Figure 3
(a) Supercapacitor charging using the voltage waveforms \(v_c(t)=V_{cc} \left( {t}/{t_{ss}}\right) ^{p}\) with \(t_{ss}=27 \text {s}\) and \(p=1.0\) and 0.1 (i.e. \(E_{10}^c\) and \(E_{01}^c\)) and the resulting time-charge profiles. (b) Illustrates the corresponding discharging voltage waveforms (i.e. \(E_{10}^d\) and \(E_{01}^d\)). Experimental measurements are plotted in solid lines and simulations are represented by dashed lines. (c) Flowchart representing the process and equations of the electric variables during charge (i.e. applied voltage, accumulated charge, and corresponding current), and voltage during discharge into a constant resistor (the device is considered. to be a fractional-order supercapacitor of impedance \(Z=R_s+1/C_{\alpha }s^{\alpha }\) and being charged with a voltage function \(v_c(t)=V_{cc} \left( {t}/{t_{ss}}\right) ^p\)).
