## 2 Methods
### Modelling and Simulation of the District  
The simulation section of the study includes some further methodological stages:  
1. On-site investigation of the district: multiple visits to the buildings were conducted between 2020 and 2022. Comprehensive data, including details about the building envelope, energy systems, occupancy levels, internal loads, lighting and equipment, and energy bill usage, were systematically gathered. 2. District energy modeling and model calibration: This phase was executed within the Energy Plus modelling and simulation environment. All relevant data obtained during the on-site investigations were input into the models. A calibration procedure was executed, focusing on refining the accuracy of key variables that carried uncertainty. 3. Towards the level of Positive Energy District, renovation, and energy efficiency measures: several solutions for enhancing energy efficiency and energy generation were introduced and implemented in the calibrated model. The subsequent calculation involved assessing the impact of these modifications on the overall energy consumption and verifying the achievement of the definition of the Positive Energy District. The buildings models were developed in accordance with the available modelling information to mirror the existing district geometry. Screenshots in Figure 4 depict the  
Figure 3: Overview of the used architecture for buildings monitoring and data collection and storage. The building energy simulation was performed utilizing non-steady state calculations within the Energy Plus environment. The computation of air temperature and heat flows employed the heat balance method. Internal loads, encompassing lighting, occupancy, and appliances, were determined based on data acquired during the on-site investigation. Additionally, details on energy system usage, schedules, and occupancy information were derived from on-site surveys. The modeling of energy systems adopts a simplified approach, treating them as thermal ideal loads, and uses fixed efficiencies for the various components of the energy systems. A validation procedure was performed to compare baseline energy use (3 years energy bills for electricity and gas) with the actual models, in order check their reliability with a monthly base for validation for both electricity and gas energy consumption which is aimed at guaranteeing a lower than 10% error with this timestep. Once the existing district was modelled and validated, renovation and renewable energy solutions were designed, modelled, and simulated in an energy plus environment to investigate the potential of the district to be a positive energy. The district renovation simulation incorporates the modelling and simulation of several technical solutions:  
Figure 4: (**a**) Anguel Guimera Public School, (**b**) Museum of La Noguera, (**c**) Xalet Montiu, (**d**) Educative Service of La Noguera, and (**e**) Library Margarida de Monferrat. * External wall insulation coating (polystyrene): applied to buildings including Xalet Montiu, Servei Educatiu de la Noguera, Angel Guimera Public School, and Biblioteca Margarida de Monfterrat. * Roof external insulation coating (polystyrene): implemented in Xalet Montiu, Servei Educatiu de la Noguera, Angel Guimera Public School, and Biblioteca Margarida de Monfterrat. * Window substitution: windows with a thermal transmittance up to 1.6 W/m\({}^{2}\cdot\)K and a Solar Heat Gain Coefficient (SHGC) of 0.6 are introduced to Angel Guimera Public School and Xalet Montiu. * Replacement of lighting bulbs and heating/cooling generators: commercially available, state-of-the-art heat pumps (air or water-based) with Coefficient of Performance (COP) and an Energy Efficiency Ratio (EER) greater than 4.5 are implemented. * Photovoltaic generation systems installation: deployed on surfaces facing south, southeast, and south-west, as well as on on-site close surfaces, such as parking areas.