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Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches

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  • Guanglei Wang

    (The Australian National University)

  • Hassan Hijazi

    (The Australian National University
    Los Alamos National Laboratory)

Abstract

Planning and operating a power grid is a nontrivial exercise due to conflicting objectives, nonlinear constraints and uncertainties at multiple decision levels. Considerable research work has been dedicated to independently solve different aspects of the overall problem. This survey provides a detailed review of state-of-the-art techniques in mathematical optimization trying to address challenges in this area. We also provide a set of open problems and research perspectives.

Suggested Citation

  • Guanglei Wang & Hassan Hijazi, 2018. "Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches," Computational Optimization and Applications, Springer, vol. 71(2), pages 553-608, November.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:2:d:10.1007_s10589-018-0015-1
    DOI: 10.1007/s10589-018-0015-1
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    1. Ahmad Khan, Aftab & Naeem, Muhammad & Iqbal, Muhammad & Qaisar, Saad & Anpalagan, Alagan, 2016. "A compendium of optimization objectives, constraints, tools and algorithms for energy management in microgrids," Renewable and Sustainable Energy Reviews, Elsevier, vol. 58(C), pages 1664-1683.
    2. Antonio Frangioni & Claudio Gentile, 2006. "Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints," Operations Research, INFORMS, vol. 54(4), pages 767-775, August.
    3. Fattahi, Salar & Ashraphijuo, Morteza & Lavaei, Javad & Atamtürk, Alper, 2017. "Conic relaxations of the unit commitment problem," Energy, Elsevier, vol. 134(C), pages 1079-1095.
    4. Alarcon-Rodriguez, Arturo & Ault, Graham & Galloway, Stuart, 2010. "Multi-objective planning of distributed energy resources: A review of the state-of-the-art," Renewable and Sustainable Energy Reviews, Elsevier, vol. 14(5), pages 1353-1366, June.
    5. Dzung T. Phan, 2012. "Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow," Operations Research, INFORMS, vol. 60(2), pages 275-285, April.
    6. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    7. Viral, Rajkumar & Khatod, D.K., 2012. "Optimal planning of distributed generation systems in distribution system: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(7), pages 5146-5165.
    8. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    9. Warren P. Adams & Hanif D. Sherali, 1986. "A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems," Management Science, INFORMS, vol. 32(10), pages 1274-1290, October.
    10. Antonio J. Conejo & Miguel Carrión & Juan M. Morales, 2010. "Decision Making Under Uncertainty in Electricity Markets," International Series in Operations Research and Management Science, Springer, number 978-1-4419-7421-1, December.
    11. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    12. Hassan Hijazi & Pierre Bonami & Gérard Cornuéjols & Adam Ouorou, 2012. "Mixed-integer nonlinear programs featuring “on/off” constraints," Computational Optimization and Applications, Springer, vol. 52(2), pages 537-558, June.
    13. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    14. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    15. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    16. Álvaro Lorca & X. Andy Sun & Eugene Litvinov & Tongxin Zheng, 2016. "Multistage Adaptive Robust Optimization for the Unit Commitment Problem," Operations Research, INFORMS, vol. 64(1), pages 32-51, February.
    17. Bruce L. Miller & Harvey M. Wagner, 1965. "Chance Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 13(6), pages 930-945, December.
    18. Gülpınar, Nalan & Pachamanova, Dessislava & Çanakoğlu, Ethem, 2013. "Robust strategies for facility location under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(1), pages 21-35.
    19. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    20. Baños, R. & Manzano-Agugliaro, F. & Montoya, F.G. & Gil, C. & Alcayde, A. & Gómez, J., 2011. "Optimization methods applied to renewable and sustainable energy: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 15(4), pages 1753-1766, May.
    21. Warren Adams & Hanif Sherali, 2005. "A Hierarchy of Relaxations Leading to the Convex Hull Representation for General Discrete Optimization Problems," Annals of Operations Research, Springer, vol. 140(1), pages 21-47, November.
    22. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    23. Melkote, Sanjay & Daskin, Mark S., 2001. "An integrated model of facility location and transportation network design," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(6), pages 515-538, July.
    24. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    25. Burak Kocuk & Hyemin Jeon & Santanu S. Dey & Jeff Linderoth & James Luedtke & Xu Andy Sun, 2016. "A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching," Operations Research, INFORMS, vol. 64(4), pages 922-938, August.
    26. Erdinc, O. & Uzunoglu, M., 2012. "Optimum design of hybrid renewable energy systems: Overview of different approaches," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(3), pages 1412-1425.
    27. Warren P. Adams & Hanif D. Sherali, 1990. "Linearization Strategies for a Class of Zero-One Mixed Integer Programming Problems," Operations Research, INFORMS, vol. 38(2), pages 217-226, April.
    28. Burak Kocuk & Santanu S. Dey & X. Andy Sun, 2016. "Strong SOCP Relaxations for the Optimal Power Flow Problem," Operations Research, INFORMS, vol. 64(6), pages 1177-1196, December.
    29. Jae Ho Kim & Warren B. Powell, 2011. "Optimal Energy Commitments with Storage and Intermittent Supply," Operations Research, INFORMS, vol. 59(6), pages 1347-1360, December.
    30. Aharon Ben-Tal & Arkadi Nemirovski, 2001. "On Polyhedral Approximations of the Second-Order Cone," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 193-205, May.
    31. Miles Lubin & Iain Dunning, 2015. "Computing in Operations Research Using Julia," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 238-248, May.
    32. Gamarra, Carlos & Guerrero, Josep M., 2015. "Computational optimization techniques applied to microgrids planning: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 48(C), pages 413-424.
    33. C. Gentile & G. Morales-España & A. Ramos, 2017. "A tight MIP formulation of the unit commitment problem with start-up and shut-down constraints," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 177-201, March.
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    Cited by:

    1. Sander Claeys & Marta Vanin & Frederik Geth & Geert Deconinck, 2021. "Applications of optimization models for electricity distribution networks," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 10(5), September.
    2. Ogunmodede, Oluwaseun & Anderson, Kate & Cutler, Dylan & Newman, Alexandra, 2021. "Optimizing design and dispatch of a renewable energy system," Applied Energy, Elsevier, vol. 287(C).

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