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An Application of Lagrangian Relaxation to Scheduling in Power-Generation Systems

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  • John A. Muckstadt

    (Cornell University, Ithaca, New York)

  • Sherri A. Koenig

    (Exxon Corporation, Florham Park, New Jersey)

Abstract

Two major decisions are made when scheduling the operations of a fossil-fuel power-generating system over a short time horizon. The “unit commitment” decision indicates what generating units are to be in use at each point in time. The “economic dispatch” decision is the allocation of system demand among the generating units in operation at any point in time. Both these decisions must be considered to achieve a least-cost schedule over the short time horizon. In this paper we present a mixed integer programming model for the short time horizon power-scheduling problem. The objective of the model is to minimize the sum of the unit commitment and economic dispatch costs subject to demand, reserve, and generator capacity and generator schedule constraints. A branch-and-bound algorithm is proposed using a Lagrangian method to decompose the problem into single generator problems. A sub gradient method is used to select the Lagrange multipliers that maximize the lower bound produced by the relaxation. We present computational results that indicate the technique is capable of solving large problems to within acceptable error tolerances.

Suggested Citation

  • John A. Muckstadt & Sherri A. Koenig, 1977. "An Application of Lagrangian Relaxation to Scheduling in Power-Generation Systems," Operations Research, INFORMS, vol. 25(3), pages 387-403, June.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:3:p:387-403
    DOI: 10.1287/opre.25.3.387
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    Cited by:

    1. Maturana, Jorge & Riff, Maria-Cristina, 2007. "Solving the short-term electrical generation scheduling problem by an adaptive evolutionary approach," European Journal of Operational Research, Elsevier, vol. 179(3), pages 677-691, June.
    2. Fattahi, Salar & Ashraphijuo, Morteza & Lavaei, Javad & Atamtürk, Alper, 2017. "Conic relaxations of the unit commitment problem," Energy, Elsevier, vol. 134(C), pages 1079-1095.
    3. Yau, Sheena & Kwon, Roy H. & Scott Rogers, J. & Wu, Desheng, 2011. "Financial and operational decisions in the electricity sector: Contract portfolio optimization with the conditional value-at-risk criterion," International Journal of Production Economics, Elsevier, vol. 134(1), pages 67-77, November.
    4. Ramteen Sioshansi and Ashlin Tignor, 2012. "Do Centrally Committed Electricity Markets Provide Useful Price Signals?," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4).
    5. Claude Lemaréchal, 2007. "The omnipresence of Lagrange," Annals of Operations Research, Springer, vol. 153(1), pages 9-27, September.
    6. C. L. Tseng & C. A. Li & S. S. Oren, 2000. "Solving the Unit Commitment Problem by a Unit Decommitment Method," Journal of Optimization Theory and Applications, Springer, vol. 105(3), pages 707-730, June.
    7. Dotzauer, Erik, 2003. "Experiences in mid-term planning of district heating systems," Energy, Elsevier, vol. 28(15), pages 1545-1555.
    8. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    9. Jiang, Yuzhou & Sioshansi, Ramteen, 2024. "A computationally efficient approach to optimizing offers in centrally committed electricity markets," European Journal of Operational Research, Elsevier, vol. 317(1), pages 25-42.
    10. Briest, Gordon & Lauven, Lars-Peter & Kupfer, Stefan & Lukas, Elmar, 2022. "Leaving well-worn paths: Reversal of the investment-uncertainty relationship and flexible biogas plant operation," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1162-1176.
    11. Johnson, Raymond B. & Oren, Shmuel S. & Svoboda, Alva J., 1997. "Equity and efficiency of unit commitment in competitive electricity markets," Utilities Policy, Elsevier, vol. 6(1), pages 9-19, March.
    12. Ramteen Sioshansif & Ashlin Tignor, 2012. "Do Centrally Committed Electricity Markets Provide Useful Price Signals?," The Energy Journal, , vol. 33(4), pages 96-118, October.
    13. Steeger, Gregory & Rebennack, Steffen, 2017. "Dynamic convexification within nested Benders decomposition using Lagrangian relaxation: An application to the strategic bidding problem," European Journal of Operational Research, Elsevier, vol. 257(2), pages 669-686.
    14. Payal Mitra & Soumendu Sarkar & Tarun Mehta & Atul Kumar, 2022. "Unit Commitment in a Federalized Power Market: A Mixed Integer Programming Approach," Working papers 323, Centre for Development Economics, Delhi School of Economics.
    15. Kaleta, Mariusz & Toczylowski, Eugeniusz, 2008. "Restriction techniques for the unit-commitment problem with total procurement costs," Energy Policy, Elsevier, vol. 36(7), pages 2439-2448, July.
    16. Richter, Lucas & Lehna, Malte & Marchand, Sophie & Scholz, Christoph & Dreher, Alexander & Klaiber, Stefan & Lenk, Steve, 2022. "Artificial Intelligence for Electricity Supply Chain automation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 163(C).
    17. L. A. C. Roque & D. B. M. M. Fontes & F. A. C. C. Fontes, 2014. "A hybrid biased random key genetic algorithm approach for the unit commitment problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 140-166, July.
    18. Jinyeong Lee & Kyungcheol Shin & Young-Min Wi, 2024. "Decentralized Operations of Industrial Complex Microgrids Considering Corporate Power Purchase Agreements for Renewable Energy 100% Initiatives in South Korea," Sustainability, MDPI, vol. 16(13), pages 1-23, June.
    19. Raymond B. Johnson & Alva J. Svoboda & Claudia Greif & Ali Vojdani & Fulin Zhuang, 1998. "Positioning for a Competitive Electric Industry with PG&E's Hydro-Thermal Optimization Model," Interfaces, INFORMS, vol. 28(1), pages 53-74, February.
    20. Heejung Park, 2022. "A Unit Commitment Model Considering Feasibility of Operating Reserves under Stochastic Optimization Framework," Energies, MDPI, vol. 15(17), pages 1-22, August.
    21. Samer Takriti & Benedikt Krasenbrink & Lilian S.-Y. Wu, 2000. "Incorporating Fuel Constraints and Electricity Spot Prices into the Stochastic Unit Commitment Problem," Operations Research, INFORMS, vol. 48(2), pages 268-280, April.
    22. Dong, Jizhe & Li, Yuanhan & Zuo, Shi & Wu, Xiaomei & Zhang, Zuyao & Du, Jiang, 2023. "An intraperiod arbitrary ramping-rate changing model in unit commitment," Energy, Elsevier, vol. 284(C).
    23. Feng, Chenjia & Shao, Chengcheng & Wang, Xifan, 2021. "CSP clustering in unit commitment for power system production cost modeling," Renewable Energy, Elsevier, vol. 168(C), pages 1217-1228.
    24. Samer Takriti & John R. Birge, 2000. "Lagrangian Solution Techniques and Bounds for Loosely Coupled Mixed-Integer Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 91-98, February.

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