AC Breakdown Voltage and Partial Discharge Activity in Synthetic Ester-Based Fullerene and Graphene Nanofluids

This paper deals with the study of the AC breakdown voltage (BDV) and partial discharges (PDs) activity of synthetic ester-based nanofluids (NF) with two kinds of carbonic nanoparticles (NPs), namely graphene (Gr) and fullerene (C60); the synthetic ester (SE) being Midel 7131. The BDV measurement was achieved at various concentrations of NPs and different electrodes gap distances, while the partial discharges activity was studied only at the optimal concentration that gave the best improvements of BDV. First, a detailed improved procedure for preparing our NFs is presented. Then, the zeta potential measurements are performed on these NFs, and their stability is checked. After the preparation and characterization of samples, the BDVs and PDs parameters are measured according to IEC 60156 (modified gap distance) and IEC 60270 standards, respectively. Finally, conformity of the experimental data with Normal and Weibull distributions is examined, and the BDV at cumulative probabilities of 1% and 50% are then deduced. It is shown that BDV outcomes for all studied liquids obey both Normal and Weibull distributions, and the BDVs at cumulative probabilities of 1% and 50% are improved. Moreover, adding Gr and C60 nanoparticles at different concentrations enhances the BDV values for investigated electrode gaps (0.1 to 2.0mm). The best improvement is obtained with a concentration of 0.4 g/L for 0.5mm and 0.7mm electrode gap with fullerene and Graphene nanoparticles, respectively. For a 2mm gap distance, the best improvements are of about 12.67% and 16.64% with 0.4g/L of C60 and 0.3 g/L of Gr, respectively. It is also shown that the addition of C60 significantly reduces the activity of partial discharges compared to pure SE, while the addition of Gr destroys the partial discharges resistance of pure SE.


I. INTRODUCTION
The concept of fluids mixed with nanoscale particles (called nanofluids) was first proposed by Choi and Eastman [1] in 1995 for their use in equipment/systems where cooling is required. They found indeed that this kind of fluid has better thermal conductivity, thermal diffusivity and convective heat transfer coefficient than the base fluid. Since then, much work has been engaged in the development of nanofluids and the analysis of the other properties they can have. So, it has been reported that the addition of some specific nanoparticles allows to improve significantly the dielectric properties of liquid insulators [2]- [9]. The heat transfer and insulating The associate editor coordinating the review of this manuscript and approving it for publication was Nagarajan Raghavan .
properties are two fundamental properties required for some applications such high voltage power transformers.
In the present work, we are more particularly interested in the insulating properties of nanofluids. Various types of nanoparticles (conducting, semi-conducting and insulating) and insulating liquids (mineral oils, synthetic and natural esters) have been investigated. So, it has been reported that synthetic ester (SE)-based nanofluids (NFs) with iron oxide (Fe 3 O 4 ), aluminum oxide (Al 2 O 3 ), and silicon dioxide (SiO 2 ) nanoparticles (NPs) show a better AC breakdown voltage (AC BDV) compared to pure SE [4], [10]. Duzkaya et Beroual [6] showed that natural ester (NE)-based NFs with semi-conductive NPs (zinc-oxide, ZnO) can improve the AC BDV by about 5%. This enhancement is obtained with a concentration of 0.1 g/L. In the case of mineral oil, the enhancement reaches 75% of AC BDV with Al 2 O 3 NPs at a concentration of 0.05 g/L [11]. They observed a correlation between the size of NPs and dielectric strength; the smallest NPs give the best improvement on AC BDV. Hussain et al. [12] studied the effect of the addition of three NPs (iron oxide ''Fe 3 O 4 '', cobalt oxide ''Co 3 O 4 '', and iron phosphide ''Fe 3 P'') on the insulation performances of synthetic ester and natural ester (NE)-based nanofluids. All the NFs show enhancements in the dielectric strength. The optimal improvements were achieved with Fe 3 P NFs (SE and NE) at a concentration of 0.002wt.% (0.02g/L). Those enhancement are 20.2 and 31.4%, for SE and NE-based NFs, respectively. Khaled and Beroual [13] reported experimental results concerning conductive NPs (Fe 3 O 4 ) at various concentrations on the dielectric strength of mineral oil, synthetic and natural esters. The AC BDV was doubled with mineral oil-based NFs and enhanced by about 48% with SE-based NFs at a concentration of 0.4 g/L. While with NE-based NFs, the addition of Fe 3 O 4 had no significant influence on the insulation performance; the improvement did not exceed 7%. Furthermore, Sima et al. [14] investigated the possible implication of the conductivity and permittivity of three NPs of metal oxides on the transformer oil performances. Ionization models of transformer oil-based NFs were developed. This model indicates that NPs whose conductivity or permittivity is not equal to that of the base liquid have increased saturation charges on their interface, which significantly affects/slows down the evolution of the streamers by enhancing the dielectric strength of NFs.
