Expanding the Scope: Modified Fortescue Theory for Frequency Unbalance Resolution in Control Strategies

Karim Mansouri, Brahim Metoui, Cristian Nichita, Amr Yousef and Ezzeddine Touti ()
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Karim Mansouri: IREENA Laboratory, UR 4642, Nantes University, 37 bd de l’Université, 44600 Saint-Nazaire, France
Brahim Metoui: MACS Laboratory, LR16ES22, University of Gabes, Gabes 6072, Tunisia
Cristian Nichita: Groupe de Recherche en Electrotechnique et Automatique du Havre, University Le Havre Normandie, 75 rue Bellot, 76058 Le Havre Cedex, France
Amr Yousef: Electrical Engineering Department, College of Engineering, University of Business and Technology, Jeddah 21589, Saudi Arabia
Ezzeddine Touti: Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia

Mathematics, 2025, vol. 13, issue 21, 1-26

Abstract: To analyze unbalanced electrical systems, the mathematical technique “symmetrical components method” developed by Charles LeGeyt Fortescue in the early 20th century has been very successful in this field. By decomposing three-phase systems into three symmetrical components: positive sequence, negative sequence, and zero sequence, the Fortescue theory provides an important analyzing method. It allows for the calculation of these symmetrical components, which helps in understanding and addressing issues related to unbalance in amplitude within electrical systems. This theory deals only with amplitude unbalances in electrical systems to analyze and solve those problems. Since this technique is limited only to amplitude unbalance, our objective is to propose a modified Fortescue theory, which will resolve frequency unbalance problems in electrical systems. The new balanced components, at the conclusion of this new theory, will be used as references to be assigned in the adopted control strategies in a subsequent research paper.

Keywords: frequency unbalance; amplitude unbalance; Fortescue theory; symmetrical components; electrical systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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