Improved Valve-Point Optimization Algorithm for Economic Load Dispatch Problem with Non-convex Fuel Cost Function

- Journal title : The Journal of The Institute of Internet, Broadcasting and Communication
- Volume 15, Issue 6, 2015, pp.257-266
- Publisher : The institute Of Webcasting, Internet And Telecommunication
- DOI : 10.7236/JIIBC.2015.15.6.257

Title & Authors

Improved Valve-Point Optimization Algorithm for Economic Load Dispatch Problem with Non-convex Fuel Cost Function

Lee, Sang-Un;

Lee, Sang-Un;

Abstract

There is no polynomial-time algorithm that can be obtain the optimal solution for economic load dispatch problem with non-convex fuel cost functions. Therefore, electrical field uses quadratic fuel cost function unavoidably. This paper proposes a valve-point optimization (VPO) algorithm for economic load dispatch problem with non-convex fuel cost functions. This algorithm sets the initial values to maximum powers for each generator. It then reduces the generation power of generator i with an average power cost of to a valve point power . The proposed algorithm has been found to perform better than the extant heuristic methods when applied to 13 and 40-generator benchmark data. This paper consequently proves that the optimal solution to economic load dispatch problem with non-convex fuel cost functions converges to the valve-point power of each generator.

Keywords

Economic Dispatch;Optimization;Valve-effect;Valve-point;

Language

Korean

References

1.

A. A. El-Fergany, "Solution of Economic Load Dispatch Problem with Smooth and Non-Smooth Fuel Cost Functions Including Line Losses Using Genetic Algorithm," International Journal of Computer and Electrical Engineering, Vol. 3, No. 5, pp. 706-710, doi:10.7763/IJCEE.2011.V3.407, Oct. 2011.

2.

B. Shaw, S. Ghoshal, V. Mukherjee, and S. P. Ghoshal, "Solution of Economic Load Dispatch Problems by a Novel Seeker Optimization Algorithm," International Journal on Electrical Engineering and Informatics, Vol. 3, No. 1, pp. 26-42, doi:10.15676/ijeei.2011.3.1.3, Mar. 2011.

3.

L. S. Coelho and V. C. Mariani, "Combining of Chaotic Differential Evolution and Quadratic Programming for Economic Dispatch Optimization with Valve-Point Effect," IEEE Trans. on Power Systems, Vol. 21, No. 2, doi:10.1109/TPWRS. 2006.873410, May 2006.

4.

S. H. Ling, H. K. Lam, F. H. F. Leung, and Y. S. Lee, "Improved Genetic Algorithm for Economic Load Dispatch with Valve-point Loadings," The 29th Annual Conference of the IEEE Industrial Electronics Society, Vol. 1, pp 442-447, doi: 10.1109/IECON.2003.1280021, Nov. 2003.

5.

T. A. A. Victoire and A. E. Jeyakumar, "Hybrid PSO-SQP for Economic Dispatch with Valve-point Effect," Electric. Power Systems Research, Vol. 71, No. 1, pp. 51-59, doi: 10.1016/j.epsr.2003.12.017, Sep. 2004.

6.

N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay, "Evolutionary Programming Techniques for Economic Load Dispatch," IEEE Trans. on Evolutionary Computing, Vol. 7, No. 1, pp. 83-94, doi: 10.1109/TEVC.2002.806788, Feb. 2003.

7.

Y. Hou, L. Lu, X. Xiong, and Y. Wu, "Economic Dispatch of Power Systems Based on the Modified Particle Swarm Optimization Algorithm," IEEE/PES Transmission and Distribution Conference and Exhibition, pp. 1-6, doi:10.1109/ TDC.2005.1546751, Aug. 2005.

8.

R. Goncalves, C. Almeida, J. Kuk, and M. Delgado, "Solving Economic Load Dispatch Problem by Natural Computing Intelligent Systems," 15th International Conference on Intelligent System Applications to Power Systems (ISAP), pp. 1-6, 8-12, doi:10.1109/ISAP.2009.5352843, Nov. 2009.

9.

J. S. Al-Sumait, J. K. Sykulski, and A. K. Al-Othman, "Solution of Different Types of Economic Load Dispatch Problems Using a Pattern Search Method," Electric Power Components and Systems. Vol. 36, No. 3, pp. 250-265, doi:10.1080/15325000701603892, Mar. 2008.

10.

