Various embodiments include a hybrid energy system that includes a gas-turbine generator (GTG), an energy storage device configured to store energy that is coupled to an inverter, with the GTG and energy storage device coupled to a low side of a step-up transformer, and methods of operating such hybrid energy systems to meet power output contract requirements or provide power for industrial power applications that exhibit load swings. Some methods of operation include controlling power output from and charging of the storage device so as to satisfy a contract schedule of electric power output. Some methods of operation include discharging a portion of stored energy of the energy storage device to satisfy swing loads of the industrial application and charging the energy storage device by the GTG between swing loads.