Characterizing and modeling electrical energy storage devices is essential for their proper integration in larger systems. However, basic circuit elements, i.e. resistors, inductors, and capacitors, are not well-suited to explain their complex frequency-dependent behaviors. Instead, fractional-order models, which are based on non-integer-order differential equations in the time-domain and include for instance the constant phase element (CPE), are mathematically more fit to this end. Here, the electrical power and energy of fractional-order capacitance and inductance are derived in both steady-state and transient conditions, and verified using a number of commercial supercapacitors and fractional-order coils. A generalized expression for the energy stored in a supercapacitor/fractional-order inductor is derived and found to depend on the capacitance/inductance and the dispersion coefficient of the device, as well as on the properties of the applied voltage waveform. © 2016 Elsevier Ltd.
Fouda M.E., Elwakil A.S., Radwan A.G., Allagui A.
Capacitor; Energy; Fractional-order inductor; Power; Supercapacitor
Energy, Vol. 111, PP. 785 to 792, Doi: 10.1016/j.energy.2016.05.104