You don't say what the alternator is but I am guessing it will be a 50 Hz / 415 V or 60 Hz / 208 V and either 2 or 4 pole.
If so, you need to run at 1500 rpm for a 4 pole 50 Hz alternator, 1800 rpm for a 4 pole 60 Hz, 3000 rpm for 2 pole 50 Hz and 3600 rpm for 2 pole 3600 rpm.
The speed controls the output frequency. The speed should be the same from no load to full load. The alternator will have a voltage regulator to make sure that the output voltage is constant.
You need to control the throttle valve. Solenoid valves are almost always on/off so all you would want that for is to shut it off.
A good way is to have a stepper motor control the throttle. You can measure the frequency by looking at the main output voltage, via a small transformer.
Small generators up to 5 kVA often use lawn mower engines. Small generators need speed control just the same as large generators and lawn mowers need speed control to stop the blades going supersonic with no load while being able to produce maximum power when the grass gets tall and wet.
Lawn mowers usually use centrifugal or vane governors. Both have a light spring to hold the throttle open, which is closed as the engine speeds up by either weights moving out due to centrifugal force, or air from the cooling fan blowing on the vane. Either of those methods would be fine and might be easier to get working.
With a 50kVA alternator you should look at something to kill the ignition if it goes too fast. It would be a lot worse than an lawnmower going mad.