Convex quadratic relaxations for mixed-integer nonlinear programs in power systems

Hijazi, Hassan Lionel; Coffrin, Carleton James; Hentenryck, Pascal Van

doi:10.1007/s12532-016-0112-z

Title: Convex quadratic relaxations for mixed-integer nonlinear programs in power systems

Abstract

Here, this paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semidefinite programming relaxations. Finally, three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations.

Authors:

^[1];

^[2]; Hentenryck, Pascal Van ^[3]

The Australian National University, Canberra (Australia)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Michigan, Ann Arbor, MI (United States)

Publication Date:: Sat Oct 15 00:00:00 EDT 2016

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1469547

Report Number(s):: LA-UR-18-21065
Journal ID: ISSN 1867-2949

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Mathematical Programming Computation

Additional Journal Information:: Journal Volume: 9; Journal Issue: 3; Journal ID: ISSN 1867-2949

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Mixed-integer nonlinear programming; Global optimization; Convex relaxation; Optimal power flow; Optimal transmission switching; Capacitor placement

Citation Formats


                    Hijazi, Hassan Lionel, Coffrin, Carleton James, and Hentenryck, Pascal Van. Convex quadratic relaxations for mixed-integer nonlinear programs in power systems.  United States: N. p., 2016. 
Web.  doi:10.1007/s12532-016-0112-z.

Copy to clipboard


                    Hijazi, Hassan Lionel, Coffrin, Carleton James, & Hentenryck, Pascal Van. Convex quadratic relaxations for mixed-integer nonlinear programs in power systems.  United States.  https://doi.org/10.1007/s12532-016-0112-z

Copy to clipboard


                    Hijazi, Hassan Lionel, Coffrin, Carleton James, and Hentenryck, Pascal Van. Sat .  
"Convex quadratic relaxations for mixed-integer nonlinear programs in power systems".  United States.  https://doi.org/10.1007/s12532-016-0112-z.  https://www.osti.gov/servlets/purl/1469547.

Copy to clipboard


                    
@article{osti_1469547,

  title        = {Convex quadratic relaxations for mixed-integer nonlinear programs in power systems},

  author       = {Hijazi, Hassan Lionel and Coffrin, Carleton James and Hentenryck, Pascal Van},

  abstractNote = {Here, this paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semidefinite programming relaxations. Finally, three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations.},

  doi          = {10.1007/s12532-016-0112-z},

  journal      = {Mathematical Programming Computation},

  number       = 3,

  volume       = 9,

  place        = {United States},

  year         = {Sat Oct 15 00:00:00 EDT 2016},

  month        = {Sat Oct 15 00:00:00 EDT 2016}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/s12532-016-0112-z

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

AMPL: A Mathematical Programing Language
book, January 1989

Fourer, Robert; Gay, David M.; Kernighan, Brian W.
Algorithms and Model Formulations in Mathematical Programming
DOI: 10.1007/978-3-642-83724-1_12

Radial Distribution Load Flow Using Conic Programming
journal, August 2006

Jabr, R.A.
IEEE Transactions on Power Systems, Vol. 21, Issue 3, p. 1458-1459
DOI: 10.1109/TPWRS.2006.879234

Optimal capacitor placement on radial distribution systems
journal, January 1989

Baran, M. E.; Wu, F. F.
IEEE Transactions on Power Delivery, Vol. 4, Issue 1
DOI: 10.1109/61.19265

Worst-Case Interdiction Analysis of Large-Scale Electric Power Grids
journal, February 2009

Salmeron, Javier; Wood, Kevin; Baldick, Ross
IEEE Transactions on Power Systems, Vol. 24, Issue 1
DOI: 10.1109/TPWRS.2008.2004825

YALMIP : a toolbox for modeling and optimization in MATLAB
conference, January 2004

Lofberg, J.
2004 IEEE International Symposium on Computer Aided Control Systems Design, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508)
DOI: 10.1109/CACSD.2004.1393890

Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
journal, December 1976

McCormick, Garth P.
Mathematical Programming, Vol. 10, Issue 1
DOI: 10.1007/BF01580665

