Effect of Conducting, Semi-Conducting and Insulating Nanoparticles on AC Breakdown Voltage and Partial Discharge Activity of Synthetic Ester: A Statistical Analysis

This paper is aimed at studying the influence of conducting (Fe3O4), semi-conductive (ZnO), and insulating (ZrO2, SiO2, and Al2O3) nanoparticles (NPs) at various concentrations on the AC dielectric strength of MIDEL 7131 synthetic ester (SE) and partial discharges activity. First, a detailed and improved procedure for preparing nanofluids (NFs) in five concentrations ranging from 0.1 g/L to 0.5 g/L is presented, including high-speed agitation and ultrasonication. Then, the long-term stability is checked based on zeta potential analysis. After preparing and characterizing the NF samples, the following step is to measure their AC breakdown voltage (BDV). Due to the limitation of the high voltage supply (Baur system), the tests are performed according to IEC 60156 standard (2.5 mm gap distance) only with ZnO, ZrO2, and SiO2 NPs, and for comparison, tests are executed for all considered NPs with an electrodes gap of 2 mm. It is shown that the addition of Fe3O4 (20 nm), ZnO (25 nm), ZrO2 (20–30 nm), SiO2 (10–20 nm), Al2O3 (20–30 nm), and Al2O3 (50 nm) NPs improves the dielectric strength of synthetic ester upon an optimal concentration which gives the highest AC BDV. SiO2 (10–20 nm) and Al2O3 (20–30 nm) manifest their best improvement at 0.3 g/L, while for the other NFs, the best improvement is observed at 0.4 g/L. Further, the Anderson–Darling goodness-of-fit test is performed on the experimental data to check their conformity with the Extreme value (EV), normal, and Weibull distributions; the normal and EV fit curves are plotted and used to evaluate the breakdown voltages at probabilities of 1%, 10%, and 50%. It is shown that the AC breakdown voltage outcomes for most investigated nanofluids mostly obey the three EV, normal, and Weibull distributions. Then, the best combinations (nature of NP and optimal concentration), namely Fe3O4 (20 nm, 0.4 g/L), Al2O3 (20–30 nm, 0.3 g/L), and Al2O3 (50 nm, 0.4 g/L) NPs, that highly enhance the AC BDV of SE are chosen for a partial discharge activity investigation and comparison with pure SE. It is shown that the addition of those NPs significantly reduces the activity of partial discharges compared to pure SE.


Introduction
Nowadays, nanotechnology has emerged as one of the most exciting and advancing areas in science and engineering. Most academic centers and industries around the globe have been occupied in focusing on nanoscale research as a part of miniaturization/proficiency in devices. As an indication, biological and medical communities exploit the properties of nanomaterials for a variety of applications under the terms nanobiology and nanomedicine [1,2]. The size of biological structures or molecules is quite close to those materials. Therefore, they could add functions to those structures/molecules. This immense integration allows reliable diagnostic or rapid drug administration tools [3,4]. Moreover, electronic chips or integrated circuits are already nano-scaled component-based

Samples Preparation
The two-step method was executed for preparing the NFs samples, as depicted in Figure 1. The base liquid cannot be used in its initial state, and it needs to be purified; the purification was made using a micro-membrane filter and a vacuum pump to remove impurities. Oleic acid (used as a surfactant) was then added, and the mixture was stirred for five minutes using the high-speed rotor-stator mixer at 13,000 rpm. The mass ratio of oleic acid (OA) to base liquid is 0.75 wt.%. This concentration was based on previous work within the research team [20]; the evolution of zeta potential versus concentration of OA has been examined, and the 0.75 wt.% gives the best compromise. Next, the desired weight of powder NPs was dispersed within the base liquid, and the mixture is agitated for 20 min. Five concentrations are considered, ranging from 0.1 to 0.5 g/L (0.01 to 0.05 wt.%). Finally, the samples of NFs are subjected to an ultrasound agitation for two hours to uniformize the mixture and reach a stable colloid. The Ultrasonic Liquid Processors device (500 W, 20 kHz) with 25 mm low-intensity solid probe operates in a pulsed mode (i.e., 10 s of operation and 5 s of rest) with an amplitude set of 60%. After every 30 min, the ultrasonic equipment is rested for 5 min to avoid overheating NF samples and extend the equipment lifetime, especially the solid probe. Note that the volume of the prepared NFs is 400 mL for each concentration and type of NPs.

Stability of Nanofluids
The stability was considered to be the most significant issue facing NFs. Unfor nately, this has proven to be a severe impediment to the widespread usage of those uids, especially for those applications that need a considerable volume, as the case power transformers. Thus, particular attention should be paid to this step for a pro outcome concerning colloid stability. Many techniques for checking the stability were ported in the literature, including zeta potential (ζ-potential) analysis [27]. The ζ-poten analysis appears to be the most efficient and less time-consuming method to check stability of NFs [27,28]. The stability depends on the ζ-potential value; a schematic pres tation is depicted in Figure 2. For the absolute values between 0 and 10 mV, the NF considered unstable, and action is needed to overcome this. In contrast, for the absolute values higher than 30 mV, the NFs are considered hig stable; between the two ranges, the NFs are stable [28]. The hydrodynamic diameter a ζ-potential measurements were performed thrice using a Zetasizer Nano (ZS) instrum (Malvern, UK). As a supplement to zeta potential measurements, the Zetasizer Nano p vides the electrical conductivity of NF samples. Therefore, the spectral absorbance of e sample was checked before performing the measurement. All samples whose spectral sorbance is less than 100 could perform the zeta potential analysis as explained in a p vious work [20]. Hence, only three concentrations (0.1, 0.2, and 0.3 g/L) were conside according to the absorbance measurement.

