## 2 Materials and Methods  
In this section, the method employed to carry out this study is presented. The Section 3 details crucial aspects of the dynamic simulation model used for the investigated buildings. This model evaluates the heating load of each building, considering different hourly trends of heat gain and heating plant activation. The dynamic simulations are implemented in the TRNSYS environment with a time step of 0.05 h. The building simulation model is based on TRNSYS Type56, a well-known type commonly used for building dynamic simulations [24]. This model is applied to buildings with various geometries and shapes in the Naples municipality, as described in the Section 4.  
The proposed energy refurbishment scenarios compared with the reference system involve boiler replacement and the use of thermal insulation materials. The comparison between the reference scenario and the retrofit scenario is possible thanks to a standardized process. Both the buildings (ante and post retrofit) are identical in terms of geometry, orientation, weather location, use, and boundary conditions, with fixed thermophysical features and energy parameters. Therefore, the energy class of the retrofitted building is identified by evaluating the primary energy consumption, which is compared with that of the reference building.  
The methodology of this research is very detailed, and the approach is not overly simplistic. In fact, compared to the widely used tools that evaluate the energy class of buildings based on the semi-stationary approach, the presented method is based on a dynamic simulation model of the whole building. Therefore, all the main inputs and outputs of the system are evaluated at each time step of the simulation for all days of the winter season, overcoming the limitations of the semi-stationary models widely adopted in commercial applications for their simplified approach.  
The results of the dynamic simulations detailed in the Section 5 are discussed for the entire heating season, considering different penetration scenarios of the considered actions for 25% and 100% of the buildings in the Naples municipality. In this study, two scenarios--25% and 100% transformation--were chosen to represent partial and full adoptions of energy efficiency measures. The 25% scenario models a conservative approach, while the 100% scenario reflects the maximum potential energy savings if all eligible buildings are upgraded. This contrast offers a clear understanding of the range of possible outcomes. The methodology, however, is flexible and can accommodate other transformation percentages depending on policy goals or scenarios.  
The energy refurbishment actions are determined using the same criterion previously adopted for the Superbonus incentive, an economic funding course in Italy up to 2023, which covers the total cost of refurbishment actions. The Superbonus incentive applies to various building types, including condominiums, private homes, and public buildings. Key measuresinclude thermal insulation and upgrading outdated heating systems to more efficient ones. While insulation is effective, it involves high capital costs and long payback periods. In contrast, replacing heating systems results in significant energy savings. Another potential measure not addressed in this study is installing thermostatic valves in radiator-based systems, which also offers energy-saving benefits. To obtain this incentive, the energy refurbishment must improve the building energy class by at least two levels [25]. The energy class is determined by comparing the primary energy consumption of the existing building with that of a reference building, as specified in the legislation [10]. Energy, economic, and environmental analyses were also performed for all the considered building geometries.