Application of semidefinite optimization techniques to problems in electric power systems

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[1]  Jesse T. Holzer,et al.  Implementation of a Large-Scale Optimal Power Flow Solver Based on Semidefinite Programming , 2013, IEEE Transactions on Power Systems.

[2]  A. Grothey,et al.  Local Solutions of Optimal Power Flow , 2013 .

[3]  Aharon Ben-Tal,et al.  Lectures on modern convex optimization , 1987 .

[4]  Paul A. Trodden,et al.  Local Solutions of the Optimal Power Flow Problem , 2013, IEEE Transactions on Power Systems.

[5]  Franz Rendl,et al.  Semidefinite Relaxations for Integer Programming , 2010, 50 Years of Integer Programming.

[6]  K. M. Nor,et al.  Improved three-phase power-flow methods using sequence components , 2005, IEEE Transactions on Power Systems.

[7]  E. Handschin,et al.  Continuation three-phase power flow: a tool for voltage stability analysis of unbalanced three-phase power systems , 2005, IEEE Transactions on Power Systems.

[8]  J. Baillieul,et al.  Geometric critical point analysis of lossless power system models , 1982 .

[9]  M. Ilić Network theoretic conditions for existence and uniqueness of steady state solutions to electric power circuits , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[10]  H. Chiang,et al.  Impact of generator reactive reserve on structure-induced bifurcation , 2009, IEEE Power & Energy Society General Meeting.

[11]  Timothy A. Davis,et al.  Algorithm 837: AMD, an approximate minimum degree ordering algorithm , 2004, TOMS.

[12]  B. C. Lesieutre,et al.  Counterexample to a Continuation-Based Algorithm for Finding All Power Flow Solutions , 2013, IEEE Transactions on Power Systems.

[13]  I. Hiskens,et al.  Convexity of the set of feasible injections and revenue adequacy in FTR markets , 2005, IEEE Transactions on Power Systems.

[14]  Masakazu Kojima,et al.  Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion , 2011, Math. Program..

[15]  Mulukutla S. Sarma,et al.  Power System Analysis and Design , 1993 .

[16]  Joseph H. Eto,et al.  Cost of Power Interruptions to Electricity Consumers in the United States (U.S.) , 2006 .

[17]  C. W. Taylor Power System Voltage Stability , 1993 .

[18]  Dima Grigoriev,et al.  Complexity of Null-and Positivstellensatz proofs , 2001, Ann. Pure Appl. Log..

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

[20]  Y.-Y. Hong,et al.  Three-phase optimal harmonic power flow , 1996 .

[21]  J. Teng A direct approach for distribution system load flow solutions , 2003 .

[22]  Silvia Lamonaca,et al.  Unbalanced Three-Phase Optimal Power Flow for Smart Grids , 2011, IEEE Transactions on Industrial Electronics.

[23]  Heng Chen Cascaded Stalling of Induction Motors in Fault-Induced Delayed Voltage Recovery (FIDVR) , 2011 .

[24]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[25]  Daniel K. Molzahn,et al.  A Sufficient Condition for Global Optimality of Solutions to the Optimal Power Flow Problem , 2014, IEEE Transactions on Power Systems.

[26]  R.J. Thomas,et al.  On voltage collapse in electric power systems , 1989, Conference Papers Power Industry Computer Application Conference.

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

[28]  B. Lesieutre,et al.  A Sufficient Condition for Power Flow Insolvability With Applications to Voltage Stability Margins , 2012, IEEE Transactions on Power Systems.

[29]  J.R. Marti,et al.  A generalised three-phase power flow method for the initialisation of EMTP simulations , 1998, POWERCON '98. 1998 International Conference on Power System Technology. Proceedings (Cat. No.98EX151).

[30]  Xiaoqing Bai,et al.  A semidefinite programming method with graph partitioning technique for optimal power flow problems , 2011 .

[31]  James S. Thorp,et al.  An efficient algorithm to locate all the load flow solutions , 1993 .

