of health using electrochemical impedance spectroscopy and the relaxation effect,” Journal of Energy Storage, vol. 43, p. 103210, 2021.
[22] S. Tairov and L. Stevanatto, “State-of-charge estimation of lead-acid batteries by using multi-frequency ac tests,” International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, vol. 5, pp. 7984–7991, 2016.
[23] A. De Angelis, E. Buchicchio, F. Santoni, A. Moschitta, and P. Carbone, “Uncertainty characterization of a practical system for broadband measurement of battery eis,” IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1–9, 2022.
[24] Y. Fu, J. Xu, M. Shi, and X. Mei, “A fast impedance calculation based battery state-of-health estimation method,” IEEE Transactions on Industrial Electronics, 2021.
[25] B. Bullecks, R. Suresh, and R. Rengaswamy, “Rapid impedance measurement using chirp signals for electrochemical system analysis,” Computers & Chemical Engineering, vol. 106, pp. 421–436, 2017.
[26] D. Klotz, M. Sch¨onleber, J. Schmidt, and E. Ivers-Tiff´ee, “New approach for the calculation of impedance spectra out of time domain data,” Electrochimica Acta, vol. 56, no. 24, pp. 8763–8769, 2011.
[27] A. Nikolian, J. Jaguemont, J. De Hoog, S. Goutam, N. Omar, P. Van Den Bossche, and J. Van Mierlo, “Complete cell-level lithium-ion electrical ecm model for different chemistries (nmc, lfp, lto) and temperatures (- 5° c to 45°c)–optimized modelling techniques,” International Journal of Electrical Power & Energy Systems, vol. 98, pp. 133–146, 2018.
[28] S. S. Madani, E. Schaltz, and S. Knudsen Kær, “An electrical equivalent circuit model of a lithium titanate oxide battery,” Batteries, vol. 5, no. 1, p. 31, 2019.
[29] X.-Z. R. Yuan, C. Song, H. Wang, and J. Zhang, Electrochemical impedance spectroscopy in PEM fuel cells: fundamentals and applications. Springer Science & Business Media, 2009.