A Novel Sigmoid Fractional Binary Swarm Intelligent Solution for Optimal Reactive Power Dispatch
6 affiliations
- 1Department of Electrical Engineering, COMSATS University Islamabad, Islamabad 44000, Pakistan
- 2Zero Emission Technologies Innovation Center, University of Tabuk, Tabuk 47913, Saudi Arabia
- 3Department of Electrical Engineering, Faculty of Engineering, University of Tabuk, Tabuk 47913, Saudi Arabia
- 4Department of Electrical Engineering, Dong-A University, Busan 49315, Republic of Korea
- 5Department of ICT Integrated Safe Ocean Smart Cities Engineering, Dong-A University, Busan 49315, Republic of Korea
- 6Faculty of Engineering and Technology, Gomal University, Dera Ismail Khan 29050, Pakistan
Abstract
Reliable, economical, and secure operation of a power system depends heavily on how well its reactive power is managed. Optimal reactive power dispatch (ORPD) coordinates generator voltage magnitudes, transformer tap settings, and switched shunt compensation so that bus voltages stay within acceptable limits and transmission losses are kept low. Because these controls interact through nonlinear power-flow relations, and because tap positions and shunt banks are physically discrete while generator voltages are continuous, the problem is non-convex, multimodal, and mixed-integer. Continuous optimizers must round their solutions and therefore never search the discrete space directly, while conventional single-lag velocity updates discard the information of earlier iterations and lose swarm diversity. To address both limitations simultaneously, a sigmoid fractional binary particle swarm optimization–gravitational search algorithm (FBPSOGSA) is proposed. The velocity is updated through a truncated Grünwald–Letnikov fractional-order expansion of depth four, which retains a weighted memory of the four most recent velocities, and is mapped to a bit-switching probability through a sigmoid (S-shaped) transfer function that drives the discrete controls directly in binary space. The method is validated on the IEEE 30-bus test system for two objectives. For active power loss minimization, the FBPSOGSA attains 5.4877 MW at a fractional order of 0.2, the lowest value among all compared methods, corresponding to improvements of 19.57% over FAHLCPSO, 13.44% over OGSA, 0.96% over KHA, and 0.89% over GSA. For voltage deviation minimization, it attains 0.1059 p.u. at a fractional order of 0.1, again the lowest among all compared methods, with improvements of 15.82% over PSOGSA, 9.80% over FPSOGSA, 8.07% over FHPSO, and 64.26% over KHA. All reported control settings satisfy the system operating constraints, and the consistency of the solutions is confirmed over 25 independent runs.
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BibTeX
@article{muhammad2026novel,
title = {{A Novel Sigmoid Fractional Binary Swarm Intelligent Solution for Optimal Reactive Power Dispatch}},
author = {Yasir Muhammad and Muhammad Zeeshan and Abdul Wadood and Shahbaz Khan and Hani Albalawi and Herie Park and Byung O Kang and Aamir Nawaz},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10100700},
url = {https://www.mdpi.com/2504-3110/10/10/700},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Novel Sigmoid Fractional Binary Swarm Intelligent Solution for Optimal Reactive Power Dispatch
AU - Yasir Muhammad
AU - Muhammad Zeeshan
AU - Abdul Wadood
AU - Shahbaz Khan
AU - Hani Albalawi
AU - Herie Park
AU - Byung O Kang
AU - Aamir Nawaz
PY - 2026
DA - 2026/10/04
JO - Fractal and Fractional
DO - 10.3390/fractalfract10100700
UR - https://www.mdpi.com/2504-3110/10/10/700
AB - Reliable, economical, and secure operation of a power system depends heavily on how well its reactive power is managed. Optimal reactive power dispatch (ORPD) coordinates generator voltage magnitudes, transformer tap settings, and switched shunt compensation so that bus voltages stay within acceptable limits and transmission losses are kept low. Because these controls interact through nonlinear power-flow relations, and because tap positions and shunt banks are physically discrete while generator voltages are continuous, the problem is non-convex, multimodal, and mixed-integer. Continuous optimizers must round their solutions and therefore never search the discrete space directly, while conventional single-lag velocity updates discard the information of earlier iterations and lose swarm diversity. To address both limitations simultaneously, a sigmoid fractional binary particle swarm optimization–gravitational search algorithm (FBPSOGSA) is proposed. The velocity is updated through a truncated Grünwald–Letnikov fractional-order expansion of depth four, which retains a weighted memory of the four most recent velocities, and is mapped to a bit-switching probability through a sigmoid (S-shaped) transfer function that drives the discrete controls directly in binary space. The method is validated on the IEEE 30-bus test system for two objectives. For active power loss minimization, the FBPSOGSA attains 5.4877 MW at a fractional order of 0.2, the lowest value among all compared methods, corresponding to improvements of 19.57% over FAHLCPSO, 13.44% over OGSA, 0.96% over KHA, and 0.89% over GSA. For voltage deviation minimization, it attains 0.1059 p.u. at a fractional order of 0.1, again the lowest among all compared methods, with improvements of 15.82% over PSOGSA, 9.80% over FPSOGSA, 8.07% over FHPSO, and 64.26% over KHA. All reported control settings satisfy the system operating constraints, and the consistency of the solutions is confirmed over 25 independent runs.
SN - 2504-3110
ER -