Usually the folowing tests can be done to help identify possible problems with a Generator. Disconnect the incoming cables and open the Y connection on the neutral. You now have three separate windings available for testing.
PI - Polarization Index Test
Consists of connecting a 1000V megger from Phase A to ground with the other two phases grounded. Run the 1000V test for 10 minutes and record the meg Ohms after each minute, take the 10 minute reading divided by the 1 minute reading to get the PI of the winding. Do the same test on each winding. The higher the PI value the better the insulation system is.
You should run this test on the Rotor as well.
Winding Resistance
Use a Ductor or DLRO (Digital Low Resistance Ohmmeter) unit. It measures the DC resistance of a circuit. Connect it to each winding one at a time and get a winding resistance for each winding. Can help identify shorted turns. Generally they should be fairly close to the same value.
Run this test on the Rotor as well.
DC Hipot (Can be a distructive test)
If your machine is 11Kv then the peak voltage is 11Kv X Sqrt(2) = 15.5Kv. You can use a DC Hipot to test the insulation system by applying a voltage above the 15.5Kv DC and take milliamp reading as you go up. The test is potenitally distructive because if you have an insulation problem with the Generator this will find it and probably make it much worse. (Rewind time) Some people still use this test at reduced levels.
PF (Power Factor Test).
This test is usually done at a voltage well under the rating of the Generator so is considered a nondistructive test. Most PF test sets designed to be used for testing Transformers but it can be adapted to test Generators. Generally it is the year to year comparisons that will mean something not necessarily the first time you run the test.
You met also check out the NETA website they provide testing specifications on most all electrical equipment.