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What voltage?

The load is a little over 2kW, so the output needs to be rated no less than 2.5kW continuous (assuming the load is continuous).

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The voltage is regulated by the number of field windings versus stator windings, multiplied by the voltage added to the field from a DC source. Phase factors and operating power factors will also affect the total kiloVolt-Ampere output of a generator. this is often factored in for household emergency generators and a generalized rating is given for a 220 volt output. for a 2049 watt load at 220 volts a single phase generator with with an output of 2500 watts or more should be used. The phase factor would be 1:1, power factor negligible (unless hooked to the power grid), and motor(generator) efficiency is about 96% typically. Adjusting for a 25% peak load (when items turn on and off) then:

(2049w/0.96)x1.25 = 2668 watts , a 2500 watt generator will handle it if not all things attached to it start at the same time.

This is equivalent to a 100amp circuit load at 220 volts or 200amps at 110 volts. (circuit breakers), most houses require a 200 or 300 amp service (add up all the circuit breakers in use in the box.)

note: single breakers are typically 110 volt and double breakers are typically 220 volts, when adding up breaker's amperage double the load for double breakers to compare the loading at 110 volts.

example:

Circuit box has 2 double (220v) breakers, stove/oven 30 amp, water heater 45amp, and 12 15 amp single breakers (110v) the total load for the service is:

(30 x 2)+(45 x 2) + (12 x 15) = 330 amps (@110 v) or 165 amp service (@220v)

165 amps x 220 volts = 33000 volt-amperes , because emergency generators are rated at 220 volts the kilowatt output needed is 1.65 x 125% = 206.25 kw @ 220 volts

For industrial generator ratings: volt-amperes = kilowatts x power factor x phase factor (3 phase generation phase factor is 1.732, power factor is adjusted by adjusting the field voltage) , these do not apply with emergency generators. {volts x amperes = watts}

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Q: What size generator needed for 2049 watt loads?
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