High Power Constant Current Power Supply Designs

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Thanks Elvee. This looks like it should work. I think I'll need to raise the supply voltage as the process requires 15VDC to conduct current.
Not at all: the circuit as drawn will work as of 8V, but this could easily be lowered to ~4V if required (even lower with some mods).
If you need 15V across the cell to start with, this circuit will more or less do it, but at very low currents.
At full current, to get 15V out, you'll need about 17V in.
Any CCS will drop some voltage; if it is of great concern, you can always use Hall-effect sensing and common source OP devices, but these are costly complications that are best avoided using a sufficient input voltage for example.
Is R24 and R29 correct?
Yes, if required their value can be altered according to your needs
Is Q12 acting as a driver and an output?
Mainly as a driver, but it will also contribute 1 or 2 amp to the output current.

Note that the transistor types are just given as examples: 2N6259, BD182, 2N3771 and many others would work equally well, but the 3055 is so cheap and common that it looks like an obvious choice
 
It's been a long slow dragged out build, but my supply is almost ready for a test run. I need to do some adjustments in the software yet, but it seems to function correctly so far.

I've got a microcontroller taking care of transformer and relay controls as well as temperature monitoring and fan controls. Another microcontroller controls current, shutdown timers and front panel display.
 

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