Besides AC breakdown voltage investigations and the possible mechanisms, partial discharges (PDs) of NFs is still little considered. Jin et al. [15], [16] compared the PDs activity in mineral oil with mineral oil-based NFs with fullerene and silica NPs at 0.01wt.%. It showed that the inception voltage was enhanced by about 20% with silica and by about 10% with fullerene. They assumed that the hydrophilic behavior of silica NFs can reduce the moisture content, hence enhancing the PD resistivity. Also, the discharge magnitudes of NFs were reduced by about 60% with silica and 36% with C 60 compared to pure mineral oil. Atiya et al. [17] compared mineral oil-based NFs with alumina (Al 2 O 3 ) impregned pressboard (NFs impregned pressboard, NIP) (with mineral oil impregned pressboard (M-OIP) in terms of PD activity. They reported that NIP manifests higher inception voltages than M-OIP. Furthermore, at different applied voltages, they observed that the addition of NPs reduces the generation rate of PDs pulses. The PDs current was also reduced in case of NIP at positive and negative polarity. The same authors investigated the effect of the type and the size of NPs; they were the first to propose that the electrical double layer (EDL) around NPs could affect the PDs activity [18]. They concluded that the larger the NP are, the more resistant to the activity of PDs is. Imani et al. [19] showed that PDs tend to be initiated predominantly at positive half-cycle by increasing the concentration of conductive NPs (Fe 3 O 4 ), unlike pure liquid, which mainly appears at negative half-cycle. According to them, this alternation could be due to the electrohydrodynamic behavior of Fe 3 O 4 NF and to the orientation of the magnetizable magnetic NPs under sinusoidal voltage.
The present work aims to study the effect of two carbonic NPs, namely, fullerene (C 60 ) and graphene (Gr) on the performances of synthetic ester (SE)-based nanofluids with respect to the AC breakdown voltage and PDs activity. The AC breakdown voltage (AC-BDV) of SE is compared to those nanofluids at different concentrations and electrodes gap distances in a sphere-sphere configuration. PDs activity at optimal concentrations is considered. First, section two presents the procedure for preparing and characterizing nanofluids samples, the BDV and PD measurements methodology. Then, in section three, the results of BDV tests are presented, and the conformity with Weibull and normal distribution laws is carried out for one specific gap distance; the results of PDs tests according to IEC 60270 are also presented. Finally, section four discusses the results and the possible physicochemical processes implicated in BDV and PDs activity.

A. SAMPLE'S PREPARATION
The base liquid used in this study is synthetic ester MIDEL 7131 transformer oil supplied by M&I Materials, UK; the    Table 1. Graphene (Gr), and fullerene (C 60 ) nanoparticles with a purity of 99.5% are supplied by SkySpring Nanomaterials and Sigma-Aldrich, respectively. The fullerene NPs are spherical, while those of graphene are lamellar NPs. The average diameters of C 60 and Gr, the thickness of Gr, the density of C 60 and Gr NPs are given in Table 2.
Two main methods for preparing nanofluids were reported. The first one consists of combining nanoparticles synthesis and NFs preparation in a single step (one-step method), where nanoparticles are directly prepared by physical vapor deposition or a liquid chemical method. In this method, the drying, storage, transport, and dispersion processes of NPs are avoided [45]. Hence, NPs agglomeration is minimized, and fluid stability is increased. However, the downside of this method is the limited volume of the prepared NFs, which constrains its range of applications. That has been the method of choice used so far, before the recent shift to the two-step method. The second method proposes a two-step technique to prepare NFs. In the first processing step, nanoparticles, nanofibers, or nanotubes are produced as a dry powder by suitable techniques [2], [45]. Then, the nanosized powder is dispersed in the fluid. This stepwise method isolates the synthesis of NPs from the preparation of NFs [45]. As a result, agglomeration could occur in both steps, especially during NPs drying, storing, and transporting. This method is problematic as agglomeration leads to the fall of clusters under gravity, decreases thermal conductivity, and affects the dielectric properties. To address this issue, some techniques such as ultrasonic agitation (treatment) and the addition of surfactants to the fluids are often used to minimize particle aggregation and improve dispersion behavior.
