A modularized battery system made up of integrated battery building blocks has been brought into sight recently. The battery building block system has advantages such as no external equalizers, no centralized converters, reduced power and voltage stresses, easy reconfiguration and customization, control of thermal distribution, etc. However, the control of charging the building block system faces challenges in stabilizing the system while distributing different power to different modules. This paper recognizes the battery building block system as a single-input and multiple-output system (SIMO). The system features an input-series and outputindependent (ISOI) architecture, where the inputs of the converters are connected in series while the output of each converter is independently supplying different load. The modeling and control of the ISOI system are demonstrated. A two-level supervised distributed control method is proposed and analyzed to achieve the stable power distribution control with simulation and experiment validation.