## 2 Material and Methods
### Multi-Criteria Decision Support System (MCDSS) for Photovoltaic Set Identification
#### 2.3.1. Mapped Input Data  
The mapped input data consist of three essential components: (i) climate conditions, (ii) installation requirements, and (iii) PV database. These elements provide information to support the next steps of the MCDSS, allowing the selection and sizing of photovoltaic systems in different contexts and locations. The first essential component is Climate Conditions, which offer definitions of geographic coordinates, cloudiness index, clearness index, solar irradiation patterns, ambient temperature, and other relevant environmental factors. These data are fundamental for calculating the energy generation capacity of photovoltaic systems at different times of the year and under various weather conditions. The geographic coordinates are obtained directly from the global positioning system (GPS), which provides precise information about the specific location of a given place. These data are essential for analysing and planning photovoltaic systems, as they help determine solar exposure and the ideal angle of solar panels. Information about cloudiness, clarity, and temperature indices is also obtained from reliable meteorological sources, such as national weather websites. In the case of Brazil, for example, these data can be extracted from the National Institute of Meteorology (INMET) [51]. These indices provide valuable insights into local weather conditions, including cloud presence, atmospheric transparency, and temperature variations throughout the day and seasons. Solar irradiance, measured in units of W/m\({}^{2}\) (watt per square metre), represents the instantaneous amount of energy received from the Sun in a specific region. Accurately sizing a photovoltaic (PV) system for electricity generation requires calculating the maximum, minimum, and average annual solar irradiance throughout the day and the average annual solar irradiance during peak hours. This assessment is crucial for optimising system performance, since these factors collectively impact the availability and intensity of solar energy, highlighting the importance of comprehensive analysis and consideration during system design and implementation. The amount of solar irradiance reaching the Earth's surface is influenced by various factors, including geographical features, cloud cover, clearness index, temperature, and other atmospheric conditions. Therefore, Equation (1) estimates the irradiation received at the top of the atmosphere in a specific region in each period [52]. \[I_{\Delta t}=\frac{W_{0}}{r^{2}}\left\{(t_{2}-t_{1})\cdot sin\delta\cdot sin \phi+\frac{12}{\pi}\cdot cos\delta\cdot cos\phi\cdot[sin(\tau_{2})-sin(\tau_{1}) ]\ \right\}, \tag{1}\]  
where \(I_{\Delta t}\) is the average intensity of local irradiation during the interval (\(\Delta_{t}\)), which is measured in W/m\({}^{2}\) (watt per square metre); \(W_{0}\) is a solar constant whose value is 1380 W/m\({}^{2}\); \(r\) is the ratio between the current distance of the Sun in relation to Earth and the average distance from the Sun to Earth; \(t_{1}\) and \(t_{2}\) are the beginning and end times of the interval \(\Delta_{t}\); \(\delta\) is the Sun's declination; \(\phi\) is the latitude of the studied location and \(\tau\) is the hourly angle of the Sun; \(\tau_{1}\) is the hourly angle of the Sun corresponding to \(t_{1}\) and \(\tau_{2}\) is the hourly angle of the Sun corresponding to \(t_{2}\). Equation (2) simplifies Equation (1) for a given period, keeping the variable \(\delta\) and \(\phi\). \[I_{0}=\frac{W_{0}}{r^{2}}\cdot sin\alpha, \tag{2}\]  
where \(I_{0}\) is the instantaneous intensity of irradiation at the location, \(\alpha\) is the solar elevation angle, and \(r\) is the ratio of the current distance from the Sun to the Earth. \(r\) is determined by Equation (3), and \(\alpha\) is determined by Equation (4).