A 55 Amp alternator running at full output will not keep up with the demand when the inverter is running at full output.
With electricity, there are losses and duty cycles to think about. Available supply should ALWAYS be greater than anticipated demand. How much greater depends on duty cycle.
Most cheap inverters are not rated for 100% duty cycle. In other words a 1500 Watt inverter is not designed to output 1500 Watts for hours on end. To get 1500 Watts out you would want to get a much larger inverter, 2000 Watts minimum, ideally 3000 Watts.
Now your 105 Amp alternator is not rated to put out 105 Amps 100% of the time either. You really need TWO 105 Amp alternators to do the job.
By the time all is said and done, you've got way more into it than a cheap clone 2000 Watt inverter generator, which only run about $500.
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