I've seen that many online schematics for using ultracapacitors as power sources place the ultracaps in series in order to increase the voltage that they can be charged to, lowering the capacitance of the circuit drastically while preserving the total energy. For example, 5 pieces of 2.7v 100F capacitors might be placed in series, bringing the voltage rating up to about 13.5v and the capacitance down to 20F. Now, ultracaps can't be used as direct replacements for batteries since their voltage drops quickly. So they'd need a buck, boost, or buck-boost converter to utilize the full capacity. For this example, let's try to get 12 volts at 750mA. Would it be more efficient / get more energy out using a buck-boost converter with a 13.5v, 20F setup, or using a boost converter with a 2.7v, 600F setup, or a 5.4v, 300F setup, etc?
Edit: Sorry, I meant for these setups to include balancing systems.
Best Answer
Well, unless some kind of charge-balancer is used, most types of energy storage devices in series (batteries, capacitors, etc.) will charge unevenly. Since a supercap may be rated +/- 10% in capacity, imagine what happens when strung together and charged in series: the one with the -10% capacitance charges first, and the voltage across it goes higher than the others. Most supercaps are pretty picky about maximum voltage, and violating this will shorten their life. Now charge equalization can be done on a series set, such as KA7OEI's blog. They discuss a lithium-iron-phosphate pack that wasn't charging correctly and how they "fixed" it by utilizing a crowbar circuit for each cell. Any number of variants could be employed here. So it doesn't matter much what number are placed in series - any in series is taking a risk.
As for the best type of converter, in general, one DC-DC converter is always going to be better than two, since there are always more losses with more components. So if possible, buck or boost are generally more efficient than SEPIC or other combinational converters simply because there is one of them.
Using the capacitors in parallel with a boost converter would solve the issue of equalization and not require any charge balancing, so seems the simpler route. At first glance.
Note that 12v * 0.75A = 9W of output power. Assuming 90% boost efficiency, current draw from the supercaps would be a minimum of (9W + 10% = 9.9W so say 10W), P=EI, 10W=2.7v*I, I=10W/2.7v, I=3.7A. Some supercaps cannot supply much current at all, or do so with little efficiency and much loss. So make sure the caps chosen can handle much more than this current. When the caps discharge, their voltage drops... so Ohm's law dictates that to get 9W out of the boost regulator at 10% capacitor voltage (0.27v), 10W=0.27v/I, I=10W/0.27v, I=37A! That is going to require some good boost circuit design. Also, whatever is used to charge the caps, must be regulated to never go above 2.7v.
Now 600F sounds like a lot of capacitance and it is... but in terms of bulk energy density the supercaps may leave you disappointed. If constructed, you may eventually decide that a 12v lead-acid battery would last longer and cost far less. The self-discharge rate of such caps is fairly high, so they will not hold energy for years or even months. Of course if this is for a backup battery scenario that is normally powered and charging, then it would be more reasonable.