A method for controlling a power generation system connected to a weak grid may generally include operating a power converter of the system so as to produce current at or above a power factor threshold associated with a power factor operating requirement for the system, detecting that a generator speed of the system has increased over a period of time, detecting that a local reference voltage for the system has decreased within the same period of time over which the generator speed has increased and adjusting the operation of the power converter to produce current at a reduced power factor below the power factor threshold so as to increase a real power output of the system.