Price-based dynamic optimal power flow with emergency repair

In a scenario involving damaged lines or equipment, healthy regions of a network with distributed energy resources can operate through islanded microgrids. With this, the hourly demand constraint is flexible and the dynamic optimal power flow (DOPF) follows a price signal, making use of inter-temporal technologies to maximize the power utility’s profit; this is known as price-based DOPF (PB-DOPF). Repair crews must also be dispatched to affected locations when restoring the network, which is known as the emergency order (EO) scheduling problem. This article proposes a mathematical model for co-optimization of the interdependent PB-DOPF and EO scheduling problems, in order to minimize the PB-DOPF cost in a horizon. The problem is formulated as a mixed-integer linear programming model with linearized three-phase power flow. An algorithm is implemented to perform the PB-DOPF and repair crew dispatches over a horizon with multiple EOs incidences, integrating a pre-scheduling methodology to handle the computational complexity. The optimization process focuses on systematically improving the solution by releasing the route and keeping track of the results related to the solution progress. Computational tests are carry on IEEE 123-bus and IEEE 8500-node distribution systems, constructing the benchmark cases with the proposed algorithm and its other two variations.