*3.6. Multi-Objective Optimisation Procedure*

Designing and configuring the optimal system sizing for a hybrid decentralized energy system is a complex process. There are a number of non-linear phenomena being simulated, as well as many potential design objectives and constraints. The chosen objective functions considering both cost and carbon reduction are the NPV and the equivalent GWP. The objective functions rely on varying the capacities of the PV solar, wind, battery, and RHFC installations at the site.

The NSGA-II uses a heuristic evolutionary learning algorithm with a population of potential design solutions within the defined constraints. It then ranks the population based on a non-dominated sorting, producing a pareto front of optimal solutions by minimizing both objective functions [36]. Each individual in the population was determined based on the simulation of the model of a one-year period and evaluating the two objectives. The best-performing individuals are passed to the next generation, whereas a combination of mutations and created offspring (crossover) determines the remaining individuals. NSGA-II provides several advantages including the use of elitism and reduced computational complexity [67]. The solving process for NSGA-II implementation is shown in Figure 7. The algorithm also requires inputs, including the population size, number of offspring, stopping conditions, and variable constraints, as shown in Table 4. The lower limit for all system assets was set to zero, while the upper limit was set to 200 kW in line with the adopted REC regulation for this study. The *pymoo* module created and maintained by Blank et al. [68] was used to implement the NSGA-II algorithm in Python.

**Figure 7.** Hybrid energy system model approach with multi-objective optimisation algorithm NSGA-II solving process.


**Table 4.** Initialisation parameters and constraints of the NSGA-II optimisation algorithm.

The input parameters were set into the simulation model with the selected objective functions and run within the NSGA-II algorithm. The optimisation ran to the maximum allowed generations before terminating. Due to the bound nature of the problem, the component capacity variables start as a random distribution, from which the non-dominated solutions on the pareto front are derived. Well-performing individuals are moved forward to the next generation, as well as a selection of offspring and individuals that have experienced random mutation. As the generations progress, the population steadily converges on a large set of non-dominated solutions that align with the pareto front between the best system economics and decarbonisation performance, denoted by the objective functions of cost savings and emissions intensity. The graph in Figure 8 shows the convergence of the objective function products during the progression through the first 200 generations of the hybrid system optimisation, which will converge towards a single value.

**Figure 8.** Convergence of the optimisation pareto front as shown by an aggregated scalar objective function minimising towards a single value.

#### **4. Results and Discussion**

#### *4.1. Optimisation Results of the Hybrid Energy Generation and Storage Renewable Energy Community*

The primary case studied was the hybrid architecture consisting of both a lithium battery and an RHFC. Within the resulting pareto front in Figure 9a, each point on the graph represents a different combination of design capacities ranging from the configuration able to achieve the highest economic returns to the system able to deliver the lowest net carbon output. The lifetime cost savings potential ranges from approximately EUR 130k to EUR 186k, while the emission intensity ranges from 82 to 140 gCO2*e*/kWh. It is interesting to note that the savings do not start at zero, implying that below EUR 130k returns, the configuration was able to increase in economic performance as well as decarbonisation before reaching an inflection point. At this point, it is clear that the net savings were able to continue increasing, while the net emissions reached its minimum and began to climb again. At the other end of the front, the gradient began to increase as both the returns increase but also the emissions intensity. This continued up to the point where the system can no longer provide additional savings without an exponential increase in embedded emissions and therefore environmental impact.

**Figure 9.** Key outputs from the multi-objective optimisation process, indicating relationship between cost reduction and climate impact of the system design.

The resulting pareto front presents several crucial outcomes and challenges for providing a low cost and net-zero energy system. Firstly, an inherent trade-off relationship was observed between the ability to decarbonise and ensure net profitability. Secondly, the REC architecture, within the context and constraints of the study, can reduce carbon emissions by over 75% compared to local grid usage. However, this is a hard limit due to the capacity factors of the components and the embedded carbon within the system during manufacturing. Additionally, trying to decrease the carbon emissions further only incurs a financial penalty, which would be hard to incentivise to the REC members.

