Over time, the number of smart grids installed worldwide is gradually increasing. However, the major portion of the required electricity is still being produced by traditional large-scale and centralized power systems. The main requirement, then, is to study and develop mathematical methods that attend the integration between the two systems previously announced. In this paper, a novel model that addresses this issue is presented. The model minimizes the total operating cost of the large-scale system considering the participation of the smart grid as a dynamic entity, entailing a close relationship between both systems. This approach distinguishes the novel proposal from others that solve similar situations by taking into account the two systems in isolation. Besides, the models that represent the most common organizational structures of the smart grids are also presented in this paper. They are needed to develop the integrated model. Many similar problems in the literature are solved by implementing decomposition techniques, which might obtain a local optimum different from the global one. By contrast, problems with this proposal are solved by using mixed-integer linear programming models that ensure the reaching of a global optimum. The real test case is the integrated Argentine large-scale system and the Armstrong smart grid. Results indicate that the novel model can reach solutions that are 5% lower in comparison with the traditional techniques of considering in isolation. Efficient CPU times enable the possibility of promptly obtaining solutions if there is any change in the parameters. In addition, other benefits, apart from the economical reductions, are also achieved. Operating information closer to the reality of both systems is obtained because it considers the effects of the smart grid in large-scale system solving.