Procedure for Breakdown Voltage Measurement
The breakdown voltage measurements have been performed in compliance with I 60156 standard method using a commercially available BAUR system. The test bench c sists of an oil tank with a capacity of 400 mL, an electrodes system with adjustable g distance, and a high voltage generator that can reach 100 kV RMS (50 Hz). According IEC 60156 [29], the BDV test is performed in a sphere-sphere electrode configuration 12.5 mm diameter, with a spacing of 2.5 mm. The voltage is applied continuously with increment of 2 kV/s until breakdown occurs.
Fe3O4 and Al2O3 NFs show superior dielectric strength, exceeding the oil tester li tation (100 kV); for that reason, a reduced electrode gap to 2 mm is considered to comp the breakdown voltage of the six NPs. In addition, the BDV test is carried out for NFs which the breakdown occurs for an electrodes gap of 2.5 mm (i.e., ZnO, ZrO2, and SiO

Stability of Nanofluids
The stability was considered to be the most significant issue facing NFs. Unfortunately, this has proven to be a severe impediment to the widespread usage of those liquids, especially for those applications that need a considerable volume, as the case for power transformers. Thus, particular attention should be paid to this step for a proper outcome concerning colloid stability. Many techniques for checking the stability were reported in the literature, including zeta potential (ζ-potential) analysis [27]. The ζ-potential analysis appears to be the most efficient and less time-consuming method to check the stability of NFs [27,28]. The stability depends on the ζ-potential value; a schematic presentation is depicted in Figure 2. For the absolute values between 0 and 10 mV, the NF is considered unstable, and action is needed to overcome this.

Stability of Nanofluids
The stability was considered to be the most significant issue facing NFs. Un nately, this has proven to be a severe impediment to the widespread usage of tho uids, especially for those applications that need a considerable volume, as the c power transformers. Thus, particular attention should be paid to this step for a outcome concerning colloid stability. Many techniques for checking the stability w ported in the literature, including zeta potential (ζ-potential) analysis [27]. The ζ-po analysis appears to be the most efficient and less time-consuming method to che stability of NFs [27,28]. The stability depends on the ζ-potential value; a schematic p tation is depicted in Figure 2. For the absolute values between 0 and 10 mV, the considered unstable, and action is needed to overcome this. In contrast, for the absolute values higher than 30 mV, the NFs are considered stable; between the two ranges, the NFs are stable [28]. The hydrodynamic diamet ζ-potential measurements were performed thrice using a Zetasizer Nano (ZS) instr (Malvern, UK). As a supplement to zeta potential measurements, the Zetasizer Nan vides the electrical conductivity of NF samples. Therefore, the spectral absorbance o sample was checked before performing the measurement. All samples whose spect sorbance is less than 100 could perform the zeta potential analysis as explained in vious work [20]. Hence, only three concentrations (0.1, 0.2, and 0.3 g/L) were cons according to the absorbance measurement.

Procedure for Breakdown Voltage Measurement
The breakdown voltage measurements have been performed in compliance w 60156 standard method using a commercially available BAUR system. The test benc sists of an oil tank with a capacity of 400 mL, an electrodes system with adjustab distance, and a high voltage generator that can reach 100 kV RMS (50 Hz). Accord IEC 60156 [29], the BDV test is performed in a sphere-sphere electrode configura 12.5 mm diameter, with a spacing of 2.5 mm. The voltage is applied continuously w increment of 2 kV/s until breakdown occurs.
Fe3O4 and Al2O3 NFs show superior dielectric strength, exceeding the oil teste tation (100 kV); for that reason, a reduced electrode gap to 2 mm is considered to co the breakdown voltage of the six NPs. In addition, the BDV test is carried out for In contrast, for the absolute values higher than 30 mV, the NFs are considered highly stable; between the two ranges, the NFs are stable [28]. The hydrodynamic diameter and ζ-potential measurements were performed thrice using a Zetasizer Nano (ZS) instrument (Malvern, UK). As a supplement to zeta potential measurements, the Zetasizer Nano provides the electrical conductivity of NF samples. Therefore, the spectral absorbance of each sample was checked before performing the measurement. All samples whose spectral absorbance is less than 100 could perform the zeta potential analysis as explained in a previous work [20]. Hence, only three concentrations (0.1, 0.2, and 0.3 g/L) were considered according to the absorbance measurement.

Procedure for Breakdown Voltage Measurement
The breakdown voltage measurements have been performed in compliance with IEC 60156 standard method using a commercially available BAUR system. The test bench consists of an oil tank with a capacity of 400 mL, an electrodes system with adjustable gap distance, and a high voltage generator that can reach 100 kV RMS (50 Hz). According to IEC 60156 [29], the BDV test is performed in a sphere-sphere electrode configuration of 12.5 mm diameter, with a spacing of 2.5 mm. The voltage is applied continuously with an increment of 2 kV/s until breakdown occurs. Fe 3 O 4 and Al 2 O 3 NFs show superior dielectric strength, exceeding the oil tester limitation (100 kV); for that reason, a reduced electrode gap to 2 mm is considered to compare the breakdown voltage of the six NPs. In addition, the BDV test is carried out for NFs in which the breakdown occurs for an electrodes gap of 2.5 mm (i.e., ZnO, ZrO 2 , and SiO 2 ). Three series of six measurements have been performed, giving 18 points considered sufficient for the statistical analysis [13,16]. Next, the conformity of AC BDV data for 2 mm and 2.5 mm electrode gaps to the extreme value (EV), Weibull, and normal distributions were analyzed using Anderson-Darling statistics. The EV distribution is rarely used to analyze AC-BDV data [13], unlike the widely used Weibull and normal distributions. Finally, the voltages corresponding to 1%, 10%, and 50% risk levels were determined using the normal and EV distributions.

