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Towards energy savings in large-scale non-orthogonal multiple access (NOMA) networks, we investigate power and load optimization for multi-cell and multi-carrier NOMA systems in this paper. To capture the coupling relation of mutual interference among cells, firstly, we extend a load-coupling model from orthogonal multiple access (OMA) to NOMA networks. Next, with this analytical tool, we formulate the considered optimization problem in NOMA-based load-coupled systems, where optimizing load, power, and determining decoding order are the key aspects in the optimization. Theoretically, we prove that the minimum network energy consumption can be achieved by using all the time-frequency resources in each cell to deliver users' demand. To achieve the optimal load and enable efficient power optimization, we develop a power-adjustment algorithm. Numerical results demonstrate promising energy-saving gains of NOMA over OMA in large-scale cellular networks, in particular for the high-demand and resource-limited scenarios.