Distribution System Restoration via Subgradient-Based Lagrangian Relaxation

Lagrangian relaxation with subgradient iterations is applied to the problem of optimal restoration of distribution systems after a blackout. The method breaks the restoration horizon into intervals and develops a restoration plan by finding the status of each of the feeders at each time interval. The Lagrangian relaxation approach allows a computationally efficient calculation of the timing and selection of feeders to be energized. The subgradient iterative approach relates to the selection of a vector of Lagrange multipliers in the optimization process. A restoration index obtained from the dual formulation of the problem is also shown. This index identifies the feeders that are closer to restoration. The proposed algorithm applies to radially configured distribution systems and is an operator-permissive, automated approach. Examples are shown including a 100-feeder restoration case.