Abstract
Increasing uncertainties in electricity prices, load demand, and renewable energy generation pose significant challenges for optimal microgrid operation in deregulated electricity markets. This paper proposes a self-adaptive Gravitational Search Algorithm (SGSA), which enhances the standard GSA by incorporating a self-adaptive mutation operator with two movement strategies to mitigate premature convergence and improve solution quality. To model uncertainties in load demand, market prices, and renewable outputs, the 2 m-Point Estimation Method (PEM) is employed as a computationally efficient alternative to conventional stochastic approaches. The proposed SGSA-PEM framework is applied to a low-voltage microgrid consisting of microturbines, phosphoric acid fuel cells, photovoltaic units, wind turbines, and battery storage. Simulation results indicate that the integration of battery storage reduces the total generation cost by up to 49.7%, while renewable energy penetration increases by approximately 10% during peak demand periods. Furthermore, comparative analysis shows that SGSA achieves lower operating costs and converges about 25% faster than standard GSA and Particle Swarm Optimization (PSO). The results confirm that the proposed framework provides a computationally efficient and robust solution for probabilistic microgrid energy management under uncertainty.
Data availability
All data generated or analysed during this study are included in this published article.
Abbreviations
- DER:
-
Distributed Energy Resources (microturbines, fuel cells, photovoltaic units, wind turbines, and battery storage)
- MGCC:
-
Microgrid Central Controller (distributed generation and load management controller)
- SGSA:
-
Self-Adaptive Gravitational Search Algorithm (the modified GSA that implements adaptive mutation strategies)
- PEM:
-
2 m-Point Estimation Method (type used for model uncertainties in load, prices, and renewable outputs)
- GSA:
-
Gravitational Search Algorithm, a metaheuristic optimization methodology based on Newtonian Gravity
- PSO:
-
Particle Swarm Optimization (a heuristic optimization algorithm)
- OPF:
-
Optimal Power Flow (a method for microgrid power dispatch)
- FESS:
-
Flywheel Energy Storage System (used for load support mode in islanded)
- Mean_k, t:
-
Mean position for all particles in dimension t at iteration k in SGSA
- Gl_k, t:
-
Global best position in dimension t at iteration k in SGSA
- α:
-
The learning rate for probability updates in SGSA, set to 0.142
- Prb1, Prb2:
-
Probabilities of mutating with mutation strategies 1 and 2 in SGSA
- Accum1, Accum2:
-
Accumulators for the probabilities used to update the mutation strategy using strategy 1 and strategy 2, respectively in SGSA
- PDG :
-
The power output from the distributed generators (including but not limited to microturbines, PV, and wind turbines)
- Ctotal :
-
The total generation cost of the microgrid, expressed in (€)
- Rpen :
-
The renewable percentage penetration (%)
- µX :
-
Mean of the input random variable X in PEM (e.g., load demand, market price)
- σX :
-
Standard deviation of the input random variable X in PEM
- ξX, i :
-
Location of the i-th concentration point in PEM for variable X
- wX, i :
-
Weight of the i-th concentration point in PEM for variable X
- Z:
-
Output random variable in PEM (e.g., total cost, power output)
- E[Zk]:
-
k-th moment of the output random variable Z in PEM
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Acknowledgements
This work was funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No. (DGSSR-2025-02-01318).
Funding
This work was funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under Grant No. (DGSSR-2025-02-01318).
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Emad M. Ahmed: conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing – review & editing, visualization. Zaki A. Zaki: conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing – review & editing, visualization. Mehrdad Ahmadi Kamarposhti: conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing – original draft, writing – review & editing, visualization, supervision, project administration, funding acquisition. El Manaa Barhoumi: conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing – review & editing, visualization. Ilhami Colak: conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing – review & editing, visualization. All authors have read and agreed to the published version of the manuscript.
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Ahmed, E.M., Zaki, Z.A., Kamarposhti, M.A. et al. Probabilistic operational management of a renewable-based microgrid considering uncertainties using the self-adaptive gravitational search algorithm. Sci Rep (2026). https://doi.org/10.1038/s41598-026-42839-8
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DOI: https://doi.org/10.1038/s41598-026-42839-8