Optimal Transmission Switching With Contingency Analysis
journal, August 2009

Hedman, K. W.; O'Neill, R. P.; Fisher, E. B.
IEEE Transactions on Power Systems, Vol. 24, Issue 3
DOI: 10.1109/TPWRS.2009.2020530

Analysis of Electric Grid Security Under Terrorist Threat
journal, May 2004

Salmeron, J.; Wood, K.; Baldick, R.
IEEE Transactions on Power Systems, Vol. 19, Issue 2
DOI: 10.1109/TPWRS.2004.825888

Using mixed-integer programming to solve power grid blackout problems
journal, March 2007

Bienstock, Daniel; Mattia, Sara
Discrete Optimization, Vol. 4, Issue 1
DOI: 10.1016/j.disopt.2006.10.007

Mixed-integer nonlinear programs featuring “on/off” constraints
journal, August 2011

Hijazi, Hassan; Bonami, Pierre; Cornuéjols, Gérard
Computational Optimization and Applications, Vol. 52, Issue 2
DOI: 10.1007/s10589-011-9424-0

Solving the capacitor placement problem in a radial distribution system using Tabu Search approach
journal, January 1996

Yann-Chang Huang,
IEEE Transactions on Power Systems, Vol. 11, Issue 4
DOI: 10.1109/59.544656

Convex Models of Distribution System Reconfiguration
journal, February 2012

Taylor, Joshua A.; Hover, Franz S.
IEEE Transactions on Power Systems, Vol. 27, Issue 3, p. 1407-1413
DOI: 10.1109/TPWRS.2012.2184307

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems
journal, December 2011

Ruiz, Juan P.; Grossmann, Ignacio E.
Computers & Chemical Engineering, Vol. 35, Issue 12
DOI: 10.1016/j.compchemeng.2011.01.035

Zero Duality Gap in Optimal Power Flow Problem
journal, February 2012

Lavaei, Javad; Low, Steven H.
IEEE Transactions on Power Systems, Vol. 27, Issue 1
DOI: 10.1109/TPWRS.2011.2160974

Trilinear Monomials with Positive or Negative Domains: Facets of the Convex and Concave Envelopes
book, January 2004

Meyer, C. A.; Floudas, C. A.
Frontiers in Global Optimization. Nonconvex Optimization and Its Applications
DOI: 10.1007/978-1-4613-0251-3_18

Reduction constraints for the global optimization of NLPs
journal, January 2004

Liberti, Leo
International Transactions in Operational Research, Vol. 11, Issue 1
DOI: 10.1111/j.1475-3995.2004.00438.x

Linear Relaxations for Transmission System Planning
journal, November 2011

Taylor, Joshua A.; Hover, Franz S.
IEEE Transactions on Power Systems, Vol. 26, Issue 4
DOI: 10.1109/TPWRS.2011.2145395

Strategic stockpiling of power system supplies for disaster recovery
conference, July 2011

Coffrin, Carleton; Van Hentenryck, Pascal; Bent, Russell
2011 IEEE Power & Energy Society General Meeting, 2011 IEEE Power and Energy Society General Meeting
DOI: 10.1109/PES.2011.6039414

Physics of power networks makes hard optimization problems easy to solve
conference, July 2012

Sojoudi, S.; Lavaei, J.
2012 IEEE Power & Energy Society General Meeting. New Energy Horizons - Opportunities and Challenges, 2012 IEEE Power and Energy Society General Meeting
DOI: 10.1109/PESGM.2012.6345272

Convex Relaxation for Optimal Power Flow Problem: Mesh Networks
journal, January 2015

Madani, Ramtin; Sojoudi, Somayeh; Lavaei, Javad
IEEE Transactions on Power Systems, Vol. 30, Issue 1
DOI: 10.1109/TPWRS.2014.2322051

Semidefinite programming for optimal power flow problems
journal, July 2008

Bai, Xiaoqing; Wei, Hua; Fujisawa, Katsuki
International Journal of Electrical Power & Energy Systems, Vol. 30, Issue 6-7, p. 383-392
DOI: 10.1016/j.ijepes.2007.12.003

