In this paper, a green and robust optimization model is introduced to minimize network power consumption, which allows fluctuations of traffic demands between source‐destination pairs in the network. Our model is based on the green hose model, where the traffic is bounded by just total outgoing and incoming amount at each node. In addition to the green hose model, we use the ellipsoidal uncertainty set to allow a different type of fluctuations in traffic demands. Here, the total amount of squared errors in traffic demands is bounded by a constant which controls the total admissible fluctuations over the network. Applying the conic duality, we formulate our model in the form of mixed‐integer second order cone programming (MISOCP) problem. Furthermore, we establish a relationship between our model and the green hose model with bound of link traffic (HLT) model, an developed version of the hose model known as the HLT. Numerical results demonstrate that each of the MISOCP problems can be solved to its optimality in a reasonable time by a general MISOCP solver, and that the proposed model has different tendency in performance with the green hose and green HLT models