Modelling supercapacitors leakage behaviour using a fractional-order model

A fractional-order circuit model is explored to represent the leakage/self-discharge behaviour of commercially available supercapacitors. This fractional order-model is composed of two elements, a fractional-order capacitor with impedance Z = 1/CαSα and a parallel resistance Rp, which set the discharge based on the time constant τ = (RpC)1/α and order α. Self-discharging data was collected from a 3 F PowerStor, 1 F Panasonic, and 350 F Maxwell supercapacitors after being charged and left in a floating state while monitoring the device terminal voltage. The parameters for the fractional-order model that best fit the experimental data were extracted using a nonlinear least-squares optimization routine, yielding τ = 6.39 Msec and α = 0.292 for the PowerStor device, τ = 137.2 Msec and α = 0.383 for the Panasonic device and τ = 53.63 Msec and α = 0.715 for the Maxwell device. The MATLAB simulated responses using the extracted parameters show maximum relative errors < 1.1% compared to the experimental data. © 2017 IEEE.