In this work, the two-step method has been employed to prepare the nanofluid samples. As well as being simple, the method is practical and thus suitable for our lab-scale needs (volume and stability). The preparation steps for NFs are shown in Figure 1. The synthetic ester is first purified (removal of impurities) using a micro membrane filter and a vacuum pump. Oleic acid (supplied by Sigma-Aldrich) is then added with a mass ratio to Ester of 0.75wt.%. The assessment of the optimal mass ratio will be presented in the following section. The mixture is stirred for five minutes using the high-speed rotor-stator disperser (Misceo ''250 F'', 400W, 13000 rpm, and shear rate of 20m/s) at room temperature to mix the solution. Therefore, the NFs are prepared by dispersing the nanoparticles at concentrations ranging from 0.1 to 0.5 g / L (0.01 to 0.05wt.%). The NFs then undergo stirring for 20 minutes with the disperser to better disperse the nanoparticles in the ester. Subsequently, the samples of NFs are subjected to an ultrasound process for two hours to avoid agglomeration and sedimentation caused by attractive/repulsive forces. The ultrasound device (500W, 20kHz, 25mm low-intensity solid probe) operates in pulsed mode ([10s 5s], i.e., 10 sec of operation and 5 sec of rest).

B. OLEIC ACID OPTIMAL CONCENTRATION
To assess the effect of the oleic acid (OA) concentration on the NFs stability and determine the suitable concentration added to the samples, zeta potential is measured and compared for different OA concentrations ranging from 0.1 to 1.0wt.%. Five concentrations of NPs ranging from 0.1 to 0.5 g/L are investigated. However, because of the material limitation, only three concentrations of NPs (namely, 0.1; 0.2, and 0.3 g/L) are analyzed in the long-term stability. This limitation, defined as the maximum concentration needed for zeta potential measurements (0.3g/L for C 60 and 0.2g/L for Gr), was fairly described in Malvern's user manual, which depends on the optical properties and the size of particles [46]. Therefore, a simple and efficient way to check test feasibility is by measuring absorbance value before performing zeta potential measurement. For absorbance values less   than 100, zeta potential test will be accurate and conclusive, else the measurement will not be considered. Figures 2 -4 show the absolute value of zeta potential evolution versus OA concentration, considering different NFs with the different types and concentrations of NPs. Those figures show that for most cases, 0.75 wt. % of OA appear as the best compromise of concentration. Since, beyond specific surfactant concentration, the extra quantity of surface agent could form what is called micelles. This concentration called the critical micellar concentration or CMC that must be avoided, as the surface tension does not reduce further above the CMC [47].

C. CHARACTERIZATION AND STABILITY EVALUATION OF NANOFLUID
After preparing the nanofluids (NFs), the following action is to characterize them and determine their long-term stability. This is important due to the correlation between the stability of these liquids and the desired properties. Several works have shown that heat transfer properties are closely related to its stability and, even more than that, its insulating properties [48]- [50]. Therefore, particular attention was attached to this step. Several technics for the stability evaluation have been used and proven to be effective [45], including (i) sedimentation and centrifugation techniques, (ii) Zeta potential (ζ ) analysis, and (iii) Spectral absorbance analysis. The hydrodynamic diameter of fullerene NPs and Zeta Potential (ζ -potential), as well as the electrical conductivity of the NFs samples, were determined thrice on a Zetasizer Nano (NS) instrument (Malvern, UK). The measurement of hydrodynamic diameter gives the first indication about the dispersion behavior of colloids and inquiry the presence of some or many clusters in the sample. Figure 5 shows the size distribution of C 60 in MIDEL 7131 for a specified concentration (0.1 g/L). We note that the fullerene distribution presents an average size higher than the declared by the supplier (4 -8nm). The observed difference is may be due to the fact that the NPs are coated with oleic acid, which increases their average size. Unlike C 60 NPs which are spherical, the Gr NPs are lamellar (non-spherical). Since hydrodynamic diameter measurements are not suited using Dynamic Light Scattering Analysis (DLS-A) technique in the case of non-spherical particles. Other techniques can be used with these particles to produce high-quality images, such as Transmission electron microscopy (TEM) and Scanning Electron Microscopy (SEM) [14], [51]. Still, those techniques are not recommended for applications that need checking the long-term stability of many samples. So, zeta potential measurement appears to be the most proper technic for applications that need effective and rapid conclusions about longterm stability. The ζ -potential and electrical conductivity were measured one week after preparation; a summary of the results is given in Table 3. ζ -potential value is a chief sign of colloid stability. It intimates the potential difference between particle surface, covered with opposite and rigidly attached ions, and the neutrality point [47]. It is known that absolute zeta potential values between 0 and 10mV indicate an unstable colloid, and a surface modification or other appropriate action is needed, while if the value is between 10 and 30mV, the NFs are stable; beyond 30mV, the nanofluids become VOLUME 10, 2022  highly stable [52]. Hence, our values indicate that our NFs are highly stable.
