Supercapacitors in Constant-Power Applications: Mathematical Analysis for the Calculation of Temperature

A set of analytical equations for the calculation temperature in supercapacitors operating constant-power applications is presented this paper. Although main operation modes are constant-current and charge discharge, study was focused on latter, since both sources loads act as systems a wide range power conversion facilities. The starting point classical supercapacitor model based electrical thermal parameters provided by manufacturers or also obtained experimental means. proposed mathematical analysis so-called incomplete gamma function that presents two major advantages over previously existing methods. Firstly, it not necessary to solve any differential system means numerical methods, which reduces required computational effort. Secondly, no simplifications relief calculations made computation variable. new formulation renders valid solutions even high-power demand situations. Moreover, can be expressed time other variable charging discharging processes. Therefore, formulas especially remarkable dimensioning supercapacitors.