DOI: 10.11648/j.ijepe.20261505.11 ISSN: 2326-960X

Hybrid Renewable Energy Supply System for Remote Villages of Grid in Madagascar Using Linear Programming by Simplex Method and Genetic Algorithms

Solofo Rakotoniaina, Iderana Indoniavo, Harlin Andriatsihoarana
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This paper details the development of a linear model to optimize the sizing of a hybrid renewable energy supply system (HRESS) for remote rural villages in developing countries. The model studied is defined by its energy supply versatility to rural household consumers. It includes electrical energy, thermal energy for cooking, and also muscular energy used for transport and manual work related to the HRESS and agriculture. For HRESS design, the approach optimizes the objective function related to total annual cost. Our optimization methodology is organized around simplex and genetic algorithms. They are simple to implement and compatible with linear programming. First, we use the deterministic simplex method for model design; second, we use a genetic algorithm as a heuristic to optimize the multi-criteria objective function. The simplex method yields a solution based on weighting coefficients α for cost, β: for CO 2 emissions, and γ : for renewable energy sources. Our approach provides a three-dimensional Pareto front (total cost, CO 2 emissions, and share of renewable sources). To demonstrate the design process of HRESS, a numerical study is drawn from the fishing village of Lavanono, located in the extreme south of Madagascar. In the context of minimizing total cost Z, the single economic-criterion method demonstrates a preference for non-renewable energy sources. Specifically, the implementation of the simplex and genetic algorithm methods results in the selection of diesel generators for 100% of the electricity supply, with a production of 128,551 kWh, and firewood for 100% of the energy for cooking, with a production of 379,600 kWh. The novelty of our approach lies in the integration of human and animal muscle power into the HRESS. The optimization of this approach yields 12 workers (1,382 kWh) and 10 beef domestic power (5,760 kWh) in the HRESS. The aforementioned amount is equivalent to Z=38,052 USD. The three-dimensional Pareto front is utilized to achieve a sustainable HRESS. The intermediate compromise is as follows: an 80% share of renewable energy sources: agrivoltaics, wind, and biogas. Agrivoltaics and wind power together provide 80% of the electricity supply. The diesel generator supplies the remaining 20%. It is estimated that biogas accounts for approximately 40% of clean cooking in the village of Lavanono. The emission limit of HRESS is set at 150 tons of carbon dioxide per year. In this case, the total cost of the project becomes Z = 70,500 USD.

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