Frequency dependent piecewise fractional-order modelling of ultracapacitors using hybrid optimization and fuzzy clustering

The usage of ultracapacitors for development of energy storage devices and alternative power sources is increasing at a very rapid rate. However accuracy in selection of ultracapacitor model parameter plays key role in the design of such devices, especially in applications involving wide operating frequency. Ultracapacitors are known to exhibit fractional dynamics and the model parameters vary significantly with frequency. This paper proposes a piecewise modelling and parameter estimation approach for ultracapacitors using a hybrid optimization and fuzzy clustering approach. The proposed modelling technique has been applied over impedance frequency response data acquired from a commercially available ultracapacitor. The model is able to represent the experimental data over different operating points with reduced number of model parameters. Comparative numerical simulations have been carried out to validate the benefits of the proposed approach. The estimated parameters revealed the disparity in the frequency dependent behavior of ultracapacitors and standard electrolytic capacitors.