Mathmatical equivalents aside.. In practice, I've found most manufacturers want you to have about 2 pto hp per kw of generated electrical power.. I know there is 'fat' in there.. But just weight till the first really big 30-40-50 (inductive) motor load hits that "15kw" genny head with a 20 pto hp tractor powering it... I think you would be amazed at what would happen...
I was running about a 23pto hp tractor on the northern 12.5 kw genny, and hitting it with 20a inductive loads as well as some constant incandescent loads, and some 'test' electroninc loads, like a tv and radio.. looking for frequency and undervotlage distortion. While the genny did take a few minot rpm hits on large loads.. all stayed withing the 'green' zone indicated on the meter... If that had been a 20pto hp tractor.. I think I might have hit some out of range votlages / freq's. I'd prefer to have excess engine if I wanted to run at full rated watts, and also have surge capability. Course.. same can be said of the genny. If I had the money, I would much prefer to run a 12kw genny head at 8 kw, vs buying an 8kw head and running it at 8kw. It gives you so much excess surge power, pluss if your pto power source is ever upgraded, you are good to go. I know keep a 33 and 67 pto hp tractor ready for my pto gen if the lamps go out... I've no doubt the extra available hp will help stabilize governor movement during high load cut in's.. etc..
just my .02
Soundguy