An electric power system includes an engine, a generator, a drivetrain including a driveshaft, and an energy storage system having a flywheel. In an implementation, a parallel-path continuously variable transmission is structured to transfer energy between the flywheel and the driveshaft, and in another implementation a parallel-path continuously variable transmission transfers energy between the engine and the generator. The transmission includes a variator and a differential geartrain. An electric motor is coupled to the flywheel and charges the flywheel such that stored flywheel energy is available for bringing up engine speed from a standby state and/or to accommodate generator load changes with limited generator speed changes.