École Nationale Supérieure de
Techniques Avancées

Abstract

The Optimal Power Flow (OPF) can be formulated as a Quadratically Constrained Quadratic Problem (QCQP). The rank one Semi-Definite Programming (SDP) provides either the optimal solution when there is no duality gap or a tight lower bound. Small-to-medium-sized SDP instances are efficiently solved by Interior Points (IP) state-of-art solvers. Moreover, chordal extension and clique decomposition on the power network graph enable the resolution of large instances. However, some instances still remain unsolvable due to numerical matters: memory issues are handled by clique decomposition but solvers do not succeed to fully achieve convergence. In order to ensure convergence, we propose a column generation algorithm exploiting the decomposed structure coming from cliques. This iterative dual approach involves two stages: resolution of a master problem and resolution of a smaller SDP subproblem for each clique. Stabilization methods such as conic-bundle are used to improve standard column generation efficiency. First computational results on small MATPOWER instances (networks from 2 to 14 buses) are presented. Key-words: large-scale OPF – rank relaxation – large-scale SDP – column generation - conic-bundle