My TYM has around 36 HP at the PTO. The PTO generators I see out there are primarily two ranges:
1. Around 13 - 15 KW which requires a HP in the upper 20s.
2. Around 25 KW which requires a HP in the upper 40s.
If I used a generator larger than rated for my tractor but I am only pulling around 16 - 20 KW, would this create problems? As long my tractor can maintain the 540 rpm, am I OK regarding providing clean power to my home?
16-20 kW on a 25kW generator is no problem for the generator. Going above 18kw load may be a problem for the tractor (using the 2 Hp/ kw rule of thumb)
Don't get "upside down" or start chasing your tail when sizing things. (E.g. Size tractor big enough for generator or size generator big enough for tractor? etc.. etc..) That is, it's the actual house loads that will determine the...uhm...load. (Thanks you Capatain Obvious!) (House loads are typically not constant as they turn off and on). Once house loads are known, then it's a matter of what will trip (generator circuit breaker) or stall (engine) when the load goes beyond the weakest link.
Having the engine as the weak link isn't a bad thing, but typically one sizes the gen "set" so that the gen's circuit breaker trips before engine rpms dip (and thus voltage and frequency dip) and/or stalls. Whether an overload causes engine to stall, or whether the voltage dip causes an increased current demand and breaker trips first probably depends on what type of house loads you have (e.g. motor typ vs. (resistive) heat element).
....and for this discussion we are totally ignoring electrical motor starting loads ("in rush current") and the motor & gen's ability to start them. That gets into rotating mass inertia (engine and generator's), governor's response times, engine speed-torque curves, the motor inrush current (winding impedance/efficiency), acceptable voltage/freq dips, how prior loaded generator is when motor in question kicks on, etc...
That is, sometimes a generator/motor set has to be up-sized to START the load, not just sized to run it; or loads have to be started in a particular order to not overload genny.