In this paper we focus on the design of the power system for off-grid cellular base stations powered by a photovoltaic (PV) solar panel and a battery. Several papers already tackled this problem, with different approaches, modeling either the day-to-day behavior, or the hourly dynamics. In addition, the meteorological characteristics were modeled using a variable number of levels. Different approaches produced different results, hardly comparable. In this paper, we discuss the choice of parameter quantization for time, weather, and energy storage, with the objective of deriving guidelines for the development of accurate and credible models that can support the power system design. Our investigation shows that quantization has an important impact on the mathematical model outputs. Hence, quantization must be carefully taken into account, to achieve a correct dimensioning of the power system.