Demand response has recently become a topic of active research. Most of work however considers only the balance between aggregate load and supply, and abstracts away the underlying power network and the associated power flow constraints and operating constraints. In this paper, we study demand response in a radial distribution network, by formulating it as an optimal power flow problem that maximizes the aggregate user utilities and minimizes the power line losses, subject to the power flow

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... traints and operating constraints. As the resulting problem is non-convex and difficult to solve, we propose a convex relaxation that is usually exact for the real-world distribution circuits. We then propose a distributed algorithm for the loadserving entity to set the price signal to coordinate the users' demand response so as to achieve the optimum. Numerical examples show that the proposed algorithm converges fast for real-world distribution systems.