Partial Discharges Measurement under AC 50 Hz Stress
The partial discharges (PDs) activity in both SE and the three SE-based NFs that give the best improvement in AC BDV tests are conducted in compliance with IEC 60270 standard method; in this case, Fe 3 O 4 (20 nm) and Al 2 O 3 (50 nm) at optimal concentration 0.4 g/L and Al 2 O 3 (20-30 nm) at optimal concentration 0.3 g/L. An industrial Omicron PDs system detection was used for this purpose. The PDs test is performed in a needle-plane electrode configuration; the gap between the two electrodes is 5 mm. The tip radius of curvature is 10 µm, while the plane electrode has a 35 mm diameter. The applied voltage is varied, and its RMS value follows the profile depicted in Figure 3; the voltage rises and falls with a speed of 1 kV/s, 13 kV as the maximum value on the plateau, maintained for 32 s, and 5 s of rest is respected between two successive tests from the same series. This voltage profile is repeated five times for each sample, which underwent five PDs tests for each liquid. So, the collected values present the average of five measurements.
Nanomaterials 2022, 12,2105 and 2.5 mm electrode gaps to the extreme value (EV), Weibull, and normal distr were analyzed using Anderson-Darling statistics. The EV distribution is rarely analyze AC-BDV data [13], unlike the widely used Weibull and normal distribu nally, the voltages corresponding to 1%, 10%, and 50% risk levels were determin the normal and EV distributions.

Partial Discharges Measurement under AC 50 Hz Stress
The partial discharges (PDs) activity in both SE and the three SE-based NFs the best improvement in AC BDV tests are conducted in compliance with IEC 6027 ard method; in this case, Fe3O4 (20 nm) and Al2O3 (50 nm) at optimal concentratio and Al2O3 (20-30 nm) at optimal concentration 0.3 g/L. An industrial Omicron PD detection was used for this purpose. The PDs test is performed in a needle-plane e configuration; the gap between the two electrodes is 5 mm. The tip radius of cur 10 μm, while the plane electrode has a 35 mm diameter. The applied voltage is var its RMS value follows the profile depicted in Figure 3; the voltage rises and fal speed of 1 kV/s, 13 kV as the maximum value on the plateau, maintained for 32 s of rest is respected between two successive tests from the same series. This voltag is repeated five times for each sample, which underwent five PDs tests for each li the collected values present the average of five measurements. For the comparison and quantification of PD activity, we are interested in inception voltage (PDIV), PD extinction voltage (PDEV) during raise and fallin respectively, and average charge (Qavg), peak charge (Qpeak), and number of PDs ( during the voltage plateau (at 13 kV RMS). It is about the average charge and the of PDs per second (NPD/s) during the 32 s, while Qpeak is the highest charge rec the same interval. In addition, the phase-resolved PDs pattern is also compared a ted for the four liquids.

Stability of Nanofluids
As mentioned above, the hydrodynamic diameter and zeta potential measu are performed on the NFs samples. However, hydrodynamic diameter analysis give an affirmative indication of the stability of NFs. For that reason, one concent considered in this analysis for the six NFs to show the dispersion behavior and lo agglomerations/clusters present in the liquid. Figure 4 shows the size distribution For the comparison and quantification of PD activity, we are interested in the PD inception voltage (PDIV), PD extinction voltage (PDEV) during raise and falling times, respectively, and average charge (Q avg ), peak charge (Q peak ), and number of PDs (NPDs/s) during the voltage plateau (at 13 kV RMS). It is about the average charge and the number of PDs per second (NPD/s) during the 32 s, while Q peak is the highest charge recorded in the same interval. In addition, the phase-resolved PDs pattern is also compared and plotted for the four liquids.

Stability of Nanofluids
As mentioned above, the hydrodynamic diameter and zeta potential measurements are performed on the NFs samples. However, hydrodynamic diameter analysis does not give an affirmative indication of the stability of NFs. For that reason, one concentration is considered in this analysis for the six NFs to show the dispersion behavior and look at  Figure 4 shows the size distributions of different SE-based NFs for a specified concentration (0.1 g/L). For all NF samples, it was noticed that maximum intensities reveal sizes higher than the declared ones by the supplier (Figure 4b). Since the observed/measured diameter using Dynamic Light Scattering (DLS) does not exclusively consider the particle size, unlike to NPs size measurement by microscopy technics (SEM and TEM); oleic acid envelopes the NP, possibly leading to an overestimation (an increase of the size), thus to larger sizes than expected. [30]. Furthermore, from what the suppliers claim, Fe 3 O 4 (20 nm), ZnO (25 nm), and Al 2 O 3 (50 nm) NPs should present a size distribution with a high peak around a specific diameter (theoretically around the declared sizes), and ZrO 2 (20-30 nm), SiO 2 NPs (10-20 nm), and Al 2 O 3 (20-30 nm) should be much larger (large variation sizes with a smaller peak), while only ZrO 2 (20-30 nm) and Al 2 O 3 (20-30 nm) NPs fit this description. does not exclusively consider the particle size, unlike to NPs size measurement by microscopy technics (SEM and TEM); oleic acid envelopes the NP, possibly leading to an overestimation (an increase of the size), thus to larger sizes than expected. [30]. Furthermore, from what the suppliers claim, Fe3O4 (20 nm), ZnO (25 nm), and Al2O3 (50 nm) NPs should present a size distribution with a high peak around a specific diameter (theoretically around the declared sizes), and ZrO2 (20-30 nm), SiO2 NPs (10-20 nm), and Al2O3 (20-30 nm) should be much larger (large variation sizes with a smaller peak), while only ZrO2 (20-30 nm) and Al2O3 (20-30 nm) NPs fit this description.  For the zeta potential analysis, the measurement is performed for the three concentrations in which the absorbance values are below 100, which indicates the test feasibility. Table 3 gives a summary of ζ-potential and electrical conductivity results for three concentrations taken one week after the preparation. According to the results, SiO2 (10-20 nm) NF is highly stable, while the other NFs are stable. We could speculate this to the size difference (contact surface); SiO2 (10-20 nm) is the smaller NPs, which should provide a more significant contact surface NPs/liquid than the other NPs.
Note that after three weeks, we did not observe sedimentation. However, if the zeta potential indicates that NFs remain stable, this cannot be a guarantee of stability for several years and the lifetime of the transformer.  For the zeta potential analysis, the measurement is performed for the three concentrations in which the absorbance values are below 100, which indicates the test feasibility. Table 3 gives a summary of ζ-potential and electrical conductivity results for three concentrations taken one week after the preparation. According to the results, SiO 2 (10-20 nm) NF is highly stable, while the other NFs are stable. We could speculate this to the size difference (contact surface); SiO 2 (10-20 nm) is the smaller NPs, which should provide a more significant contact surface NPs/liquid than the other NPs.
Note that after three weeks, we did not observe sedimentation. However, if the zeta potential indicates that NFs remain stable, this cannot be a guarantee of stability for several years and the lifetime of the transformer.

