Capacity sizing and calculating cost savings for residential households in a rapidly evolving energy market, influenced by fluctuating electricity prices and changing government incentives, is a highly complex problem. The key challenges stem from multiple interacting factors, including retail electricity prices, the desired payback period, household size, applicable electricity schemes, and the capacity factor of the photovoltaic (PV) system. The nominal power output of the solar energy system is constrained by both the specifications and the number of installed inverters and PV panels. As solar generation is intermittent and non-dispatchable, it is inherently weather-dependent and often unable to align with the dynamic fluctuations in household electricity consumption. From a financial modelling perspective, the length of the accounting period directly determines the time resolution of the model, influencing both the accuracy of cash flow estimation and investment decision-making. The proposed two-level investment planning model is based on the process network synthesis approach. At the upper level of the process model, solar generation technologies, including inverters and solar panels, are technically and economically assessed. At the lower level, which represents the load consumption side, the periodical energy balances for production, storage, demand, and purchase are considered. In order to accurately evaluate the solar energy system, the model is developed with both a monthly framework and a detailed hourly framework. The time resolution allows the model to account for grid intake, electricity sold, and storage inventory conditions over the defined periods, ultimately providing the optimal sizing for a solar system equipped with battery storage. Case studies are conducted to investigate the effects of household size, extended payback periods, varying retail electricity prices, and grid reliability. These scenarios demonstrate the key parameters that significantly influence the economic feasibility and optimal sizing of the solar energy system, which are discussed in detail in this paper.