Anomalous diffusion models in frequency-domain characterization of lithium-ion capacitors

Lithium ion capacitors (LICs) have urgent application demands in the field of transportation and renewable energy. In order to better understand the applicable scope and limitations of this kind of energy storage device, frequency-domain testing and modeling are particularly indispensable. In this paper, the frequency-domain characteristics of LICs is analyzed. It is found that the diffusion segment has more obvious non-ideal feature. Two frequency-domain models are proposed to describe the anomalous phenomena in diffusion process. The models realize non-idealized expression by introducing the ordinary diffusion model into fractional differentiation. One of the models is derived from a continuous time random walk scheme with macro constraints, which is introduced for the first time to describe the frequency-domain characteristics of supercapacitors to the best of our knowledge. A matched parameter identification method is presented. The corresponding model parameters can be obtained quickly by combining theoretical calculation and numerical analysis. Finally, the adaptability of the two models are verified through a series of working conditions at different temperatures, voltages and life periods.