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AIMS Mathematics

2026, Volume 11, Issue 6: 19242-19285. doi: 10.3934/math.2026783
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Adaptive fractional-order moth flame swarm intelligence algorithm for optimal reactive power dispatch and stability enhancement in power grids

  • 1.
    Department of Electrical Engineering, COMSATS University Islamabad Attock campus, Pakistan
  • 2.
    Department of Electrical Engineering, College of Engineering, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 12271, Saudi Arabia
  • 3.
    Zero Emission Technologies Innovation Center, University of Tabuk, Tabuk 47913, Saudi Arabia
  • 4.
    Department of Electrical Engineering, Faculty of Engineering, University of Tabuk, Tabuk 47913, Saudi Arabia
  • 5.
    Department of Electrical Engineering, Dong-A University, Busan 49315, Republic of Korea
  • 6.
    Department of ICT Integrated Safe Ocean Smart Cities Engineering, Dong-A University, Busan 49315, Republic of Korea
  • Published: 30 June 2026

  • MSC : 90C59, 90C30, 34A08, 68T20

  • This paper presents a fractional-order swarm intelligence optimization framework for solving the optimal reactive power dispatch (ORPD) problem in modern power grids. The proposed method integrates fractional calculus into the moth-flame optimization algorithm to capture the memory and hereditary characteristics inherent in complex power systems. The fractional-order formulation enhances information exchange among candidate solutions and improves the exploitation capability of the search process. The resulting fractional-order moth-flame optimization (FMFO) algorithm was applied to IEEE benchmark power systems to minimize real power losses and voltage deviations while considering flexible alternating current transmission system (FACTS) device constraints. Simulation results demonstrate significant performance improvements, achieving active power loss reductions of 17.53% in the IEEE-30 bus system, 43.32% in the modified IEEE-30 bus network, and 22.5% in the IEEE-57 bus system. Furthermore, voltage deviation was reduced by up to 84% in the IEEE-57 benchmark system. Statistical evaluations confirm the robustness, stability, and superior convergence behavior of the proposed fractional-order swarm optimization framework compared with conventional optimization techniques, demonstrating its effectiveness for intelligent power system operation.

    Citation: Babar Sattar Khan, Affaq Qamar, Abdul Wadood, Hani Albalawi, Herie Park, Byung O Kang. Adaptive fractional-order moth flame swarm intelligence algorithm for optimal reactive power dispatch and stability enhancement in power grids[J]. AIMS Mathematics, 2026, 11(6): 19242-19285. doi: 10.3934/math.2026783

    Related Papers:

  • This paper presents a fractional-order swarm intelligence optimization framework for solving the optimal reactive power dispatch (ORPD) problem in modern power grids. The proposed method integrates fractional calculus into the moth-flame optimization algorithm to capture the memory and hereditary characteristics inherent in complex power systems. The fractional-order formulation enhances information exchange among candidate solutions and improves the exploitation capability of the search process. The resulting fractional-order moth-flame optimization (FMFO) algorithm was applied to IEEE benchmark power systems to minimize real power losses and voltage deviations while considering flexible alternating current transmission system (FACTS) device constraints. Simulation results demonstrate significant performance improvements, achieving active power loss reductions of 17.53% in the IEEE-30 bus system, 43.32% in the modified IEEE-30 bus network, and 22.5% in the IEEE-57 bus system. Furthermore, voltage deviation was reduced by up to 84% in the IEEE-57 benchmark system. Statistical evaluations confirm the robustness, stability, and superior convergence behavior of the proposed fractional-order swarm optimization framework compared with conventional optimization techniques, demonstrating its effectiveness for intelligent power system operation.



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