In a gas turbine power generator system, when there is an increase in the demand of a user system, a battery system supplies a supplemental electric power which is given by adding an added electric power to a difference between a current output of the power generator and the increased demand. Because the supplemental electric power is greater than the difference between the current output of the generator and the increased demand by the added electric power, the load acting upon the gas turbine engine is correspondingly reduced even from the preceding steady state so that the gas turbine engine can quickly accelerate to the level that matches the increased demand of the user system. Therefore, the battery system is required to supply electric power only for a relatively short time as compared to the case where the supplemental electric power is equal to the difference between the output of the power generator and the demand, and the capacity of the battery system may be smaller than the case where the battery meets the entire demand while the gas turbine engine is being accelerated.
