Distributed service restoration for active distribution networks based on alternating direction method of multipliers

Chapter 11 proposes a distributed optimal service restoration strategy based on the alternating direction method of multipliers (ADMMs). In the presence of a permanent fault, an optimized self-healing scheme minimizes the unsupplied demand while maintaining the faulted section of the network isolated. The service restoration of the self-healing scheme is a combinatorial optimization problem whose computational complexity grows exponentially with the number of binary variables. To resolve this issue, a distributed optimal service restoration strategy based on the ADMM is proposed. Firstly, the optimal service restoration problem is formulated as a mixed-integer nonlinear programming (MINLP) model, including decomposable radiality constraints. The decision variables of the problem are the status of the remote-controlled switches, load zones, and load shedding at each controllable demand. Operational constraints, such as current and voltage magnitude constraints, distributed generation capacity constraints, and radial topology constraints, are respected in the optimization problem. Then, the MINLP model is transformed into a mixed-integer second-order cone programming (MISOCP) model. Finally, the MISOCP model is decomposed and solved using an ADMM-based algorithm. Through the proposed decomposition, the service restoration problem is distributed among the zones of the distribution system. The proposed distributed strategy can provide optimal service restoration solutions in reasonable time without a central controller.