SOLUTION TO NONCONVEX ECONOMIC DISPATCH PROBLEM WITH VALVE POINT EFFECT BY HARMONY SEARCH ALGORITHM

Öz

In literature, economic power dispatch problems are generally categorized as convex and nonconvex optimization problems. In this study, harmony search algorithm (HSA) has been used for the solution of the economic dispatch problem with valve point effect. In these this kind of problems, fuel cost curve increases as sinusoidal oscillations. In the solution of the problem B loss matrix has been used for the calculation of the line losses. Total fuel cost has been minimized under electrical constraints. HSA method has been applied to three different test systems one with 6 buses 3 generators, the other with 14 buses 5 generators (IEEE) and the last one with 30 buses 6 generators (IEEE). The solution of the test systems have been obtained by improving a programme in MATLAB R2010a. The obtained optimum solution values have been compared with optimum solution values obtained by the application of different methods in literature and the results of them have been discussed.

Anahtar Kelimeler

• Economic power dispatch,Valve point effects,Non-convex functions,Harmony search algorithm

VALF NOKTA ETKİLİ KONVEKS OLMAYAN EKONOMİK GÜÇ DAĞITIM PROBLEMLERİNİN HARMONİ ARAMA ALGORİTMASIYLA ÇÖZÜMÜ

Öz

Literatürde ekonomik güç dağıtım problemleri konveks ve konveks olmayan olarak iki grupta incelenmektedir. Bu çalışmada valf nokta etkili konveks olmayan ekonomik güç dağıtım probleminin çözümü için harmoni arama algoritması (HAA) kullanılmıştır. Bu tür problemlerde yakıt maliyet eğrisi sinüzoidal dalgalanmalar şeklinde artmaktadır. Problemin çözümünde hat kayıplarının hesaplanması için B kayıp matrisi kullanılmıştır. Toplam yakıt maliyeti elektriksel kısıtlar altında minimize edilmiştir. HAA metodu 6 baralı 3 generatörlü, 14 baralı 5 generatörlü (IEEE) ve 30 baralı 6 generatörlü (IEEE) olmak üzere üç farklı test sistemine uygulanmıştır. MATLAB R2010a’da bir program geliştirilerek test sistemlerinin çözümleri elde edilmiştir. Bulunan optimal çözüm değerleri, literatürde farklı metotlar uygulanarak bulunan optimal çözüm değerleriyle karşılaştırılmış ve sonuçlar tartışılmıştır.

Anahtar Kelimeler

• Ekonomik güç dağıtımı,Valf nokta etkileri,Konveks olmayan fonksiyonlar,Harmoni arama algoritması

Kaynakça

1. [1] Yaşar, C., Özyön, S., “A new hybrid approach for nonconvex economic dispatch problem with valve-point effect”, Energy, Volume 36, Issue 10, s.5838-5845, October 2011.
2. [2] Malik T.N., Asar A., Wyne M.F., Akhtar S., "A new hybrid approach for the solution of nonconvex economic dispatch problem with valve-point effects", Electric Power Systems Research, Vol.80, No.9, s.1128-1136, 2010.
3. [3] Özyön S., Yaşar C., Temurtaş H., "Diferansiyel gelişim algoritmasının valf nokta etkili konveks olmayan ekonomik güç dağıtım problemlerine uygulanması - Differential evolution algorithm approach to nonconvex economic power dispatch problems with valve point effect", 6th International Advanced Technologies Symposium (IATS’11), Electrical & Electronics Technologies Papers, Vol.4, EAE-40, s.181-186, 16-18 May 2011, Elazığ, TURKEY.
4. [4] Yuan X., Wang L., Zhang Y., Yuan Y., "A hybrid differential evolution method for dynamic economic dispatch with valve-point effects", Expert systems with applications, Vol.36, No.2, Part. 2, s.4042-4048, 2009.
5. [5] Labbi Y., Attous D., "Big bang – big crunch optimization algorithm for economic dispatch with valve-point effect", Journal of Theoretical and Applied Information Technology, Vol.16, No.1, s.48-56, 2010.
6. [6] Lin W.M., Gow H.J., Tsay M.T., "A Partition Approach Algorithm for nonconvex Economic Dispatch", Electrical Power and Energy Systems, Vol.29, No: 5, s. 432-438, 2007.
7. [7] Selvekumar A.I., Thanushkodi K., "Anti-Predatory Particle Swarm Optimization: Solution to Nonconvex Economic Dispatch Problems", Electrical Power Systems Research, Vol.78, No.1, s. 2-10, 2008.
8. [8] Chaturvedi K.T., Pandit M., Srivastava L., "Particle swarm optimization with time varying acceleration coefficients for non-convex economic power dispatch", Electrical Power and Energy Systems, Vol.31, No.6, s. 249-257, July 2009.

9. [9] Panigrahi B.K., Yadav S.R., Tiwari M.K.,"A clonal algorithm to solve economic load dispatch", Electric Power Systems Research, Vol.77, No.10, s.1381-1389, 2007.
10. [10] Da-kuo H., Fu-li W., Zhi-zhong M., "Hybrid genetic algorithm for economic dispatch with valve-point effect", Electric Power Systems Research, Vol.78, s.626-633, 2008.
11. [11] Guerrero R.E.P., Maldonado J.R.C., “Economic power dispatch with non-smooth cost functions using differential evolution", Power Symposium 2005, NAPS 2005, Proceedings of the 37th Annual North American, s.183-190, 2005.
12. [12] Michalewicz Z., Schoenauer M., "Evolutionary algorithm for constrained parameter optimization problem", Evolutionary Computation, Vol.4, No.1, s.1-32, 1996.
13. [13] Özyön, S., Yaşar, C., Özcan G., Temurtaş, H., “Valf nokta etkili konveks olmayan ekonomik güç dağıtım problemlerine yapay arı koloni algoritması (ABC) yaklaşımı - An artificial bee colony algorithm (ABC) aproach to nonconvex economic power dispatch problems with valve point effect”, Ulusal Elektrik-Elektronik Bilgisayar Sempozyumu (FEEB 2011), Bildiri Kitabı-1, s. 294-299, 05-07 Ekim 2011, Elazığ, TÜRKİYE.
14. [14] Wood A. J., Wollenberg B. F., "Power Generation Operation and Control ", New York-Wiley, 1996.
15. [15] Ayvaz M. T., Karahan, H., Gürarslan, G., “Su dağıtım şebekelerinin armoni araştırması optimizasyon tekniği ile optimum tasarımı” 5. Kentsel Altyapı Ulusal Sempozyumu, Bildiriler Kitabı, s.188-202, 2007.
16. [16] Geem ZW, Kim JH, Loganathan GV., “A new heuristic optimization algorithm: harmony search” Simulation, Vol.76, No.2, s.60-68, 2001.
17. [17] Lee KS, Geem ZW. “A new structural optimization method based on the harmony search algorithm” Computers and Structures, Vol.82 No.9-10, s.781-798, 2004.
18. [18] Lee KS, Geem ZW. “A new meta-heuristic algorithm for continues engineering optimization: harmony search theory and practice” Computer Method Application Mech. Eng., Vol.194, s.3902–3933, 2004.
19. [19] Mahdavi M, Fesanghary M, Damangir E. “An improved harmony search algorithm for solving optimization problems” Applied Mathematics and Computation, vol.188, s.1567–1579, 2007.