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During system restoration, it is critical to utilize the available black-start (BS) units to provide cranking power to non-black-start (NBS) units in such a way that the overall system generation capability will be maximized. The corresponding optimization problem is combinatorial with complex practical constraints that can vary with time. This paper provides a new formulation of generator start-up sequencing as a mixed integer linear programming (MILP) problem. The linear formulation leads to an optimal solution to this important problem that clearly outperforms heuristic or enumerative techniques in quality of solutions or computational speed. The proposed generator start-up strategy is intended to provide an initial starting sequence of all BS or NBS units. The method can provide updates on the system MW generation capability as the restoration process progresses. The IEEE 39-Bus system, American Electric Power …