Power system operation faces an increasing level of uncertainties from renewable generation and demand, which may cause large-scale congestion under an ineffective operation. This article applies energy storage (ES) to reduce system peak and the congestion by the robust optimization, considering the uncertainties from the ES state-of-charge (SoC), flexible load, and renewable energy. First, a deterministic operation model for the ES, as a benchmark, is designed to reduce the variance of the branch power flow based on the least-squares concept. Then, a robust model is built to optimize the ES operation with the uncertainties in the severest case from the load, renewable energy, and ES SoC that are converted into branch flow budgeted uncertainty sets by the cumulant and Gram–Charlier expansion methods. The ES SoC uncertainty is modeled as an interval uncertainty set in the robust model, solved by the duality theory. These models are demonstrated on a grid supply point to illustrate the effectiveness of a congestion management technique. Results illustrate that the proposed ES operation significantly improves system performance in reducing the system congestion. This robust optimization-based ES operation can further increase system flexibility to facilitate more renewable energy and flexible demand without triggering the large-scale network investment.