Both fans run permanently when AC is on
 

Hi I'm new here and need some help please. I have a 1999 Audi A3 1.8L (non Turbo).

Some time ago I noticed that the main (bigger) radiator fan did not come on when it should. I removed it and found that it had burned out, presumably because it stayed on permanently. I also noticed that the 30A fuse (left one on top of the battery) burned and damaged the fuse holder and possibly the circuitry underneath, because now when I pull the new fuse the fans keep on running. (I will fix this soon.)

Any ways, so I bought a new fan and this is what I found:
When the AC is off, the fans operate normally. They both come on and off and maintain operating temperature. I also noticed that at times they run at a higher speed, like they should.

But, when the AC is on, both fans run permanently, even when the car is cold. I have reason to believe that they even run when I drive at higher speeds on the highway. And surely it should not be like this.

Based on these symptoms, I think that I have ruled out the temperature switch, because the fans do come on and go off at 90 degrees like they should when the AC is off. Also, when I pull the plug at the switch the fans no longer come on. As such, the problem seems to be related to the AC system. Is it not only the smaller fan that should run when the AC is on, or do both come on? I thought that when the AC is on the smaller one should run, and the bigger one only comes on when the rad gets hot?

I am hoping someone can provide me with some advice on what this might be. Being that the fans will run permanently when the AC is on, I am worried that the new fan will burn out as well.

Also, does this model have a fan control unit or are the fans controlled by the ECU? If it has a control unit, will it be located underneath the battery? I tried to look in from the side but don't see anything there except the main wiring harness seems to pass through underneath.

Thank you. I would very much appreciate it if someone can help me.

Follow up: I opened the little black box on top of the battery to see if I see any abnormalities, but there was none. Am I correct in saying that the 30A fuse on the left is the fan's fuse? Since the circuitry is normal, the fan should stop when I pull this fuse, but instead when I pull it the fan goes to high speed.