## 3 Tests of the Developed PD Monitoring System on Power Transformers
### Test of the System on 31.5 MVA Power Transformer
The conducted data analysis proves that in the monitored power transformer:  
* Partial discharges were registered every day, and their activity was the highest mainly for hours from 8:45 a.m. to 5:45 p.m. (these time intervals are indicated in Figure 32 as grey bands). The sum of PD pulses from this time intervals constitutes 68.9% of all registered pulses. Figure 32: Partial discharges intensity characteristics, voltage, load, and oil temperature characteristics registered during 8-days-operation of the monitoring system on the 31.5 MVA substation power transformer. * The peak intensity of partial discharges occurred between 1:00 p.m. and 3:00 p.m. In this short period, almost one-quarter (24.4 %) of all PD pulses were detected. * The Pearson correlation coefficient between the hourly distribution of the UHF and AE pulses for sensor ISO-002-ADW/UHF-1 was \(r=0.87\) with significance \(p=0.001\) (very strong positive correlation), and for sensor ISO-002-ADW/UHF-2 it was \(r=0.45\) with significance \(p=0.027\) (moderate positive correlation). Both hourly distributions of the UHF and AE pulses are presented in Figure 33.
* The hourly distribution of the PD pulses registered with the high-frequency current transformer ISO-002-HF was correlated the most with the distribution obtained for the AE transducer (\(r=0.68\), \(p<0.001\)) and the UHF antenna (\(r=0.62\); \(p=0.001\)) of the sensor ISO-002-ADW/UHF-1. In the case of the sensor ISO-002-ADW/UHF-2 the correlation was lower at the level of \(r=0.44\) with significance \(p=0.029\) for the distribution obtained for the AE transducer and \(r=0.22\) with significance \(p=0.031\) for the distribution obtained for the UHF antenna. * The voltage value was changing in a narrow range from 113.3 to 117.6 kV, wherein the average, variance, and standard deviation were, respectively, equal to \(M=115.3\) kV, \(s^{2}=0.47\), and \(SD=0.69\). Due to the small voltage variation, it was decided not to investigate its influence on partial discharges intensity. * During the 8-days-operation of the system, the power transformer was loaded with relatively low power from only 0.68 to 11.34 MVA, which constituted, respectively, 2.15% and 36.00% of its rated power. The average value of the load was equal to \(M=5.31\) MVA, variance \(s^{2}=6.16\), and standard deviation \(SD=2.48\). * The oil temperature was changing in a wide band from 14.0 to 36.1 \({}^{\circ}\)C. It was observed that daily \"hills\" and local peaks of the oil temperature curve overlap the period of higher activity of partial discharges. (from 8:45 a.m. to 5:45 p.m.) (see Figure 32). In turn, for daily \"valleys\" of the oil temperature curve, a clear reduction or complete disappearance of the partial discharges activity was observed. In order to test the hypothesis relating to the influence of the level of oil temperature on partial discharges intensity in the monitored power transformer, it was decided to conduct a one-way analysis of variance (ANOVA) for independent samples. One of the main assumptions of the ANOVA is that the independent variable consists of two or more categorical, independent, and equinumerous groups. The categorization of the daily oil temperature values (independent variable) was carried out using tertiles, in order to obtain three equinumerous groups. The \"low\" temperature category was ascribed to lower tertile, whereas \"moderate\" and \"high\" temperature categories to middle and higher tertiles, respectively. Since the assumption of homogeneity of variance was violated ([PERSON]'s test for equality of variances was statistically significant), therefore the Brown-Forsythe and Welch F-ratios are reported. The results of both robust tests of equality of means are listed in Table 6. The results of the analysis showed that the compared groups differ from one another statistically, which means that the oil temperature level differentiates the number  
Figure 33: Hourly distribution of the UHF and AE pulses for sensor: (**a**) ISO-002-ADW/UHF-1 and (**b**) ISO-002-ADW/UHF-2. of PD pulses.