# Optimizing Sustainable Energy Transitions in Small Isolated Grids Using Multi-Criteria Approaches
## 4 Results and Discussion
### Multi-Objective Optimization
Otherwise, in all likelihood, the optimal system would have used this technology to a greater extent. The objective is to meet the island's energy demand using a mix of renewable energy sources, but minimizing dependence on fossil fuels, i.e., diesel generation remains an option for backup purposes. Then, consequently, the limits for diesel generators (0-13 MW) range from the current values to total elimination:  
\[ \begin{array}{c}PotentialInstalledPower\leq x_{Diesel}\leq CurrentInstalledPower (MW)\\ Constraint:\\ 0\leq x_{Diesel}\leq 13.04\\ \end{array}  \tag{9}\]  
Given that El Hierro is an island, the energy supply must always meet or exceed the demand to prevent shortages since there is no possibility of connection to an external grid. This constraint can be formulated as follows:  
\[ \begin{array}{c}Generation(x)-Demand\ \geq 0\\ \end{array}  \tag{10}\]  
When optimizing El Hierro's energy grid using EPLANopt and EnergyPLAN, the goal is to find the best balance between competing objectives like minimizing total annual cost and lifecycle CO\({}_{2}\) emissions. This leads to identifying a Pareto front, which is an important concept in multi-objective optimization. In a two-objective optimization problem, the Pareto front can be visualized as a curve in a two-dimensional plot where each axis represents one of the objectives, i.e., the total annual cost vs. lifecycle CO\({}_{2}\) emissions. Points on this curve represent the Pareto-optimal solutions. The EPLANopt framework uses multi-objectiveoptimization techniques to weigh the trade-offs between different goals and identify Pareto-optimal solutions. These solutions can offer valuable insights into the best combination of renewable energy sources, storage technologies, and backup generators (if needed) to meet energy demands while also minimizing costs and emissions. The EPLANopt script was launched using baseline data, allowing for a comprehensive energy system analysis. The results of this optimization process are illustrated in Figure 10, which shows the Pareto front and all the simulations, including the dominated solutions. Each point on the Pareto front signifies a different mix of energy sources and technologies that collectively offer a balance between minimizing costs and reducing CO\({}_{2}\) emissions. The blue points represent dominated solutions, while the red points depict the Pareto front. The green points labeled (D) and (WH) highlight the above-analyzed scenarios. Point (D) represents the alternative option of just operating with diesel, whereas point (WH) represents the actual situation with the wind-hydro plant. As can be seen in Figure 10, the change between diesel generation and the current diesel/wind-hydro plant mix has led to a substantial reduction in emissions, but with an appreciable increase in costs. It is therefore necessary to make progress on both fronts to continue to reduce emissions and at the same time, if possible, costs. The reference case, i.e., the actual current energy setup and the situation with only the conventional power plant, are compared against the numerous points on the Pareto front. The existence of numerous Pareto optimal solutions demonstrates the value of multi-objective optimization in energy system design and planning. By simultaneously considering economic and environmental objectives, the optimization process can identify solutions that offer significant improvements over the current or alternative setups. Remarkably, many solutions significantly reduce CO\({}_{2}\) emissions without an increase in the total annual costs, compared to the reference case (WH). This finding highlights the potential for achieving environmental benefits through system optimization without compromising economic efficiency. Figure 10: Pareto-optimal solutions found with EPLANopt.