In this paper, a real-time demand response (DR) framework and model for a smart distribution grid is formulated. The model is optimized in a distributed manner with the Lagrangian relaxation (LR) method. Consumers adjust their own hourly load level in response to real-time prices (RTP) of electricity to maximize their utility. Because the convergence performance of existing distributed algorithms highly relies on the selection of the iteration step size and search direction, a novel approach termed Lagrangian multiplier optimal selection (LMOS) is proposed to overcome this difficulty. Via sensitivity analysis, the energy demand elasticity of consumers can be effectively estimated. Then the LMOS model Can be established to optimize the Lagrangian multipliers in a relatively small linearized neighborhood. The salient feature of LMOS is its capability to optimally determine the Lagrangian multipliers during each iteration, which greatly improves the convergence performance of the distributed algorithm. Case studies based on a distribution grid with the number of consumers ranging from 10 to 100 and a real-world distribution grid demonstrate that the proposed method greatly outperforms the prevalent approaches, in terms of both efficiency and robustness. (C) 2017 Elsevier Ltd. All rights reserved.