Nevertheless, it was observed that the absolute value of ζ -potential decreases when increasing the concentration. We could speculate that this could be due to the increased surface area or the reduced quantity of light scattered by particles. Unlike the zeta potential value, the electrical conductivity increases with the concentration because Gr and C 60 are excellent conductors materials [29], [36]. Additionally, the electrical conductivity of SE-based NFs with Gr was higher than that with C 60 for the same concentration, depicted in Table 3. According to the literature, this behavior may be due to the fact that Gr conducts more than C 60 [29]. With its flat surface, the graphene nanomaterial poses a slight resistance to the crossing electrons, meaning the material has exceptionally high electron mobility result in high conductivity.
In addition to zeta potential and electrical conductivity values measured one week after the sample preparation, zeta potential evolution over time seems interesting as a stability criterion. Figure 6 shows the absolute value of zeta potential measurements of SE-based C 60 and Gr nanofluids over seven weeks at a concentration of 0.1 g/L. It is observed that the zeta potential shows no obvious signs of decay, and all values are above the lower limit of 30mV, which indicates that our NFs are highly stable.

D. BREAKDOWN VOLTAGE MEASUREMENT
Breakdown voltage measurements are conducted using oil tester BAUR DTA 100 C. The method of applying and measuring voltage is the same for all tests. After the sample positioning and distance setting, a wait time of ten minutes is respected before running the test. According to the IEC 60156 [53], the electrodes consist of two spheres of 12.5mm diameter, separated by a distance of 2.5mm. The other electrode gaps were ensured using hold plates ranging from 0.1 to 2.0mm. The voltages increment is 2kV/s until the breakdown occurs. Two minutes between each measure and the next are respected for all series; each series consists of six measurements. Three NF samples are prepared and tested for each concentration. Thus, each type of NF is subjected to three series of tests (that is a total of 18 measurements). After each series (i.e. 6 measurements), the NF sample is changed.
So, for statistical analysis, we should have sufficient data for specific electrode sets and concentrations. Hence, three series are measured for a distance of 2mm (breakdown in case of NFs do not occur with 2.5mm, AC-BDV > 100kV). The AC-BDV data were then analyzed using Weibull and normal distributions. Those methods are the most used for analyzing the AC-BDV so far. Finally, the voltages corresponding to the cumulative probability of 1% and 50% are determined, and the p-value is calculated.

E. PARTIAL DISCHARGES MEASUREMENT UNDER AC 50 Hz STRESS
The partial discharges (PDs) activity in both SE and SE-based C 60 and Gr NFs at optimal concentration is conducted in compliance with IEC 60270 standard method using an industrial Omicron PDs system detection. The PDs test is performed in a needle-plane electrodes configuration with a gap spacing of 5mm. The tip radius of curvature is 10µm, while the plane electrode has a 30mm diameter. Figure 7 shows the profile of the voltage RMS value applied to all samples; the voltage rises and falls with 1kV/s speed, 12kV as the maximum value, kept for 30s, and 5s of rest is respected between two successive tests. This voltage profile is applied five times for each sample, which that underwent five PDs tests for each liquid. A microscope monitoring of the needle tip before and after demonstrates that those series of PDs tests does not affect the condition of the needle.
During the tests, the PDs inception voltages (PDIVs), extinction voltages (PDEVs), average charge (Qavg), peak charge (Qpeak), and number of PDs (NPDs/s) are measured. Note that Qavg represents the average of the PDs charge magnitude and NPD/s the number of PDs per second during the 30s of the maximum applied voltage. In addition, the phase-resolved PDs pattern is also compared for the three liquids.

A. MEAN VALUE OF BREAKDOWN VOLTAGE
The mean value of the voltage and standard deviation of each series are calculated according to equations (1) and (2).
U i is the measured voltage, and ''n'' is the number of tests per series. According to the IEC 60156, ''n'' refers to number of tests per series. Figures 8. (a) and 8. (b) give the mean values of BDV for different SE-based NFs with fullerene (C 60 ) and graphene (Gr), respectively, for a specific distance equal to 2mm. We have mentioned before that the BDs does not occur for a 2.5mm gap distance because of the 100kV limitation of oil tester.
