Ah, the never ending debate about balancing your super capacitors. This is a tough one, and I'll tell you why. There are many different methods of balancing for super capacitors, but it seems that everyone has a different preference. This information can be hard to find. As well, most methods of balancing will limit the charge and discharge limits of your super capacitor. Meaning that you will possibly negate the function of the balancing circuit, or damage your balancing circuit if you charge at a high current, or discharge at a high current. Custom balancing circuits are available, but they are expensive, and still have limitations. Yes, even for Maxwell balancing circuits.
Personally, I prefer to make a bank and charge it to only 75-80% MAX of the total charge voltage. For instance, if I have a 15v bank of capacitors in series, I will only charge to 12.5-13v. This will slightly waste on capacity, but you're not going to have any over-charging issues, as all of the caps in the bank will all be charged to 75-80% of the maximum charge. You can try this for yourself.
There are many other options, such as using a resistor divider network, diodes, and active bleeder circuits. I've found a wonderful little forum discussion (Thanks to ultracapacitors.org). The problem with zener diodes is you will need high wattage zeners that will likely require heat sinks. The problem with the resistor divider network is that you will either have to implement high resistance resistors and charge EXTREMELY SLOWELY, or use high wattage low-resistance resistors, and you will bleed a TON of energy off in the process. There really is a lot to it. The problem is that most balancing circuitry theory is based around capacitors that are extremely small in comparison to super capacitors.
See this link for forum discussion:
If you are willing to sacrifice some capacity, then my preferred method is the way to go. I plan on doing some experiments in the future, but instead of providing direct information that I have not personally verified, I suggest having a look through the document posted above. This is a very heated topic of conversation.
When in series, the voltages on each capacitor will vary mainly due to each individual leakage current. It is HIGHLY recommended that you use the same capacitance values in your series banks. This is because if you have a capacitor with high capacitance and a capacitor with low capacitance, they're going to discharge at different speeds based on the load. Some have more than others which leads to voltage imbalance. If you measure the voltage on each individual capacitor in a bank, you will see just this; different voltage on each of them. Again, if you only charge to 75-80% of the maximum charge, you're going to have different voltages on each of the capacitors, but they will all be well within the charge limit range.
IN REGARDS TO THE SCHEMATIC POSTED FOR THIS TOPIC:
Many thanks to David A. Johnson P.E . (Professional Engineer) for this circuit. The document behind this circuit can be found here:
By far, this is the best balancing circuit I've come across. It is a custom circuit for a 3v load, but it can easily be modified to suit other needs. I'll go through the circuit theory, but be sure to check out the link above! The 9v 300mA MAX solar panel is charging a set of three super series super capacitors. The 1N5819 diode blocks power from entering back through the solar panel. The charge off the super capacitors enters into a 3v regulator that powers the load (Load circuit not seen here). When using solar panels, you don't necessarily have to limit the charge with a resistor, as you won't damage the solar cell if drawing ALL of the energy it is creating. When using a wall transformer combined with say an LM317 variable DC power supply IC, it is EXTREMELY important to use a charge limiting resistor.
Each capacitor has its own charge limiter circuit, and I have to say that it is ingenius! Each of the three capacitors is tied to a comparator circuit. Each comparator circuit acts to drain the capacitor down to 2.65v if the voltage at the positive input surpasses 1.2v. This is where customization comes into play. You can use this circuit as a reference, and really go to town with your modiification. These capacitors have a charge limit of 2.7v. The engineer who designed this wanted each cap to be charged to a maximum of 2.65v (Three of them is series would equal 7.95v). That 7.95v is then fed into a 3v voltage regulator, which is redundant for this discussion. There is a 33k ohm protective resistor in series with the 1.2v zener diode that sets the 1.2v reference at the negative input of the comparator. At the positive input of the comparator, there is a resistor network that is comprised of a 75k and a 68k resistor.
2.65v / (75 + 68) = 0.01853...
0.0185 x 68 = 1.26v (roughly)
This calculation means that when we see the voltage on the capacitor rise to 2.65v, we see more than 1.2v at the positive input.
When there is 2.65v or more on each capacitor, there will be roughly 1.26v at the positive input of the comparator. When there is more voltage at the positive input than there is at the negative input, the comparator output is turned on, activating the FET, which drains the voltage down to less than 2.65v. When the voltage on the capacitor is less than 2.65v, the voltage at the positive input of the comparator is lower than the voltage at the negative input, which then turns the comparator off. When the comparator is off, the FET is not draining. The current being drained along the FET is limited by a 2.2 Ohm 1W resistor. I believe that the 10k ohm resistor between the 1.2v zener diode and the negative input is used to eliminate an offset voltage and is recommended in the data sheet.
The operational amplifiers being used as comparators are micro powered. This means that the VCC, or power supply voltage requirement is very low; in this case it is 1.6v-5.5v. What is really cool about this circuit is that the DC ground is not used for reference in the top two comparator circuits. The negative reference points are the negative leads of each super capacitor, which makes the working voltage for each circuit is the voltage on each of the individual capacitor.