Electric power systems face the risk of outages due to extreme weather events, cyber-attack, human errors, and other unforeseen circumstances. A power grid that is resilient to these unfortunate events has become a consistent theme in literature and media. One approach to improve the grid's resilience is by decentralizing the grid into smaller controllable units called microgrids. This dissertation focuses on the control and operation of islanded microgrids for black start restoration (BSR). Two operation modes were identified based on islanded microgrids' primary control for BSR. These modes are the single master operation (SMO) and multi-master operation (MMO) modes. These two control approaches were used to develop two sequential multi-step BSR methods for islanded microgrids. The first part of this dissertation presents the BSR formulation for SMO microgrids. The restoration problem was formulated as a mixed-integer linear programming (MILP) problem. The frequency response of the isochronous synchronous-machine based generator (ISMG) was derived and validated through transient simulation. The frequency response was then used to characterize the ramp rate and the settling time of the ISMG. With these characterizations, the BSR can minimize total restoration time and maximize energy restored. The developed BSR method was studied on a modified IEEE 123 node test feeder. The second part of this dissertation provides studies of the use of MMO microgrids for BSR. The MMO microgrids were assumed to be operating with conventional droop control. Before developing the BSR method, two novel linear power flow (LPF) formulations for islanded droop-controlled microgrids were derived. These two LPF formulations were extended to develop optimal power flow (OPF) formulations as a quadratic programming (QP) and a mixed-integer quadratic programming (MIQP) problem to minimize cost. These formulations were followed by a MILP formulation to realize a novel BSR method for MMO microgrids with the derived LPF equations incorporated as the power flow constraint. Extensive case studies were used to validate and verify the developed BSR method. Because the MMO microgrid can have multiple master DGs per microgrid, they are expected to improve islanded microgrids' resilience compared to SMO microgrids which have one master DG per microgrid.