An algorithmic framework for convex mixed integer nonlinear programs
journal, May 2008

Bonami, Pierre; Biegler, Lorenz T.; Conn, Andrew R.
Discrete Optimization, Vol. 5, Issue 2
DOI: 10.1016/j.disopt.2006.10.011

A Linear-Programming Approximation of AC Power Flows
journal, November 2014

Coffrin, Carleton; Van Hentenryck, Pascal
INFORMS Journal on Computing, Vol. 26, Issue 4
DOI: 10.1287/ijoc.2014.0594

Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow
journal, April 2012

Phan, Dzung T.
Operations Research, Vol. 60, Issue 2
DOI: 10.1287/opre.1110.1036

Optimal capacitor placement using deterministic and genetic algorithms
journal, January 2000

Delfanti, M.; Granelli, G. P.; Marannino, P.
IEEE Transactions on Power Systems, Vol. 15, Issue 3
DOI: 10.1109/59.871731

SCIP: solving constraint integer programs
journal, January 2009

Achterberg, Tobias
Mathematical Programming Computation, Vol. 1, Issue 1
DOI: 10.1007/s12532-008-0001-1

DC Power Flow Revisited
journal, August 2009

Stott, B.; Jardim, J.; Alsac, O.
IEEE Transactions on Power Systems, Vol. 24, Issue 3
DOI: 10.1109/TPWRS.2009.2021235

A non-incremental model for optimal control of reactive power flow
journal, November 1996

Wang, Zhuding; Peng, Du; Feng, Qishan
Electric Power Systems Research, Vol. 39, Issue 2
DOI: 10.1016/S0378-7796(96)01112-1

A comparison of the AC and DC power flow models for LMP calculations
conference, January 2004

Overbye, T. J.
37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the
DOI: 10.1109/HICSS.2004.1265164

Inverter VAR control for distribution systems with renewables
conference, October 2011

Farivar, Masoud; Clarke, Christopher R.; Low, Steven H.
DOI: 10.1109/SmartGridComm.2011.6102366

Optimal reactive power planning using evolutionary algorithms: a comparative study for evolutionary programming, evolutionary strategy, genetic algorithm, and linear programming
journal, January 1998

Lee, K. Y.; Yang, F. F.
IEEE Transactions on Power Systems, Vol. 13, Issue 1
DOI: 10.1109/59.651620

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments
journal, January 2010

Bienstock, Daniel; Verma, Abhinav
SIAM Journal on Optimization, Vol. 20, Issue 5
DOI: 10.1137/08073562X

Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes
journal, June 2004

Meyer, Clifford A.; Floudas, Christodoulos A.
Journal of Global Optimization, Vol. 29, Issue 2
DOI: 10.1023/B:JOGO.0000042112.72379.e6

MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education
journal, February 2011

Zimmerman, Ray Daniel; Murillo-Sanchez, Carlos Edmundo; Thomas, Robert John
IEEE Transactions on Power Systems, Vol. 26, Issue 1
DOI: 10.1109/TPWRS.2010.2051168

Transmission Switching in Security-Constrained Unit Commitment
journal, November 2010

Khodaei, Amin; Shahidehpour, Mohammad
IEEE Transactions on Power Systems, Vol. 25, Issue 4
DOI: 10.1109/TPWRS.2010.2046344

Optimal Transmission Switching
journal, August 2008

Fisher, E. B.; O'Neill, R. P.; Ferris, M. C.
IEEE Transactions on Power Systems, Vol. 23, Issue 3
DOI: 10.1109/TPWRS.2008.922256

Perspective reformulations of mixed integer nonlinear programs with indicator variables
journal, May 2010

Günlük, Oktay; Linderoth, Jeff
Mathematical Programming, Vol. 124, Issue 1-2
DOI: 10.1007/s10107-010-0360-z

SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
journal, January 1999

Toh, K. C.; Todd, M. J.; Tütüncü, R. H.
Optimization Methods and Software, Vol. 11, Issue 1-4
DOI: 10.1080/10556789908805762

