  The need to restore and keep the grid running or fast restoration during
emergencies such as extreme weather conditions is quite apparent given the
reliance of other infrastructure on electricity. One promising approach to
electricity restoration is the use of locally available energy resources to
restore the system to form isolated microgrids. In this paper, we present a
black start restoration method that forms islanded microgrids after a blackout.
The master DGs in the formed microgrids are coordinated to work together
through droop control. Several constraints, including incentive-based demand
response (DR) with direct load control (DLC) and distributed generator (DG)
operation constraints, were formulated and linearized to realize a
mixed-integer linear programming (MILP) restoration model. To improve
compactness and to ensure that the model is neither under-sized nor over-sized,
a pre-processing graph analysis approach was introduced which helps to
characterize the least number of restoration steps needed to optimally restore
the microgrid. Studies were performed on a modified IEEE 123 node test feeder
to evaluate the effects of demand response, non-dispatchable DGs, and choice of
restoration steps on the quality of the restoration solution.
