Shameless plug to my recently published paper! It's open source so you should be able to view it.
Supercapacitors do not behave like other capacitors (obvious if you've used one). Mainly in that their charge profile is not linear due to an internal distribution of time constants. This means that you can charge a SC up to 1V, say, for 1s, then go open circuit and the voltage will seemingly drop, or sag. If you do the same test but hold the 1V charge for 2s the sag will be less.
Conversely, and more importantly from a safety perspective, you can short out a SC, i.e. discharge it to 0V, leave it open circuit for a minute, and the voltage will have rebounded positively. So that SC you thought was "flat" has seemingly recharged itself! If you have a decent bank of these that could give you "a wee tingle" to quote Big Clive! Interesting since there is no electrochemistry in a SC like there is in a battery.
What does this mean for us though? Well as a researcher I am obviously very low in the TRLs so bear that in mind, but we actually know very little about how these devices actually work. Modelling simulations that you may get in software may not be representative of real life (e.g. Matlab, LTSpice, etc).
Also, do not assume that the charge characteristics are linear, in that if your 5V SC is at 2V5 it is at 50% SoC. It might be if you have held it at 2V5 for a long time (mins, hours, days, we don't know?) but certainly not if it has only just reached this voltage, unlike, say, a ceramic or electrolytic.
Food for thought, hope you find this an interesting insight to some of the work I am doing here at Loughborough University!