Abstarct: This thesis implements home energy management system to achieve the integrated management of electrical and thermal energy in a smart home, taking into account the residents welfare. Energy resources are electricity and natural gas networks, a solar water heater, a photovoltaic unit, and a storage unit. Electrical and thermal loads are categorized in three types: i) time-flexible loads, ii) power-flexible loads and iii) fixed loads. In order to overcome the uncertainties in the production of solar sources and the external temperature of the home, two different uncertainty models are used: i) single-scenario forecast, and ii) prediction intervals. Thus, the energy management problem is transformed into deterministic and robust optimization models. Using the real-world data of solar irradiance and external temperature collected from smart power microgrid at Shahrood University of Technology, two optimization models are implemented and compared. baxsed on the simulation results, choosing a conservative strategy through the robust optimization model compared to the deterministic model can guarantee the decision feasibility, but at the expense of reducing the level of residents welfare. Additionally, considering lixnking constraints among loads and sources, on one hand, rises the residents welfare, but on the other hand, increases energy costs.