This paper provides models for managing and investigating the power flow of a grid-connected solar photovoltaic (PV) system with an energy storage system (ESS) supplying the residential load. This paper presents a combination of models in forecasting solar PV power, forecasting load power, and determining battery capacity of the ESS, to improve the overall quality of the power flow management of a grid-connected solar PV system. Big data tools were used to formulate the solar PV power forecasting model and load power forecasting model, in which real historical solar electricity data of actual solar homes in Australia were used to improve the quality of the forecasting models. In addition, the time-of-use electricity pricing was also considered in managing the power flow, to provide the minimum cost of electricity from the grid to the residential load. The output of this model presents the power flow profiles, including the solar PV power, battery power, grid power, and load power of weekend and weekday in a summer season. The battery state-of-charge of the ESS was also presented. Therefore, this model may help power system engineers to investigate the power flow of each system of a grid-connected solar PV system and help in the management decision for the improvement of the overall quality of the power management of the system.