An S$\ell_1$LP-Active Set Approach for Feasibility Restoration in Power Systems

TL;DR

This paper introduces an active set approach based on L1 linear programming to restore power network feasibility after disturbances by optimally shedding load, enabling vulnerability assessment and stress testing.

Contribution

It presents a novel optimization framework combining nonsmooth penalties and active-set heuristics for power system feasibility restoration under attack or disturbance.

Findings

Algorithm achieves quadratic convergence in certain cases

Framework effectively quantifies network vulnerability

Method enables stress testing of power systems

Abstract

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. Besides suggesting an optimal response to a given attack, our approach can be used to quantify disruption, thereby enabling "stress testing" to be performed and vulnerabilities to be identified. 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 quadratic 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.