Convex relaxation of optimal power flow: A tutorial

This is a short survey of recent advances in the convex relaxation of the optimal power flow problem. Our focus is on understanding structural properties, especially the underlying convexity structure, of optimal power flow problems rather than different computational algorithms.

[1]  D. R. Fulkerson,et al.  Incidence matrices and interval graphs , 1965 .

[2]  William F. Tinney,et al.  Optimal Power Flow Solutions , 1968 .

[3]  O. Alsac,et al.  Fast Decoupled Load Flow , 1974 .

[4]  Robert E. Tarjan,et al.  Algorithmic Aspects of Vertex Elimination on Graphs , 1976, SIAM J. Comput..

[5]  Charles R. Johnson,et al.  Positive definite completions of partial Hermitian matrices , 1984 .

[6]  M. E. Baran,et al.  Optimal capacitor placement on radial distribution systems , 1989 .

[7]  M. E. Baran,et al.  Optimal sizing of capacitors placed on a radial distribution system , 1989 .

[8]  R. G. Cespedes,et al.  New method for the analysis of distribution networks , 1990 .

[9]  Hsiao-Dong Chiang,et al.  On the existence and uniqueness of load flow solution for radial distribution power networks , 1990 .

[10]  B. Stott,et al.  Further developments in LP-based optimal power flow , 1990 .

[11]  H. Chiang A decoupled load flow method for distribution power networks: algorithms, analysis and convergence study , 1991 .

[12]  Francisco D. Galiana,et al.  A survey of the optimal power flow literature , 1991 .

[13]  Yves Colin de Verdière,et al.  Multiplicities of Eigenvalues and Tree-Width of Graphs , 1998, J. Comb. Theory B.

[14]  Stephen P. Boyd,et al.  Applications of second-order cone programming , 1998 .

[15]  R. Adapa,et al.  A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches , 1999 .

[16]  A. G. Expósito,et al.  Reliable load flow technique for radial distribution networks , 1999 .

[17]  R. Adapa,et al.  A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods , 1999 .

[18]  J. Momoh Electric Power System Applications of Optimization , 2000 .

[19]  Henry Wolkowicz,et al.  Handbook of Semidefinite Programming , 2000 .

[20]  Deqiang Gan,et al.  Stability-constrained optimal power flow , 2000 .

[21]  R. Saigal,et al.  Handbook of semidefinite programming : theory, algorithms, and applications , 2000 .

[22]  Shuzhong Zhang,et al.  Quadratic maximization and semidefinite relaxation , 2000, Math. Program..

[23]  Kazuo Murota,et al.  Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework , 2000, SIAM J. Optim..

[24]  J.A. Momoh Mini Cogeneration Schemes in Mexico , 2001, IEEE Power Engineering Review.

[25]  Katsuki Fujisawa,et al.  Exploiting sparsity in semidefinite programming via matrix completion II: implementation and numerical results , 2003, Math. Program..

[26]  Charles R. Johnson,et al.  On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph , 2003 .

[27]  Hein van der Holst,et al.  Graphs whose positive semi-definite matrices have nullity at most two , 2003 .

[28]  Masakazu Kojima,et al.  Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations , 2003, Comput. Optim. Appl..

[29]  R. Belmans,et al.  Usefulness of DC power flow for active power flow analysis , 2005, IEEE Power Engineering Society General Meeting, 2005.

[30]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[31]  R. Jabr Radial distribution load flow using conic programming , 2006, IEEE Transactions on Power Systems.

[32]  R. Jabr,et al.  A Conic Quadratic Format for the Load Flow Equations of Meshed Networks , 2007, IEEE Transactions on Power Systems.

[33]  K. Fujisawa,et al.  Semidefinite programming for optimal power flow problems , 2008 .

[34]  K. Pandya,et al.  A SURVEY OF OPTIMAL POWER FLOW , 2008 .

[35]  Xiaoqing Bai,et al.  Semi-definite programming-based method for security-constrained unit commitment with operational and optimal power flow constraints , 2009 .

[36]  O. Alsaç,et al.  DC Power Flow Revisited , 2009, IEEE Transactions on Power Systems.

[37]  David Tse,et al.  Geometry of feasible injection region of power networks , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[38]  Javad Lavaei,et al.  Power flow optimization using positive quadratic programming , 2011 .

[39]  Joshua A. Taylor,et al.  Conic optimization of electric power systems , 2011 .

[40]  K. Mani Chandy,et al.  Inverter VAR control for distribution systems with renewables , 2011, 2011 IEEE International Conference on Smart Grid Communications (SmartGridComm).

[41]  K. Mani Chandy,et al.  Optimal power flow over tree networks , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[42]  R. Jabr Exploiting Sparsity in SDP Relaxations of the OPF Problem , 2012, IEEE Transactions on Power Systems.

[43]  M. B. Cain,et al.  History of Optimal Power Flow and Formulations , 2012 .

[44]  F. S. Hover,et al.  Convex Models of Distribution System Reconfiguration , 2012, IEEE Transactions on Power Systems.

[45]  K. Mani Chandy,et al.  Equivalence of branch flow and bus injection models , 2012, 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[46]  David Tse,et al.  Optimal Distributed Voltage Regulation in Power Distribution Networks , 2012, ArXiv.

[47]  Steffen Rebennack,et al.  Optimal power flow: a bibliographic survey I , 2012, Energy Systems.

[48]  S. Low,et al.  Zero Duality Gap in Optimal Power Flow Problem , 2012, IEEE Transactions on Power Systems.

[49]  Steffen Rebennack,et al.  Optimal power flow: a bibliographic survey II , 2012, Energy Systems.

[50]  J. Lavaei,et al.  Physics of power networks makes hard optimization problems easy to solve , 2012, 2012 IEEE Power and Energy Society General Meeting.

[51]  Na Li,et al.  Exact convex relaxation of OPF for radial networks using branch flow model , 2012, 2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm).

[52]  Ufuk Topcu,et al.  On the exactness of convex relaxation for optimal power flow in tree networks , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[53]  Na Li,et al.  Distributed Optimization in Power Networks and General Multi-agent Systems , 2013 .

[54]  David Tse,et al.  Geometry of injection regions of power networks , 2011, IEEE Transactions on Power Systems.

[55]  Ufuk Topcu,et al.  Exact convex relaxation for optimal power flow in distribution networks , 2013, SIGMETRICS '13.

[56]  Steven H. Low,et al.  Optimal Power Flow in Direct Current Networks , 2013, IEEE Transactions on Power Systems.

[57]  Branch flow model: Relaxations and convexification , 2014, 2014 IEEE PES T&D Conference and Exposition.

[58]  Javad Lavaei,et al.  Geometry of Power Flows and Optimization in Distribution Networks , 2012, IEEE Transactions on Power Systems.

[59]  K. Mani Chandy,et al.  Quadratically Constrained Quadratic Programs on Acyclic Graphs With Application to Power Flow , 2012, IEEE Transactions on Control of Network Systems.

[60]  Babak Hassibi,et al.  Equivalent Relaxations of Optimal Power Flow , 2014, IEEE Transactions on Automatic Control.