A hybrid energy storage system is configured to control pulsed power. A first dynamo-electric machine is coupled to an inertial energy storage device and has multiple input stator windings configured to accept input power from a source. A polyphase output stator winding is configured to deliver electric power having a first response time to a DC bus. A secondary energy storage system is coupled to the DC bus and is configured to convert its stored energy to electric power in a bidirectional manner. A second dynamo-electric machine has an input stator winding and at least one polyphase output stator winding coupled to a converter, the converter coupled to a DC output. A polyphase boost exciter is configured to derive energy from the DC bus and excite the second machine input stator winding, wherein the second machine is configured to be excited at a faster rate than the first response time of the first machine.