Hi,
- 15W with 24V says everything (including resistance) R = 38.4ohm.
but you said:
I have designed temperature controller
supplied with 400V AC able to drive 8kW heating power into loads with resistance range 128mOhms ... 20 Ohms (400V max, 250A max)
--> What I want to say: I was confused by the "24V
supply" --> in my eyes you don´t want 24V as supply voltage, but as ouptut voltage (= heater voltage). I understand now.
Temperature is linear with power. If my circuit outputs a voltage then P is proportional to V^2, if it outputs a current then I is proportional to I^2. Therefore, T is proportional to I^2 or V^2 (not sqrt of either).
This all is correct. Thus you need to compensate for the "square" that happens "outside" your controller. You need the square-root inside your controller.
this would reduce my resolution to 12 bits
True, but 12 bits is well enough for a temperautre controller. It´s a 1:4096 range (in steady state). If I understood correctly, then you have a feedbacked system.
Example: In my home there we have a 1 bit controller (ON/OFF bimetall thermostat with internal heater) and it maintains room temperautre fairly constant, even when outside temperature varies widely.
Don´t forget: with a regulation loop you have an additional parameter "time".
Some questions: Do you really think that your power supply output voltage is stable within 0.025%? And do you think that your heater resistance is stable within 0.025% over temperature and time?
Mind: copper changes it´s resistance about 0.4% per °C. This is 16 times the error you need - and this with a variation of a single °C!
--> Start to really develop your system ... with specifications and error estimation.
Klaus
added:
Onother - maybe interesting - calculation: 15W / 4096 is about 3.7mW. This is less than the sun transmits on a square with about 2mm of length.