# A Methodology for Exploiting Smart Prosumers' Flexibility in a Bottom-Up Aggregation Process
## 4 Case Studies
### Case Study 1--Passive User (No PV System, No Batteries)  
From the data of the disaggregated load diagram, it is possible to develop the \"potential flexibility diagram\" for each individual controllable device, which represents the sign and maximum flexibility value that the device can provide at each hour of the day (Figure 7). Specifically, a positive flexibility value represents the opportunity to increase the prosumer's instantaneous energy consumption; conversely, a negative one represents the opportunity to decrease the instantaneous energy consumption. According to a typical Italian double-tariff contract in 2020 for domestic end-users [29], the energy cost per hour is assumed to equal to 0.188 \(\upcels\)/kWh from 8:00 to 19:00 and 0.182 \(\upcels\)/kWh in the rest of the day, while the dissatisfaction cost of every controllable device was estimated considering the habits of a typical residential prosumer [28; 29; 30] and is represented in Figure 8. It should be emphasized that the way in which the algorithm  
Figure 6: Residential users’ disaggregated power profile. operates is not influenced by the price of electricity paid by the user. The tariff conditions only influence the economic value of the offer. The simulation has been carried out considering two different DR requests for the whole day, and in particular:  
* A request to increase the power consumption in the time interval 06:45-07:00;
* A request to decrease the power consumption in the time interval 14:45-15:00. When the DSO requests a flexibility amount (and the admitted tolerance) to be delivered in a specific time interval, the VAE informs all the EMS that could contribute, and each EMS interested in participating in the provision of the flexibility service communicates to  
Figure 8: Dissatisfaction cost d per hour of each controllable device. Figure 7: Potential flexibility diagrams. the VAE its power level expected in the time interval indicated by the DSO and elaborates a list of all flexibility offers that the prosumer could produce, including the price of each offer and the IDs of the appliances involved. If the EMS is able to submit independently an offer that satisfies the flexibility request received from the DSO, that offer is presented to the VAE. Otherwise, the aggregation process starts: the EMS interacts with the other EMSes by forming groups or aggregates, each characterized by an overall offer consisting of a variation in power supplied at a given price. In this simulation, it was hypothesized that the prosumer selected for the winner cluster offers the tuple quantity/price in Table 1.  
At the same time, the potential flexibility diagrams are updated, as shown in Figure 10, following the criteria described in Section 2: in the specific case, the flexibility values associated with the boiler are set to zero for the remaining hours of the day. For the flexibility request at 14:45, the same process is repeated, but with the uploaded input data. At this point, the aggregation algorithms in the VAE are carried out again, and it was supposed that the prosumer had been selected for the winner cluster with the tuple quantity/price in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline \(\Delta\)**P [W]** & **Price [c]** & **Devices Involved** \\ \hline
1458 & 0.47 & Boiler \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Winner Offer at 6.45. \begin{table}
\begin{tabular}{c c c} \hline \hline \(\Delta\)**P [W]** & **Price [c]** & **Devices Involved** \\ \hline \hline \(-\)2000 & 0.2961 & Dishwasher \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Winner Offer at 14.45. Figure 9: Comparison between the updated and original daily load diagrams after the load shifting action. The load diagram was then updated as shown in Figure 11, considering a load shift action at 15:15. Finally, the potential flexibility diagrams were updated, and, in particular, the flexibility values associated with the dishwasher were set to zero for the remaining hours of the day (Figure 12).