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Normally, generators real and reactive power generation depends on the load according to the power balance equation. According to the load/demand power factor at the generators would be adjusted.
to inform at what PF u can get max Active Power.
Power Factor shown on Generator Name Plate is a Generator Manufacturer advise that how much Power Facor at Load side can be handled by the given generator without affecting its Normal Operation / Output Electrical Characteristics.
As Load side Power Factor further lowers in an Electrical System, Source Output in KW starts getting limited.