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.
Highlights
This paper is a comparative study of the multiple RC, Oustaloup and Grünwald–Letnikov approaches for time domain implementations of fractional-order battery models
constant phase elements (CPEs) are used instead of capacitors because when they are connected in parallel with a resistor forming a ZARC element, φ represents the depression often observed in the semi-circles in the impedance plot of a Li-ion cell
The three main approaches adopted in the literature for the implementation of the time-domain response of battery fractional order models (FOM) were introduced and compared in terms of accuracy, computational requirements and suitability for the time-domain identification of battery impedance
Summary
Energy storage systems (ESSs) are among the most critical components concerning the full adoption of renewable energy sources and electric transportation [1]. The parameters of an ECM can be fitted from voltage and current data obtained during specific operating conditions [6] These circuit components are often insufficient for modelling the dynamics of electrochemical processes such as charge and mass transfers and double layer capacitance in a battery, due to the spatial distribution of those processes [10]. The second goal was to understand for which of the three cases the timedomain identification of the FOM leads to a correct frequency-domain response, keeping the impedance model meaningful This analysis may serve as a guide for the selection of implementation approaches for FOMs in EMS applications.
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