Abstract : Recently, saving energy for backbone networks has raised an increasing concern for network operators. Since traffic load has a small influence on power consumption, the most common approach is to put unused links into sleep mode to save energy. To guarantee QoS, all traffic demands should be routed without violating capacity constraints. In this work, we consider to save energy with Open Shortest Path First (OSPF) protocol. From the perspective of traffic engineering, we argue that stability in routing configuration also plays an important role in QoS. In details, frequent changes in network configuration (link weights, slept and activated links) to adapt with traffic fluctuation in daily time cause network oscillation. We propose a novel optimization method of link weight so as to limit the changes in network configurations in multi-period traffic matrices. We formally define the problem and model it as Mixed Integer Linear Program (MILP). We then propose efficient heuristic algorithm that is suitable for large networks. Simulation results with real traffic traces on three different networks show that our approach achieves high energy savings and less pain for QoS (in term of less changes in network configuration).