# Methods for Aggregation and Remuneration of Distributed Energy Resources
## 5 Results
### Aggregation of Resources  
The aggregation results are related to the resource distributions inside each group, for a total of K number of groups. The aggregation is based on the K-Means clustering algorithm, and its inputs are the scheduled energy obtained before in the optimization, and the respective costs considered. The aggregation methods are applied for each period individually, i.e., a period must be chosen to undertake the aggregation analysis. Thus, the results shown in this subsection are relative to period 12. Firstly, it is presented the results regarding the method that does not require the clustering algorithm, the third, shown in Table 4. Regarding the methods 1 and 2, these are shown in Table 5.  
\begin{table}
\begin{tabular}{c l c c c} \hline \hline  & & **Group** & **Scheduled (kWh)** & **\# of Resources** \\ \hline \multirow{4}{*}{**Distributed Generation**} & Wind & 1 & 310.26 & 4 \\  & Photovoltaic & 2 & 173.81 & 20 \\  & Biomass & 3 & 34.34 & 1 \\ \cline{2-5}  & \multicolumn{2}{c}{**Total**} & \multicolumn{2}{c}{**518.42**} & **25** \\ \hline \multirow{4}{*}{**Demand Response**} & Domestic & 1 & 12.21 & 8 \\  & Small commerce & 2 & 3.34 & 2 \\  & Medium commerce & 3 & 12.23 & 4 \\  & Large commerce & 4 & 13.18 & 4 \\  & Industrial & 5 & 10.56 & 2 \\ \cline{2-5}  & \multicolumn{2}{c}{**Total**} & \multicolumn{2}{c}{**51.53**} & **20** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results for the Third Aggregation Method.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Producers**} & \multicolumn{4}{c}{**Consumers**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**Method 1**} & \multicolumn{2}{c}{**Method 2**} & \multicolumn{2}{c}{**Method 1**} & \multicolumn{2}{c}{**Method 2**} \\ \hline \multirow{2}{*}{
\begin{tabular}{c} **Cluster** \\ **Scenario** \\ \end{tabular} } & \multirow{2}{*}{**Group**} & **Scheduled** & **\# of** & **Scheduled** & **\# of** & **Scheduled** & **\# of** & **Scheduled** & **\# of** \\  & & **(kWh)** & **Resources** & **(kWh)** & **Resources** & **(kWh)** & **Resources** & **(kWh)** & **Resources** \\ \hline \multirow{4}{*}{\(\text{K}=\text{4}\)} & 1 & 145.42 & 12 & 310.26 & 4 & 13.80 & 9 & 7.18 & 4 \\  & 2 & 310.26 & 4 & 145.42 & 12 & 10.56 & 2 & 25.41 & 8 \\  & 3 & 34.34 & 1 & 34.34 & 1 & 13.18 & 4 & 8.37 & 6 \\  & 4 & 28.39 & 8 & 28.39 & 8 & 13.98 & 5 & 10.56 & 2 \\  & 5 & - & - & - & - & - & - & - \\  & 6 & - & - & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results for the aggregation methods 1 and 2.  
The results regarding all the methods for producers show that the resource distribution starts to be affected in the third cluster scenario; the total number of groups equal to 6. For consumers, the type of method used and the cluster scenario change the distribution of resources amongst the groups.  
One can see that in the third method of aggregation, it is obtained the groups according to the resource classification; however, this can also be seen through the other methods. Taking into consideration each group's total schedule, there are groups with the same amount in the different methods, for example, 34.34 kWh is the biomass resource group in aggregation method 3, but also group 3 in method 1, and group 3 in method 2 has the same total energy scheduled. This can also be seen considering the photovoltaic resource's group in method 3 (310.26), with group 2 and 1 from method 1 and 2, respectively.  
This suggests that the clustering k-means, given the energy scheduled and cost, can identify this pattern of producer's type without actually being served as input. These group similarities between methods starts to fade with the increase in the number of groups when considering the methods 1 and 2, since method 3 remains the same. Regarding the consumer's clustering, these similarities mentioned before can also be seen, especially for industrial consumers that retain the same amount of energy schedule through the different methods and clustering scenarios.