AC Breakdown Voltage Test for 2 mm Electrodes Gap
As explained in the previous section, the breakdown does not occur at a 2.5 mm electrode gap with Fe 3 O 4 (20 nm) and Al 2 O 3 (20-30 and 50 nm) NFs; the AC BDV with a 2 mm electrode gap distance is also considered to compare the six NPs under the same experimental conditions, which is the purpose of this subsection. Figure 5a-f shows the mean and max/min AC BDV for Synthetic Ester and Fe 3 O 4 (20 nm), ZnO (25 nm), ZrO 2 (20-30 nm), SiO 2 (10-20 nm), and Al 2 O 3 (20-30 and 50 nm) NFs at different concentrations, respectively. Whatever the type and concentration of the used NPs, the enhancement of the BDV in NFs was remarkable compared to the pure SE. In addition, adding NPs reduces the standard deviation of AC BDV which mainly increases the slope in the statistical analysis, thence enhancing the BDV at low-risk levels. Furthermore, the type and concentrations of NPs play a significant role in increment percentage. Synthetic ester-based ZnO (25 nm, ZrO 2 (20-30 nm), and SiO 2 (10-20 nm) NPs manifested the best improvements of around 20% compared to pure SE, while the best improvements with Fe 3 O 4 (20 nm) and Al 2 O 3 (20-30 and 50 nm) NFs NPs were between 37% and 44% concerning pure SE. Those improvements were compared and plotted, as depicted in Figure 6. It was noted that all NFs samples reveal an optimal concentration of around 0.3 and 0.4 g/L. Note that with the optimal concentration of SiO 2 (10-20 nm) and Al 2 O 3 (20-30 nm) NPs that is 0.3 g/L, the BDV is improved by 20.30% and 44.12%, respectively, as shown in Figure 5d,e. Up to 0.3 g/L, a slight lowering for the same Al 2 O 3 NPs of 50 nm is remarked compared to the smaller Al 2 O 3 of 20 nm NPs; a reversed tendency is observed beyond 0.4 g/L. With 0.4 g/L Al 2 O 3 (50 nm), the enhancement is 42.13% compared to pure SE ( Figure 5f). Khaled and Beroual have also carried out conceptually similar work [15,16] in which Al 2 O 3 (13 and 50 nm) NPs dispersed within mineral oil and synthetic ester, where they showed a similar tendency: the smallest particles provide a lower optimal concentration. With

AC Breakdown Voltage Test for 2.5 mm Electrode Gap (IEC 60156)
Following the IEC 60156 standard (2.5 mm electrode gap), among the six tested NPs, the breakdown occurs only with ZnO (25 nm), ZrO 2 (20-30 nm), and SiO 2 (10-20 nm) NFs. Therefore, only the three NPs will be addressed in the following section. Figures 7-9 give the mean and max/min AC BDV for synthetic ester-based ZnO (25 nm), ZrO 2 (20-30 nm), and SiO 2 (10-20 nm) NFs at different concentrations, respectively. It was noted that the best enhancements of SE-based ZnO (25 nm) and ZrO 2 (20-30 nm) NFs, are about 14.28% and 11.13%, respectively, for a concentration of 0.4 g/L, as shown in Figures 7 and 8, while for SE-based SiO 2 (10-20 nm) NFs, the improvement reaches the highest BDV value for a concentration of 0.3 g/L ( Figure 9); this presents a 12.83% of improvement against pure SE.
Finally, the improvements were compared and plotted for each concentration, as depicted in Figure 10.
the standard deviation of AC BDV which mainly increases the slope in the statistical analysis, thence enhancing the BDV at low-risk levels. Furthermore, the type and concentrations of NPs play a significant role in increment percentage. Synthetic ester-based ZnO (25 nm, ZrO2 (20-30 nm), and SiO2 (10-20 nm) NPs manifested the best improvements of around 20% compared to pure SE, while the best improvements with Fe3O4 (20 nm) and Al2O3 (20-30 and 50 nm) NFs NPs were between 37% and 44% concerning pure SE. Those improvements were compared and plotted, as depicted in Figure 6. It was noted that all NFs samples reveal an optimal concentration of around 0.3 and 0.4 g/L.   (e) (f)  Note that with the optimal concentration of SiO2 (10-20 nm) and Al2O3 (20 NPs that is 0.3 g/L, the BDV is improved by 20.30% and 44.12%, respectively, as s Figure 5d,e. Up to 0.3 g/L, a slight lowering for the same Al2O3 NPs of 50 nm is re compared to the smaller Al2O3 of 20 nm NPs; a reversed tendency is observed bey g/L. With 0.4 g/L Al2O3 (50 nm), the enhancement is 42.13% compared to pure SE 5f). Khaled and Beroual have also carried out conceptually similar work [15,16] i Al2O3 (13 and 50 nm) NPs dispersed within mineral oil and synthetic ester, wh showed a similar tendency: the smallest particles provide a lower optimal concen Nanomaterials 2022, 12,2105 With Fe3O4 (20 nm), ZnO (25 nm), and ZrO2 (20-30 nm) NPs, the best enhancem about 37.70%, 19.38%, and 21.37%, respectively, for a concentration of 0.4 g/L, a in Figure 5a-c. Fe3O4 (20 nm) and Al2O3 (20-30 nm and 50 nm) NFs show the bes mances according to AC BDV; their best improvements are greater than 35% for a