It is noticed that SE-based NFs with C 60 reach the highest BDV value for a concentration of 0.4 g/L (Figure 8. (a)), which presents a 12.67% of improvement against pure SE. While with graphene, the best enhancement is about 16.64% for 0.3 g/L, as shown in figure 8. (b). Moreover, for d = 2mm, the BDV is enhanced whatever the concentration of NFs, the nature of NPs with respect to SE. Furthermore, this improvement depends on the type and concentration of nanoparticles. Hence, figure 8 highlights the optimal concentration concept as reported in [5], [13], [54]. Note that with SE-based C 60 NFs, beyond the optimal concentration (0.4 g/L), BDV seems to tend to decrease, while with graphene, this is observed beyond 0.3 g/L.
The results presented previously in figure 8 were now presented numerically in Table 4 with standard deviation (Std.) values of NFs for different concentrations of NPs. Besides improving the breakdown voltage mean value, the addition of nanoparticles provides a decreased standard deviation, mainly providing a high peak on the normal distribution histogram plot. A detailed explanation will be considered in the coming paragraphs. Thus, the slightest standard deviation was the highest peak will. In addition, the slight standard deviation provides better transformer reliability, in which the breakdown voltage at very weak cumulative probability will be enhanced.   Figure 9 depicts the percentage improvement of the AC BDV of NFs as a function of the gap distance for different concentrations. It was observed that with SE-based NFs with C 60 (Figure 9. (a)) and Gr ( Figure 9. (b)), the BDV values are increased, whatever the electrode gap and the NPs concentrations. However, the improvement is more important for SE-based NFs with C 60 than with Gr for distances up to 0.5mm. Beyond this distance, the enhancement is more important with SE-based NFs with Gr than that with C 60 . Such a difference may be due to the difference in the geometrical patterns of the two nanomaterials. The geometric structure of fullerene nanoparticles is a truncated icosahedron (dot, 0D), which looks like a soccer ball, while graphene is a crystalline two-dimensional (2D) material.
The fact that the improvement of BDV increases with the electrodes gap and passes by a maximum for a given gap (0.5mm with fullerene and 0.7mm for graphene) before decreasing could be due to the involved physicochemical processes which could be different for smaller electrode gaps than for the larger ones. Also, it is well known that the dielectric strength is higher for small gaps than for the long ones. The electric field can also explain these differences since beyond a certain electrodes gap distance, the electric field loses some of its uniformity in the sphere-to-sphere electrodes set. Note that the improvement in BDV with fullerene at 0.7mm is less than for other electrode gaps.

B. STATISTICAL ANALYSIS OF AC BREAKDOWN VOLTAGE
The most-reported statistical laws for analyzing the breakdown voltage data are Weibull and normal distributions. Anderson -Darling and Shapiro -Wilk conformity tests are conducted on experimental data to check their conformity with those distributions. The Anderson-Darling statistic measures how well the data follow a particular distribution. The better the distribution fits the introduced data, the smaller this statistic will be, while the Shapiro -Wilk statistic measures how well the data follow the normal distribution. The p-value computation allows checking if the data come from a particular distribution. If the p-value is less than a chosen alpha (0.05), reject the null hypothesis that the data come from those distributions. Figures 10. (a) and 10. (b) show the Weibull probabilities plots of the AC BDV of SE and SE-based nanofluids with fullerene and graphene, respectively, for different concentrations of NPs, for d = 2mm. The shape, scale, number of samples (N), Anderson-Darling (AD), and p-values are shown in the supplements of these figures. The shape value, also known as the Weibull slope, indicates the slope of the linear fit characteristic, while the scale value indicates failure degree. Note that, beyond the concentration of 0.3 g/L, the slope is around ten to eleven. Thus, except at a concentration of 0.1 and 0.2 g/L with significant cumulative probability (more than 0.95), the AC BDV of NFs are higher than that of synthetic ester, whatever the nature and size of nanoparticles. Table 5 summarizes the computed p-values for the investigated nanofluids samples and the decision about conformity to Weibull distribution. We noticed that all NFs samples obey Weibull distribution according to p-value computation.   Table 6 gives the AC breakdown voltages at 1% and 50% cumulative probability for the two studied NFs, deduced from Weibull distribution plots. This table shows the voltage for each probability and the enhancement of NFs concerning SE.

