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We consider the scenario of a low voltage microgrid populated by a number of distributed microgenerators. We focus on the problem of obtaining a dynamic model that describes the input-output relation between complex power commands sent to the microgenerator inverters and the voltage measurements across the network. Such a model is intended as a necessary tool in the design of distributed and centralized control algorithms for the provision of ancillary services in the power distribution grid. Because this model is to be used for the design of such algorithms, we look for an analytical derivation instead of a simulative tool. The proposed model is linear and explicitly contains the network parameters and topology. Simulation shows how the proposed model approximates well the behavior of the original nonlinear system.