Energy Efficiency of a Resistor-Fractional Order Capacitor Series Circuit During Charging from a DC Voltage Source

Fractional-order derivatives offer a significant advantage in modeling complex electrical and electronic systems by providing higher accuracy and flexibility compared to classical integer-order derivative approaches. This method allows for the precise description of the dynamic behavior of energy storing circuit elements, particularly supercapacitors. In recent years, the fractional-order circuit elements have found widespread use in a wide range of applications, from filter designs and control systems to energy storage applications and signal processing. In this study, the energy loss incurred during the charging of a capacitor, modeled using a fractional-order derivative element in series with a resistor and driven by a DC source, is analytically examined. The analysis is conducted using the Caputo definition of the fractional derivative. The results are then compared with the energy loss in a classical R–C circuit. The findings indicate that the energy loss in a fractional-order capacitor-resistor circuit during charging differs from that in an integer-order counterpart. It is found to be dependent on the fractional order α. .Fractional-order modeling of the capacitor is needed to calculate the charging efficiency of such a circuit accurately.