Minimizing total costs for distribution power grids considering harmonics and uncertainty of wind speed and solar radiation

Le Chi Kien, Nguyen Dinh Phu, Thang Trung Nguyen, Thai Dinh Pham and Minh Phuc Duong

PLOS ONE, 2026, vol. 21, issue 9, 1-34

Abstract: Nowadays, distributed renewable energy generation sources are increasingly popular and strongly impact the traditional power grid. Therefore, determining the appropriate penetration of these sources is a big challenge because of the randomness of the renewable electricity output. This study applies a robust and stable algorithm, called the modified coyote optimization algorithm (MCOA), to determine an optimal solution for the effective integration of wind turbine and photovoltaic distributed generation units (WT-PVDGUs) in different-scale power grids of IEEE 33 buses and 69 buses. For the first case, the primary goal is to minimize the combined costs of investment, operation, and maintenance (OM) of WT-PVDGUs, energy purchase for loads, and energy loss during distribution while mitigating the harmfulness of harmonics on power quality and load operation. The study applies Weibull and Beta probability distribution functions (pdfs) to predict the output power of WT-PVDGUs to enhance the quality of the found feasible solutions. The obtained results from the suggested method are compared with five other active methods to demonstrate the superiority of MCOA with total cost savings of up to 25.56% ($4.1811 million) for the first system and 27.05% ($4.9090 million) for the second system over the 20-year project life cycle. In addition, in the second case, the optimal solution from MCOA achieves a loss reduction of up to 65.51% in the first system and 69.17% in the second system. These results are better than dozens of recently published methods. Not only that, but the voltage profile is also raised to the best range, and the total and individual harmonic distortions are mitigated and meet the IEEE Std. 519 thanks to the optimal installation of units in the power grids. Therefore, this study has significantly contributed to reducing total costs, eliminating the harmful effects of harmonics, and dealing with uncertainty regarding renewable energies.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0355399

DOI: 10.1371/journal.pone.0355399

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