IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v71y2018i2d10.1007_s10589-018-0015-1.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-018-0015-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-018-0015-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Bruce L. Miller & Harvey M. Wagner, 1965. "Chance Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 13(6), pages 930-945, December.
    3. 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.
    4. 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.
    5. 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.
    6. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    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. Antonio Frangioni & Claudio Gentile, 2006. "Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints," Operations Research, INFORMS, vol. 54(4), pages 767-775, August.
    9. 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.
    10. 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.
    11. Fattahi, Salar & Ashraphijuo, Morteza & Lavaei, Javad & Atamtürk, Alper, 2017. "Conic relaxations of the unit commitment problem," Energy, Elsevier, vol. 134(C), pages 1079-1095.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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, September.
    18. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    19. 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.
    20. Miles Lubin & Iain Dunning, 2015. "Computing in Operations Research Using Julia," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 238-248, May.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    27. 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.
    28. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    29. 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.
    30. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    31. 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.
    32. 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.
    33. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Walid Ben-Ameur & Adam Ouorou & Guanglei Wang & Mateusz Żotkiewicz, 2018. "Multipolar robust optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 395-434, December.
    2. Steffen Rebennack, 2022. "Data-driven stochastic optimization for distributional ambiguity with integrated confidence region," Journal of Global Optimization, Springer, vol. 84(2), pages 255-293, October.
    3. Marla, Lavanya & Rikun, Alexander & Stauffer, Gautier & Pratsini, Eleni, 2020. "Robust modeling and planning: Insights from three industrial applications," Operations Research Perspectives, Elsevier, vol. 7(C).
    4. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    5. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    6. Mavromatidis, Georgios & Orehounig, Kristina & Carmeliet, Jan, 2018. "A review of uncertainty characterisation approaches for the optimal design of distributed energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 88(C), pages 258-277.
    7. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    8. Han, Biao & Shang, Chao & Huang, Dexian, 2021. "Multiple kernel learning-aided robust optimization: Learning algorithm, computational tractability, and usage in multi-stage decision-making," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1004-1018.
    9. Xuejie Bai & Yankui Liu, 2016. "Robust optimization of supply chain network design in fuzzy decision system," Journal of Intelligent Manufacturing, Springer, vol. 27(6), pages 1131-1149, December.
    10. Hanks, Robert W. & Weir, Jeffery D. & Lunday, Brian J., 2017. "Robust goal programming using different robustness echelons via norm-based and ellipsoidal uncertainty sets," European Journal of Operational Research, Elsevier, vol. 262(2), pages 636-646.
    11. Longsheng Sun & Mark H. Karwan & Changhyun Kwon, 2018. "Generalized Bounded Rationality and Robust Multicommodity Network Design," Operations Research, INFORMS, vol. 66(1), pages 42-57, 1-2.
    12. Wang, Fan & Zhang, Chao & Zhang, Hui & Xu, Liang, 2021. "Short-term physician rescheduling model with feature-driven demand for mental disorders outpatients," Omega, Elsevier, vol. 105(C).
    13. Zhi Chen & Melvyn Sim & Peng Xiong, 2020. "Robust Stochastic Optimization Made Easy with RSOME," Management Science, INFORMS, vol. 66(8), pages 3329-3339, August.
    14. Feng, Wei & Feng, Yiping & Zhang, Qi, 2021. "Multistage robust mixed-integer optimization under endogenous uncertainty," European Journal of Operational Research, Elsevier, vol. 294(2), pages 460-475.
    15. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    16. Liu, Kanglin & Li, Qiaofeng & Zhang, Zhi-Hai, 2019. "Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 79-101.
    17. Wei Liu & Li Yang & Bo Yu, 2021. "KDE distributionally robust portfolio optimization with higher moment coherent risk," Annals of Operations Research, Springer, vol. 307(1), pages 363-397, December.
    18. Shao-Wei Lam & Tsan Sheng Ng & Melvyn Sim & Jin-Hwa Song, 2013. "Multiple Objectives Satisficing Under Uncertainty," Operations Research, INFORMS, vol. 61(1), pages 214-227, February.
    19. Fu, Chenyi & Zhu, Ning & Ma, Shoufeng & Liu, Ronghui, 2022. "A two-stage robust approach to integrated station location and rebalancing vehicle service design in bike-sharing systems," European Journal of Operational Research, Elsevier, vol. 298(3), pages 915-938.
    20. Mehdi Karimi & Somayeh Moazeni & Levent Tunçel, 2018. "A Utility Theory Based Interactive Approach to Robustness in Linear Optimization," Journal of Global Optimization, Springer, vol. 70(4), pages 811-842, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:71:y:2018:i:2:d:10.1007_s10589-018-0015-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.