Application of Chaotic Maps to Economic Load Dispatch Problem

Yıl 2024, Cilt: 14 Sayı: 3, 1630 – 1639, 15.09.2024

Mehmet Safa Aydın , Ertuğrul Çam

https://doi.org/10.31466/kfbd.1530071

Öz

This paper aims to solve the economic load dispatch problem (ELD) by using random numbers generated by chaotic maps with particle swarm optimization (PSO). The randomly generated coefficients r1 and r2 in the velocity equation of the PSO algorithm are generated by three different chaotic map methods namely logistic map, gaussian map, and tent map. As a result, three different methods are proposed: PSO with logistic map (LMPSO), PSO with Gaussian map (GMSPO), and PSO with tent map (TMPSO). These algorithms are applied to a 40-unit test system that includes transmission line losses, and the results are compared with the standard PSO algorithm. Each algorithm was run 50 times, and the maximum, minimum, and average values were recorded. All the proposed methods found lower costs than the standard PSO algorithm. Although the lowest cost was achieved with the GMPSO algorithm, the LMPSO algorithm was observed to be more successful on average.

Anahtar Kelimeler

Economic Load Dispatch, Particle Swarm Optimization, Chaotic Maps, Optimization

Kaynakça

• Adarsh, B. R., Raghunathan, T., Jayabarathi, T., & Yang, X.-S. (2016). Economic dispatch using chaotic bat algorithm. Energy, 96, 666–675. https://doi.org/https://doi.org/10.1016/j.energy.2015.12.096
• Alataş, B. (2007). Kaotik Haritalı Parçacık Sürü Optimizasyonu Algoritmaları Geliştirme.
• Arul, R., Velusami, S., & Ravi, G. (2013). Chaotic firefly algorithm to solve economic load dispatch problems. 2013 International Conference on Green Computing, Communication and Conservation of Energy (ICGCE), 458–464. https://doi.org/10.1109/ICGCE.2013.6823480
• Balamurugan, R., & Subramanian, S. (2007). Self-Adaptive Differential Evolution Based Power Economic Dispatch of Generators with Valve-Point Effects and Multiple Fuel Options. International Journal of Electrical and Computer Engineering, 1, 543–550. https://api.semanticscholar.org/CorpusID:11392605
• Barati, H., & Sadeghi, M. (2018). An efficient hybrid MPSO-GA algorithm for solving non-smooth/non-convex economic dispatch problem with practical constraints. Ain Shams Engineering Journal, 9(4), 1279–1287. https://doi.org/10.1016/j.asej.2016.08.008
• Barisal, A. K., & Prusty, R. C. (2015). Large scale economic dispatch of power systems using oppositional invasive weed optimization. Applied Soft Computing Journal, 29, 122–137. https://doi.org/10.1016/j.asoc.2014.12.014
• Burak Demir, F., Tuncer, T., Fatih Kocamaz, A., Turgut, M., Üniversitesi Bilgisayar, Ö., & Bölümü, T. (2019). Lojistik-Gauss Harita Tabanlı Yeni Bir Kaotik Sürü Optimizasyon Yöntemi.
• Doğru, A. S., Temel, B., & Eren, T. (2019). Comparison of Particle Swarm Optimization and Bat Algorithm Methods in Localization of Wireless Sensor Networks. Uluslararası Muhendislik Arastirma ve Gelistirme Dergisi, 793–801. https://doi.org/10.29137/umagd.668724
• Eke, İ., SAKA, M., & Tezcan, S. (2023). Kaotik Parçacık Sürü Optimizasyonu Kullanarak Ekonomik Yük Dağıtımı Probleminin Çözümüsolutıon Of The Economıc Load Dıspatch Problem Usıng Chaotıc Partıcle Swarm Optımızatıon. Mühendislik Bilimleri ve Tasarım Dergisi, 11, 957–965. https://doi.org/10.21923/jesd.1293964
• Hassan, M. H., Kamel, S., Salih, S. Q., Khurshaid, T., & Ebeed, M. (2021). Developing Chaotic Artificial Ecosystem-Based Optimization Algorithm for Combined Economic Emission Dispatch. IEEE Access, 9, 51146–51165. https://doi.org/10.1109/ACCESS.2021.3066914
• Onan, A. (2013). Metasezgisel Yöntemler ve Uygulama Alanları. Çukurova Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 17(2), 113–128. https://dergipark.org.tr/en/pub/cuiibfd/issue/4144/54418
• Rezaie, H., Kazemi-Rahbar, M. H., Vahidi, B., & Rastegar, H. (2018). Solution of combined economic and emission dispatch problem using a novel chaotic improved harmony search algorithm. Journal of Computational Design and Engineering, 6(3), 447–467. https://doi.org/10.1016/j.jcde.2018.08.001
• Sudhakaran, M., Raj, P. A. .-. D. .-. V, & Palanivelu, T. G. (2007). Application of Particle Swarm Optimization for Economic Load Dispatch Problems. 2007 International Conference on Intelligent Systems Applications to Power Systems, 1–7. https://doi.org/10.1109/ISAP.2007.4441694
• Tanyıldızı, E., & Cigalı, T. (2017). Kaotik Haritalı Balina Optimizasyon Algoritmaları. Fırat Üniversitesi Mühendislik Bilimleri Dergisi, 29(1), 307–317. https://doi.org/10.35234/fumbd.314671
• Tao, Z., & Jin-ding, C. (2009). A new chaotic PSO with dynamic inertia weight for economic dispatch problem. 2009 International Conference on Sustainable Power Generation and Supply, 1–6. https://doi.org/10.1109/SUPERGEN.2009.5347916
• Walters, D. C., & Sheble, G. B. (1993). Genetic algorithm solution of economic dispatch with valve point loading. IEEE Transactions on Power Systems, 8(3), 1325–1332. https://doi.org/10.1109/59.260861
• Xu, Z., Yang, H., Li, J., Zhang, X., Lu, B., & Gao, S. (2021). Comparative study on single and multiple chaotic maps incorporated grey wolf optimization algorithms. IEEE Access, 9, 77416–77437.
• Younes, M., & Benhamida, F. (2011). Genetic algorithm-particle swarm optimization (GA-PSO) for economic load dispatch. Przeglad Elektrotechniczny, 4, 369–372.
• Zaraki, A., & Othman, M. F. Bin. (2009). Implementing particle swarm optimization to solve economic load dispatch problem. SoCPaR 2009 – Soft Computing and Pattern Recognition, 60–65. https://doi.org/10.1109/SoCPaR.2009.24

