The energy consumption of a building is a parameter that holds a key role in the context of building energy performance enhancement. As buildings continue to grow in complexity because of the need for more sustainable technical solutions, dynamic energy modelling tools offer new opportunities for their management and comprehension. Accurate parameter screening is crucial for understanding the relationship between model inputs and outputs, especially as models reflect the building's complexity. In the context of model calibration and verification, a comprehensive overview of the developed model is essential before the availability of monitored data. Global Sensitivity Analysis (GSA) is a powerful tool for such a goal. The work presented advances previous research by employing a more sophisticated version of the TRNSYS-based dynamic model of the UniZEB Living Lab at University of Padova (Italy). This approach studies the most influential parameters affecting energy demand, enabling the identification of potential regulatory, technological or user-centered improvements. The findings aim to enhance the precision and reliability of energy models, contributing to the design and optimization of energy-efficient buildings.