Polynomial SDP cuts for Optimal Power Flow

摘要: The use of convex relaxations has lately gained considerable interest in Power Systems. These play a major role providing quality guarantees for non-convex optimization problems. For the Optimal Flow (OPF) problem, semidefinite programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from lack scalability. In this work, we introduce an exact reformulation relaxation, formed by set polynomial constraints defined space real variables. new can be seen as “cuts”, strengthening weaker second-order cone relaxations, and generated lazy iterative fashion. formulation handled standard nonlinear solvers, enjoying better stability computational efficiency. This approach benefits recent results on tree-decomposition methods, reducing dimension underlying matrices. As side result, present Kirchhoff's Voltage Law reveal existing link between these cycle original three dimensional Preliminary show significant gain efficiency compared solver approach.