AC Breakdown Voltage Test for 2.5 mm Electrode Gap (IEC 60156)
Following the IEC 60156 standard (2.5 mm electrode gap), among the six test the breakdown occurs only with ZnO (25 nm), ZrO2 (20-30 nm), and SiO2 (10-20 n Therefore, only the three NPs will be addressed in the following section. Figures the mean and max/min AC BDV for synthetic ester-based ZnO (25 nm), ZrO2 (20and SiO2 (10-20 nm) NFs at different concentrations, respectively. It was noted best enhancements of SE-based ZnO (25 nm) and ZrO2 (20-30 nm) NFs, are abou and 11.13%, respectively, for a concentration of 0.4 g/L, as shown in Figures 7 and for SE-based SiO2 (10-20 nm) NFs, the improvement reaches the highest BDV va concentration of 0.3 g/L ( Figure 9); this presents a 12.83% of improvement again SE. Finally, the improvements were compared and plotted for each concentration picted in Figure 10.   With Fe3O4 (20 nm), ZnO (25 nm), and ZrO2 (20-30 nm) NPs, the best enhancem about 37.70%, 19.38%, and 21.37%, respectively, for a concentration of 0.4 g/L, a in Figure 5a-c. Fe3O4 (20 nm) and Al2O3 (20-30 nm and 50 nm) NFs show the bes mances according to AC BDV; their best improvements are greater than 35% for

AC Breakdown Voltage Test for 2.5 mm Electrode Gap (IEC 60156)
Following the IEC 60156 standard (2.5 mm electrode gap), among the six tes the breakdown occurs only with ZnO (25 nm), ZrO2 (20-30 nm), and SiO2 (10-20 n Therefore, only the three NPs will be addressed in the following section.

Statistical Analysis of AC Breakdown Voltage Data
Extreme value (EV), normal, and Weibull distributions are used to analyze the conformity of breakdown voltage outcomes. Contrary to the popular statisti (i.e., Weibull and normal) [16,20,25,31], EV has been rarely considered to adjust th imental AC BDV outcomes [13]. EV distribution combines Gumbel, Frechet, and distribution [13]; hence probability fit curves of the experimental results are plotte EV and normal distribution. Those latter are used then to estimate the voltage at risk levels. Therefore, the most crucial BDV levels should be estimated at 1%, 1 50% risk levels. Before estimating those voltages, a goodness-of-fit test should formed to check if the data came from a population with a specific distributio distribution obeys the experimental data, the voltages could be estimated, and the thence present a good estimation.
Nevertheless, the conformity of the experimental data was investigated u Anderson-Darling test. The Anderson-Darling (AD) statistic is a goodness-o mainly used to decide whether a sample of size n is drawn from a specified distr most commonly whether the sample data is drawn from a normal distribution. T has been successfully extended to the other distributions [32]. Anderson-Darlin

Statistical Analysis of AC Breakdown Voltage Data
Extreme value (EV), normal, and Weibull distributions are used to analyze the conformity of breakdown voltage outcomes. Contrary to the popular statist (i.e., Weibull and normal) [16,20,25,31], EV has been rarely considered to adjust th imental AC BDV outcomes [13]. EV distribution combines Gumbel, Frechet, and distribution [13]; hence probability fit curves of the experimental results are plott EV and normal distribution. Those latter are used then to estimate the voltage at risk levels. Therefore, the most crucial BDV levels should be estimated at 1%, 1 50% risk levels. Before estimating those voltages, a goodness-of-fit test should formed to check if the data came from a population with a specific distributio distribution obeys the experimental data, the voltages could be estimated, and th thence present a good estimation.
Nevertheless, the conformity of the experimental data was investigated u Anderson-Darling test. The Anderson-Darling (AD) statistic is a goodness-o mainly used to decide whether a sample of size n is drawn from a specified dist most commonly whether the sample data is drawn from a normal distribution. has been successfully extended to the other distributions [32]. Anderson-Darlin ness-of-fit is performed to check if the experimental data comes from EV, norm

Statistical Analysis of AC Breakdown Voltage Data
Extreme value (EV), normal, and Weibull distributions are used to analyze and test the conformity of breakdown voltage outcomes. Contrary to the popular statistical laws (i.e., Weibull and normal) [16,20,25,31], EV has been rarely considered to adjust the experimental AC BDV outcomes [13]. EV distribution combines Gumbel, Frechet, and Weibull distribution [13]; hence probability fit curves of the experimental results are plotted using EV and normal distribution. Those latter are used then to estimate the voltage at specific risk levels. Therefore, the most crucial BDV levels should be estimated at 1%, 10%, and 50% risk levels. Before estimating those voltages, a goodness-of-fit test should be performed to check if the data came from a population with a specific distribution. If the distribution obeys the experimental data, the voltages could be estimated, and the results thence present a good estimation.
Nevertheless, the conformity of the experimental data was investigated using the Anderson-Darling test. The Anderson-Darling (AD) statistic is a goodness-of-fit test mainly used to decide whether a sample of size n is drawn from a specified distribution, most commonly whether the sample data is drawn from a normal distribution. This test has been successfully extended to the other distributions [32]. Anderson-Darling goodnessof-fit is performed to check if the experimental data comes from EV, normal, and Weibull distribution. The conformity is then decided according to the p-value, depending on the AD value [32,33]. Based on the statistics, if the p-value (probability value) is higher than the significance level, alpha (α), there is enough evidence to accept the hypothesis that the data come from a specific distribution. The p-values of 0.05 were considered statistically significant [13,16,33], and from the AD test, the p-value for the EV, normal, and Weibull distributions were calculated and compared to the significance level.

