## 4 Conclusions  
When reviewing the wind and solar behavior of the four selected locations, it was concluded that the level of solar radiation presented by Puerto Bolivar was higher than that presented by Texas, Beijing, and Bremen. Only Texas presented a similar behavior due to the fact that both regions are desert zones. As for the wind speed, the behavior presented was much more variable, with each region presenting its peak at different times of the year. The highest peaks occurred in the first three months of the year in all four locations.  
Similarly, the simulation allowed us to conclude that the implementation of a PEM cell as a support to wind and solar generation system was very effective in meeting variable energy demand. The PEM cell, together with a PID system, was able to deliver the necessary energy in spite of the fact that in some seasons of the year, the climatic conditions to cover the demand were not available, as was observed in Texas for the load profile 2. This control system was strongly affected by the high peaks in the input variables over time. This can be appreciated in the first three months of the year in Bremen. The high wind supply made it difficult for the hybrid trigeneration system to maintain a stable power output by increasing the settling time, which could cause problems by exceeding the demanded load.  
In addition, the evaluation of the performance of the controller through the indicators IAE, ISE, TTAE, and ITSE, showed that the PID used presented a shorter error stabilization time when the changes in the load were smoother, and the error was given by radiation levels, and wind speeds lower than necessary, forcing the PID to vary the molar flow of \(H_{2}\) and \(O_{2}\).  
The results allow us to conclude that the difficulty of controlling a multivariable process such as a hybrid generation system is not limited only in the number of variables, but also by the interaction that exists between the subsystems (wind turbine, fuel cell, and solar photovoltaic system). The degree of interaction will determine whether the control strategy to control the process should be decentralized or centralized. Therefore, it is necessary to have interaction measures to help make such a decision, as is the case of the relative gain matrix, which is a heuristic technique without a strong theoretical basis, but rigorous connections have been established between the relative gain matrices and the stability for systems from their transfer functions. Thus, a relative gain matrix is proposed to advance in the study of the stability of multivariable control systems of hybrid energy generation processes.  
In the ITSE, it was observed that the second load profile in the study generated a lower stabilization time than the first one, due to the smooth variation in the load demanded from the system. In this indicator, the load profile was 27% lower on average for the four locations, with Puerto Bolivar standing out as the location that presented the smallest difference from the others, reaching a 19% difference between the profiles due to the variability in the study period for wind and solar resources.  
Conceptualization: G.V.O.; Methodology: G.V.O. and J.D.F.; Software: G.V.O., J.D.F., and J.P.R.; Validation: G.V.O., J.D.F., and J.P.R.; Formal Analysis: G.V.O., J.D.F., and J.P.R.; Investigation: G.V.O., J.D.F., and J.P.R.; Resources: G.V.O. and J.P.R.; Writing--Original Draft Preparation: G.V.O. and J.P.R.; Writing--Review and Editing: J.D.F. and J.P.R.; Funding Acquisition: G.V.O., and J.P.R. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Universidad del Atlantico and Universidad Francisco de Paula Santander.  
This research was supported by Universidad Francisco de Paula Santander and the Mechanical Engineering Program of Universidad del Atlantico. The Kai Research Group supports [PERSON] and [PERSON].  
The authors declare no conflict of interest.