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It is starting to look really good! It's still early, but why are you using rheostats rather than a constant resistor setup for setting the cell voltages? I would think once you know what ohm resistors to put in there that it wont' change. Again, still early, only had one cup of coffee so far.
More than likely. I have 3 cells that zero out and three that don't.
Its going to be trial and error to get it right. I don't know enough about capacitors. I know what They do and what they are used for but that's about it. What I don't know how to size one for the application.
For your application, I would think a 100-500µf for the specific voltage you are running would be plenty. Not a lot of current going though that board unless you need to put them on the main power line lol.
They will only store what they are supplied with. Just like the caps on an ESC that make the plug spark when you first plug it in, then they absorb some of the current demand while also smoothing out the current and reducing noise in the line.
If you are worried about when the voltage in the line goes down, you can always put a small resistor across the leads to help drain it faster. Most high voltage electronics such as PSU's where high voltage comes in and low voltage comes out have drain resistors on the caps so the caps don't try to kill you when you open up the case.