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Unexplainable design fault
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amyk:
Have you considered using an integrated protection IC like a DW01?
Lesolee:

--- Quote from: Pentoad on January 16, 2020, 07:59:40 pm ---I have also noticed that sometimes just touching the output of the voltage reference using my multimeter probe fixes the problem until the board is powered again. The multimeter wasn't even switched on when I did this.

--- End quote ---
That is a classic symptom of oscillation. You have multiple boards, some of which work and some don't. You must probe it with a scope, not just a DVM. Q2_Drain is a key place to look with a scope. Look at the start up timing using a digital storage oscilloscope.

Remember that the scope probe itself can suppress oscillations. If it always starts up correctly when the scope is connected, that is another clue.

I designed one of these myself, where each cell was around 1kg (that is BIG).  The circuit needs to be protected against single faults, requiring more circuitry to prevent failed over-charge signals etc.
Pentoad:
C2 is essential to prevent the comparator oscillating at high frequencies when both its inputs are at the same voltage. Without the capacitor, the output oscillates at possibly a few hundred kilohertz which causes Q1 to heat up severely. I also tried adding a load resistor to the voltage reference which didn't help. When I have an oscilloscope attached to the reference, the problem doesn't arise at all, possibly due to its 47pf input capacitance. I will try adding different capacitors to the reference to see if that helps.
Lesolee:
You might also want to consider using a 100R resistor in series with the gate of Q2, right up close to its gate leg. The device itself can like to oscillate.
TerminalJack505:
To prevent oscillation due to noise it is best to configure your comparator with some hysteresis as others have suggested.  You can do this by replacing the capacitor with a very large resistor.

I've attached simulations of that portion of your circuit as-is as well as with a 1M Ohm resistor in place of the capacitor.  Both are being fed a noisy input that is near the reference voltage.

Notice the following:

* The cap will allow the non-inverting input to be pushed below GND when the output switches from high to low.  This risks putting the LM239 into latch-up.
* With a cap, the non-inverting input eventually settles back down at the same voltage it was at before so it won't really prevent oscillation due to input noise--maybe just reduce the frequency.
* With a 1M Ohm resistor, the non-inverting input's voltage will swing +/- approximately 30mV.  Thus, preventing false triggers.  The amount of hysteresis can be changed by changing the feedback resistor's size.
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