The rising penetration of renewable energy introduces greater volatility and uncertainty into energy systems. Energy storage systems (ESS) play a vital role in enhancing system flexibility and stability. However, frequent charge–discharge cycles lead to significant degradation of storage devices, reducing their economic efficiency and lifespan. This paper proposes a two-stage robust optimization framework under high renewable penetration, explicitly considering battery degradation. The first stage determines the optimal capacity configuration of distributed energy resources, including PV, wind, gas turbines, and ESSs. The second stage optimizes operational strategies under worst-case uncertainty in renewable generation and load, while accounting for the degradation cost and cycle life of the ESS. A linearized degradation model is developed based on depth-of-discharge (DoD), and the overall problem is solved using a Column-and-Constraint Generation (C&CG) algorithm. Simulation results demonstrate that the proposed approach effectively balances investment and operation, reduces degradation-related costs, and ensures reliable performance under uncertainty.