## 2 Materials and Methods
### A Hypothetical Smart Home  
A hypothetical home was designed as a starting point for creating the Digital Twin. Different types of appliances were chosen to be introduced into the home based on their commonality in European households and their availability in the GREen ENergy Dataset (GREEND) [32] ([[https://www.andreatonello.com/greend-energy-metering-data-set/](https://www.andreatonello.com/greend-energy-metering-data-set/)]([https://www.andreatonello.com/greend-energy-metering-data-set/](https://www.andreatonello.com/greend-energy-metering-data-set/)) accessed on 15 May 2024) and the UK Domestic Appliance-Level Electricity (UK-DALE) [33] ([[https://jack-kelly.com/data/](https://jack-kelly.com/data/)]([https://jack-kelly.com/data/](https://jack-kelly.com/data/)) accessed on 15 May 2024) datasets. These two datasets were selected among a variety of open-source datasets made available as additional materials of scientific papers because they provide a large number of appliances, and minimize the geographic variations in appliance usage patterns. Our hypothetical home is composed of 6 rooms, each hosting several smart appliances. The details are presented in Table 1.  
For each appliance type, a specific appliance available in one of the buildings included in the GREEND or UK-DALE datasets was chosen as a representative sample. Table 2 shows the details of the selected appliances, including the source dataset, the building, the manufacturer, and the model. The preferred sources were buildings 3 and 5 of the GREEND dataset, as they had a large number of appliance data and reasonable consumption values. Other buildings in GREEND were discarded, as they either contained insufficient usage data or the consumption data were highly unrealistic, indicating measurement errors. The appliance types that were either unavailable or unsuitable in GREEND were instead chosen  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Room** & **Appliances** \\ \hline Corridor & Lamp \\ Living room & Air conditioning split, lamp, radio, television \\ Kitchen & Dishwasher, fridge with a combined freezer, lamp, microwave \\ Bedroom \#1 & Air conditioning split, desktop computer, lamp \\ Bedroom \#2 & Air conditioning split, lamp, television \\ Bathroom & Boiler, lamp, washing machine \\ \hline \hline \end{tabular}
\end{table}
Table 1: In this table, for each room of the hypothetical home, the relative smart appliances are listed.  
from the UK-DALE dataset. Because no information about individual air conditioning splits was available, the whole-home air conditioning consumption was used instead, which corresponded to the three splits being controlled collectively.  
A limitation of the GREEND and UK-DALE datasets is that they do not record the operation mode of appliances at a given time. This information is required to assign a specific consumption value to each operation mode and to estimate its duration. A possible solution to this problem is identifying the operation mode of appliances from the power consumption data using unsupervised learning methods, such as applying clustering techniques to the raw energy values. However, this approach can work only for simple appliances, such as lamps or televisions, but not for complex ones, such as fridges or washing machines, which may have different _operation cycles_. For example, a washing machine might draw no power for a short period while the clothes soak, and then use a lot of power for a spin cycle. Both of these cycles are part of the same operation mode, but there is no way to recognize this when clustering the raw data. Furthermore, methods based on raw data are also susceptible to noisy points and outliers; thus, they often lead to poor clustering results [34]. For this reason, the first step of our work was to identify a method for operation mode recognition. This is illustrated in the following subsection.