# Selection of Features Based on Electric Power Quantities for Non-Intrusive Load Monitoring
## 3 Database Creation
### Signal Processing  
In order to be able to evaluate all the electrical quantities in Table 1, the time signals stored in the BLUED database have been processed through a standard scheme, described in the following. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Measurement Unit** & **Definition** & \\ \hline Active power & W & \(P=P_{1}+P_{H}\) & (7) \\ Fundamental active power & W & \(P_{1}=V_{1}I_{1}cos\theta_{1}\) & (8) \\ Harmonic active power & W & \(P_{H}=V_{0}I_{0}+\sum\limits_{h\
eq 1}V_{h}h_{l}cos\theta_{h}\) & (9) \\ Fundamental reactive power & Var & \(Q_{1}=V_{1}I_{1}sin\theta_{1}\) & (10) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definitions of the considered power quantities under non-sinusoidal conditions, according to [25]. Before to proceed with the evaluation of the electrical quantities of interest, according to a generic timeline such as the one represented in Figure 1, it is important to focus on a specific section of both voltage and current signals. Given \(t_{e}\), the time instant in which an event occurs for the generic device, a 2 s time window, centered in \(t_{e}\), is selected. Consequently, the selected portion of the signal is divided in 8 observation windows (\(ow_{1},\leavevmode\
obreak\ ow_{2},\dots,\leavevmode\
obreak\ ow_{8}\)), each one 15 cycles long (250 ms at the 60 Hz rated frequency). For each observation window, a calculation window is selected, by considering 10 cycles starting from the first zero-crossing in the voltage signal. Then, the fast Fourier transform (FFT) is applied to each calculation window of both voltage and current signals. In particular, since the bandwidth of the acquisition system for the BLUED database was limited to 300 Hz, only the frequency components up to the 5 th order have been considered to evaluate all four electric parameters by means of Equations (7)-(10). This results in eight \begin{table}
\begin{tabular}{c c c} \hline \hline
**Appliance Label** & **Appliance Name** & **Number of Recorded Events** \\ \hline
101 & Desktop Lamp & 25 \\
103 & Garage Door & 23 \\
108 & Kitchen Aid Chopper & 12 \\
111 & Fridge & 546 \\
118 & Computer A & 45 \\
120 & Laptop B & 14 \\
123 & DVR—Blue ray player & 33 \\
127 & Air Compressor & 20 \\
129 & TV & 53 \\
131 & Printer & 146 \\
134 & Iron & 40 \\
140 & Monitor & 222 \\
147 & Backyard lights & 16 \\
149 & Office lights & 53 \\
150 & Closet lights & 21 \\
151 & Upstairs hallway light & 17 \\
152 & Hallways Stairs lights & 58 \\
155 & Kitchen overhead light & 56 \\
156 & Bathroom upstairs lights & 97 \\
157 & Dining room overhead light & 32 \\
158 & Bedroom lights & 18 \\
159 & Basement light & 38 \\ \hline \hline \multicolumn{3}{c}{**TOT:**} & **1585** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Lists of the considered appliances from BLUED dataset. Figure 1: Representation of a generic timeline. values for each one of the four parameters: four values for the pre-event period and four values for the post-event period, stored in a matrix \(\mathbb{P}\in\Re^{4*8}\):  
\[\mathbb{P}=\left[ \begin{array}{ccc}P(\sigma w_{1})&\cdots&P(\sigma w_{8})\\ P_{1}(\sigma w_{1})&\cdots&P_{1}(\sigma w_{8})\\ P_{H}(\sigma w_{1})&\cdots&P_{H}(\sigma w_{8})\\ Q_{1}(\sigma w_{1})&\cdots&Q_{1}(\sigma w_{8})\end{array}