After replace A/C system it is not blowing cold air and there is a burning smell

The compressor is not supposed to be engaged all the time. If you smelled the clutch then more then likely the clutch has locked up and is not able to release. If you check power at the compressor I imagine it will not have power all the time but the compressor will still be engaged. If this is the case then your clutch is locked to the compressor and will not disengage. At that point, you can try and replace the clutch but if it were me, I would go ahead and take the compressor back if you purchased this as a unit.

https://www.2carpros.com/articles/car-air-conditioner-not-working-or-is-weak

Let me know if you have questions and we can figure out next steps.

I understand it stays engaged all the time but to determine what is causing it to stay on, we need to check voltage at the compressor. Basically this will tell us if it is being commanded on all the time and if not, then the clutch is seized.

More then likely this is the clutch being seized. However, if the compressor doesn't cool at all then we need to check pressures to determine if the compressor has failed or if the clutch is just not disengaging.

I suspect the compressor has failed and not just the clutch because if the compressor doesn't disengage, I would expect there to be cold air coming out until the system built up too much pressure. The fact that the compressor stays on and there is no cold air, I suspect the compressor is not building any pressure and checking the high and low side pressures will tell us that.

https://www.2carpros.com/articles/car-air-conditioner-not-working-or-is-weak

You are welcome. Let us know what you find. I am curious about this one. Thanks