Polynomial SDP cuts for Optimal Power Flow

Hassan Hijazi, Carleton Coffrin, Pascal Van Hentenryck
2016 2016 Power Systems Computation Conference (PSCC)  
The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing quality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF) problem, the semidefinite programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from a lack of scalability. In this work, we introduce an exact reformulation of the SDP relaxation, formed by a set of polynomial
more » ... ints defined in the space of real variables. The new constraints can be seen as "cuts", strengthening weaker second-order cone relaxations, and can be generated in a lazy iterative fashion. The new formulation can be handled by standard nonlinear programming solvers, enjoying better stability and computational efficiency. This new approach benefits from recent results on tree-decomposition methods, reducing the dimension of the underlying SDP matrices. As a side result, we present a formulation of Kirchhoff's Voltage Law in the SDP space and reveal the existing link between these cycle constraints and the original SDP relaxation for three dimensional matrices. Preliminary results show a significant gain in computational efficiency compared to a standard SDP solver approach.
doi:10.1109/pscc.2016.7540908 dblp:conf/pscc/HijaziCH16 fatcat:tikylatj6rccbdxd3pmtlwr2yq