Due to its high short-term variability, solar-photovoltaic power in isolated industrial grids faces a challenge of grid reliability. Storage systems can provide grid support but come at a high cost that requires carefully evaluating power capacity needs. Battery sizing methodologies are now the focus of many studies, with a global upward trend in detailed modelling and complex optimization. However, although solar variability can be the source of uncertainties and battery oversizing, it rarely features as an input in scenarios. This study proposes several solar variability scenarios thanks to the wavelet-variability model and two variability metrics. These scenarios are employed as inputs in two sizing methodologies to compare the resulting battery capacity and draw conclusions on the role of modelling complexity and scenario identification. Results show that neglecting the photovoltaic power plant smoothing effect leads to an overestimation of the battery power support of 51%. In the other hand, complex dynamic modelling may reduce the battery power capacity by 25%. The economic analysis shows that a proper combination of variability scenario and battery sizing methodology may reduce the levelized costs of electricity by 3%.