# Optimizing Sustainable Energy Transitions in Small Isolated Grids Using Multi-Criteria Approaches
## 4 Results and Discussion
### Multi-Objective Optimization  
The shift towards sustainable and efficient energy systems is a complex challenge as the most suitable configuration that balances multiple, often conflicting, objectives must be selected. In smart energy systems, the optimization problem typically involves minimizing objectives, such as total annual cost, lifecycle GHG emissions, energy losses, or other relevant factors. These objectives can be in conflict, meaning that improving one objective may come at the expense of another. To address this challenge, multi-objective optimization techniques are employed to identify optimal solutions representing the best trade-offs between the competing objectives. As mentioned, the EnergyPLAN software is used to conduct the current analysis. Although this software is a simulation tool rather than an optimization model, it allows for analyzing any conceivable energy system scenario. Scripts in other tools like MATLAB or Python can simulate different scenarios where various constraints and objectives can \begin{table}
\begin{tabular}{c c c} \hline
**Technology** & **Results for 2023 Simulation** \\ \hline Diesel power plant & & \\ \hline Installed diesel power & & 13.04 MW \\ Generation & & 31.41 GWh \\ Average CF & & 27.50\% \\ Peak CF & & 59.13\% \\ \hline Annual costs & & 4.278 M EUR 1 \\ Fixed operation costs & & 6.10\% \\ Variable costs & & 4.017 M EUR & 93.90\% \\ Annual investment costs & & 0 M EUR & --- \\ \hline Hydro–wind plant & & \\ \hline \multicolumn{3}{c}{Wind} \\ \hline Installed wind power & & 11.50 MW \\ Generation & & 23.93 GWh \\ Average CF & & 23.75\% \\ Peak CF & & 67.05\% \\ \hline Annual costs & & 1.471 M EUR 1 \\ Fixed operation costs & & 30.66\% \\ Annual investment costs 1 & & 1.02 M EUR & 69.34\% \\ \hline \multicolumn{3}{c}{Hydro storage} \\ \hline Installed pump power & & 6 MW \\ Installed turbine power & & 11.30 MW \\ Storage capacity & & 225 MWh \\ Energy pumped & & 7.52 GWh \\ Hydro pump average CF & & 14.31\% \\ Hydro pump peak CF & & 100\% \\ Energy turbinated & & 2.78 GWh \\ Turbine average CF & & 2.76\% \\ Turbine peak CF & & 67.05\% \\ \hline \multicolumn{3}{c}{Annual costs} & \multicolumn{2}{c}{2.410 M EUR 1} \\ Fixed operation costs & & 0.685 M EUR & 28.42\% \\ Annual investment costs1 & & 1.725 M EUR & 71.58\% \\ \hline \multicolumn{3}{c}{Total annual costs} & \multicolumn{2}{c}{8.159 M EUR} \\ \hline \multicolumn{3}{c}{GHG emissions} & \multicolumn{2}{c}{24.063 kt} \\ \hline \end{tabular} 1  
\end{table} 
Table 5: Overview of the main features of the current generating systems. be implemented. For example, EPLANopt is publicly accessible under the GNU Lesser General Public License and published on a GitLab repository [31]. EPLANopt is used as an optimization framework that interfaces with EnergyPLAN to optimize the energy system while considering multiple conflicting objectives. This tool uses a multi-objective evolutionary algorithm (MOEA) built on the Python library DEAP. The MOEA in EPLANopt is designed to find optimal future energy mixes that satisfy minimum criteria for various energy strategies and energy system costs [68]. EPLANopt allows for the definition of optimization problems with EnergyPLAN as the underlying simulation model. The problem must be specified by decision variables, constraints and objective functions to find the optimal arrangement of the energy generation system. Based on Equation (1), the general multi-objective optimization problem to minimize total annual cost and lifecycle CO\({}_{2}\) emissions can be defined:  
\[\underset{x}{min}\left[ \begin{matrix}Total\ Annual\ Cost\ [M\&]\\ CO_{2}\ Life\ Cycle\ Emissions\ (tons)\end{matrix} \right] \tag{4}\]  
In the context of El Hierro's energy grid, the decision variables may include the installed capacities of various technologies, such as wind power, solar photovoltaics, hydropower, energy storage and diesel generators. The optimization problem may be subject to various constraints, such as usually the installable capacity limits of each technology.