1) WEIBULL PROBABILITY ANALYSIS
In most cases, nanofluids BDV was higher than that of SE, regardless of the type and concentrations of NPs; Khaled et Beroual [4] reported such results in the case of SE-based NFs with metals oxides NPs. The addition of nanoparticles significantly improves the 1% probability BDV, and this improvement can reach 50% in the case of SE-based NFs with graphene at a concentration of 0.3g/L. However, the same type and concentration of NPs allow having the best improvement in the mean value.
2) SHAPIRO-WILK NORMALITY TEST Figures 11 and 12 give the histograms of the breakdown voltage distribution of the tested samples for an electrode gap of d = 2mm. Those histograms can give a general idea of the shape. It is observed at first glance that the experimental data also obey the normal distribution. To confirm this VOLUME 10, 2022 conformity, two numerical measures of shape provide a more precise evaluation which is called 'measures of shape,' and more precisely, 'Skewness and Kurtosis': Skewness indicates the amount and direction of skew (deviation from horizontal symmetry), and Kurtosis indicates how tall, and sharp the central peak is relative to a standard bell curve. Hence, to prove normal univariate distribution, skewness and Kurtosis values should be between −3 and +3 [4], and they are equal to zero in the case of standard normal distribution.
Matlab software was used to compute these two parameters, and the results are depicted in Table 7. It appears that except SE/C 60 (0.2 g /L) and SE/Gr (0.2 and 0.3 g /L) nanofluids cases, for which their Kurtosis is higher than three, all other samples provide satisfactory Kurtosis values. However, according to Khaled et Beroual [4], Kurtosis values higher than three do not exclude the data from normality. Furthermore, all Kurtosis values are positive. These distributions with positive Kurtosis values are called leptokurtic distribution, with a high peak, resulting in a small standard deviation value.
Nevertheless, the Shapiro-Wilk normality test on the experimental data should be conducted via p-value to verify the conformity with normal distribution. Therefore, the Matlab program was extended to compute those values and compare them with the alpha value. Table 8 summarizes the p-values for investigated NFs samples and the conformity to normal distribution. We observe that the p-value calculated for the experimental data for SE and SE-based NFs with fullerene and graphene are higher than the significance value (α = 0.05). Thus, they do all obey normal distribution. Furthermore, we observe that with all SE-based NFs with Gr (0.1 g/L) whose p-value is close to   unity, the normal distribution fits perfectly the experimental data. SE-based NF with C 60 at 0.4 g/L are higher than that in pure SE. The opposite is observed with SE-based Gr NF at 0.3 g/L, which presents a poor PDIVs value. In the case of fullerene, this was enhanced by about 5.1% and was worsened by about 33.33% with graphene. Furthermore, the lower Qavg, Qpeak, and NPDs/s for SE-based C 60 NF demonstrates that fullerene NPs enhanced the performance of the SE liquid with a lower PDs activity. On the other hand, graphene NPs deteriorates the fluid behavior increasing the PDs activity at the same voltage level. The PDEVs results show that the pure SE gives the best extinction voltage compared to the two NFs. It was decreased by about 14.98% with C 60 and by about 39.4% with Gr. Figures 13 -15 show the PDs patterns of SE, SE-based NF with C 60 at 0.4 g/L, and SE-based NF with Gr at 0.3 g/L, respectively, at 12kV (RMS) voltage level after 30s. For all three cases, it was observed that the PDs activity began with the appearance of PDs at the peak of negative polarity (270 • electrical degrees), and just after at the peak of positive polarity (90 • electrical degrees) with less number of PDs but a higher charge level. Furthermore, it was noticed that C 60 NF ( Figure 14) shows the lowest activity in terms of PDs activity compared to pure SE. However, unlike C 60 , Gr NF exhibits the more important PDs activity, both at the positive and negative polarities. Based on partial discharge measurements, with a higher PDIV and a lower PDs activity, it can be said that the addition of fullerene NPs enhances the performance of the pure liquid against PDs activity.

A. AC BRE AKDOWN VOLTAGE OF FULLERENE AND GRAPHENE NANOFLUIDS
Conformity check-in of two statistical laws was conducted on our samples using the p-value calculation for one specific 5630 VOLUME 10, 2022   gap distance. Then, these values were compared to the significance value (α = 5%) to validate the conformity. It appears from those results that the experimental data of breakdown voltages for all investigated nanofluids samples obey both Weibull and normal distributions. Thus, these results confirm those reported by elsewhere in which breakdown voltages data of nanofluids and their host liquids usually obey normal and Weibull distributions [5], [13], [20].
