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A Polynomial-Time Algorithm with Tight Error Bounds for Single-Period Unit Commitment Problem

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Abstract

This paper proposes a Lagrangian dual-based polynomial-time approximation algorithm for solving the single-period unit commitment problem, which can be formulated as a mixed-integer quadratic programming problem and proven to be NP-hard. Tight theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are provided. Computational results support the effectiveness and efficiency of the proposed algorithm for solving large-scale problems.

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References

  1. Tseng, C. L.: On power system generation unit commitment problems, Ph.D. Dissertation, University of California, Berkeley (1996)

  2. Padhy, N.P.: Unit commitment — A bibliographical survey. IEEE Transactions on Power Systems 19, 1196–1205 (2004)

    Article  Google Scholar 

  3. Lu, C., Deng, Z., Fang, S. C., Jin, Q., Xing, W.: Fast computation of global solutions to the single-period unit commitment problem. Journal of Combinatorial Optimization (2019). https://doi.org/10.1007/s10878-019-00489-9

  4. Galiana, F.D., Motto, A.L., Bouffard, F.: Reconciling social welfare, agent profits, and consumer payments in electricity pools. IEEE Transactions on Power Systems 18, 452–459 (2003)

    Article  Google Scholar 

  5. Padberg, M.W., VanRoy, T.J., Wolsey, L.A.: Valid linear inequalities for fixed charge problems. Operations Research 33, 842–861 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  6. Frangioni, A., Gentile, C., Grande, E., Pacifici, A.: Projected perspective reformulations with applications in design problems. Operations Research 59, 1225–1232 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Motto, A.L., Galiana, F.D.: Unit commitment with dual variable constraints. IEEE Transactions on Power Systems 19, 330–338 (2004)

    Article  Google Scholar 

  8. Dang, C., Li, M.: A floating-point genetic algorithm for solving the unit commitment problem. European Journal of Operational Research 181, 1370–1395 (2007)

    Article  MATH  Google Scholar 

  9. Jiang, R., Zhang, M., Li, G., Guan, Y.: Two-stage network constrained robust unit commitment problem. European Journal of Operational Research 234, 751–762 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Rong, A., Hakonen, H., Lahdelma, R.: A variant of the dynamic programming algorithm for unit commitment of combined heat and power systems. European Journal of Operational Research 190, 741–755 (2008)

    Article  MATH  Google Scholar 

  11. Dai, H., Zhang, N., Su, W.: A literature review of stochastic programming and unit commitment. Journal of Power and Energy Engineering 3, 206–214 (2015)

    Article  Google Scholar 

  12. Wu, L., Shahidehpour, M.: Security-constrained unit commitment with uncertainties. In: Chen, Hong (ed.) Power Grid Operation in a Market Environment: Economic Efficiency and Risk Mitigation. John Wiley & Sons, New Jersey (2016). https://doi.org/10.1002/9781119083016.ch5

    Chapter  Google Scholar 

  13. Tahanan, M., van Ackooij, W., Frangioni, A., Lacalandra, F.: Large-scale unit commitment under uncertainty: A literature survey. 4OR Quarterly Journal of the Belgian 13, 115–171 (2015)

    MATH  Google Scholar 

  14. Yamin, H.Y.: Review on methods of generation scheduling in electric power systems. Electric Power Systems Research 69, 227–248 (2004)

    Article  Google Scholar 

  15. Chen, C.L., Wang, S.C.: Branch-and-bound scheduling for thermal generating units. IEEE Transactions on Energy Conversion 8, 184–189 (1993)

    Article  Google Scholar 

  16. Huang, K.Y., Yang, H.T., Huang, C.L.: A new thermal unit commitment approach using constraint logic programming, Proceedings of the 20th International Conference on Power Industry Computer Applications, 176–185 (1997)

  17. Frangioni, A., Furini, F., Gentile, C.: Approximated perspective relaxations: A project and lift approach. Computational Optimization and Applications 63, 705–735 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  18. Nieva, R., Inda, A., Frausto, J.: CHT: A digital computer package for solving short term hydro-thermal coordination and unit commitment problems. IEEE Transactions on Power Systems 1, 168–174 (1986)

    Article  Google Scholar 

  19. Lowery, P.G.: Generating unit commitment by dynamic programming. IEEE Transactions on Power Apparatus and Systems PAS–85, 422–426 (1966)

