This study introduces a mixed integer secondorder cone programming (MISOCP) model called the green Ellipsoid model for power saving in communication networks. The goal of this research is to optimize power consumption in communication networks by applying the conic optimization technique which is an emerging branch of research. The consumed power in communication networks is minimized considering network data variation using robust optimization. We apply the ellipsoidal uncertainty set to grant a variation in the network data and presented the model in the form of MISOCP. To scale down the total energy utilization in the network, the study proposes shutting down some unnecessary links throughout the entire network. By identifying and deactivating these redundant or unused links, the overall power consumption is reduced. Based on the numerical results obtained, the proposed green Ellipsoid model demonstrates the ability to save consumed power in comparison to the existing green Hose approach. The results indicate that the green Ellipsoid model exceeds the green Hose approach in terms of power savings. This suggests that the introduced model is more adequate in optimizing power utilization and achieving energy efficiency in the communication networks. An additional advantage of the green Ellipsoid model is its ability to accommodate data variation across the network through a single parameter. Acknowledging that MISOCP is a known NP-hard problem, the study also proposes an improved method to minimize computation time. This is achieved by leveraging optimization software tools that make the model tractable. By utilizing these tools, the presented model can be efficiently solved within an acceptable time.