  When a major outage occurs on a distribution system due to extreme events,
microgrids, distributed generators, and other local resources can be used to
restore critical loads and enhance resiliency. This paper proposes a
decision-making method to determine the optimal restoration strategy
coordinating multiple sources to serve critical loads after blackouts. The
critical load restoration problem is solved by a two-stage method with the
first stage deciding the post-restoration topology and the second stage
determining the set of loads to be restored and the outputs of sources. In the
second stage, the problem is formulated as a mixed-integer semidefinite
program. The objective is maximizing the number of loads restored, weighted by
their priority. The unbalanced three-phase power flow constraint and
operational constraints are considered. An iterative algorithm is proposed to
deal with integer variables and can attain the global optimum of the critical
load restoration problem by solving a few semidefinite programs under two
conditions. The effectiveness of the proposed method is validated by numerical
simulation with the modified IEEE 13-node test feeder and the modified IEEE
123-node test feeder under plenty of scenarios. The results indicate that the
optimal restoration strategy can be determined efficiently in most scenarios.
