The electrical power sector has entered an era of decarbonizing energy generation by accommodating more Renewable Energy Sources (RES), especially solar energy in the power grid. However, high penetration of such a resource has negative impacts on the power network such as power fluctuations, reverse power flows and voltage rises. Energy Storage (ES) offers an effective solution to addressing those challenges while improving the load factor as well as the utilization of network infrastructures. This paper proposes a new framework to integrate Community Energy Storage (CES) units in an existing residential community system with rooftop solar Photovoltaic (PV) units. In this framework, three analytical approaches are respectively developed to handle three important parameters of the CES integration (i.e. locations, sizes and operational characteristics) to enhance network performances. Firstly, a simple approach is developed on the basis of a Center of Gravity (COG) theory to determine the location of CES for minimizing the annual energy loss. Secondly, a new analytical formulation based on a load following control method is presented to identify the properrated capacity of CES and its hourly dispatch strategy for achieving a desired annual load factor. Lastly, a technique to estimate the optimal operational characteristic of CES is proposed for flattening the daily demand profile and improving the voltage profile. The proposed framework is tested on a 19-bus test system while considering the probability of PV generation along with load variations. The numerical results show that the developed framework can bring the system load factor to a maximum of 0.76, at which the penetration levels of CES and PV are at 22% and 5% respectively while reducing the energy loss by 24.21% and enhancing the voltage profile significantly. The results also indicate that 22% CES penetration can reduce the annual purchased energy cost from the grid by 11.1% and the annual energy loss cost by 36.88%, where the system accommodates respective PV penetration levels of 5% and 50%.