A vehicle includes an engine, an electric machine, a battery, and at least one controller. The vehicle may further comprise a port for supplying power to a load external to the vehicle. The controller is programmed to operate the engine at a power level based on a difference between a battery voltage and a reference voltage such that a power output by the electric machine reduces the difference. The power level may define an engine operating point that minimizes fuel consumption. The operating point may be an engine torque and an engine speed. The power level may be further based on a state of charge of the battery. The electric machine may be operated to cause the engine to rotate at an engine speed corresponding to the selected power level. The difference may be caused by varying power drawn by a load external to the vehicle.