# (Ultra)capacitor Series vs. Parallel with (Buck-)boost converter

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.

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.

Each ultracap will store the same amount of energy. Therefore in principle it doesn't matter whether they are connected in series, or in parallel.

In practice, because of losses in power supply converters, resistive and diode thresholds, they tend to work a bit more efficiently with a higher voltage and a lower current. A lower current is generally easier to wire externally as well. For the same size controller chip, you'll be able to process more power at higher voltages.

Therefore, stack your caps in series (for which you must employ some form of over-voltage and reverse voltage protection, even if you don't go as far as full charge balancing). Once you are in the 12v to 24v range, that's probably the sweet spot for available converters. Don't go above 36v, you start to worry about insulating high voltages above that. Don't go below 5v, currents are starting to rise and efficiency really fall off below that.

To temper your enthusiasm for different configurations, remember that you're only talking about a few percentage points of efficiency, not 2x or 5x energy differences.

I happen to do this sort of thing for a living! At much higher voltages and currents, but the principle is the same. I dropped several capacitors of your specs into our calculators to see what would happen. There are a few critical pieces of information you'll need before you can really answer your question.

1) What is the drop-out voltage of your regulator? If your regulator shuts down at .1V input, no big loss. But if your regulator shuts down at 10V, then you have to series caps above that, and the overwhelming majority of the energy will still be left in the caps when you stop operating!

2) The ESR of the caps burns off some of your energy, and at a constant-power load the equation to figure out how much becomes a non-linear differential equation. (Solution here.) Comparing five in parallel to five in series, that's a 25x change in ESR! Assuming a 100% efficient regulator running down to .1V, 5 of these in parallel gives you 120 seconds of operation, and 5 in series gives you only 20 seconds! (Assuming end-of-life values.) The difference is almost entirely because of the ESR!

3) Can your regulator both buck and boost? If it can only boost, and you need exactly 12V (not 12V or more) then putting your caps in series to get 13.5V at full charge changes the topology of your regulator away from a straight boost topology. SEPIC would be my choice for that.

4) What is the efficiency of your regulator at different operating points? There's a good chance it's optimized around a particular input voltage, and the efficiency goes down the further you get away from that voltage. So all other things being equal, the less your voltage changes, the better off you'll be.

Based on all that, you'll probably get the best results by optimizing a boost regulator to run and drop out at an extremely low voltage, and using the caps in parallel. Flyback might be a good topology for that kind of power level and application

• A typical boost regulator (that can deliver 12V) won't function below 1V. So a 2.7V super capacitor will have around 30% of it's power unusable. Capacitors in series won't have that problem but capacitance decrease and as you said ESR also increases. So which is better? Commented Dec 7, 2018 at 2:00