A Two-Stage Stochastic Model to Optimize the Number of Photovoltaic Panels in Smart Homes Considering the Impact of Air Pollution and Uncertainty in Daily Power Generation

Abstract

The growing demand for energy and environmental challenges have made optimizing energy consumption in the residential sector—a sector that accounts for 33.2% of energy use in Iran—essential for addressing the energy crisis, frequent power outages, and environmental pollution. This study develops a two-stage stochastic integer mathematical model to determine the optimal number of solar panels while providing an energy consumption scheduling plan for smart home appliances. The model incorporates technical, environmental, and economic factors, including installation space, air pollution levels, solar panel costs, and energy prices. A major source of uncertainty is the daily electricity generation capacity of solar panels, which varies throughout the year. To address this, the model treats each day as a scenario and is solved using GAMS software by converting the stochastic model into a scenario-based one. Given that solving the model with 365 daily scenarios is computationally intensive, a scenario reduction method using averaging was applied, reducing the number of scenarios to 12—one for each month. Results show that in countries with high energy prices, such as Germany, installing between 15 and 76 solar panels is economically viable. In contrast, in Iran, where energy prices are subsidized, installing up to 11 panels is cost-effective. Additionally, higher air pollution levels increase the optimal number of panels, and smart management of household appliances can reduce costs by up to 25%.