Branch Flow Model: Relaxations and Convexification—Part I
We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results.
© 2013 IEEE. Open access. Manuscript received May 11, 2012; revised July 22, 2012, November 18, 2012, January 04, 2013, and March 01, 2013; accepted March 03, 2013. Date of publication April 23, 2013; date of current version July 18, 2013. This work was supported by NSF through NetSE grant CNS 0911041, DoE's ARPA-E through grant DE-AR0000226, the National Science Council of Taiwan (R. O. C.) through grant NSC 101-3113-P-008-001, SCE, the Resnick Institute of Caltech, Cisco, and the Okawa Foundation. A preliminary and abridged version has appeared in . Paper no. TPWRS-00424-2012. The authors would like to thank S. Bose, K. M. Chandy, and L. Gan of Caltech; C. Clarke, M. Montoya, and R. Sherick of the Southern California Edison (SCE); and B. Lesieutre ofWisconsin for helpful discussions.
Published - 06507355.pdf
Submitted - 1204.4865v4.pdf