## 2 Materials and Methods
### Methodology for Online Monitoring of PDs in Tested Power Transformers
Localizing PD sources using the TDoA technique in the transformer tank area where the AE sensors of the PDtracker Portable system recorded acoustic emission pulses (if PDs were detected when the monitoring systems were activated or during their routine inspection on the following day, acoustic emission monitoring was immediately halted, and efforts were made to locate the PD source). When two different detection methods are used simultaneously in the study of PD monitoring in transformers, an important issue is to assess the degree of convergence of the results obtained. To perform an objective analysis, it was decided to use the confusion matrix and appropriate agreement metrics, which allow for an accurate determination of how closely the results of both methods agree. The confusion matrix is a tool that allows for a detailed presentation of the results of two monitoring methods, in this case, UHF and AE, in the form of a table comparing the results of both techniques in terms of their ability to detect PD pulses. In the classic confusion matrix for two methods, where each of them can indicate \"1\" (PD pulse detected) or \"0\" (no PD pulse), four basic categories are distinguished:  
* True positive (TP): The number of cases in which both methods detected a PD pulse during the same period. This means that both systems correctly recorded the presence of a discharge. In this case, there is a low probability that both the UHF and AE methods were recording interference at the time. * False positive (FP): The number of cases in which one method recorded a PD pulse and the other did not. This suggests that one of these methods was more sensitive in detecting PD or may have captured interference signals. * False negative (FN): The number of cases in which one method did not detect a pulse recorded by the other method. Here, the reasons may be identical to those in false positive cases. * True negative (TN): The number of cases in which both methods did not record any PD pulse. This means that both methods are consistent in identifying periods without discharges or are too sensitive to detect them, e.g., in a situation where the generated PD pulses had low energy. Figure 3: Schematic diagram of the online PD monitoring conducted simultaneously using the acoustic emission (AE) and ultra-high-frequency (UHF) methods: CH1–CH8—acoustic emission sensors; L1, L2, and L3—windings of individual transformer phases; TC—on-load tap changer; ODV—oil drain valve; PDA—Qualitrol CMD01591 rod antenna; NGA—external noise-gating antenna; AE—acoustic emission measurement system (PDtracker Portable); UHF—ultra-high-frequency measurement system (Qualitrol Portable PDM). The confusion matrix in this context enables the assessment of the agreement of both PD monitoring methods, allows the examination of how often both methods agree in their results, and also identifies cases where there are differences in the detection of PD phenomena. On the basis of the confusion matrix, various agreement metrics can be calculated, which allow a more precise determination of the degree of similarity between the results obtained from two measurement methods. Among the various agreement metrics, Accuracy Index and Jaccard Index were selected as they best correspond to the specificity of comparing two simultaneously applied methods for PD detection. Accuracy Index is one of the basic measures that determines how often both methods give the same results, i.e., both simultaneously record or do not record PD pulses. It is the ratio of the number of cases in which both methods give the same result (TP + TN) to the total number of cases (TP + TN + FP + FN):  
\[\text{Accuracy Index}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+ \text{EN}} \tag{1}\]  
The Jaccard Index measures the similarity between two data sets, in this case, the results of two monitoring methods.