The graph in Figure 9b displays the capacities of PV solar, wind power, battery, fuel cell, and electrolyser systems with the final population arranged by the two objective functions. The best economic outcome is on the left, while the best environmental outcome is on the right. It can be observed that all systems generally tend towards an increase in capacity as the emissions improve. This is most likely because a larger total off-grid capacity has a higher self-consumption rate, and therefore is relying less on the grid which has a high emissions intensity of 325 gCO2*e*/kWh. The REC was consequently able to reduce emissions to a greater extent. This, of course, negatively impacts the economics of the REC as more capital has to be invested into a more substantial design. It appears from the graph that the wind power, as well as the fuel cell and electrolyser which make up the RHFC are most sensitive to changes in the objective functions. The following section explores the chosen optimal design, and details why the capacities affect the objective functions in this way.

#### *4.2. Best Hybrid System Design for the Renewable Energy Community*

The pareto front provides a range of potential non-dominated solutions in which neither objective function is favoured over the other. There are several methods that can be used to choose a nominally 'best' system from the population to perform further analysis. Based on the research conducted by Wang and Rangaiah [69], it was chosen to use simple additive weighting (SAW). SAW normalises both objective function values, where zero is

the worst possible result and one is the most improved. The values are then summed for each member of the population to find the best overall solution.

$$\begin{cases} F\_{\overline{ij}} = \frac{f\_{\overline{ij}}}{f\_{\overline{j}}^{+}} & \text{for a maximization criterion, where } f\_{\overline{i+}} = \max\_{i \in \mathcal{m}} f\_{\overline{ij}}\\ F\_{\overline{ij}} = \frac{f\_{\overline{ij}}}{f\_{\overline{j}}^{-}} & \text{for a maximization criterion, where } f\_{\overline{i-}} = \min\_{i \in \mathcal{m}} f\_{\overline{ij}} \end{cases} \tag{16}$$

$$A\_{\overline{i}} = \sum\_{j=1}^{n} F\_{\overline{ij}} \tag{17}$$

*Fij* is the normalised set of objective functions *j* for the pareto population *i* and *fij* is the initial set. *fi*<sup>+</sup> and *fi*<sup>−</sup> are the maximum and minimum criteria of the set, respectively. *Ai* then provides the best set of design variables to use in the hybrid REC, given in Table 5. The system was then simulated to perform analysis of all performance indicators.


**Table 5.** Optimal installed capacities of the energy system assets.

Figure 10 contains two one-week sample periods obtained from the simulation, displaying the balance of each asset and their contribution to balancing the total REC load. Typical summer and winter periods are used to observe the seasonal variation in the system response. The REC load was higher on average during the summer period, leading to increased reliance and leading the energy grid to fill gaps in the consumption requirement when the ESS was unavailable. The winter period, by contrast, was able to satisfy the load requirement with the exception of some short periods. This shows that although the REC can operate largely off-grid, it is still beneficial from both an economic and emissions perspective to remain grid-connected from the short period when the REC generation and hybrid storage cannot fully balance the consumption. The hydrogen system requires a maximum storage of 1835k, which was evaluated from the simulation as the storage required to avoid any state-of-charge limits. The value therefore is a worst-case scenario for the system, as it is likely that a smaller storage would be chosen in accordance with the installation space available within the REC. Given the lower heating value (LHV) of hydrogen and the average fuel cell efficiency of 46%, the system would require approximately 14 Nm<sup>2</sup> of hydrogen stored at 35bar to supply the required quantity of a one-year period.

Table 6 below shows a full breakdown of the economic and environmental performance of each grouped asset. The solar array was able to deliver the most energy to the REC due to the high capacity of 71 kW, but also the higher solar potential on the island of Formentera of 4.7 kWh/m2, compared to London, UK, of 2.9 kWh/m2. Energy generated from wind provides the next greatest portion of over 24%, the benefit of which is that energy is generated during the night period as well as the day to charge the battery and a steady quantity of hydrogen. The battery itself was relatively small compared to the other components at 14 kWh and responds only when the energy generated is no longer available in excess of supply. The fuel cell and electrolyser were sized at 20 kW and 18 kW, respectively. It is interesting to note that the electrolyser was smaller in power input capacity than the fuel cell, even though the efficiencies would dictate the fuel cell would need approximately half the rated power of the electrolyser to achieve the same capacity factor. The increased generation from wind power over more of the simulation may allow the electrolyser to run for longer periods and make up the fuel cell's lower efficiency.

**Figure 10.** Energy generation hour-by-hour breakdown by source. Example shown includes typical summer and winter weeks.

**Table 6.** The economic and environmental performance of the different REC assets in the optimal design configuration.

