The hard start capacitor is not used to "store" energy. The capacitor is used to generate a phase shift in current to the start windings. In other words, it generates a starting torque using the start winding. A larger cap, like a hard start cap, will cause higher current in the starting winding, and hence a higher starting torque. In a hard start kit, this extra current and torque, if left on, would cause a high current over heating of the motor, and eventual failure. So the cap in the hard start kit is only applied momentarily during startup.
As I had said earlier, this higher starting current will result in a higher draw from the AC supply. It is possible that the higher current will be offset by the shorter time for startup. Generators have two limitations: copper and iron. Copper is the size (gauge) of wire. Heavier wire can handle more current with less losses. So heavier wire can provide more current with less losses in the windings (due to resistance). You will therefore have lower voltage drop. With smaller wire, during heavy current draws the voltage will sag more below the design voltage.
Iron refers to the amount on iron in the laminated magnetic structure of the generator's stator. As current goes up, so does the magnetic fields in the iron of the stator. At high currents, the iron can reach "saturation" which is the point where the iron can not increase it's magnetic strength any more - it is saturated. This is kind of a hard limit on the output of the generator. So on a big inrush like the AC, you have the inertia of the generator to provide energy (rotational). The copper may cause the voltage to droop at high currents, but if you hit field saturation, you are at a hard limit on current.
The desire to build cheaply, common in many import units, means saving on copper and iron. This is why many low cost gen sets have such a low ratio between the full load and surge ratings. A heavier, more conservative build will have more margins and therefore a higher surge rating.
paul
