Zero Duality Gap in Optimal Power Flow Problem

Citations Over TimeTop 1% of 2011 papers

Abstract

The optimal power flow (OPF) problem is nonconvex and generally hard to solve. In this paper, we propose a semidefinite programming (SDP) optimization, which is the dual of an equivalent form of the OPF problem. A global optimum solution to the OPF problem can be retrieved from a solution of this convex dual problem whenever the duality gap is zero. A necessary and sufficient condition is provided in this paper to guarantee the existence of no duality gap for the OPF problem. This condition is satisfied by the standard IEEE benchmark systems with 14, 30, 57, 118, and 300 buses as well as several randomly generated systems. Since this condition is hard to study, a sufficient zero-duality-gap condition is also derived. This sufficient condition holds for IEEE systems after small resistance (10 -5 per unit) is added to every transformer that originally assumes zero resistance. We investigate this sufficient condition and justify that it holds widely in practice. The main underlying reason for the successful convexification of the OPF problem can be traced back to the modeling of transformers and transmission lines as well as the non-negativity of physical quantities such as resistance and inductance.

Related Papers

• → Stable zero duality gaps in convex programming: Complete dual characterisations with applications to semidefinite programs(2009)31 cited
• → Robust duality for the uncertain multitime control optimization problems(2022)16 cited
• → Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap(2017)8 cited
• → Strong duality in optimization: shifted power reformulation(2015)4 cited
• → Universal duality in conic convex optimization(2006)8 cited