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This paper addresses the problem of the optimal stabilization of DC microgrids using a hierarchical control design. A recursive optimal power flow formulation is proposed in the tertiary stage that ensures the global optimum finding due to the convexity of the proposed quadratic optimization model in determining the equilibrium operative point of the DC microgrid as a function of the demand and generation inputs. An exact feedback controller with integral action is applied in the primary and secondary controller layers, which ensures asymptotic stability in the sense of Lyapunov for the voltage variables. The dynamical model of the network is obtained in a set of reduced nodes that only includes constant power terminals interfaced through power electronic converters. This reduced model is obtained by applying Kron’s reduction to the linear loads and step nodes in the DC grid. Numerical simulations in a DC microgrid with radial structure demonstrate the effectiveness and robustness of the proposed hierarchical controller in maintaining the stability of all the voltage profiles in the DC microgrid, independent of the load and generation variations.

Hierarchical Control for DC Microgrids Using an Exact Feedback Controller with Integral Action