A power system is disclosed. The power system may have an engine with a desired operating speed range, and a generator mechanically driven by the engine to produce electrical power directed to an external load. The power system may also have a power storage device associated with at least one of the engine and the generator, and a controller in communication with the engine and the power storage device. The controller may be configured to determine a speed of the engine deviating from the desired operating range, and to activate the power storage device to absorb or supplement at least a portion of the electrical power directed to the external load based on the determination.