The conventional approach for the control of distribution networks, in the presence of active generationand/or controllable loads and storage, involves a combination of both frequency and voltage regulation atdifferent time scales. With the increased penetration of stochastic resources, distributed generation anddemand response, this approach shows severe limitations in both the optimal and feasible operation ofthese networks, as well as in the aggregation of the network resources for upper-layer power systems. Analternative approach is to directly control the targeted grid by defining explicit and real-time setpointsfor active/reactive power absorptions/injections defined by a solution of a specific optimization problem;but this quickly becomes intractable when systems get large or diverse. In this paper, we address thisproblem and propose a method for the explicit control of the grid status, based on a common abstractmodel characterized by the main property of being composable. That is to say, subsystems can be aggre-gated into virtual devices that hide their internal complexity. Thus the proposed method can easily copewith systems of any size or complexity. The framework is presented in this Part I, whilst in Part II weillustrate its application to a CIGRÉ low voltage benchmark microgrid. In particular, we provide imple-mentation examples with respect to typical devices connected to distribution networks and evaluate ofthe performance and benefits of the proposed control framework.