This paper analyzes the behavior of residential solar-powered electrical energy storage systems. For this purpose, a simulation model based on MATLAB/Simulink is developed. Investigating both short-time and seasonal hydrogen-based storage systems, simulations on the basis of real weather data are processed on a timescale of 15 min for a consideration period of 3 years. A sensitivity analysis is conducted in order to identify the most important system parameters concerning the proportion of consumption and the degree of self-sufficiency. Therefore, the influences of storage capacity and of storage efficiencies are discussed. A short-time storage system can increase the proportion of consumption by up to 35 percentage points compared to a self-consumption system without storage. However, the seasonal storing system uses almost the entire energy produced by the photovoltaic (PV) system (nearly 100% self-consumption). Thereby, the energy drawn from the grid can be reduced and a degree of self-sufficiency of about 90% is achieved. Based on these findings, some scenarios to reach self-sufficiency are analyzed. The results show that full self-sufficiency will be possible with a seasonal hydrogen-based storage system if PV area and initial storage level are appropriate.