[32]  R. Belmans,et al.  A literature survey of Optimal Power Flow problems in the electricity market context , 2009, 2009 IEEE/PES Power Systems Conference and Exposition.

[33]  M. Pavella,et al.  Direct methods for studying dynamics of large-scale electric power systems - A survey , 1985, Autom..

[34]  Ian Dobson,et al.  Voltage collapse precipitated by the immediate change in stability when generator reactive power limits are encountered , 1992 .

[35]  Venkataramana Ajjarapu,et al.  A practical minimum load shedding strategy to mitigate voltage collapse , 1998 .

[36]  D. Shirmohammadi,et al.  A three-phase power flow method for real-time distribution system analysis , 1995 .

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

[38]  Franz S. Hover,et al.  Conic relaxations for transmission system planning , 2011, 2011 North American Power Symposium.

[39]  Leigh Tesfatsion,et al.  DC Optimal Power Flow Formulation and Solution Using QuadProgJ , 2006 .

[40]  Pravin Varaiya,et al.  Foundations of direct methods for power system transient stability analysis , 1987 .

[41]  J. Gross,et al.  Graph Theory and Its Applications , 1998 .

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

[43]  Hadi Saadat,et al.  Power System Analysis , 1998 .

[44]  Gabriel Valiente,et al.  Algorithms on Trees and Graphs , 2002, Springer Berlin Heidelberg.

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

[46]  Y. Tamura,et al.  A Load Flow Calculation Method for Ill-Conditioned Power Systems , 1981, IEEE Transactions on Power Apparatus and Systems.

[47]  Y. Tamura,et al.  Relationship Between Voltage Instability and Multiple Load FLow Solutions in Electric Power Systems , 1983, IEEE Transactions on Power Apparatus and Systems.

[48]  Johan Löfberg,et al.  Pre- and Post-Processing Sum-of-Squares Programs in Practice , 2009, IEEE Transactions on Automatic Control.

[49]  Daniel K. Molzahn,et al.  Examining the limits of the application of semidefinite programming to power flow problems , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[50]  Thomas J. Overbye,et al.  Improved techniques for power system voltage stability assessment using energy methods , 1991 .

[51]  V. Venkatasubramanian,et al.  Complementary limit induced bifurcation theorem and analysis of Q limits in power-flow studies , 2007, 2007 iREP Symposium - Bulk Power System Dynamics and Control - VII. Revitalizing Operational Reliability.

[52]  I. Dobson,et al.  New methods for computing a closest saddle node bifurcation and worst case load power margin for voltage collapse , 1993 .

[53]  P. Damrongkulkamjorn,et al.  Security-constrained unit commitment using Mixed-Integer Programming with Benders Decomposition , 2010, ECTI-CON2010: The 2010 ECTI International Confernce on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology.

[54]  Thomas J. Overbye,et al.  A new method for finding low-voltage power flow solutions , 2000, 2000 Power Engineering Society Summer Meeting (Cat. No.00CH37134).

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

[56]  Jan M. Maciejowski,et al.  An efficient algorithm for mixed integer semidefinite optimisation , 2003, Proceedings of the 2003 American Control Conference, 2003..

[57]  Javad Lavaei,et al.  Geometry of power flows in tree networks , 2012, 2012 IEEE Power and Energy Society General Meeting.

[58]  Daniel K. Molzahn,et al.  Sufficient conditions for power flow insolvability considering reactive power limited generators with applications to voltage stability margins , 2013, 2013 IREP Symposium Bulk Power System Dynamics and Control - IX Optimization, Security and Control of the Emerging Power Grid.

[59]  Shuai Lu,et al.  Load modeling and calibration techniques for power system studies , 2011, 2011 North American Power Symposium.

[60]  David Tse,et al.  Distributed algorithms for optimal power flow problem , 2011, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[61]  Chao Yang,et al.  Severe Multiple Contingency Screening in Electric Power Systems , 2008, IEEE Transactions on Power Systems.

[62]  R. Seydel Practical bifurcation and stability analysis : from equilibrium to chaos , 1994 .

