This paper is the first of a two-part paper presenting a multiperiod generalized network flow model of the integrated energy system in the United States. Part I describes the modeling approach used to evaluate the economic efficiencies of the system-wide energy flows, from the coal and natural gas suppliers to the electric load centers. Under the proposed problem formulation, fuel supply and electricity demand nodes are connected via a transportation network, and the model is solved for the most efficient allocation of quantities and corresponding prices. The methodology includes physical, economic, and environmental aspects that characterize the different networks. Part II of this paper provides numerical results that demonstrate the application of the model.