The system was simulated by Matlab software, where the daily load curve, grid cutoff hours, and the monthly solar radiation are considered. The design of this system and specifics of its components are presented in this paper. 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 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. 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. This status represents a real problem for different sectors. The electricity in Gaza, Palestine, is limited and scheduled for 4-10 hours per day due to political reasons.