Power and energy analysis of fractional-order electrical energy storage devices. (15th September 2016) - Fouda, M.E.; Elwakil, A.S.; Radwan, A.G.; Allagui, A.
Abstract: 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. Highlights: Accurate expression for the electrical energy stored in a supercapacitor is derived. Stored energy depends on the capacitance, dispersion factor and voltage waveform. A dissipated-to-stored energy ratio in supercapacitors is derived. A maximum operating frequency for a supercapacitor is suggested. Results are verified on commercial supercapacitors and fractional-order coils.