I. Introduction
Integrated with smart infrastructures, communication architectures, advanced control technologies, etc., a smart grid is expected to be much more efficient and reliable [1], [2] compared with the traditional power grid. Due to the existence of intelligent controllable electrical devices and advanced communication networks [3] , distributed control and optimization [4] become possible and also desirable in a smart grid [5], [6]. Compared with the conventional centralized approach, the distributed one will be more scalable and robust, which is more applicable for smart grid. Especially, distributed energy management (DEM) is a critical and notable problem in the operation of a smart grid [7].