Modeling, simulation, and optimization methods are used in the present study to design grid-tied and off-grid solar PV systems for super-efficient electrical appliances for residential buildings. The principal objective of this study is to design a renewable energy system to serve the electric load of super-efficient appliances with high penetration of renewable resources and low greenhouse gas emissions and cost of energy. Hourly calculations using optimization method are used to study the daily and yearly performance and the cost of the renewable energy systems. A comparison between the performance of the grid-tied and off-grid solar PV systems using conventional and super-efficient appliances in Dubai is presented. The comparison includes the total power production from the solar PV system, the power purchased from the grid, the extra power sold to the utility grid, the power used to meet the electrical load of the appliances, the excess power, the renewable fraction, the greenhouse gas emissions, and the levelized cost of energy. The results of the simulation show that the integration of super-efficient appliances powered with the grid-tied solar power system is a good option to control the energy consumption of the residential buildings and to reduce the cost of electricity and greenhouse gas emissions: low building energy consumption (reduction by half of the electrical power consumption: from 62.91 to 30.78 kWh/day using super-efficient appliances); all the electrical power demand for the building is met without shortage; the power systems produce low excess power (0.29–1.82%) compared to the off-grid power system; all the extra power from the solar PV is sold back to the grid to reduce the cost of energy, high renewable fraction (68% of the total energy served to the load is produced from solar PV), low-cost of electricity (12% reduction of the cost of energy compared to the utility grid), and low greenhouse gas emissions (45–51% reductions of the CO2, NOX, and SO2 emissions compared to the conventional electrical appliances).