The need for electrical power gradually increases every year due to population growth and economic development in particular in developing countries. The primary sources of electricity are usually fossil fuels such as coal, natural gas, oil etc. and major part of them is imported by those countries. This is unfortunately a typical indication of the energy dependence and play strategic role in economic development of the developing countries since some cannot switch to renewable energy use despite they have abundant renewable energy potential. The fact that the use of renewable energy is not widespread in those countries and it can be seen as not making enough investment by the government or private sector. This potential can be utilized by using on-grid/ off-grid renewable systems in particular wind-PV systems ranging from power ratings of 1 to 10 kW in remote areas. To make such systems economic, power balance between generation and consumption should be maintained at hourly time slots in the day. One way to do that is to solve a discrete optimization problem and the solution can be achieved by a mathematical model satisfying the given constraints in a certain location. Unit sizing of a low power off-grid renewable system to meet power demand for a typical residential home in a location is achieved and the outcomes are meaningful and encouraging for widening renewable energy applications worldwide.