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This paper presents a convex relaxation of a class of smart building-grid energy management models using a semi-definite programming approach. A smart building-grid energy system is roughly defined as an interconnection of buildings and electric power grid energy resources within a clearly defined boundary, here called a smart site. A smart site is a strategic or self-interested entity that seeks to maximize some utility function subject to all applicable technical and budget constraints. The utility function is here a measure of energy efficiency. A smart site may purchase energy from or sell energy to its external environment. On one hand, traditional building energy management systems have focused on meeting the energy requirements of one or more buildings assuming that the buildings are connected to a strong or infinite-capacity utility grid. On the other hand, electric grid management systems have traditionally modeled relatively large sites as single grid nodes with simple lump load models. The contribution of the present paper is two-fold: to provide a general model that integrates and extends building and energy management models, and (b) to develop a convex relaxation of the ensuing model a solution of which yields a global lower bound. The proposed approach also provides a means to test whether any solution, for example, obtained using a heuristic method, is global, and the corresponding optimality gap.