Estimation of Supercapacitor Energy Storage Based on Fractional Differential Equations

In this paper, new results on using only voltage measurements on supercapacitor terminals for estimation of accumulated energy are presented. For this purpose, a study based on application of fractional–order models of supercapacitor charging/discharging circuits is undertaken. Parameter estimates of the models are then used to assess the amount of the energy accumulated in supercapacitor. The obtained results are compared with energy determined experimentally by measuring voltage and current on supercapacitor terminals. All the tests are repeated for various input signal shapes and parameters. Very high consistency between estimated and experimental results fully confirm suitability of the proposed approach and thus applicability of the fractional calculus to modelling of supercapacitor energy storage.