I asked for a complete explanation.

I guess this is another one of those "Top-Secret" projects that we seem to see so much of.

My guess is that Super-Capacitors are not going
to be the Magic-Silver-Bullet that You may be thinking they will be.
They will not practically replace Batteries except in
extremely niche applications such as temporary memory retention.
.
.
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It's basically for a car starter battery.
The supercaps are there for two reasons:

1. To provide power to the starter motor when required (given their extremely low IR, they will be preferentially used).
2. To protect equipment. One reason it's not always a good idea to use a battery with a BMS under the bonnet, is that if the battery is completely full, the BMS disables charging. This can create a voltage spike that can damage equipment. The supercaps ensure this does not occur.

The supercaps are more than capable of starting the engine without the batttery connected.

If you need any further information, please let me know.

 

I have seen a super-capacitor "battery substitute" with adequate capability to crank an engine. For the price of that super-cap package I could easily buy quite a few standard automotive "12 volt" batteries.
And as for the concern about an automotive alternator charging system "running away" when the battery management package switches off, at least in my vehicles that does not happen when the battery becomes disconnected. Possibly it might be a problem in a vehicle with a mechanical relay voltage regulator that was poorly designed. Maybe.

 

And still, why a battery management system for any part of this project??To charge a super capacitor all you need is a current limited DC voltage source. The current does not need to be regulated, just within the battery's charging limits range.