Polygeneration systems with thermal energy storage represent promising solutions to achieve energy saving and emissions reduction in the civil sector. The definition of customer-oriented design and operation strategies represents a most challenging task, in order to maximize the profitability and make the investment attractive. A large potential is often recognized for the installation of centralized plants serving a cluster of buildings located over a small area; in such cases the design problem becomes extremely complex and the analyst needs reliable instruments to identify the optimal solution. This paper in two parts presents a scientific tool for the optimization of design and operation for complex polygeneration plants serving a number of buildings with heat, cooling and electricity. The method is flexible with respect to boundary conditions as concerns the power exchange with the public grid, the tariff structure and the normative constraints. In Part I of the paper the method is described, focusing the attention on the most conceptual aspects. The Mixed Integer Linear Programming algorithm is also presented and error analyses are performed for each of the figures adopted, in order to assess the robustness of the method. In Part II of this paper the tool will be extensively applied to some explicative case studies, in order to better clarify its potential in supporting energy analysts and decision makers. (C) 2013 Elsevier Ltd. All rights reserved.