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Intermittent nature of renewable energies and random nature of moving loads negatively influence the power system transient stability. Energy storage can enhance the system response by providing short-term energy sources. However, fast dynamic storage systems require advanced controllers to stabilize the transients. This paper introduces the application of a decentralized overlapping decomposition controller in transient stability of renewable energy penetrated storage-based power systems. In a battery-based power system there exists strongly coupled state variables shared among areas. Large-scale controllers can decouple the system state variables and stabilize the oscillations. Here, the model of battery storage is obtained considering the battery's state of charge and the droop in power electronic interfaces. The overlapping decomposition decentralized controller demonstrates an enhanced transient stability performance under variable state of charge in various capacity of storage devices.