**Shailendra Rajput 1, Alon Kuperman 2, Asher Yahalom <sup>1</sup> and Moshe Averbukh 1,\***


Received: 29 July 2020; Accepted: 3 September 2020; Published: 4 September 2020

**Abstract:** The specific power storage capabilities of double-layer ultracapacitors are receiving significant attention from engineers and scientific researchers. Nevertheless, their dynamic behavior should be studied to improve the performance and for efficient applications in electrical devices. This article presents an infinite resistor–capacitor (r–C) chain-based mathematical model for the analysis of double layer ultracapacitors. The internal resistance and capacitance were measured for repetitive charging and discharging cycles. The magnitudes of internal resistance and capacitance showed approximately ±10% changes for charge-discharge processes. Electrochemical impedance spectroscopy investigations revealed that the impedance of a double-layer ultracapacitor does not change significantly in the temperature range of (−30 ◦C to +30 ◦C) and voltage range of (0.3376–2.736 V). The analysis of impedance data using the proposed mathematical model showed good agreement between the experimental and theoretical data. The dynamic behavior of the ultracapacitor was successfully represented by utilizing the proposed infinite r–C chains equivalent circuit, and the reverse Fourier transform analysis. The r–C electrical equivalent circuit was also analyzed using the PSIM simulation software to study the dynamic behavior of ultracapacitor parameters. The simulation study yields an excellent agreement between the experimental and calculated voltage characteristics for repetitive charging-discharging processes.

**Keywords:** ultracapacitor; equivalent circuit; Fourier transform; internal resistance
