Application of Chaotic Maps to Economic Load Dispatch Problem

Mehmet Safa Aydın; Ertuğrul Çam

doi:10.31466/kfbd.1530071

EN TR

Application of Chaotic Maps to Economic Load Dispatch Problem

Abstract

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.

Keywords

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

Kaotik Haritaların Ekonomik Yük Dağıtımı Problemine Uygulanması

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

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Details

Primary Language

English

Subjects

Power Plants

Journal Section

Research Article

Authors

Mehmet Safa Aydın ^*
0000-0002-2219-8121
Türkiye

Ertuğrul Çam
0000-0001-6491-9225
Türkiye

Publication Date

September 15, 2024

Submission Date

August 8, 2024

Acceptance Date

August 27, 2024

Published in Issue

Year 2024 Volume: 14 Number: 3

DOI

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

IZ

https://izlik.org/JA24ND38EA

APA

Aydın, M. S., & Çam, E. (2024). Application of Chaotic Maps to Economic Load Dispatch Problem. Karadeniz Fen Bilimleri Dergisi, 14(3), 1630-1639. https://doi.org/10.31466/kfbd.1530071

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