Statistical Analysis of AC Breakdown Voltage Outcomes for 2 mm Electrodes Gap
The Anderson-Darling goodness-of-fit was performed on experimental data of the six NFs at different concentrations for the 2 mm electrode gap in which the breakdown occurs at this gap distance; the results are shown in Table 4. It was noticed that the p-value is higher than the significance level for most cases, and therefore, the experimental data obey the three distributions for those higher than the significance level. According to these results, the experimental data of AC BDV for the 2 mm electrode gap fit better to the normal distribution than the EV and Weibull distributions. In addition, the EV and Weibull gave quite the same p-values since the Weibull is a particular case of EV [13].  (20-30 nm), and Al 2 O 3 (50 nm) NFs versus AC BDV for different concentrations; they show how the breakdown data fit each case's corresponding normal and EV probability lines. From those plots, the BDV at risk levels (1%, 10%, and 50%) are evaluated from normal and EV distribution fit curves and presented in Table 5a,b. The BDV at 1% and 10% risk levels (U 1% and U 10% ) are essential information about the reliability of the HV apparatuses since they represent their voltage limit for safe/continuous operation and the lowest possible AC BDV, while the BDV at 50% (U 50% ) is an estimation of the expected mean BDV [25].
It resorts from the results in Table 5a,b that the addition of the Fe 3 O 4 (20 nm), ZnO (25 nm), ZrO 2 (20-30 nm), SiO 2 (10-20 nm), Al 2 O 3 (20-30 nm), and Al 2 O 3 (50 nm) NPs could not only enhance the mean AC BDV (from 50% risk level) but also improve the AC BDV at 1% and 10% risk levels. Mainly, the addition of these NPs strongly affects the U 1% rather than U 10% and U 50% , exceeding 75% of improvement with Fe 3 O 4 (20 nm) and  (20-30 nm), and Al2O3 (50 nm) NFs versus AC BDV for different concentrations; they show how the breakdown data fit each case's corresponding normal and EV probability lines. From those plots, the BDV at risk levels (1%, 10%, and 50%) are evaluated from normal and EV distribution fit curves and presented in Table 5a,b. The BDV at 1% and 10% risk levels (U1% and U10%) are essential information about the reliability of the HV apparatuses since they represent their voltage limit for safe/continuous operation and the lowest possible AC BDV, while the BDV at 50% (U50%) is an estimation of the expected mean BDV [25].   (20-30 nm), and Al2O3 (50 nm) NFs versus AC BDV for different concentrations; they show how the breakdown data fit each case's corresponding normal and EV probability lines. From those plots, the BDV at risk levels (1%, 10%, and 50%) are evaluated from normal and EV distribution fit curves and presented in Table 5a,b. The BDV at 1% and 10% risk levels (U1% and U10%) are essential information about the reliability of the HV apparatuses since they represent their voltage limit for safe/continuous operation and the lowest possible AC BDV, while the BDV at 50% (U50%) is an estimation of the expected mean BDV [25].       It resorts from the results in Table 5a,b that the addition of the Fe3O4 (20 nm), ZnO (25 nm), ZrO2 (20-30 nm), SiO2 (10-20 nm), Al2O3 (20-30 nm), and Al2O3 (50 nm) NPs could not only enhance the mean AC BDV (from 50% risk level) but also improve the AC BDV at 1% and 10% risk levels. Mainly, the addition of these NPs strongly affects the U1% rather than U10% and U50%, exceeding 75% of improvement with Fe3O4 (20 nm) and Al2O3 (20-30 and 50 nm) compared to pure SE. Still, Fe3O4 (20 nm) and Al2O3 (20-30 and 50 nm) give the best U10% and U50% compared to ZnO (25 nm), ZrO2 (20-30 nm), and SiO2 (10-20 nm) NFs.

