# Privacy-Preserving Overgrid: Secure Data Collection for the Smart Grid
## 5 Experiments
### Numerical Results  
In this section, we analyze the ability of PP-Overgrid to respond to realistic DSO requests, by considering 10 sub-nodes for each real node joining the Overgrid, a total number of \(N=100\) real nodes and a network degree of 5 or 20. We assume that the DSO updates its power constraint signal every 15 minutes and that each node can adapt the consumption of flexible loads in a purely proportional fashion. In other words, \(p_{i}\) being the initial power demand of node \(i\) and \(p_{i\_new}\) the power demand after the DR scheme, we consider that it is feasible to perform a proportional reduction \(p_{i_{new}}=\frac{P_{DSO}}{pN}\cdot p_{i}\) at each node \(i\), in order to meet the DSO request \(P_{DSO}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline \# & **Name** & **Type** & **Description** \\ \hline
1 & AC & HVAC & Central air conditioner outdoor unit energy use in kWh \\ \hline
2 & Boil\_g\_e & HVAC & Hydronic loop electric pump energy use in kWh \\ \hline
3 & DHP & HVAC & Ductless heat pump total energy use in kWh. Includes both outdoor and indoor units \\ \hline
4 & ER & HVAC & Zonal electric resistance heater energy use in kWh. \\ \hline
5 & ER\_2 & HVAC & Additional zonal electric resistance heater energy use in kWh. \\ \hline
6 & ER\_3 & HVAC & Additional zonal electric resistance heater energy use in kWh. \\ \hline
7 & ER\_4 & HVAC & Additional zonal electric resistance heater energy use in kWh. \\ \hline
8 & ER\_5 & HVAC & Additional zonal electric resistance heater energy use in kWh. \\ \hline
9 & Furn & HVAC & Electric furnace resistance heating element energy use in kWh \\ \hline
10 & Furn\_AH & HVAC & Central forced air system air handler energy use in kWh. Includes air handlers for gas furnaces, electric resistance furnaces, central air conditioners, and heat pumps. \\ \hline
11 & HP\_in & HVAC & Air source heat pump system auxiliary resistance element energy use in kWh. Located indoors; at the air handler, the elements provide additional heat. \\ \hline
12 & HP\_in\_2 & HVAC & Additional air source heat pump system auxiliary resistance element energy use in kWh. Located indoors, at the air handler, the elements provide additional heat \\ \hline
13 & HP\_out & HVAC & Air source heat pump outdoor unit energy use in kWh. Records energy use for both heating and cooling. \\ \hline
14 & HP\_out\_2 & HVAC & Additional air source heat pump outdoor unit energy use in kWh. Records energy use for both heating and cooling. \\ \hline
15 & PTAC & HVAC & Packaged terminal air conditioner energy use in kWh \\ \hline
16 & PTHP & HVAC & Packaged terminal heat pump energy use in kWh \\ \hline
17 & Dryer & Appliance & Clothes dryer energy use in kWh. Includes heating element, drum motor, and exhaust fan energy. \\ \hline
18 & Dwash & Appliance & Dishwasher energy use in kWh. \\ \hline
19 & Cwash & Appliance & Clothes washer energy use in kWh \\ \hline
20 & Cwash\_2 & Appliance & Additional clothes washer energy use in kWh \\ \hline
21 & DHW\_1 & DHW & Primary electric resistance tank water heater energy in kWh \\ \hline
22 & DHW\_2 & DHW & Secondary electric resistance tank water heater energy in kWh \\ \hline
23 & DHW\_HP & DHW & Heat pump water heater energy use in kWh. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of residential loads identified as flexible. Figure 8 shows the aggregated power demand of PP-Overgrid when applying the DR (red curve) and without applying the DR scheme (green curve), together with the \(P_{DSO}\) signal (blue curve) sent by the DSO. For completeness, the figure also shows the results without applying the privacy preserving scheme, i.e., without sub-nodes (\(n=1\)). In all the considered scenarios, for a network degree \(D=5\) or \(D=20\), the results show that the DR scheme is able to meet the DSO constraints, since the red curve closely matches the blue one.