Jointly Constrained Biconvex Programming
journal, May 1983

Al-Khayyal, Faiz A.; Falk, James E.
Mathematics of Operations Research, Vol. 8, Issue 2
DOI: 10.1287/moor.8.2.273

Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem
journal, March 2016

Madani, Ramtin; Ashraphijuo, Morteza; Lavaei, Javad
IEEE Transactions on Power Systems, Vol. 31, Issue 2
DOI: 10.1109/TPWRS.2015.2411391

A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods
journal, January 1999

Momoh, J. A.; El-Hawary, M. E.; Adapa, R.
IEEE Transactions on Power Systems, Vol. 14, Issue 1
DOI: 10.1109/59.744495

A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches
journal, January 1999

Momoh, J. A.; Adapa, R.; El-Hawary, M. E.
IEEE Transactions on Power Systems, Vol. 14, Issue 1
DOI: 10.1109/59.744492

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
journal, April 2005

Wächter, Andreas; Biegler, Lorenz T.
Mathematical Programming, Vol. 106, Issue 1
DOI: 10.1007/s10107-004-0559-y

Convex relaxation for optimal power flow problem: Mesh networks
conference, November 2013

Madani, Ramtin; Sojoudi, Somayeh; Lavaei, Javad
2013 Asilomar Conference on Signals, Systems and Computers
DOI: 10.1109/acssc.2013.6810520

Strategic planning for power system restoration
report, November 2011

Bent, Russell W.; Coffrin, Carleton; Van Hentenryck, Pascal
DOI: 10.2172/1119647

Strategic Planning for Power System Restoration
conference, April 2012

Coffrin, Carleton; Van Hentenryck, Pascal; Bent, Russell
First International Symposium on Uncertainty Modeling and Analysis and Management (ICVRAM 2011); and Fifth International Symposium on Uncertainty Modeling and Anaylsis (ISUMA), Vulnerability, Uncertainty, and Risk
DOI: 10.1061/41170(400)22

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs
text, January 2005

Bonami, Pierre; Biegler, Lorenz; Conn, Andrew
Carnegie Mellon University
DOI: 10.1184/r1/6466718

Promises of conic relaxation for contingency-constrained optimal power flow problem
conference, September 2014

Madani, Ramtin; Ashraphijuo, Morteza; Lavaei, Javad
2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
DOI: 10.1109/allerton.2014.7028573

Optimal capacitor placement using deterministic and genetic algorithms
conference, January 1999

Delfanti, M.; Granelli, G. P.; Marannino, P.
PICA'99 - Power Industry Computer Applications Conference, Proceedings of the 21st International Conference on Power Industry Computer Applications. Connecting Utilities. PICA 99. To the Millennium and Beyond (Cat. No.99CH36351)
DOI: 10.1109/pica.1999.779515

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems
text, January 2018

Ruiz, Juan P.; Grossmann, Ignacio E.
Figshare
DOI: 10.1184/r1/6467621

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs
text, January 2006

Bonami, Pierre; Biegler, Lorenz T.; Conn, Andrew R.
Carnegie Mellon University
DOI: 10.1184/r1/6703619

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems
text, January 2018

Ruiz, Juan P.; Grossmann, Ignacio E.
Figshare
DOI: 10.1184/r1/6467621.v1

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs
text, January 2006

Bonami, Pierre; Biegler, Lorenz T.; Conn, Andrew R.
Carnegie Mellon University
DOI: 10.1184/r1/6703619.v1

A Linear-Programming Approximation of AC Power Flows
preprint, January 2012

Coffrin, Carleton; Van Hentenryck, Pascal
arXiv
DOI: 10.48550/arxiv.1206.3614

Works referencing / citing this record:

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations
journal, November 2018

Bynum, Michael; Castillo, Anya; Watson, Jean‐Paul
AIChE Journal, Vol. 65, Issue 7
DOI: 10.1002/aic.16508

