Im on your side and am for you. Hey for years when I was a Secondary Power Distribution Design Engineer we tried and did indeed add capacitance all the time to improve power factor and I tried to explain below the theory of how it works AND BELIEVE ME IT DOES so add capacitors n take some measurements until you achieve the correct values and post back and let us know and CONGRATULATIONS is what I say. I am not in the habit of name calling, I try to help when I can.
If your genny is any good quality at all a 4 KW ought to start a 10 to 12 amp motor load no problem is my best guess subject to the load and specs and quality of the genny and again if you can add capacitance to balance out an otherwise heavy inductive load I guarantee the power factor will improve. Unless you develop a switching system to precisely remove it I still dont see adding resistance to lessen the current and drop the voltage to power a motor as the best method for start ups, but Im for you if you do so let us know how that works and with some good data IM ALWAYS WILLING TO LEARN A NEW TRICK OR TWO YA SEE...
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