IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v72y2019i2d10.1007_s10589-018-0047-6.html
   My bibliography  Save this article

A partial outer convexification approach to control transmission lines

Author

Listed:
  • S. Göttlich

    (University of Mannheim)

  • A. Potschka

    (Heidelberg University)

  • C. Teuber

    (University of Mannheim)

Abstract

In this paper we derive an efficient optimization approach to calculate optimal controls of electric transmission lines. These controls consist of time-dependent inflows and switches that temporarily disable single arcs or whole subgrids to reallocate the flow inside the system. The aim is then to find the best energy input in terms of boundary controls in combination with the optimal configuration of switches, where the dynamics is driven by a coupled system of hyperbolic differential equations. We use a well-known three-step optimization approach based on the idea of partial outer convexification, for which we establish that the analytical requirements for its application hold for each fixed spatial discretization of the underlying partial differential equation, provided that combinatorial constraints are only pointwise in time. A comparison with a direct solver yields very promising results, also for problems with from an application viewpoint important switch up-time and down-time constraints, which are not pointwise in time and thus not fully covered by theory.

Suggested Citation

  • S. Göttlich & A. Potschka & C. Teuber, 2019. "A partial outer convexification approach to control transmission lines," Computational Optimization and Applications, Springer, vol. 72(2), pages 431-456, March.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:2:d:10.1007_s10589-018-0047-6
    DOI: 10.1007/s10589-018-0047-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-018-0047-6
    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/s10589-018-0047-6?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. Falk Hante & Sebastian Sager, 2013. "Relaxation methods for mixed-integer optimal control of partial differential equations," Computational Optimization and Applications, Springer, vol. 55(1), pages 197-225, May.
    2. J. T. Linderoth & M. W. P. Savelsbergh, 1999. "A Computational Study of Search Strategies for Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 173-187, May.
    3. VAN ROY, Tony J., 1983. "Cross decomposition for mixed integer programming," LIDAM Reprints CORE 496, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Juan Pablo Vielma & Shabbir Ahmed & George Nemhauser, 2010. "Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions," Operations Research, INFORMS, vol. 58(2), pages 303-315, April.
    5. M. W. P. Savelsbergh, 1994. "Preprocessing and Probing Techniques for Mixed Integer Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 6(4), pages 445-454, November.
    6. Sebastian Sager & Michael Jung & Christian Kirches, 2011. "Combinatorial integral approximation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(3), pages 363-380, June.
    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. Dominik Garmatter & Margherita Porcelli & Francesco Rinaldi & Martin Stoll, 2023. "An improved penalty algorithm using model order reduction for MIPDECO problems with partial observations," Computational Optimization and Applications, Springer, vol. 84(1), pages 191-223, January.

    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. Kumar Abhishek & Sven Leyffer & Jeff Linderoth, 2010. "FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 555-567, November.
    2. Sven Leyffer & Paul Manns & Malte Winckler, 2021. "Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation," Computational Optimization and Applications, Springer, vol. 79(1), pages 193-221, May.
    3. Christoph Buchheim & Renke Kuhlmann & Christian Meyer, 2018. "Combinatorial optimal control of semilinear elliptic PDEs," Computational Optimization and Applications, Springer, vol. 70(3), pages 641-675, July.
    4. Marvin Severitt & Paul Manns, 2023. "Efficient Solution of Discrete Subproblems Arising in Integer Optimal Control with Total Variation Regularization," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 869-885, July.
    5. Lluís-Miquel Munguía & Geoffrey Oxberry & Deepak Rajan & Yuji Shinano, 2019. "Parallel PIPS-SBB: multi-level parallelism for stochastic mixed-integer programs," Computational Optimization and Applications, Springer, vol. 73(2), pages 575-601, June.
    6. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    7. Codas, Andrés & Camponogara, Eduardo, 2012. "Mixed-integer linear optimization for optimal lift-gas allocation with well-separator routing," European Journal of Operational Research, Elsevier, vol. 217(1), pages 222-231.
    8. Christensen, Tue R.L. & Labbé, Martine, 2015. "A branch-cut-and-price algorithm for the piecewise linear transportation problem," European Journal of Operational Research, Elsevier, vol. 245(3), pages 645-655.
    9. Bissan Ghaddar & Ignacio Gómez-Casares & Julio González-Díaz & Brais González-Rodríguez & Beatriz Pateiro-López & Sofía Rodríguez-Ballesteros, 2023. "Learning for Spatial Branching: An Algorithm Selection Approach," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1024-1043, September.
    10. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    11. Jon Lee & Daphne Skipper & Emily Speakman & Luze Xu, 2023. "Gaining or Losing Perspective for Piecewise-Linear Under-Estimators of Convex Univariate Functions," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 1-35, January.
    12. Mazzola, Joseph B. & Neebe, Alan W., 1999. "Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type," European Journal of Operational Research, Elsevier, vol. 115(2), pages 285-299, June.
    13. Pourbabai, B. & Ashayeri, J. & Van Wassenhove, L.N., 1992. "Strategic marketing, production, and distribution planning of an integrated manufacturing system," Other publications TiSEM 16c2bacb-2c2b-427e-b429-c, Tilburg University, School of Economics and Management.
    14. Jon D. Petersen & Gustaf Sölveling & John-Paul Clarke & Ellis L. Johnson & Sergey Shebalov, 2012. "An Optimization Approach to Airline Integrated Recovery," Transportation Science, INFORMS, vol. 46(4), pages 482-500, November.
    15. Altay, Nezih & Robinson Jr., Powell E. & Bretthauer, Kurt M., 2008. "Exact and heuristic solution approaches for the mixed integer setup knapsack problem," European Journal of Operational Research, Elsevier, vol. 190(3), pages 598-609, November.
    16. Cappanera, Paola & Visintin, Filippo & Banditori, Carlo, 2014. "Comparing resource balancing criteria in master surgical scheduling: A combined optimisation-simulation approach," International Journal of Production Economics, Elsevier, vol. 158(C), pages 179-196.
    17. Eduardo Rauh Müller & Eduardo Camponogara & Laio Oriel Seman & Eduardo Otte Hülse & Bruno Ferreira Vieira & Luis Kin Miyatake & Alex Furtado Teixeira, 2022. "Short-term steady-state production optimization of offshore oil platforms: wells with dual completion (gas-lift and ESP) and flow assurance," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 152-180, April.
    18. Markus Leitner & Ivana Ljubić & Martin Luipersbeck & Markus Sinnl, 2018. "Decomposition methods for the two-stage stochastic Steiner tree problem," Computational Optimization and Applications, Springer, vol. 69(3), pages 713-752, April.
    19. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2017. "Linear Reformulation of Polynomial Discrete Programming for Fast Computation," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 108-122, February.

    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:72:y:2019:i:2:d:10.1007_s10589-018-0047-6. 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.