Can I use individual capacitor IR for parallel circuit balancing resistors?

[sodoyle]

TL;DR Summary

I would like to size voltage balancing resistors for capacitors.

I am going to have several series/parallel capacitors so need balancing resistors. I understand that for series capacitors, it is wise to use voltage balancing resistors so mismatch in individual series capacitors leakage current can flow through the resistors which prevents individual capacitors from charging more than desired.

As an example, let's say the insulation resistance (IR) of a given capacitor is 50MEG. I think selecting a resistor at least one order of magnitude lower (5MEG) would be suitable. Assuming I have 2 series capacitors, I would place a resistor across each so I'd also have two series 5MEG resistors.

My question comes to parallel capacitors. If I place two capacitors in parallel, circuit theory would give an equivalent IR of 25MEG. This would mean that I now need maximum 2.5MEG balancing resistors. Thinking about it using the current divider though, it seems like 5MEG should still be fine. Let's say I still have two in series and two in parallel...if the top parallel capacitors have combined 1 mA leakage current and the bottom parallel capacitors have a combined 0.95 mA leakage current, the real impedance of each capacitor would still be 50MEG so the excess 0.5 mA would still have the same difference in impedance when "deciding" to flow through the capacitors or balancing resistor. Therefore, I think the balancing resistor sizing can be based on an individual capacitors IR and not the "equivalent IR" of the parallel branch.

Is this correct or am I off in my reasoning?

 

[Baluncore]

Maybe look at it from a time constant point of view. Each capacitor has a parallel resistor, such that the product R·C is a constant in the capacitor bank. That way, as the system voltage rises or falls, the capacitors all rise and fall in proportion.

 

[sodoyle]

Maybe look at it from a time constant point of view. Each capacitor has a parallel resistor, such that the product R·C is a constant in the capacitor bank. That way, as the system voltage rises or falls, the capacitors all rise and fall in proportion.

Looking at it from the time constant point of view it looks like the resistance would need to decrease proportionally to the increase in capacitance. In other words, if I have 4 capacitors in parallel, the balancing resistors would need to be 4x lower than the value with no parallel caps (assuming all capacitors are the same value). If that's the case, it seems reasonable only to a certain extent. At some point the resistance would get too low and losses through them would be too high. I still see why it's important to consider the dynamic response for these resistors though.

From the steady state point of view, the R·C time constant wouldn't be as important as they'll only effect the static voltage balancing. As mentioned above, the RC time constant cannot be reasonably kept the same in all cases. If I parallel 50 capacitors, it may not be feasible to have 50x lower balancing resistors simply because of the increase in power consumption.

 

[Baluncore]

If I parallel 50 capacitors, it may not be feasible to have 50x lower balancing resistors simply because of the increase in power consumption.

If you have 50 capacitors in parallel, the leakage current will be 50 times greater so you will need one resistor with 1/50th of the resistance to conduct that leakage current.

Think of each capacitor as having it's own resistor. If there are 50 capacitors, there will be 50 resistors in parallel. The time constant of any combination will remain the same.