I was confused for a long time on the excition problem until i found out that even gigawatt sized generators have 30% regulation under load.
Cheap generators achieve regulation by saturation. They waste 600 watts in the rotor and stator at no load on a brushed, 5 to 6kw 3600 rpm gen head.
You can buy an avr on ebay for $20
I dont know how much power is wasted in cheap 5kw brushless, 3rd harmonic excited generators, as i have never found one to take apart
For what its worth i removed 3 pounds of copper from a single phase 5kw generator and put 5 pounds back in. Made a nice 10 pitch, 24 slot, 2 pole 3 phase winding, very nice sine wave output.