An S`1LP-Active Set Approach for Feasibility Restoration in Power Systems

We consider power networks in which it is not possible to satisfy all loads at the demand nodes, due to some attack or disturbance to the network. We formulate a model, based on AC power flow equations, to restore the network to feasibility by shedding load at demand nodes, but doing so in a way that minimizes a weighted measure of the total load shed, and affects as few demand nodes as possible. This solution provides guidance to operators on how to minimize the impact of a disruptive event on those served by the grid. Optimization techniques including nonsmooth penalty functions, sequential linear programming, and active set heuristics are used to solve this model. We describe an algorithmic framework and present convergence results, including a superlinear convergence result for the case in which the solution is fully determined by its constraints, a situation that arises frequently in the power systems application.