Non-orthogonal multiple access (NOMA)-enabled heterogeneous networks (N-HetNets) can provide higher system capacity and spectrum efficiency by allowing multiple users cooperating in the same channel. However, traditional resource allocation algorithms are achieved under perfect channel state information (CSI) which is difficult to obtain in practical systems. In this paper, we study the total energy efficiency maximization problem in a downlink multicell N-HetNets under imperfect CSI, where the constraints of the quality of service of small-cell users, the maximum transmit power, and the cross-tier interference are considered. With the help of the ellipsoidal uncertainty sets, an iterative-based power allocation and user association algorithm is proposed based on the worst-case approach and the Lagrange dual method. Moreover, computational complexity, robust sensitivity and the impact of imperfect CSI error on user's outage probability are provided to insight the performance of the proposed algorithm. Simulation results demonstrate the robustness of the proposed algorithm.