We consider the problem of optimal reactive power compensation for the minimization of power distribution losses in a smart microgrid. We first propose an approximate model for the power distribution network, which allows us to cast the problem into the class of convex quadratic, linearly constrained, optimization problems. We then consider the specific problem of commanding the microgenerators connected to a microgrid, in order to achieve the optimal injection of reactive power. For this task, we design a randomized, leader-less, gossip-like optimization algorithm. We show how a distributed approach is possible, where microgenerators need to have only a partial knowledge of the problem parameters and of the state, and can perform only local measurements. For the proposed algorithm, we provide conditions for convergence together with an analytic characterization of the convergence speed. The analysis shows that, in radial networks, the best performance is achieved when we command cooperation among microgenerators that are neighbors in the electric topology. Numerical simulations are included to validate both the proposed model and the analytic results about the performance of the proposed algorithm.