Approximation of Supercapacitor Charging Process Using Fractional Order Transfer Functions

Abstract

The expressions of the fractional order transfer functions of the supercapacitor charging process using the most common models of representing their impedance are analytically obtained and the most optimal model for further research is chosen. The calculation of the fractional order transfer function of the supercapacitor charging process with a 1F capacity is carried out, using the averaged data of various experimental studies. Also, the obtained transition process is compared with the experimental one. Experimental studies of transition charging processes of supercapacitors with different capacities (0.22 F, 1.0 F, 4.7 F) are carried out, using a voltage divider without using an operational amplifier. The obtained transition processes are approximated by the use of compact fractional order transfer functions by the particle swarm optimization method. The estimation of the approximation accuracy for different variants of transfer functions in the time domain is performed.