It was noticed from experimental results that SE-based nanofluids with fullerene (C 60 ) and graphene (Gr) show an increased breakdown voltage compared to pure host synthetic ester (SE) under AC stress. For a given distance equal to 2mm, regardless of the concentration, SE-based NFs with Gr show a noteworthy improvement than SE-based NFs with C 60 . These improvements are between 5.5 and 12.67% with C 60 and 8.25 and 16.64% with Gr. The improvement depends not only on the nature and the concentration of nanoparticles but also on the gap distance. For most cases, from 0.1 to 0.5mm, the improvement is more important with SE-based NFs with C 60 than that with Gr, and the optimal improvement is about 28.7% at 0.5mm; beyond 0.5mm, the SE-based NFs with Gr becomes more important and op 2 timal enhancement reach 24.39% at 0.7mm. The existence of an optimal concentration for each kind of NPs could be due to the saturation of interfaces between NPs and hosting liquid by electrons. The trapping and accumulation of moving electrons would have reached a limit that the NPs interfaces cannot exceed.
In addition, the presence of NPs improves the AC breakdown voltages at 1% and 50% cumulative probability. Since unexpected collapse at a low voltage value must be considered, each sample breakdown voltage at the lowest probability (1%) is crucial for transformer safety. Therefore, it was observed that NFs with C 60 and Gr have shown an enhanced breakdown strength against pure SE at the lowest probability, especially with Gr. At 0.3 g/L of Gr NF, the best enhancement reaches 51.23%. While, with 0.5 g/L of C 60 NF, the best improvement of breakdown voltage was about 36.14%. Those results confirm the high safety of the nanofluid with Gr and C 60 .
Many research works are engaged to understand better the mechanisms/reasons responsible for improving breakdown voltage in the presence of nanoparticles, and there is almost total unanimity that the nanostructures affect the streamers development. Thus, Peppas et al. [20] tend to explain the improvement in the dielectric strength with the presence of NPs by the efficient electrons trapping resulting by nanostructures, which frustrates the development of streamers and reduces their propagation speed. On the other hand, Ibrahim et al. [5] studied the effect of particles charge on the breakdown phenomena in AC and DC stress for the first time. They conduce that the positively charged nanoparticle holds positive charges that can trap the streamer electrons. Therefore, it increases the breakdown strength of the NF. Conversely, negatively charged particles catch the electrons from the ionized oil molecules to the positive charges formed due to polarization.
A multi-core model was proposed by Tanaka et al. [55] in solid dielectrics and, more particularly, to analyze different phenomena that polymer nanocomposite dielectrics exhibit, which provides a fine structure to ''interaction zones.''. This model was served by Atiya et al. [50]. They suggest that the breakdown voltage improvement was due to the interfacial region formed around the nanoparticle. Based on the electronegativity of nanoparticles, the breakdown mechanism was proposed by preventing streamer propagation into the first and second modes, and fastmoving electrons are trapped. Hence the breakdown process is delayed. VOLUME 10, 2022 Most authors have proposed those mechanisms/reasons, and others suggest that the conductivity of nanoparticles could be one of the reasons for delaying streamer development. Through an experimental study on insulation performances of transformer oil-based NFs with conductive Fe 3 O 4 , semi-conductive TiO 2 , and insulating Al 2 O 3 nanoparticles, Sima et al. [14] proposed an ionization model of NFs. According to this model, the conductive NPs reduce the mobility of fast-moving electrons and turn them into sluggish negative charged NPs, resulting in slowing streamer propagation. Khaled and Beroual [4] tested SE-based NFs with two types of NPs, conductive (Fe 3 O 4 ) and insulating (Al 2 O 3 and SiO 2 ). They observed that conductive nanoparticles (Fe 3 O 4 ) give better enhancement than insulating nanoparticles (SiO 2 and Al 2 O 3 ). While insulating particles give fairly the same improvements of breakdown voltage. The same authors studied AC BDV of Mineral oil-based and synthetic and natural esters NFs with Fe 3 O 4 [13]. The presence of Fe 3 O 4 has doubled the BDV with mineral oil and improved it by about 48 and 7% with SE and NE, respectively. This work showed that the nature of liquid is a fundamental factor in the improvements of BDV. In addition to the conductivity of NPs, according to Hwang et al. [22], the dielectric constants of base liquid and nanoparticles explained the breakdown voltage enhancement. NPs and base liquids having close conductivities and dielectric constants cause the breakdown voltage to deteriorate; the further apart these two parameters are, the higher the breakdown voltage of NF will be.