Probabilistic N - k failure-identification for power systems
journal, January 2018

Sundar, Kaarthik; Coffrin, Carleton; Nagarajan, Harsha
Networks, Vol. 71, Issue 3
DOI: 10.1002/net.21806

Small and strong formulations for unions of convex sets from the Cayley embedding
journal, March 2018

Vielma, Juan Pablo
Mathematical Programming, Vol. 177, Issue 1-2
DOI: 10.1007/s10107-018-1258-4

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs
journal, January 2019

Nagarajan, Harsha; Lu, Mowen; Wang, Site
Journal of Global Optimization, Vol. 74, Issue 4
DOI: 10.1007/s10898-018-00734-1

A convex relaxation approach for power flow problem
journal, April 2019

Manshadi, Saeed D.; Liu, Guangyi; Khodayar, Mohammad E.
Journal of Modern Power Systems and Clean Energy, Vol. 7, Issue 6
DOI: 10.1007/s40565-019-0525-6

Network transition security for transmission switching
journal, September 2019

Tian, Shijun; Wang, Xifan; Wang, Xiuli
Journal of Modern Power Systems and Clean Energy, Vol. 7, Issue 5
DOI: 10.1007/s40565-019-0562-1

Probabilistic $N$-$k$ Failure-Identification for Power Systems
text, January 2017

Sundar, Kaarthik; Coffrin, Carleton; Nagarajan, Harsha
arXiv
DOI: 10.48550/arxiv.1704.05391

An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs
preprint, January 2017

Nagarajan, Harsha; Lu, Mowen; Wang, Site
arXiv
DOI: 10.48550/arxiv.1707.02514

Similar Records in DOE PAGES and OSTI.GOV collections:

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

Journal Article Bestuzheva, Ksenia ; Hijazi, Hassan Lionel ; Coffrin, Carleton James - INFORMS Journal on Computing

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. Next, we introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmarkmore »« less
https://doi.org/10.1287/ijoc.2019.0900

Full Text Available
Mixed Integer Nonlinear Programming Approaches to Enhance Resiliency and Response Strategies in Critical Infrastructure

Technical Report Bynum, M. ; Castillo, A. ; Knueven, B. ; ...

Motivation. Critical infrastructures are large, complex engineered systems that must be operated robustly under abnormal conditions resulting from natural hazards or intentional acts. For example, electric power systems must be robust to line faults, water utilities must rapidly mitigate contamination incidents, and computing networks must adapt to adversarial intrusions to protect critical information. Problem. It is difficult for decision-makers within resiliency analysis in critical infrastructure to optimize designs and develop effective response strategies that can account for uncertainties. Facing incomplete information and the sheer scope that a natural hazard or attack vector may incorporate, response can be ineffective without reliable,more »« less
https://doi.org/10.2172/1763233

Full Text Available
Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

Journal Article Dias, Fernando H. C. ; Hijazi, Hassan Lionel ; Rey, David - European Journal of Operational Research

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either alwaysmore »« less
https://doi.org/10.1016/j.ejor.2021.03.059

Full Text Available
Polyhedral approximation in mixed-integer convex optimization

Journal Article Lubin, Miles ; Yamangil, Emre ; Bent, Russell Whitford ; ... - Mathematical Programming

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. Here, we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class. Our approach is based on constructing polyhedral outer approximations of the convex constraints, resulting in a global solution by solving a finite number of mixed-integer linear and continuous convex subproblems. The key advance we present is to strengthen the polyhedral approximations by constructing them in a higher-dimensional space. In order tomore »« less
Cited by 27
https://doi.org/10.1007/s10107-017-1191-y

Full Text Available
An L$$_0$$L$$_1$$-norm compressive sensing paradigm for the construction of sparse predictive lattice models using mixed integer quadratic programming

