## 4 Results and Analysis
### Solution of the Deterministic Planning Problem  
#### 4.1.1 Results for the Case without Reliability Requirements  
In total, 400 optimal planning exercises were carried out, that is, 400 microgrid designs (100 for each group of clients with different load profiles obtained from CREST), which allows for the determination of the total costs of microgrids that operate connected to distribution systems. The average results obtained without reliability requirements, for each group of residential households, are presented in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Size [kW]**} & \multicolumn{2}{c}{**Annuity [USD/kW]**} & \multicolumn{2}{c}{**Annuity [USD/kW]**} \\ \cline{2-5}  & **PV + on-Grid** & **PV + Hybrid** & **Size [kW]** & **Inverter Battery** \\  & **Inverter** & **Inverter** & & **Charger** \\ \hline
[0–3] & 101.4 & 103.5 & [0–3] & 11.3 \\
[3–4] & 96.5 & 97.9 & (3–5] & 10.3 \\
[4–5] & 94.1 & 93.6 & \(>\)5 & 9.3 \\
[5–10] & 91.7 & 91.2 & & \\ \(>\)10 & 84.8 & 88.2 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Economies of scale for microgrid assets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Clients by Microgrid**} & **1** & **10** & **20** & **100** \\ \hline Panel power [kW] & 2.25 & 18.22 & 35.76 & 178.23 \\ Panel power per household [kW] & 2.25 & 1.82 & 1.79 & 1.78 \\ Inverter technology & On-grid & On-grid & On-grid & On-grid \\ \hline Investment cost per client & & & & \\
[USD/year] & 228.1 & 184.8 & 181.3 & 180.7 \\ Cost function per household & & & & \\
[USD/year] & 172.3 & 168.2 & 167.3 & 167.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average results for microgrids without reliability requirements. According to the results, the optimization algorithm decides to install panels with on-grid inverter technology, which is cheaper than hybrid inverter technology. The most important impact is reflected on the investment costs per client of the PV system, which are reduced by 20% on average for microgrids of 10, 20 and 100 clients, compared to the average of investment costs for one-client microgrids. The reduction is due to the diversity of energy consumption, which leads to a decrease in the PV capacity per customer as the number of clients per microgrid increases (Figure 6a): each box compiles the information of 100 different microgrids, where the triangle refers to the mean value of PV capacity per customer for the 100 microgrids, the orange line indicates the median value, and the limits of the rectangles represent the quartiles Q1 and Q3 (i.e., the central 50% of the microgrids in each group of 1, 10, 20 and 100 residential households). In order to show the behavior of the diversity of energy consumption, Figure 6b shows the distributions with boxplot diagrams of monthly consumption per household, together with their standard deviations for each group of 1, 10, 20 and 100 residential households. As can be seen, the diversity of energy consumption is greater in one-client groups and decreases as more residential clients are grouped. This can be noticed because each rectangle containing 50% of the data decreases as the group size increases, meaning that the results of the 100 microgrids for each group of clients become more similar as the number of customers increases. Additionally, by changing ex-post the investment costs from the data reported in Table 4, greater savings can be achieved when considering the effect of EoS (Figure 7): the investment savings derived from the diversity of the load profiles, plus the EoS, when community microgrids of 10, 20 and 100 clients are formed, is 32.2%, 33.5% and  
Figure 6: Distribution of the (**a**) PV system capacities and (**b**) monthly energy consumption by household, for groups. 33.7%, with respect to the average cost of investment for one-client microgrids (without reliability requirements).