The electricity in Gaza, Palestine, is limited and scheduled for 4-10 hours per day due to political reasons. This status represents a real problem for different sectors. This paper presents an effective solution especially for the energy supply problem in the residential sector by using an unconventional PV system which operates in stand-alone and grid-connected modes. The system includes a storage battery block with a proper capacity to secure for continuous power supply of a residential house with a daily energy load of 10 kWh. It was found that an unconventional PV system of 3.2 kWp and a storage battery block of 19.2 kWh will be able to cover the total daily energy demands of the house including the outlined electricity cutoff hours. The design of this system and specifics of its components are presented in this paper. The system was simulated by Matlab software, where the daily load curve, grid cutoff hours, and the monthly solar radiation are considered. The obtained simulation results show that the produced PV energy exceeds the load demands during nine months of the year, and thereby, a high battery state of charge (SOC) in the range of 73-84% is achieved. During the three months of the lowest solar radiation (Dec.-Feb.), the produced PV energy is equal to the load demand while the battery state of charge varies in the range of 40-49% which verifies the appropriateness of the proposed PV system. The daily energy yield of the PV system varies between 2.6 and 5.4 kWh/kWp in January and July, respectively, which corresponds to a performance ratio of 90% and 66.25%, respectively.