## 2 Methodology
### Data Resources  
One of the most important inputs for this research is the wind speed and solar radiation data. These data were the operational input variables for the hybrid trigeneration system, and they were used to evaluate the system performance and to conduct the analysis. The USA, Germany, and China were chosen because they are economies with a high impact on their regions and have made significant progress in generating clean energy. To these three nations was added Colombia, because it is the country in which the research as carried out, and it presents promising wind [37] and solar generation potential [38]. Having selected the countries, we proceeded to choose the places in these countries where we would collect data; the frequency distribution of wind speed was considered, as shown in Figure 4.  
For this, the solar potential of each country was taken into account, and data were collected in the places with the highest potential. There are several models to predict solar radiation. One of the main models was proposed both by [PERSON] [27] and [PERSON] [28] and uses daily sun hours. This method is also known as AP. Similarly, [PERSON] and [PERSON] [29] proposed a method called BC correlation, in addition to the method proposed by [PERSON] and [PERSON] [30] known as HS correlation. These methods use the minimum and maximum daily temperature in both cases, as well as theoretical values of incident extraterrestrial radiation. The model used to obtain the data in this investigation was [PERSON] and Campbell, which uses variables typical of a physical phenomenon, as seen in Equation (18). \[H=a\cdot H_{O}\cdot\left[1-e^{-b\cdot\Delta T^{c}}\right] \tag{18}\]  
where \(a\) is the transmissivity of the atmosphere, \(b\) and \(c\) are constants assigned to each region, \(H_{O}\) is the daily extraterrestrial energy and depends on the day of the year and the latitude, and \(\Delta T\) is the difference between the maximum and minimum daily temperature. As for wind speed, the prediction was made by taking into account the Weibull probability distribution, which is affected by shape parameters (\(k\) or \(\alpha\)) ranging from 1 to 3.6 and is dimensionless. This probability is also dependent on a scale parameter (\(c\), \(\theta\) or \(\beta\)) [39]. This probability is described by Equation (19). \[f(x;\alpha,\theta)=\left\{ \begin{array}{c}\frac{\alpha}{\theta^{2}}\cdot x^{ \alpha-1}\cdot e^{-(\tilde{x})^{\alpha}}\ x\geq 0\\ \\ 0\ x\leq 0\end{array} \right. \tag{19}\]  
where \(x\), \(\alpha\), and \(\theta>0\) are in m/s. This function describes the relative probability of a random variable such as wind occurring at a given time; that is, it characterizes the probable behavior of wind data remeasured by the meteorological station. Thus, the probability of a random variable to fall within a particular region is given by the integral of the density of this variable in that region. The wind potential is determined to calculate the Weibull distribution parameters by mean of the least-squares method. Weibull is a continuous and triparametric distribution. In other words, it is completely defined by three parameters, and it is the most-used model in the field of wind energy [40]. For this research, the distribution of two parameters was selected, which corresponds to the scale parameter \(c\) in m/s that determines the average wind speed in the place of study and the shape parameter \(k\) that indicates the degree of dispersion of the records. With these parameters, the frequency with which certain wind speeds are manifested in the hybrid generation system can be established. These calculated wind speed data are presented in Figure 5. This figure shows the wind speeds for Texas (USA), Bremen (Germany), Beijing (China), and Puerto Bolivar (Colombia) throughout the year 2019. In Figure 5, in the case of China, you can see the maximum wind speed of 12.9 m/s was reached on Monday 13 May. Another important value is the minimum wind speed, which happened on the first day of January, registering 2.6 m/s.