Journal Article Huang, W ; Urban, A ; Xiao, P ; ... - arXiv.org Repository

First-principles based lattice models allow the modeling of ab initio thermodynamics of crystalline mixtures for applications such as the construction of phase diagrams and the identification of ground state atomic orderings. The recent development of compressive sensing approaches for the construction of lattice models has further enabled the systematic construction of sparse physical models without the need for human intuition other than requiring the compactness of effective cluster interactions. However, conventional compressive sensing based on L1-norm regularization is strictly only applicable to certain classes of optimization problems and is otherwise not guaranteed to generate optimally sparse and transferable results, somore »« less
Full Text Available

Similar Records

Title: Convex quadratic relaxations for mixed-integer nonlinear programs in power systems

Abstract

Citation Formats

AMPL: A Mathematical Programing Language book, January 1989

Radial Distribution Load Flow Using Conic Programming journal, August 2006

Optimal capacitor placement on radial distribution systems journal, January 1989

Worst-Case Interdiction Analysis of Large-Scale Electric Power Grids journal, February 2009

YALMIP : a toolbox for modeling and optimization in MATLAB conference, January 2004

Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems journal, December 1976

Optimal Transmission Switching With Contingency Analysis journal, August 2009

Analysis of Electric Grid Security Under Terrorist Threat journal, May 2004

Using mixed-integer programming to solve power grid blackout problems journal, March 2007

Mixed-integer nonlinear programs featuring “on/off” constraints journal, August 2011

Solving the capacitor placement problem in a radial distribution system using Tabu Search approach journal, January 1996

Convex Models of Distribution System Reconfiguration journal, February 2012

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems journal, December 2011

Zero Duality Gap in Optimal Power Flow Problem journal, February 2012

Trilinear Monomials with Positive or Negative Domains: Facets of the Convex and Concave Envelopes book, January 2004

Reduction constraints for the global optimization of NLPs journal, January 2004

Linear Relaxations for Transmission System Planning journal, November 2011

Strategic stockpiling of power system supplies for disaster recovery conference, July 2011

Physics of power networks makes hard optimization problems easy to solve conference, July 2012

Convex Relaxation for Optimal Power Flow Problem: Mesh Networks journal, January 2015

Semidefinite programming for optimal power flow problems journal, July 2008

An algorithmic framework for convex mixed integer nonlinear programs journal, May 2008

A Linear-Programming Approximation of AC Power Flows journal, November 2014

Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow journal, April 2012

Optimal capacitor placement using deterministic and genetic algorithms journal, January 2000

SCIP: solving constraint integer programs journal, January 2009

DC Power Flow Revisited journal, August 2009

A non-incremental model for optimal control of reactive power flow journal, November 1996

A comparison of the AC and DC power flow models for LMP calculations conference, January 2004

Inverter VAR control for distribution systems with renewables conference, October 2011

Optimal reactive power planning using evolutionary algorithms: a comparative study for evolutionary programming, evolutionary strategy, genetic algorithm, and linear programming journal, January 1998

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments journal, January 2010

Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes journal, June 2004

MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education journal, February 2011

Transmission Switching in Security-Constrained Unit Commitment journal, November 2010

Optimal Transmission Switching journal, August 2008

Perspective reformulations of mixed integer nonlinear programs with indicator variables journal, May 2010

SDPT3 — A Matlab software package for semidefinite programming, Version 1.3 journal, January 1999

Jointly Constrained Biconvex Programming journal, May 1983

Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem journal, March 2016

A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods journal, January 1999

A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches journal, January 1999

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming journal, April 2005

Convex relaxation for optimal power flow problem: Mesh networks conference, November 2013

Strategic planning for power system restoration report, November 2011

Strategic Planning for Power System Restoration conference, April 2012

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs text, January 2005

Promises of conic relaxation for contingency-constrained optimal power flow problem conference, September 2014

Optimal capacitor placement using deterministic and genetic algorithms conference, January 1999

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems text, January 2018

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs text, January 2006

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems text, January 2018

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs text, January 2006

A Linear-Programming Approximation of AC Power Flows preprint, January 2012

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations journal, November 2018

Probabilistic N - k failure-identification for power systems journal, January 2018

Small and strong formulations for unions of convex sets from the Cayley embedding journal, March 2018