    Article  Google Scholar 

  20. Schulze, T., Grothey, A., McKinnon, K.: A stabilised scenario decomposition algorithm applied to stochastic unit commitment problems. European Journal of Operational Research 261, 247–259 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  21. Ma, H., Shahidehpour, S.M.: Transmission-constrained unit commitment based on Benders decomposition. International Journal of Electrical Power and Energy Systems 20, 287–294 (1998)

    Article  Google Scholar 

  22. Papavasiliou, A., Oren, S.S.: Multiarea stochastic unit commitment for high wind penetration in a tramsimission constrained network. Operations Research 61, 578–592 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Carøe, C. C., Schultz, R.: A two-stage stochastic program for unit commitment under uncertainty in a hydro-thermal power system. Konrad-Zuse-Zentrum für Informationstechnik (1998). https://edocs.tib.eu/files/e001/247354082.pdf

  24. Nowak, M.P., Römisch, W.: Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Annals of Operations Research 100, 251–272 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  25. Gröwe-Kuska, N., Römisch, W.: Stochastic unit commitment in hydrothermal power production planning, Application of Stochastic Programming, In: S. W. Wallace and W. T. Ziemba (ed.) MOS-SIAM Series on Optimization, Chapter 30, 633–653 (2005)

  26. Ghaddar, B., Naoum-Sawaya, J., Kishimoto, A., Taheri, N., Eck, B.: A Lagrangian decomposition approach for the pump scheduling problem in water networks. European Journal of Operational Research 241, 490–501 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  27. Dudek, G.: Adaptive simulated annealing schedule to the unit commitment problem. Electric Power Systems Research 80, 465–472 (2010)

    Article  Google Scholar 

  28. Mantawy, A.H., Abdel-Magid, Y.L., Selim, S.Z.: Integrating genetic algorithms, tabu search, and simulated annealing for the unit commitment problem. IEEE Transactions on Power Systems 14, 829–836 (1999)

    Article  Google Scholar 

  29. Selvi, V., Umarani, R.: Comparative analysis of ant colony and particle swarm optimization techniques. International Journal of Computer Applications 5, 1–6 (2010)

    Article  Google Scholar 

  30. Nagaraja, M.S.: Optimum generation scheduling for thermal power plants using artificial neural network. International Journal of Electrical and Computer Engineering 1, 135–139 (2011)

    Google Scholar 

  31. Clerc, M., Kennedy, J.: The particle swarm – explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation 6, 58–73 (2002)

    Article  Google Scholar 

  32. Ogbe, E., Li, X.: A new cross decomposition method for stochastic mixed-integer linear programming. European Journal of Operational Research 256, 487–499 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. van den Bosch, P.P.J., Honderd, G.: A solution of the unit commitment problem via decomposition and dynamic programming. IEEE Transactions on Power Apparatus and Systems PAS–104, 1684–1690 (1985)

    Article  Google Scholar 

  34. Padhy, N. P.: Hybrid Models for Unit Commitment Problems, Ph.D. Dissertation, Anna University, Chennai (1997)

  35. Fang, S.C., Xing, W.: Linear conic optimization. Science Press, Beijing (2013)

    Google Scholar 

  36. Rockafellar, R.T., Wets, R.J.B.: Variational analysis, a series of comprehensive studies in mathematics, vol. 317. Springer, Berlin (2004)

    Google Scholar 

  37. Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear programming? In: Theory and Algorithms, 3rd edn. John Wiley & Sons, New Jersey (2013)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Big Data Center of State Grid Corporation of China, Beijing, 100053, China

    Ruo-Tian Gao

  2. Department of Industrial and System Engineering, North Carolina State University, Raleigh, 27695-7906, USA

    Shu-Cherng Fang

  3. School of Economics and Management, North China Electric Power University, Beijing, 102206, China

    Cheng Lu

  4. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Wen-Xun Xing

Authors
  1. Ruo-Tian Gao
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  2. Shu-Cherng Fang
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  3. Cheng Lu
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  4. Wen-Xun Xing
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Corresponding author

Correspondence to Cheng Lu.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11771243, 12171151, and 11701177) and US Army Research Office (No. W911NF-15-1-0223).

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Gao, RT., Fang, SC., Lu, C. et al. A Polynomial-Time Algorithm with Tight Error Bounds for Single-Period Unit Commitment Problem. J. Oper. Res. Soc. China 11, 1–28 (2023). https://doi.org/10.1007/s40305-021-00376-3

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  • DOI: https://doi.org/10.1007/s40305-021-00376-3

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