In recent years, green networking has attracted a lot of attention from device manufacturers and Internet Service Providers (ISP) to reduce energy consumption. In the literature, energy-aware traffic engineering problem is proposed to minimize the total energy consumption by switching off unused network devices (routers and links) while guaranteeing full network connectiv-ity. In this work, we are interested in the problem of energy-aware Traffic Engineering while using multi-path routing (ETE-MPR) to minimize link capacity utilization in ISP backbone networks. To this end, we propose a bi-level optimization model where the upper level represents the energy management function , and the lower level refers to the deployed multi-path routing protocol. Then, we reformulate it as a one-level MILP replacing the second level problem by different sets of optimality conditions. We further use these formulations to solve the problem with classical branch-and-bound, cutting plane, and branch-and-cut algorithms. The computational experiments are performed on real instances to compare the proposed algorithms and to evaluate the efficiency of our model against the existing single-path and multi-objective approaches.