L. S. Coelho and V. C. Mariani, "An Improved Harmony Search Algorithm for Power Economic Load Dispatch," Energy Conversion and Management, Vol. 50, No. 10, pp. 2522-2526, doi:10.1016/j.enconman.2009.05.034, Oct. 2009.

11.

K. Zare, M. T. Haque, and E. Davoodi, "Solving Non-convex Economic Dispatch Problem with Valve Point Effects using Modified Group Search Optimizer Method," Electrical Power Systems Research, Vol. 84, No. 1, pp. 83-89, doi:10.1016 /j.epsr.2011.10.004, Mar. 2012.

12.

K. S. Pothiya, and S. Boonseng, "Distributed Tabu Search Algorithm for Solving the Economic Dispatch Problem," TENCON, Vol. C, pp. 484-487, doi:10.1109/TENCON.2004.1414813, Nov. 2004.

13.

R. Balamurugan and S. Subramanian, "Self-Adaptive Differential Evolution Based Power Economic Dispatch of Generators with Valve-Point Effects and Multiple Fuel Options," International Journal of Computer Science and Engineering, Vol. 1, No. 3, pp. 10-17, Mar. 2007.

14.

N. Sinha and B. Purkayastha, "PSO Embedded Evolutionary Programming Technique for Nonconvex Economic Load Dispatch," IEEE PES-Power Systems Conference and Exposition, Vol. 1, pp. 66-71, doi: 10.1109/PSCE.2004.1397447, Oct. 2004.

15.

P. Attaviriyanupap, H. Kita, E. Tanaka, and J. Hasegawa, "A Hybrid EP and SQP for Dynamic Economic Dispatch with Non-smooth Fuel Cost Function," IEEE Trans. on Power System, Vol. 22, No. 4, pp. 411-416, doi: 10.1109/MPER.2002.4312139, Apr. 2002.

16.

J. B. Park, K. S. Lee, J. R. Shin, and K. Y. Lee, "A Particle Swarm Optimization for Economic Dispatch with Non-smooth Cost Function," IEEE Trans. Power System, Vol. 20, No. 1, pp. 34-42, doi: 10.1109/TPWRS.2004.831275, Feb. 2005.

17.

A. I. Selvakumar, and K. Thanushkodi, "A New Particle Swarm Optimization Solution to Non-convex Economic Dispatch Problems," IEEE Trans. on Power Systems, Vol. 22, No. 1, pp. 42-51, doi: 10.1109/TPWRS.2006.889132, Feb. 2007.

18.

J. B. Park, W. N. Lee, and J. R. Sin, "An Improved Particle Swarm Optimization for Economic Dispatch Problems with Non-Smooth Cost Functions," International Journal of Innovations in Energy Systems and Power, Vol. 1, No. 1, pp. 1-7, doi:10.1109/PES.2006.1709300, 2006.

19.

K. T. Chaturvedi, M. Pandit, L Srivastava, "Self-organizing hierarchical particle swarm optimization for nonconvex economic dispatch," IEEE Trans. on Power Systems, Vol. 23, No. 3, pp. 1079-1087, doi:10.1109/TPWRS.2008.926455, Aug. 2008.

20.

A. Khamseh and Y. Y. Alinejad-Beromi, "Hybrid CLONAL Selection Algorithm with SA for Solving Economic Load Dispatch with Valve- Point Effect," Canadian Journal on Electrical and Electronics Engineering, Vol. 2, No. 10, pp. 463-467, 2011.

21.

K. Meng, Z. Y. Dong, H. G. Wang, K. P. Wong, "Quantum-inspired Particle Swam Optimization for Valve-point Economic Load Dispatch," IEEE Trans. on Power Systems, Vol. 25, No. 1, pp. 215-222, doi:10.1109/TPWRS.2009.2030359, Jan. 2010.

22.

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, doi:10.1109/59.476058, Nov. 1995.

23.

A. Bhattacharya, P. K. Chattopadhyay, "Biogeography- based Optimization for Different Economic Load Dispatch Problems," IEEE Trans. on Power Systems, Vol. 25, No. 2, pp. 1064-1077, doi:10.1109/TPWRS.2009.2034525, May 2010.

24.

J. B. Park, Y. W. Jeong, J. R. Shin, and K. Y. Lee, "An Improved Particle Swarm Optimization for Nonconvex Economic Dispatch Problems," IEEE Trans. on Power Systems, Vol. 25, No. 1, pp. 156-166, 10.1109/TPWRS.2009.2030293, Jan. 2010.