# Machine Learning-Based Monitoring of DC-DC Converters in Photovoltaic Applications
## 2 Materials and Methods
### Fault Classes  
To propose a prognostic approach for photovoltaic systems focused on parametric faults, the corresponding classes must be defined starting from tolerance ranges around the component nominal values. In fact, parametric faults are deviations of components from the nominal values that produce a partial loss of functionality. These variations could introduce undetectable consequences from a general point of view in the functioning of the system but by choosing appropriate measurements, the variations can be identified and localized in a specific component or in a group of components. The nominal intervals of the four passive components are defined, starting from the nominal values shown in Table 2 and applying a 15% tolerance. These variations are considered acceptable as they guarantee an output ripple lower than 10% and maintain CCM operation. The parametric failure conditions correspond to a maximum decrease of 70% for each passive component. Table 3 summarizes the operating ranges of each component. It is necessary to highlight that the single failure hypothesis is assumed because it is the most likely, and no-fault propagation is expected. This means that only one passive component at a time can be considered defective, and five classes of failure are used. The nominal working condition of the converter is called \"class 0\", and it presents all components in their nominal ranges. The other classes are summarized in Table 4.  
Therefore, the main objective of the classifier is to identify these working conditions starting from specific measurements extracted from the DC-DC converter. To make the monitoring system suitable from a practical point of view, it is important to offer a low intrusive level using as few measures as possible. For this reason, in the next paragraphs of this paper, a selection method of the measurements is proposed based on the testability level of the circuit and on the influence of the environmental conditions. All the time-domain measures considered in this work have two information contents: the first is linked to the average value of the quantities and the second to their ripples. Therefore, the dataset matrix used to train the neural classifier must contain two columns for each measurement and one column for the corresponding class. The general form of the dataset is (7),  
\[\left[ \begin{array}{cccc}Q^{1}_{1,m}&Q^{1}_{1,r}&\dots&0\\ Q^{2}_{1,m}&Q^{2}_{1,r}&\dots&0\\ \vdots&\vdots&\dots&\vdots\\ Q^{N_{5}}_{1,r}&Q^{N_{5}}_{1,r}&\dots&4\end{array} \right] \tag{7}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Fault Class** & **Description** \\ \hline
0 & Each component is in the nominal range \\
1 & Malfunction on \(L_{1}\) \\
2 & Malfunction on \(L_{2}\) \\
3 & Malfunction on \(C_{1}\) \\
4 & Malfunction on \(C_{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fault Classes. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(L_{1}\) **[mH]** & \(L_{2}\) **[mH]** & \(C_{1}\) **[\(\mu\)F]** & \(C_{2}\) **[\(\mu\)F]** \\ \hline
5 & 5 & 2.4 & 2.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Converter components. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(L_{1}\) **[mH]** & \(L_{2}\) **[mH]** & \(C_{1}\) **[\(\mu\)F]** & \(C_{2}\) **[\(\mu\)F]** \\ \hline Nominal Range & (4.25–5.75) & (4.25–5.75) & (2.04–2.76) & (2.04–2.76) \\ Malfunction Condition & (1.5–4.25) & (1.5–4.25) & (0.72–2.04) & (0.72–2.04) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Operating ranges. where, for example, \(Q^{1}_{1,m}\) is the first measure of the mean value of the quantities \(Q_{1}\) (voltage or current) and \(Q^{1}_{1,r}\) is its ripple. A significant number of samples are used for each fault class, and the total number of rows belonging to the dataset is \(N_{S}\). It should be noted that keeping the duty cycle fixed; it is possible to reduce the size of the dataset matrix and the variability of the measurements.