## 2 Methodology
### Model Description  
To carry out the simulation of the hybrid trigeneration system, a mathematical model was made for each of the three energy sources used in the work. Solar energy is obtained through the photovoltaic method, which transforms direct solar radiation into electrical energy through panels. The model adopted to simulate the photovoltaic solar panel was based on the studies conducted by [PERSON] and [PERSON] [28]. All of the relevant phenomena in the modeling of a photovoltaic panel are shown in Table 1.  
In this model, the light generated current in a PV module is calculated from the Equation (1), and the inverse saturated current is defined from the Equation (2). Furthermore, it is taken into account that the saturation current varies with the temperature of the panel, for which it is modeled and expressed, as seen in Equation (3). In Equation (4), the cell output current is described. The photovoltaic panel model allows us to describe mathematically the operation of the panel array included in the system studied and to observe its curves of current-voltage and power-voltage operating under standard conditions. The simulation allows for the observation and analysis of one or more variables as a function of time, where the input variable to the system is the annual radiation profile in the selected places, and the main output is power generated, which is regulated in the hybrid generation system according to the energy load profile. The parameters required for the simulation were obtained from the literature and technical information provided by the manufacturer of the equipment [28]. Similarly, wind energy is transformed into electrical energy by a turbine, which transforms the kinetic energy of the wind into rotational energy by the propellers. In turn, this rotational energy is transformed into electrical energy by a generator. The dynamic model used for the analysis in the simulation was the one presented by [PERSON] and [PERSON] [29], which is expressed in Equation (5). \[\frac{y(s)}{x(s)}=\frac{0.25}{s^{2}+0.7\cdot s+0.25} \tag{5}\]  
This model was developed for a Southwest Wind Power Inc. AIR 403 wind turbine. The power generated varies with wind speed and behaves as described in Figure 3.  
The power generation capacity of this turbine has a maximum speed limit of 40 miles per hour. At or above this wind speed, power generation becomes impossible. For the hydrogen cell, the model uses the expanded form of the Nemst Equation [30], which models the thermodynamic potential \(E\) and is presented in Table 2 as Equation (6). As for the concentration of dissolved oxygen at the gas-liquid interface, the [PERSON] model [31] is used, which is shown in the table as Equation (7). In addition, this model takes into account the excess voltage caused by the activation and the internal resistance, whose models were developed experimentally and are presented in Equations (8) and (9), respectively. Similarly, the output voltage of the fuel cell is modeled according to Equation (10), and the hydrogen production rate, according to [PERSON]'s law, is presented in Equation (11). \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Model** \\ \hline Light generated current in a PV module, \(I_{ph}\) [A] & \(I_{ph}=\frac{\lambda\cdot(I_{SC}+K\cdot T-298\cdot K)}{\frac{100}{e^{-1}\cdot C_ {0}}}\) (1) \\ Inverse saturated current, \(I_{rs}\) [A] & \(I_{rs}=\frac{100}{e^{-1}\cdot C_{0}}\) (2) \\ Saturation current, \(I_{O}\) [A] & \(I_{O}=I_{rs}\big{(}\frac{T}{T_{s}}\big{)}^{3}e^{\frac{s_{0}^{2}}{28\cdot K}- \frac{1}{(T_{s}-1)}}\) (3) \\ Cell output current, \(I_{pv}\) [A] & \(I_{pv}=N_{p}\cdot I_{ph}-N_{p}\cdot I_{o}e^{-\frac{s}{N_{o}\cdot(N_{o}+I_{pv} -\frac{\kappa_{p}}{N_{o}\cdot K\cdot A\cdot T})}-1}\) (4) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Photovoltaic panel model. A more detailed description of the models adopted for the development of this study can be found in the literature.