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs journal, January 2019

A convex relaxation approach for power flow problem journal, April 2019

Network transition security for transmission switching journal, September 2019

Probabilistic $N$-$k$ Failure-Identification for Power Systems text, January 2017

An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs preprint, January 2017

AMPL: A Mathematical Programing Language
book, January 1989

Radial Distribution Load Flow Using Conic Programming
journal, August 2006

Optimal capacitor placement on radial distribution systems
journal, January 1989

Worst-Case Interdiction Analysis of Large-Scale Electric Power Grids
journal, February 2009

YALMIP : a toolbox for modeling and optimization in MATLAB
conference, January 2004

Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
journal, December 1976

Optimal Transmission Switching With Contingency Analysis
journal, August 2009

Analysis of Electric Grid Security Under Terrorist Threat
journal, May 2004

Using mixed-integer programming to solve power grid blackout problems
journal, March 2007

Mixed-integer nonlinear programs featuring “on/off” constraints
journal, August 2011

Solving the capacitor placement problem in a radial distribution system using Tabu Search approach
journal, January 1996

Convex Models of Distribution System Reconfiguration
journal, February 2012

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems
journal, December 2011

Zero Duality Gap in Optimal Power Flow Problem
journal, February 2012

Trilinear Monomials with Positive or Negative Domains: Facets of the Convex and Concave Envelopes
book, January 2004

Reduction constraints for the global optimization of NLPs
journal, January 2004

Linear Relaxations for Transmission System Planning
journal, November 2011

Strategic stockpiling of power system supplies for disaster recovery
conference, July 2011

Physics of power networks makes hard optimization problems easy to solve
conference, July 2012

Convex Relaxation for Optimal Power Flow Problem: Mesh Networks
journal, January 2015

Semidefinite programming for optimal power flow problems
journal, July 2008

An algorithmic framework for convex mixed integer nonlinear programs
journal, May 2008

A Linear-Programming Approximation of AC Power Flows
journal, November 2014

Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow
journal, April 2012

Optimal capacitor placement using deterministic and genetic algorithms
journal, January 2000

SCIP: solving constraint integer programs
journal, January 2009

DC Power Flow Revisited
journal, August 2009

A non-incremental model for optimal control of reactive power flow
journal, November 1996

A comparison of the AC and DC power flow models for LMP calculations
conference, January 2004

Inverter VAR control for distribution systems with renewables
conference, October 2011

Optimal reactive power planning using evolutionary algorithms: a comparative study for evolutionary programming, evolutionary strategy, genetic algorithm, and linear programming
journal, January 1998

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments
journal, January 2010

Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes
journal, June 2004

MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education
journal, February 2011

Transmission Switching in Security-Constrained Unit Commitment
journal, November 2010

Optimal Transmission Switching
journal, August 2008

Perspective reformulations of mixed integer nonlinear programs with indicator variables
journal, May 2010

SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
journal, January 1999

Jointly Constrained Biconvex Programming
journal, May 1983

Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem
journal, March 2016

A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods
journal, January 1999

A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches
journal, January 1999

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
journal, April 2005

Convex relaxation for optimal power flow problem: Mesh networks
conference, November 2013

Strategic planning for power system restoration
report, November 2011

Strategic Planning for Power System Restoration
conference, April 2012

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs
text, January 2005

Promises of conic relaxation for contingency-constrained optimal power flow problem
conference, September 2014

Optimal capacitor placement using deterministic and genetic algorithms
conference, January 1999

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems
text, January 2018

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs
text, January 2006

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems
text, January 2018

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs
text, January 2006

A Linear-Programming Approximation of AC Power Flows
preprint, January 2012

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations
journal, November 2018

Probabilistic N - k failure-identification for power systems
journal, January 2018

Small and strong formulations for unions of convex sets from the Cayley embedding
journal, March 2018

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs
journal, January 2019

A convex relaxation approach for power flow problem
journal, April 2019

Network transition security for transmission switching
journal, September 2019

Probabilistic $N$-$k$ Failure-Identification for Power Systems
text, January 2017

An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs
preprint, January 2017