International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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An Economic Dispatch Algorithm as Combinatorial Optimization Problems

  • Min, Kyung-Il (Electrical and Electronic Engineering, Yonsei University) ;
  • Lee, Su-Won (Institute of TMS Information Technology, Yonsei University) ;
  • Moon, Young-Hyun (Electrical and Electronic Engineering, Yonsei University)
  • Published : 2008.08.31
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Abstract

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the $\lambda$-P table method is used to calculate ED for the fitness function of GA. The $\lambda$-P table method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with three kinds of ED problems, namely ED considering valve-point effects (EDVP), ED with multiple fuel units (EDMF), and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all three ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

Keywords

References

  1. A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, Wiley, New York, 1996
  2. D. C. Walters and G. B. Sheble, "Genetic algorithm solution of economic dispatch with valve point loading," IEEE Trans. on Power Systems, vol. 8, no. 3, pp. 1325-1331, Aug. 1993 https://doi.org/10.1109/59.260861
  3. P. H. Chen and H. C. Chang, "Large-scale economic dispatch by genetic algorithm," IEEE Trans. on Power Systems, vol. 10, no. 4, pp. 1919-1926, Nov. 1995 https://doi.org/10.1109/59.476058
  4. C. L. Chiang, "Improved genetic algorithm for power economic dispatch of units with valvepoint effects and multiple fuels," IEEE Trans. on Power Systems, vol. 20, no. 4, pp. 1690-1699, Nov. 2005 https://doi.org/10.1109/TPWRS.2005.857924
  5. K. P. Wong and Y. W. Wong, "Thermal generator scheduling using hybrid genetic/simulated annealing approach," IEE Proceedings Part C - Generation Transmission, and Distribution, vol. 142, no. 4, pp. 372-380, July 1995 https://doi.org/10.1049/ip-gtd:19951974
  6. K. Y. Lee, A. Sode-Yome, and J. H. Park, "Adaptive Hopfield neural network for economic load dispatch," IEEE Trans. on Power Systems, vol. 13, pp. 519-526, May 1998 https://doi.org/10.1109/59.667377
  7. W. M. Lin, F. S. Cheng, and M. T. Tsay, "An improved Tabu search for economic dispatch with multiple minima," IEEE Trans. on Power Systems, vol. 17, pp. 108-112, Feb. 2002 https://doi.org/10.1109/59.982200
  8. Y. M. Park, J. R. Won, and J. B. Park, "A new approach to economic load dispatch based on improved evolutionary programming," Eng. Intell. Syst. Elect. Eng. Commun., vol. 6, no. 2, pp. 103-110, June 1998
  9. N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay, "Evolutionary programming techniques for economic load dispatch," IEEE Trans. on Evolutionary Computation, vol. 7, no. 1, pp. 83-94, Feb. 2003 https://doi.org/10.1109/TEVC.2002.806788
  10. T. Jayabarathi, G Sadasivam, and V. Ramachandran, "Evolutionary programming based economic dispatch of generators with prohibited operating zones," Electric Power Systems Research, vol. 52, pp. 261-266, 1999 https://doi.org/10.1016/S0378-7796(99)00025-5
  11. J. B. Park, K. S. Lee, J. R. Shin, and K. Y. Lee, "A particle swarm optimization for economic dispatch with nonsmooth cost functions," IEEE Trans. on Power Systems, vol. 20, no. 1, pp. 34- 42, Feb. 2005 https://doi.org/10.1109/TPWRS.2004.831275
  12. T. A. A. Victoire and A. Ebenezer Jeyakumar, "Hybrid PSO-SQP for economic dispatch with valve-point effect," Electric Power Systems Research, vol. 71, pp. 51-59, 2004 https://doi.org/10.1016/j.epsr.2003.12.017
