Discrepancy Between Derivative Orders in Fractional Supercapacitor Models for Charging and Discharging Cycles

摘要

This paper presents results of research related to estimating a fractional order of supercapacitor models governed by non-integer differential equations. The results are determined on the basis of supercapacitors responses to voltage and current steps of different values, separately for charging and discharging cycles. The use of fractional order models makes it possible to reduce the complexity of the model and, at the same time, ensures very good compliance with the real system response. It is well known that the fractional order of the differential equations corresponds to the physicochemical properties of the supercapacitor. Three widely available supercapacitors are examined. The tests are carried out for five different values of voltage and current steps. The obtained results indicate an important dependence of the estimated non-integer order also on the conditions of their use.