Statistical Analysis of AC Breakdown Voltage Outcomes for 2.5 mm Gap Distance
Following the same steps presented in the previous subsection, the p-value for the EV, normal, and Weibull distributions were calculated and compared to the significance level for AC BDV data for 2.5 mm electrode gap ( Table 6). The concerned NPs are ZnO (25 nm), ZrO 2 (20-30 nm), and SiO 2 (10-20 nm). It was noted that the p-value is higher than the significance level for all cases except ZrO 2 (20-30 nm) NF at 0.1 g/L with normal distribution, and therefore, most of the experimental data obey the three distributions. Table 6. Hypothesis test of conformity of breakdown voltage outcomes of various nanofluids to EV, Normal, and Weibull distributions considering p-value calculation, for 2.5 mm electrode gaps. From those plots, the BDV at risk levels (1%, 10%, and 50%) are evaluated and presented in Table 7. Like those for 2 mm electrode gaps, those results for 2.5 mm show that the addition of ZnO (25 nm), ZrO 2 (20-30 nm), and SiO 2 (10-20 nm) NPs could not only enhance the mean AC BDV but also improve the AC BDV at 1% and 10% risk levels. Mainly, NPs' addition affects the U 1% more than U 10% and U 50% , exceeding 25% of improvement with the three NFs compared to pure SE. In addition, the concentrations for the optimal increments are identical to those that give the best mean AC BDV. This observation could easily be verified in Figures 17-19 below, where the line corresponding to the optimal concentrations is in the right of the others, whatever the breakdown probability.  Table 8 presents the average and standard deviation (St. Dev), as well as the increment percentage of PDIV (partial discharge inception voltage), PDEV (partial discharge extinction voltage), Qavg, Qpeak, and NPDs/s values obtained from electrical measurements for different liquids tested with a threshold detection level of 500 fC. This threshold is just above the background noise and allows the PD activity comparison of the four liquids at the same voltage level. The higher applied voltage than 13 kV RMS could lead to the pure SE breakdown and for a threshold level higher than 500 fC, the PDIV and PDEV voltage could not be measured in the case of Al2O3 NFs.   In addition, the concentrations for the optimal increments are identical to those that give the best mean AC BDV. This observation could easily be verified in Figures 17-19 below, where the line corresponding to the optimal concentrations is in the right of the others, whatever the breakdown probability.  Table 8 presents the average and standard deviation (St. Dev), as well as the increment percentage of PDIV (partial discharge inception voltage), PDEV (partial discharge extinction voltage), Qavg, Qpeak, and NPDs/s values obtained from electrical measurements for different liquids tested with a threshold detection level of 500 fC. This threshold is just above the background noise and allows the PD activity comparison of the four liquids at the same voltage level. The higher applied voltage than 13 kV RMS could lead to the pure SE breakdown and for a threshold level higher than 500 fC, the PDIV and PDEV voltage could not be measured in the case of Al2O3 NFs.   Table 8 presents the average and standard deviation (St. Dev), as well as the increment percentage of PDIV (partial discharge inception voltage), PDEV (partial discharge extinction voltage), Q avg , Q peak , and NPDs/s values obtained from electrical measurements for different liquids tested with a threshold detection level of 500 fC. This threshold is just above the background noise and allows the PD activity comparison of the four liquids at the same voltage level. The higher applied voltage than 13 kV RMS could lead to the pure SE breakdown and for a threshold level higher than 500 fC, the PDIV and PDEV voltage could not be measured in the case of Al 2 O 3 NFs.  (20-30 nm), and Al 2 O 3 (50 nm) NFs, respectively, at 13 kV (RMS) voltage level. It was observed that the PDs activity starts with the appearance of PDs at the peak of negative polarity (270 • electrical degrees) and just a few cycles later at the peak of positive polarity (90 • electrical degrees). Except for Fe 3 O 4 (20 nm) NF, a smaller number of PDs was noticed in the positive polarity than in the negative, but with a higher charge level for pure SE,  The PDIVs and PDEVs values of SE-based NFs are higher than those in pure SE in all cases. With 0.3 g/L Al2O3 (20-30 nm) NPs, the PDIV was enhanced by 24.58%, while 0.4 g/L Fe3O4 (20 nm) and Al2O3 (50 nm) NPs enhanced it by 22.95% and 24.14%, respectively. A similar tendency was observed with PDEV, i.e., 32.69%, 14.79%, and 28.66% of improvement in the case of Fe3O4 (20 nm), Al2O3 (20-30 nm), and Al2O3 (50 nm), respectively. Furthermore, a lower Qavg, Qpeak, and NPDs/s for the three NFs than pure SE was observed. Figures 20-23 show the PDs patterns of pure SE, SE-based Fe3O4 (20 nm), Al2O3 (20-30 nm), and Al2O3 (50 nm) NFs, respectively, at 13 kV (RMS) voltage level. It was observed that the PDs activity starts with the appearance of PDs at the peak of negative polarity (270° electrical degrees) and just a few cycles later at the peak of positive polarity (90° electrical degrees). Except for Fe3O4 (20 nm) NF, a smaller number of PDs was noticed in the positive polarity than in the negative, but with a higher charge level for pure SE, Al2O3 (20-30 nm), and Al2O3 (50 nm) NFs. The Fe3O4 (20 nm) NF manifests the lowest/highest activity in negative and positive polarities, respectively, unlike other NFs.

