I have a 4.2KW system and live in a sunny country area. On a hot summer's day I can get 30KW, in winter 23KW. You can't calculate accurately because there is no accurate data for solar irradiation, and because the weather is unpredictable.
A three wire home distribution service rated at 100 amps has a wattage capacity of;From L1 to L2 at 240 volts x 100 amps = 24000 watts or 24 kilowatts. From L1 to neutral at 120 volts x 100 amps = 12000 watts or 12 kilowatts. From L2 to neutral at 120 volts x 100 amps = 12000 watts or 12 kilowatts.
Watts and horsepower are directly related as they are both measurements of power. 1hp = 745.6998 watts. So 3kW = 3000W / 745.6998 W/hp = 4.023hp You need a minimum of 4hp, which will give you a max of 2982W before any losses in your generator. You should probably go with a 4.5 or 5 horse motor.