Modelling and Parameter Estimation of Super Capacitor Bank under Balanced and Unbalanced conditions

Super capacitors(SC) have gained eminence as an energy storage solution due to its high energy density,rapid charging and discharging capabilities and superior life cycle. The recent developments in modelling SCs using fractional order calculus has enabled in better understanding of charge reallocation and dynamics that happens within a SC. This paper extends this Fraction Order Model(FOM) to a $2 \times 2$ SC bank under balanced and unbalanced conditions and verify whether such a bank can be mathematically reduced to a single cell of higher voltage and current capabilities. The parameters of the bank is obtained by curve fitting methods using the experimental and simulated data and compared with the parameters of a single cell.The proposed theory is backed with substantial experimental data obtained from charge-discharge profile of a 2x2 bank of the Faradigm 360F 2.7V each.