Critical Load Restoration Method for Unbalanced Distribution Systems Based on Linear Approximation

After a major outage caused by extreme events, critical loads can be restored by distributed generators (DGs) in the distribution system. The critical load restoration problem can be formulated as a mixed-integer semidefinite program (MISDP) to model the multi-phase unbalance of the distribution system, but MISDP cannot be solved efficiently. This paper proposes a mixed-integer linear program (MILP) for critical load restoration problem based on linear approximation of power flow, which is a good estimate of nonlinear unbalanced power flow and can be solved efficiently using off-the-shelf optimization tools. In addition, to consider the operation of the post-restoration system during the outage, we extend the proposed MILP to a multi-time restoration model by adding additional time-related constraints. The accuracy and efficiency of the proposed one-snapshot restoration model are validated by numerical simulations on IEEE 13, 34, 37 and 123- node test feeders, and the effectiveness of the multi-time restoration model is demonstrated on IEEE 37-node test feeder.