Discussion
Statistical analysis was performed on the AC BDV outcomes at 2 mm and 2.5 mm electrode gaps, and conformity to EV, normal, and Weibull statistical laws were conducted based on the p-value calculation. In other words, the AD statistics were employed to compute the corresponding p-value for each sample and compare it to the significance level. The results show that the experimental data of breakdown voltages for SE and SE-based NPs are observed with a concentration 0.4 g/L. Similar results have been reported by other researchers [14,16,17,31].
The fact that there is an optimal concentration of NPs could be due to the saturation of the NPs/SE interfaces [16]; hence, the smaller particles may show their best AC BDV at lower concentrations than bigger particles. Beyond optimal concentration, an additional amount of NPs will show a lower or even negative effect on the AC BDV. Accordingly, up to 0.3 g/L, a slightly lower mean AC BDV has been observed with Al 2 O 3 (50 nm) than with Al 2 O 3 (20-30 nm); a reversed tendency is observed beyond 0.4 g/L. Khaled and Beroual reported a similar tendency with mineral oil and SE [16] Nevertheless, a minor decline in AC BDV of ZnO (25 nm), ZrO 2 (20-30 nm), and SiO 2 (10-20 nm) NFs is observed after modifying the electrodes gap to 2.5 mm. Furthermore, the optimal concentrations of those NPs are confirmed, 0.4 g/L for ZnO (25 nm), ZrO 2 (20-30 nm) and NPs, and 0.3 g/L for SiO 2 (10-20 nm) NPs, which give 14.28%, 11.13%, and 12.83% of improvements compared to SE, respectively.
Khaled and Beroual [16] examined the same SE MIDEL 7131 with Fe 3 O 4 (50 nm), SiO 2 (10-20 nm), and Al 2 O 3 (13 and 50 nm) NPs. They reported that the best improvements in breakdown voltages are obtained with Fe 3 O 4 and SiO 2 NFs at the maximum concentration of 0.4 g/L (upper limit, no optimal concentration), with Al 2 O 3 (50 nm) NF at 0.3 g/L (optimal concentration), and, at 0.05 g/L (lower limit, minimum concentration) with Al 2 O 3 (13 nm) NF. Their work suggests that the smaller the NPs, the higher AC BDV is (for the same concentration). The best improvement with SiO 2 NF is about 30% compared to pure SE, while in the present work, the optimal improvement is about 11.62% at 0.3 g/L (for 2.5 mm electrode gap). In addition, they reported a lower AC BDV breakdown voltage for a MIDEL 7131 (60 kV) compared to the results in this work (82.6 kV); likely, this is likely because they have been used an aged MIDEL 7131. The same authors investigated the effect of conductive NPs (Fe 3 O 4 ) on the AC BDV of mineral oil, synthetic and natural Esters-based NFs [34]. Their findings reveal that Fe 3 O 4 nanoparticles significantly improve AC BDV of mineral oil (MO) and synthetic ester (SE). These improvements are 100% and 48% with MO and SE-based NFs, respectively. The improvement does not exceed 7% with natural ester, unlike MO and SE, even reducing the AC BDV.
Different mechanisms have been proposed to describe the processes associated with a dielectric strength enhancement when adding a small amount of NPs to host liquids. Hwang et al. [11] introduced the electron scavenging model as a possible mechanism that depends on the relaxation time constant (τ r ). It well describes the enhancement of the insulating performances of base liquid with addressed conductive NPs (Fe 3 O 4 ), but it fails to explain the performance improvement of other NPs, even conductive ones [18]. The mechanisms by which conductive, semi-conductive, and dielectric NPs trap electrons are explained by the potential well distribution caused by induced or polarized charges [10]. The difference between conductivity or permittivity of NPs and host liquid could generate induced and/or polarized charges on the NPs/SE interface, producing electrons trapping site [10]. The formed trapping site on the interface could trap moving electrons, enhancing the base liquid's breakdown performance.
The involved mechanisms in enhancing BDV of NFs could also be discussed by considering the behavior of spherical particles (roughly assuming that the particles are spherical) suspended in a liquid and subjected to a uniform applied electric field; three cases are possible.
The first case is when the polarizability of the NP is more significant than the base liquid. That means that there are more charges inside the interface (NP side) than outside (liquid side), resulting in a surface charge density difference on both sides of the interface. So, an induced dipole is aligned with the field applied through the particle [35]. A suitable example of this case would be a conducting NP (or NP 'insulting or conducting' with a high dielectric constant) in an insulating liquid with a low dielectric constant.
The second case is when the polarizability of the NP is less significant than the base liquid, which means that there are fewer charges inside the interface (NP side) than outside (liquid side). The resulted dipole points in the opposite direction. This could be an insulating NP suspended in a liquid with a high dielectric constant or high conductivity.
The third case is when the polarizability of the NP and that of the liquid are the same, and there is no net dipole. Obviously, the second and the third cases do not correspond to our study since, in most cases, the NPs conductivity and/or permittivity is higher than that of SE.
Nevertheless, the charge polarized on the surface of the NP produces the trapping site (potential well) [10]. Electron trapping by NPs significantly slows down the streamer's development by reducing its velocity and enhancing the NFs breakdown voltage. Sima et al. [10] conducted studies investigating the depth of the potential well of conducting Fe 3 O 4 , semi-conductive TiO 2 , and insulating Al 2 O 3 NPs. They found that the potential wells of dielectric NPs are shallower than those of conductive NPs [10].
The results from the performed PDs test on Fe 3 O 4 (20 nm), Al 2 O 3 (20-30 nm), and Al 2 O 3 (50 nm) nanofluids at optimal concentrations show a considerable enhancement of PDs resistivity of pure SE. Alike, it was found that the PD inception voltage (PDIV), PD extinction voltage (PDEV) are pushed to higher voltage levels when adding Fe 3 O 4 (20 nm), Al 2 O 3 (20-30 nm), and Al 2 O 3 (50 nm) NPs to the reference SE under AC stress. Also, those NFs show a reduced Q avg , Q peak , and NPDs/s compared to SE.
According to Atiya et al. [24], the thickness of the electrical double layer (EDL) around NP plays a vital role in reducing PD activity; the thicker the EDL, the more resistive to PD. However, in our case, the zeta potential measurements show that Al 2 O 3 (50 nm) NPs show a higher zeta potential than Fe 3 O 4 (20 nm) and Al 2 O 3 (20-30 nm) NPs; hence the EDL thickness for Al 2 O 3 (50 nm) NPs is larger than that for Al 2 O 3 (20-30 nm) and Fe 3 O 4 (20 nm) NPs [24].
Depending on the properties of the NPs and the liquid used, the presence of NPs can induce electric field heterogeneity in the NF. The localized increase of the electric field can lead to PDs at the same applied voltage or at the same ionization level of the liquid. Thus, near the electrodes, high mobility electrons and low mobility ionized ions are ready to migrate under the electric field forces. The NPs then play the role of electrons and negative ion scavengers, which generate a potential well (trapping site) that reduces the electron/negative ion movement and thence PD activities [10,36]. When the trapping process is finished, nanoparticle surfaces are saturated with negative charges; hence they no longer could trap more electrons. The limit is strongly correlated with the mismatch between base liquid and NP's conductivities and/or permittivities [10,35].

Conclusions
In this work, it was shown that the AC breakdown voltage of synthetic ester-based ZrO 2 (20-30 nm), ZnO (25 nm), SiO 2 (10-20 nm), Al 2 O 3 (20-30 nm), Al 2 O 3 (50 nm), and Fe 3 O 4 (20 nm) nanofluids are improved. The improvements are the best with conductive nanoparticles (Fe 3 O 4 ) and insulating nanoparticles (Al 2 O 3 ), regardless of the size. However, the addition of insulating nanoparticles (Al 2 O 3 ) with the smallest size (20-30 nm) shows the best improvement at a lower concentration. The statistical analysis of the experimental results shows that the breakdown voltage outcomes mostly obey the EV, normal, and Weibull distributions. Additionally, it has been shown that the addition of Al 2 O 3 (20-30 nm), Al 2 O 3 (50 nm), and Fe 3 O 4 (20 nm) NPs significantly reduces the partial discharge activity compared to pure SE.