Optimal Power Flow for radial and mesh grids using semidefinite programming

Oscar D. Montoya-Giraldo, Walter J. Gil-González, Alejandro Garcés-Ruíz


This paper presents a convex formulation for optimal power flow (OPF) in both radial and meshed grids. A semidefinite programming (SDP) approximation transforms the quadratic non-convex model into a relaxed convex quadratic model, which can be more efficiently solved. This model is implemented in MATLAB using the CVX package for convex optimization. The results obtained are compared to the non-linear model of the problem implemented in GAMS and MATPOWER by using four typical systems in specialized literature (two radial and two meshed). SDP approximation demonstrated to provide accurate solutions that are close to an optimal solution of the problem in shorter computational times. Such solutions are applicable to real-time operation and control problems.


Convex approximation power flow; optimal power flow; semidefinite programming; radial grids; mesh grids.

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