Concerning the advantages of smart microgrids and the importance of selecting and using technologies accustomed to optimized planning and design of typology and capacity of supplies, demand response programs, and energy-storage charges, the existing research has focused on the optimized design of microgrids using ant colony optimization algorithm. Conditions of the optimization problem are enacted on the objective function based on technical and operational limitations of supplies and microgrids, which may lead to the limitation of response space of the problem. Additionally, a methodology is proposed for modeling and analyzing a novel design to consider the uncertainty of production and demand with reverse risk in the design of residential microgrids. The proposed methodology focuses on the uncertainty of photovoltaic production and load demand by solving twodimensional multipurpose optimization problems based on information gap decision theory (IGDT). In the mentioned approach, the photovoltaic generation's uncertainty and charge are integrated into an equation to be solved as a problem. Regardless of the likelihood density function of uncertainty parameters and without preparing a firm framework, the current method integrates wind and photovoltaic production into the microgrids. The results of the mentioned method are conclusive, which makes the problems solvable.
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