Solar power is normally the only persistent power for satellites, so the energy supply problem of onboard devices is more difficult than that of the terrestrial networks. To fit the special architecture of satellite networks, the capacitated multi-commodity minimum cost flow model with constrained link capacity was modified and extended. Meanwhile, based on the multi-coverage scheme and traffic distribution patents in satellite networks, the existing heuristic algorithms were improved to turn off the unnecessary satellites, up-down links and inter-satellite links for energy saving. Under the constraints of link utilization and routing hops increasing ratio, the closing ratios of the three parameters are up to 59%, 61% and 72% respectively, and the total energy saving ratio can be up to 65% in simulation.