Kaotik Haritaların Ekonomik Yük Dağıtımı Problemine Uygulanması

Yıl 2024, Cilt: 14 Sayı: 3, 1630 – 1639, 15.09.2024

Mehmet Safa Aydın , Ertuğrul Çam

https://doi.org/10.31466/kfbd.1530071

Öz

Bu çalışmada kaotik haritalar ile üretilen rassal sayıların parçacık sürü optimizasyonu (PSO) ile kullanılarak ekonomik yük dağıtımı probleminin (EYD) çözülmesi hedeflenmiştir. PSO algoritmasının hız denkleminde yer alan ve rastgele oluşturulan r1 ve r2 katsayıları Lojistik kaotik harita metodu ile oluşturularak Lojistik haritalı PSO (LMPSO), gauss kaotik harita metodu ile oluşturularak gauss haritalı PSO (GMPSO) ve çadır kaotik harita metodu ile oluşturularak çadır haritalı PSO (TMPSO) metotları oluşturulmuştur. Oluşturulan bu algoritmalar iletim hattı kayıplarının dahil edildiği 40 üniteli test sistemine uygulanmış ve sonuçlar standart PSO algoritması ile karşılaştırılmıştır. Her algoritma 50 defa çalıştırılmış ve maksimum, minimum ve ortalama değerler kaydedilmiştir. Önerilen metotların hepsi standart PSO algoritmasından daha düşük maliyetler bulmuştur. En düşük maliyete GMPSO algoritması ile ulaşılmış olsa da ortalamada LMPSO algoritmasının daha başarılı olduğu gözlenmiştir.

Anahtar Kelimeler

Ekonomik Yük Dağıtımı, Parçacık Sürü Optimizasyonu, Kaotik Haritalar, Optimizasyon

