Communication—The Ragone Plot of Supercapacitors Under Different Loading Conditions
Anis Allagui, Mohammed E. Fouda, Ahmed S. Elwakil
Abstract
The power-energy performance of supercapacitors is usually visualized by the Ragone plot of (gravimetric or volumetric) energy density vs power density. The energy is commonly computed from E = CV 2 /2, and the power from P = E /Δ t , which assume RC -based models. In this study, we investigate the energy-power profiles of two commercial supercapacitors discharged with three different types of loads: (i) constant current, (ii) constant power, and (iii) constant resistive load. The energy is computed as per the definition from the time-integral of its instantaneous power, i.e. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>E</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mo>∫</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi mathvariant="italic">dt</mml:mi> </mml:math> with p ( t ) = i ( t ) v ( t ). In doing so, we do not assume any specific model a priori, and we highlight the fact that supercapacitor performance depends on the type of load it supplies. We also model the experimental Ragone plot using a fractional-order model composed of a resistance and a constant phase element, and show its superiority over the standard RC model.