  Power restoration is an urgent task after a black-out, and recovery
efficiency is critical when quantifying system resilience. Multiple elements
should be considered to restore the power system quickly and safely. This paper
proposes a recovery model to solve a direct-current optimal power flow (DCOPF)
based on mixed-integer linear programming (MILP). Since most of the generators
cannot start independently, the interaction between black-start (BS) and
non-black-start (NBS) generators must be modeled appropriately. The
energization status of the NBS is coordinated with the recovery status of
transmission lines, and both of them are modeled as binary variables. Also,
only after an NBS unit receives cranking power through connected transmission
lines, will it be allowed to participate in the following system dispatch. The
amount of cranking power is estimated as a fixed proportion of the maximum
generation capacity. The proposed model is validated on several test systems,
as well as a 1393-bus representation system of the Puerto Rican electric power
grid. Test results demonstrate how the recovery of NBS units and damaged
transmission lines can be optimized, resulting in an efficient and
well-coordinated recovery procedure.
