Starting with '87 GM models, it's common to go through four to six replacement generators in the life of the vehicle. You already did what it takes to reduce the number of repeat failures; that is to replace the battery at the same time. Due to their design, these generators develop huge voltage spikes that can damage the internal voltage regulator and diodes, and interfere with computer sensor signals. The battery dampens and absorbs those spikes, but as the lead flakes off the plates as it ages, it loses its ability to do that. The battery must be replaced when replacing the generator unless it is less than about two years old.
Beyond that, you likely have a generator with a bad diode. You need a professional load tester to test for that. With one bad diode of the six, all you'll be able to get under full load is exactly one third of the generator's rated current. 30 amps from the common 90 amp generator is not enough to run the entire electrical system under all conditions. The battery will have to make up the difference until it slowly runs down over hours or days. Also, with a failed diode, "ripple" voltage will be very high. Professional load testers measure that and either list it as a value or as a relative value on a bar graph.
There is one test to perform before replacing the generator again. Use a digital voltmeter set to the 2 volt or 20 volt scale. Place one probe on the battery's positive post and the other one on the generator's large bolted-on output terminal. That voltage should stay at 0.0 volts, but typically you'll find a couple of tenths of a volt. It should never rise much more than that regardless of engine speed. If it does, inspect that wire for breaks or corrosion.
Tuesday, March 17th, 2015 AT 3:41 PM