The enhancement of breakdown voltage of SE when adding C 60 and Gr we observed are likely due to their conductivities too higher than that of the base synthetic ester liquid confirming thence the results reported elsewhere [4], [14] and to the difference in dielectric permittivities of graphene (about 6.9) and fullerene (2.2) regarding that of SE (3.2) as suggested by Hwang et al. [22]. The fact that graphene gives slightly better improvement of BDV than fullerene can be due to its higher dielectric permittivity. Also, the geometry of fullerene and graphene molecules make those molecules can act at two levels (1) as barriers in the vicinity of electrodes by reducing the injected charges into the fluid, increasing thence the initiation threshold voltage of streamers/discharges and therefore the breakdown voltage; and (2) by capturing the moving streamer electrons thence delaying the breakdown.

B. PDs ACTIVITY OF FULLERENE AND GRAPHENE NANOFLUIDS
It emerges from the above results that the addition of Fullerene NPs to SE significantly reduces the activity of PDs, unlike graphene, which tremendously destroys the PDs resistance of pure SE. The addition of C 60 increases the PDIV and reduces Qavg, Qpeak, and NPDs/s compared to the reference SE under AC stress, while Gr NF shows poor performances regarding to PDs activity. It was mentioned previously that the conductive NPs reduce the mobility of fast-moving electrons and turn them into sluggish negative charged NPs, resulting in slowing streamer propagation [14]. According to Atiya et al. [18], the electrical double layer (EDL) around the NPs captures the charge carriers, thus delaying charge accumulation via the electrode space. Therefore, since fullerene and graphene NPs are both highly conductive, it would be expected, according to this hypothesis, that both types of NPs have a favorable impact, i.e. a reduction of the activity of PDs, a slowing down the streamer development, and thence increasing the BDV. However, that is not the case: the C 60 NPs show a very favorable effect on the activity of the PDs in SE, unlike the Gr NPs. The inception voltage of PDs with fullerene is higher than that with graphene. The other explanation for this difference could be the shape of nanoparticles. NPs of C 60 that are spherical could capture more charge carriers than Gr NPs, which are lamellar (Gr). Jin et al. [16] compared the effect of hydrophilic (SiO 2 ) and hydrophobic (C 60 ) NPs on the PDs activity in mineral oil. They assume that the remarked difference in the inception voltage may be due to the hydrophilic behavior of silica NPs. These latter can reduce the moisture content improving hence PDs resistivity. The same authors also verified the ability to reduce moisture content when adding hydrophilic NPs (SiO 2 ) to mineral oil [56]. In this study, C 60 and Gr NPs are hydrophobic, and to correctly state the effect of moisture content on the PDs activity, the water content of the three liquids (i.e. SE, SE-based C 60 NF, and SE-based Gr NF) was measured twice using Mettler Toledo titrator. The obtained results show that the addition of C 60 at 0.4g/L and Gr at 0.3 g/L, increases the water content of pure SE from 33.3 to 39.2 and 46.7ppm, respectively. However, these slight differences remain far from the limit value for water content, which are 200ppm for new Midel 7131 and 400ppm for Midel 7131 in service, according to standard IEC 61099 and IEC 61203, respectively. Hence, those results do not allow such a conclusion to be drawn on the effect of the water content on the PDs activity of SE-based NF.

V. CONCLUSION
To infer, an experimental study on the effect of two carbonic nanomaterials (namely, fullerene and graphene) on the AC breakdown voltages and partial discharges activity of synthetic ester (Midel 7131)-based nanofluids has been presented. It showed that adding Gr and C 60 NPs at different concentrations improves the AC breakdown voltages. However, the improvement depends not only on the concentration but also on the electrodes gap. Indeed, from 0.1 to 0.5mm, the enhancement is more significant with SE-based NFs with fullerene (C 60 ) than that with graphene (Gr), and the optimal improvement is about 28.7% at 0.5mm; beyond 0.5mm, the SE-based NFs with Gr becomes more interesting and optimal enhancement reach 24.39% at 0.7mm.
The statistical analysis of the experimental results performed for a gap distance of 2mm, shows that the breakdown voltage data obey the normal and Weibull probabilistic laws. Note that we considered the gap distance of 2mm, the closest to the standardized distance of 2.5 mm, because of the limitation of the voltage supply (100 kV) and the fact that the breakdown did not occur for 2.5 mm.
It also showed that the addition of C 60 significantly reduces the partial discharge activity in SE while the addition of Gr destroys the partial discharge resistance of pure SE.