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Energy supply through integrated renewable energy sources (RESs) and battery systems will be of higher importance for future residential sectors. Optimal energy management and sizing for the components of residential systems can enhance efficiency, self-suffiency, and meanwhile can be cost-effective by reducing investment as well as operating costs. Accordingly, this paper proposes an exhaustive optimization model for determining the capacity of RESs, namely: wind turbines and photovoltaic (PV) systems. In this study, batteries and electric vehicles (EVs) are utilized in line with other sources to capture fluctuations of RESs. To model the uncertainties of RESs, energy prices, and load demands a linearized stochastic programming framework is applied. The proposed framework involves long-term and efficient resource development alongside with short-term management and utilization of these resources for supplying the demand load. In our study, we utilize the roulette wheel mechanism (RWM) method as well as proper probability distribution functions (PDFs) to generate scenarios for all sources of uncertainties, including wind turbines, PV systems, demand, and electricity market price. The approach is verified in two different cases, including an individual home and a larger micro-grid (MG). The results of multiple numerical simulations demonstrate the effectiveness of the proposed stochastic model.

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