Direct current (DC) network has been recognized as a promising technique, especially for shipboard power systems (SPSs). Fast resilience control is required for an SPS to survive after faults. Towards this end, this paper proposes the indices of survivability and functionality, based on which a two-phase resilience control method is derived. The on/off status of loads are determined in the first phase to maximize survivability, while the functionality of supplying loads are maximized in the second phase. Based on a comprehensive model of a DC shipboard power systems (DC-SPS), the two-phase method renders two mixed-integer non-convex problems. To make the problems tractable, we develop second-order-cone-based convex relaxations, thus converting the problems into mixed-integer convex problems. Though this approach does not necessarily guarantee feasible, hence global, solutions to the original non-convex formulations, we provide additional mild assumptions, which ensures that the convex relaxations are exact when line constraints are not binding. In the case of inexactness, we provide a simple heuristic approach to ensure feasible solutions. Numerical tests empirically confirm the efficacy of the proposed method.
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