*Article* **A Comparison of Time-Domain Implementation Methods for Fractional-Order Battery Impedance Models**

**Brian Ospina Agudelo 1,2,***∗***, Walter Zamboni 1,***<sup>∗</sup>* **and Eric Monmasson <sup>2</sup>**


**Abstract:** This paper is a comparative study of the multiple RC, Oustaloup and Grünwald–Letnikov approaches for time domain implementations of fractional-order battery models. The comparisons are made in terms of accuracy, computational burden and suitability for the identification of impedance parameters from time-domain measurements. The study was performed in a simulation framework and focused on a set of ZARC elements, representing the middle frequency range of Li-ion batteries' impedance. It was found that the multiple RC approach offers the best accuracy– complexity compromise, making it the most interesting approach for real-time battery simulation applications. As for applications requiring the identification of impedance parameters, the Oustaloup approach offers the best compromise between the goodness of the obtained frequency response and the accuracy–complexity requirements.

**Keywords:** battery impedance model; equivalent circuit model; fractional-order model; timedomain implementation
