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In this paper, we investigate energy optimization in multi-cell and multi-carrier non-orthogonal multiple access (NOMA) networks. We apply a load-coupling model for NOMA networks to capture the coupling relation of mutual interference among cells. With this analytical tool, we formulate an energy minimization problem in a NOMA-based load-coupled system, where optimizing load-rate-power allocation, and determining decoding order and user grouping are the key aspects. Theoretically, we prove that the minimum consumed energy can be achieved by using all the time-frequency resources in each cell to deliver users' demand, and allowing all the users to share resource units. From a practical perspective, we consider three types of NOMA grouping schemes, i.e., all-user grouping, partitioned and non-partitioned grouping. We develop tailored solutions for each grouping scheme to enable efficient load-rate-power optimization. These three algorithmic components are embedded into a power-adjustment framework to provide energy-efficient solutions for NOMA networks. Numerical results demonstrate promising energy-saving gains of NOMA over orthogonal multiple access in large-scale cellular networks, in particular for high-demand and resource-limited scenarios. The results also show fast convergence of the proposed algorithms and demonstrate the effectiveness of the solutions.