  13. A. I. Selvakumar and K. Thanushkodi, "A new particle swarm optimization solution to nonconvex economic dispatch problems," IEEE Trans. on Power Systems, vol. 22, pp. 42-51, Feb. 2007 https://doi.org/10.1109/TPWRS.2006.889132
  14. J. Y. Kim, H. S. Lee, and J. H. Park, "A modified particle swarm optimization for optimal power flow," KIEE J. Electr. Eng. Technol., vol. 2. no. 4, pp. 413-419, 2007 https://doi.org/10.5370/JEET.2007.2.4.413
  15. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Dover, 1998
  16. T. Li and M. Shahidehpour, "Price-based unit commitment: A case of lagrangian relaxation versus mixed integer programming," IEEE Trans. on Power Systems, vol. 20, no. 4, Nov. 2005
  17. Q. Zhai, X. Guan, and J. Cui, "Unit commitment with identical units: Successive subproblem solving method based on Lagrangian relaxation," IEEE Trans. on Power Systems, vol. 17, no. 4, Nov. 2002
  18. K. I. Min, J. G. Lee, S. J. Kim, H. S. Hong, and Y. H. Moon, "Economic dispatch algorithm by $\lambda$-P tables reflecting actual fuel cost curves," presented at the IFAC Symposium on PPS, Kananaskis, Canada, Paper No. pps 533, June 2006
  19. C. E. Lin and G. L. Viviani, "Hierarchical economic dispatch for piecewise quadratic cost functions," IEEE Trans. on Power Apparatus and Systems, vol. 103, no. 6, pp. 1170-1175, June 1984 https://doi.org/10.1109/TPAS.1984.318445
  20. F. N. Lee and A. M. Breipohl, "Reserve constrained economic dispatch with prohibited operating zones," IEEE Trans. on Power Systems, vol. 8, no. 1, pp. 246-254, Feb. 1993 https://doi.org/10.1109/59.221233
  21. K. Chandram, N. Subrahmanyam, and M. Sydulu, "Secant method for economic dispatch with generator constraints and transmission losses," KIEE J. Electr. Eng. Technol., vol. 3. no. 1, pp. 52-59, 2008 https://doi.org/10.5370/JEET.2008.3.1.052
  22. Y. H. Moon, J. D. Park, H. J. Kook, and Y. H. Lee, "A new economic dispatch algorithm considering any higher order generation cost functions," Int. Journal of Elec. Power & Energy Syst., vol. 23, pp. 113-118, May 2000
  23. M. Madrigal and V. H. Quintana, "An analytical solution to the economic dispatch problem," IEEE Power Eng. Review, pp. 52-55, Sep. 2000
  24. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution programs, Springer, 1999
  25. K. Y. Lee and M. A. El-Sharkawi, Ed., Modern Heuristic Optimization Techniques with Applications to Power Systems, IEEE Power Engineering Society (02TP160), 2002
  26. B. K. Panigrahi, S. R. Yadav, S. Agrawal, and M. K. Tiwari, "A clonal algorithm to solve economic load dispatch," Electric Power Systems Research, vol. 77, pp. 1381-1389, 2007 https://doi.org/10.1016/j.epsr.2006.10.007
  27. T. Satoh, H. Kuwabara, M. Kanezashi, and K. Nara, "Artificial life system and its application to multiple-fuel economic load dispatch problem," Evolutionary Computation CEC '02. Proceedings of the 2002 Congress, vol. 2, pp. 1432 - 1437, May 2002
  28. P. Somasundaram, K. Kuppusamy, and P. R. Kumudini Devi, "Economic dispatch with prohibited operating zones using fast computation evolutionary programming algorithm," Electric Power Systems Research, vol. 70, pp. 245-252, 2004 https://doi.org/10.1016/j.epsr.2003.12.013
  29. L. G. Papageorgiou and E. S. Fraga, "A mixed integer quadratic programming formulation for the economic dispatch of generators with prohibited operating zones," Electric Power Systems Research, vol. 77, pp. 1292-1296, 2007 https://doi.org/10.1016/j.epsr.2006.09.020