This is probably a simple problem but so unsure. 2000 7.3 started and all is good at idle. Accelerate to 1500 RMPS and alternator light comes on and volt meter shows near full scale. Pulled back in to garage and checked with real meter. With engine off 12.3 volts. Start and at idle 12.8 volts. but when RPMs go up the volts at battery do the same. I got 18.3. If I put headlights and fan on full the light comes on about 1800 RMPs.

Replace alternator or is it a battery problem or something else?

 

sounds to me like the voltage regulator in the alternator failed.

 

Make sure your wires to the alternator are good. There is usually one(yellow/white?) that leaves the alternator and is the wire the internal regulator uses to sample the voltage in the truck's wiring. If this wire is broken the regulator will lose it's reference voltage and may go wild.