Kaynakça

• Adarsh, B. R., Raghunathan, T., Jayabarathi, T., & Yang, X.-S. (2016). Economic dispatch using chaotic bat algorithm. Energy, 96, 666–675. https://doi.org/https://doi.org/10.1016/j.energy.2015.12.096
• Alataş, B. (2007). Kaotik Haritalı Parçacık Sürü Optimizasyonu Algoritmaları Geliştirme.
• Arul, R., Velusami, S., & Ravi, G. (2013). Chaotic firefly algorithm to solve economic load dispatch problems. 2013 International Conference on Green Computing, Communication and Conservation of Energy (ICGCE), 458–464. https://doi.org/10.1109/ICGCE.2013.6823480
• Balamurugan, R., & Subramanian, S. (2007). Self-Adaptive Differential Evolution Based Power Economic Dispatch of Generators with Valve-Point Effects and Multiple Fuel Options. International Journal of Electrical and Computer Engineering, 1, 543–550. https://api.semanticscholar.org/CorpusID:11392605
• Barati, H., & Sadeghi, M. (2018). An efficient hybrid MPSO-GA algorithm for solving non-smooth/non-convex economic dispatch problem with practical constraints. Ain Shams Engineering Journal, 9(4), 1279–1287. https://doi.org/10.1016/j.asej.2016.08.008
• Barisal, A. K., & Prusty, R. C. (2015). Large scale economic dispatch of power systems using oppositional invasive weed optimization. Applied Soft Computing Journal, 29, 122–137. https://doi.org/10.1016/j.asoc.2014.12.014
• Burak Demir, F., Tuncer, T., Fatih Kocamaz, A., Turgut, M., Üniversitesi Bilgisayar, Ö., & Bölümü, T. (2019). Lojistik-Gauss Harita Tabanlı Yeni Bir Kaotik Sürü Optimizasyon Yöntemi.
• Doğru, A. S., Temel, B., & Eren, T. (2019). Comparison of Particle Swarm Optimization and Bat Algorithm Methods in Localization of Wireless Sensor Networks. Uluslararası Muhendislik Arastirma ve Gelistirme Dergisi, 793–801. https://doi.org/10.29137/umagd.668724
• Eke, İ., SAKA, M., & Tezcan, S. (2023). Kaotik Parçacık Sürü Optimizasyonu Kullanarak Ekonomik Yük Dağıtımı Probleminin Çözümüsolutıon Of The Economıc Load Dıspatch Problem Usıng Chaotıc Partıcle Swarm Optımızatıon. Mühendislik Bilimleri ve Tasarım Dergisi, 11, 957–965. https://doi.org/10.21923/jesd.1293964
• Hassan, M. H., Kamel, S., Salih, S. Q., Khurshaid, T., & Ebeed, M. (2021). Developing Chaotic Artificial Ecosystem-Based Optimization Algorithm for Combined Economic Emission Dispatch. IEEE Access, 9, 51146–51165. https://doi.org/10.1109/ACCESS.2021.3066914
• Onan, A. (2013). Metasezgisel Yöntemler ve Uygulama Alanları. Çukurova Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 17(2), 113–128. https://dergipark.org.tr/en/pub/cuiibfd/issue/4144/54418
• Rezaie, H., Kazemi-Rahbar, M. H., Vahidi, B., & Rastegar, H. (2018). Solution of combined economic and emission dispatch problem using a novel chaotic improved harmony search algorithm. Journal of Computational Design and Engineering, 6(3), 447–467. https://doi.org/10.1016/j.jcde.2018.08.001
• Sudhakaran, M., Raj, P. A. .-. D. .-. V, & Palanivelu, T. G. (2007). Application of Particle Swarm Optimization for Economic Load Dispatch Problems. 2007 International Conference on Intelligent Systems Applications to Power Systems, 1–7. https://doi.org/10.1109/ISAP.2007.4441694
• Tanyıldızı, E., & Cigalı, T. (2017). Kaotik Haritalı Balina Optimizasyon Algoritmaları. Fırat Üniversitesi Mühendislik Bilimleri Dergisi, 29(1), 307–317. https://doi.org/10.35234/fumbd.314671
• Tao, Z., & Jin-ding, C. (2009). A new chaotic PSO with dynamic inertia weight for economic dispatch problem. 2009 International Conference on Sustainable Power Generation and Supply, 1–6. https://doi.org/10.1109/SUPERGEN.2009.5347916
• Walters, D. C., & Sheble, G. B. (1993). Genetic algorithm solution of economic dispatch with valve point loading. IEEE Transactions on Power Systems, 8(3), 1325–1332. https://doi.org/10.1109/59.260861
• Xu, Z., Yang, H., Li, J., Zhang, X., Lu, B., & Gao, S. (2021). Comparative study on single and multiple chaotic maps incorporated grey wolf optimization algorithms. IEEE Access, 9, 77416–77437.
• Younes, M., & Benhamida, F. (2011). Genetic algorithm-particle swarm optimization (GA-PSO) for economic load dispatch. Przeglad Elektrotechniczny, 4, 369–372.
• Zaraki, A., & Othman, M. F. Bin. (2009). Implementing particle swarm optimization to solve economic load dispatch problem. SoCPaR 2009 – Soft Computing and Pattern Recognition, 60–65. https://doi.org/10.1109/SoCPaR.2009.24

Toplam 19 adet kaynakça vardır.

Ayrıntılar

Kaynak Göster

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