This paper presents a global hierarchized control method for railway interties based on the direct singleto-three-phase AC/AC Modular Multilevel Converter with integrated split battery energy storage. The power and voltage decoupling between the converter submodules and the batteries is achieved through non-isolated dedicated DC/DC converters. The control objectives include submodule capacitor voltage and battery state of charge balancing. All possible converter operation modes are investigated by means of simulations. Moreover, potential three-phase grid asymmetries are considered and studied. In the latter, the integrated storage elements can be utilized to transfer the necessary active power to the railway network side irrespectively from three-phase grid faults.