Determination of a physically correct fractional-order model for electrolytic computer-grade capacitors

Electrolytic computer-grade capacitors (ECGCs) are vastly implemented in energy storage systems. However, their models are not accurate and simple as other kinds of capacitors. For example, ECGCs and supercapacitors share many characteristics but have some differences because of their physicochemical properties, so it is wrong to assume their electrical behaviour is equivalent. In this work, we study the discharging response of ECGCs using four models obtained from fractional differential equations (FDEs) with integer initial conditions and causal fractional definitions, that is, Caputo and conformable operators. We also recall a correct procedure to achieve models from FDEs with physical consistency of units and avoiding additional and senseless constants. Thence, we perform a fitting procedure over an experimental dataset from six ECGCs via a hybrid solving procedure powered by the cuckoo search algorithm and interior-point algorithm. Our results show that models based on the traditional ordinary differential equation give the worst description of discharge, while models containing the Mittag-Leffler function, with time to the power of fractional order as the argument, render the best description of ECGCs.

Automated summary

The study showed that the behavior of Electrolytic computer-grade capacitors (ECGCs) should not be assumed to be equivalent to supercapacitors. By utilizing models derived from fractional differential equations (FDEs) and suitable solving algorithms, a more accurate description of the discharge process of ECGCs can be achieved.