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The possibility to store energy, to exchange power and information on demand and production among grids allows us to achieve an active distribution which is of major interest for cooperative smart power grids, that are grids which can forecast demand and production and are able to exchange power in order to enhance the quality of the service. In this paper, a model to support optimal decisions in a network of cooperative grids is formalized as an original discrete and centralized problem here defined as cooperative network of smart power grids (CNSPG) problem. In the CNSPG problem, the control variables are the instantaneous flows of power in the network of grids, which can be obtained from the solution of a linear quadratic Gaussian problem on a fixed time horizon. A simple case study showing the enhancement which may be obtained from the introduction of direct connections among microgrids according to a lattice network is shown and finally discussed.