A hybrid energy storage module system includes a first power stage having a short circuit switch to connect the first power stage to a power bus, a second power stage stacked in series with the first power stage and having a short circuit switch to connect the second power stage to the power bus, and a controller. The controller is operably connected to the first and second power stage short circuit switches to discharge one of the first and second power stage through the other of the first and second power stage in a state of charge balancing mode. Aircraft electrical systems and methods of controlling connectivity of hybrid energy storage modules to electrical systems are also described.