3000 rpm is the full load speed for a 50 Hz genset. Off load the governor should maintain engine speed at no more than 3150 rpm (5% run out)
When initially starting, if the engine speed is below 3000, the governor will open the throttle fully, to bring the engine upto rated speed, but close it partially as rated speed approaches.
As Noel says, check that the throttle closes as the engine speeds up.
Once upto speed, depending on the electrical load applied to the alternator, the speed can vary between 3000 (Full load) and 3150 (No load)
Trying to shorten the run out, to control frequency more closely, can make the governing too sensitive, and unstable, so that the speed is constantly varying, even with a constant electrical load.
Hopefully, any “hunting” will gradually be damped out, by mechanical and electrical inertias
The electrical control set up should limit, and control, voltage.
Usually. lacking means of applying a full electrical load, normal practice is to set the maximum speed, unloaded, to 3150 rpm. As electrical load is applied, the speed should fall until, what ever load results in 3000 rpm, will be the maximum that the engine can deliver.
If the engine is overloaded, and the speed falls below 3,000 rpm, the frequency will be below 50 Hz, with the problems that can bring.
Overspeeding can bring electrical and mechanical problems, so is to be avoided.
HTH
Howard