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

[64]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[65]  Brian Borchers,et al.  Implementation of a primal–dual method for SDP on a shared memory parallel architecture , 2007, Comput. Optim. Appl..

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

[67]  R. Kellogg,et al.  Pathways to solutions, fixed points, and equilibria , 1983 .

[68]  S. Grijalva,et al.  Individual Branch and Path Necessary Conditions for Saddle-Node Bifurcation Voltage Collapse , 2012, IEEE Transactions on Power Systems.

[69]  Steven H. Low,et al.  Branch Flow Model: Relaxations and Convexification—Part II , 2012 .

[70]  Chen-Sung Chang,et al.  Toward a CPFLOW-based algorithm to compute all the type-1 load-flow solutions in electric power systems , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[72]  J. Yorke,et al.  Finding zeroes of maps: homotopy methods that are constructive with probability one , 1978 .

[73]  Rs Stainton,et al.  Pathways to solutions , 1984 .

[74]  Weimin Ma Dynamical systems analysis in electric power systems , 1991 .

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

[76]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[77]  Daniel Kuhn,et al.  A cutting-plane method for Mixed-Logical Semidefinite Programs with an application to multi-vehicle robust path planning , 2010, 49th IEEE Conference on Decision and Control (CDC).

[78]  F. Alvarado,et al.  Computation of closest bifurcations in power systems , 1994 .

[79]  Venkataramana Ajjarapu,et al.  The continuation power flow: a tool for steady state voltage stability analysis , 1991 .

[80]  L. Ni,et al.  Parallel processing for the load flow of power systems: the approach and applications , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[81]  Thierry Van Cutsem,et al.  Voltage Stability of Electric Power Systems , 1998 .

[82]  V. A. Venikov,et al.  Estimation of electrical power system steady-state stability in load flow calculations , 1975, IEEE Transactions on Power Apparatus and Systems.

[83]  Luis Rouco,et al.  A power flow solvability identification and calculation algorithm , 2006 .

[84]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[85]  T. Overbye A power flow measure for unsolvable cases , 1994 .

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

[87]  S. Granville,et al.  Application of interior point methods to power flow unsolvability , 1996 .

[88]  Daniel K. Molzahn,et al.  Investigation of Non-zero Duality Gap Solutions to a Semidefinite Relaxation of the Optimal Power Flow Problem , 2014, 2014 47th Hawaii International Conference on System Sciences.

[89]  P. Ju,et al.  Evaluation of methods for measuring the insolvability of power flow , 2008, 2008 Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies.

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

[91]  S. A. Naqavi,et al.  Load flow fractals , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[92]  M. Ferris,et al.  Optimal Transmission Switching , 2008, IEEE Transactions on Power Systems.

[93]  Robert E. Tarjan,et al.  Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1984, SIAM J. Comput..

[94]  B. Lesieutre,et al.  Approximate Representation of ZIP Loads in a Semidefinite Relaxation of the OPF Problem , 2014, IEEE Transactions on Power Systems.

[95]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

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

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

[98]  D. Kosterev,et al.  Load modeling in power system studies: WECC progress update , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[99]  Makoto Yamashita,et al.  Latest Developments in the SDPA Family for Solving Large-Scale SDPs , 2012 .

[100]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[101]  Leon O. Chua,et al.  Linear and nonlinear circuits , 1987 .

[102]  Georgios B. Giannakis,et al.  Economic Dispatch in Unbalanced Distribution Networks via Semidefinite Relaxation , 2012, 1207.0048.

[103]  J. F. Dorsey,et al.  A test for the existence of solutions in ill-conditioned power systems , 1991, IEEE Proceedings of the SOUTHEASTCON '91.

[104]  Georgios B. Giannakis,et al.  Distributed Optimal Power Flow for Smart Microgrids , 2012, IEEE Transactions on Smart Grid.

[105]  I. Hiskens,et al.  Exploring the Power Flow Solution Space Boundary , 2001, IEEE Power Engineering Review.