Pareto-based multi-objective whale optimization algorithm for economic-environmental optimal power flow

Abstract

This paper presents a Multi-Objective Whale Optimization Algorithm (MOWOA) for solving the Optimal Power Flow (OPF) problem in the IEEE 30-bus test system. The proposed approach simultaneously optimizes four conflicting objectives: fuel cost minimization ($/h), active power loss minimization (MW), voltage deviation minimization (p.u.), and emission reduction (ton/h). A Pareto-based archive mechanism combined with a crowding distance strategy is employed to maintain a well-distributed set of non-dominated solutions. The MOWOA effectively mimics the bubble-net hunting behavior of humpback whales to explore the multi-dimensional search space. Simulation results on the IEEE 30-bus system demonstrate that the proposed algorithm successfully generates a rich Pareto-optimal front comprising 50 non-dominated solutions. The best cost solution achieves 798.34 $/h, which is competitive with state-of-the-art single-objective methods. Comprehensive trade-off analysis reveals that a 62.7% reduction in emissions can be achieved at only a 22.7% increase in fuel cost, offering decision-makers flexible and insightful options for sustainable power system operation.

Keywords

• Optimal power flow
• Multi-objective optimization
• Whale optimization algorithm
• Pareto front
• IEEE 30-bus system

Ekonomik-çevresel optimal güç akışı için pareto tabanlı çok amaçlı balina optimizasyon algoritması

Abstract

Bu makale, IEEE 30-bara test sisteminde Optimal Güç Akışı (OPF) problemini çözmek için Çok Amaçlı Balina Optimizasyon Algoritması (MOWOA) sunmaktadır. Önerilen yaklaşım, birbiriyle çelişen dört hedefi eş zamanlı olarak optimize etmektedir: yakıt maliyetinin en aza indirilmesi ($/h), aktif güç kaybının en aza indirilmesi (MW), gerilim sapmasının en aza indirilmesi (p.u.) ve emisyon azaltımı (ton/h). İyi dağıtılmış bir domine edilmemiş çözümler kümesini korumak için Pareto tabanlı bir arşiv mekanizması, yoğunluk mesafesi (crowding distance) stratejisi ile birlikte kullanılmaktadır. MOWOA algoritması, çok boyutlu arama uzayını keşfetmek için kambur balinaların baloncuk ağı (bubble-net) avlanma davranışını taklit ederek çalışmaktadır. IEEE 30-bara test sistemi üzerinde gerçekleştirilen simülasyon sonuçları, önerilen algoritmanın 50 adet domine edilmemiş çözümden oluşan zengin bir Pareto-optimal ön cephe (Pareto front) üretmede başarılı olduğunu göstermektedir. En düşük maliyetli çözüm 798,34 $/h değerine ulaşmış olup, bu sonuç mevcut tek amaçlı en gelişmiş yöntemlerle rekabet edebilecek düzeydedir. Kapsamlı ödünleşim (trade-off) analizi, yakıt maliyetinde yalnızca %22,7’lik bir artış karşılığında emisyonların %62,7 oranında azaltılabileceğini ortaya koymaktadır. Bu durum, sürdürülebilir güç sistemi işletimi için karar vericilere esnek ve değerli seçenekler sunmaktadır.

Keywords

• Optimal güç akışı
• Çok amaçlı optimizasyon
• Balina optimizasyon algoritması
• Pareto ön cephesi
• IEEE 30-bara sistemi

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