# Statistical Investigation of Lightning Impulse Breakdown Voltage of Natural and Synthetic Ester Oils-Based Fe3O4, Al2O3 and SiO2 Nanofluids

Abderrahmane Beroual, Usama Khaled

► To cite this version:

Abderrahmane Beroual, Usama Khaled. Statistical Investigation of Lightning Impulse Breakdown Voltage of Natural and Synthetic Ester Oils-Based Fe3O4, Al2O3 and SiO2 Nanofluids. IEEE Access, 2020, 8, pp.112615-112623. 10.1109/ACCESS.2020.3003246. hal-05009819

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Distributed under a Creative Commons Attribution 4.0 International License
Received May 22, 2020, accepted June 13, 2020, date of publication June 17, 2020, date of current version June 29, 2020.

Digital Object Identifier 10.1109/ACCESS.2020.3003246

# Statistical Investigation of Lightning Impulse Breakdown Voltage of Natural and Synthetic Ester Oils-Based Fe₃O₄, Al₂O₃ and SiO₂ Nanofluids

ABDERRAHMANE BEROUAL<sup>1)</sup>, (Fellow, IEEE), AND USAMA KHALED<sup>2,3)</sup>

Corresponding author: Usama Khaled (usamakhaled@energy.aswu.edu.eg)

**ABSTRACT** The characteristics of lighting impulse breakdown voltage (LI-BDV) constitute key performance indicators of insulating materials, especially in insulations based on liquids and liquid-paper for high voltage applications. Encouraged by environmental policies worldwide, new insulating liquids have been developed in recent years. Among these are natural and synthetic esters that are currently considered as potential substitutes for traditional mineral oils due to their environmentally friendly properties. Recent technological advances have shown that the addition of specific nanoparticles (NPs) to insulating liquids can improve both the dielectric withstand voltage and the thermal behavior of liquid insulations. This paper examines the effects of some NPs on the negative LI-BDV of natural and synthetic ester liquids, namely MIDEL 1204 and MIDEL 7131, respectively. The used NPs are Fe₃O₄, Al₂O₃ and SiO₂. The LI-BDV measurements are executed in accordance with IEC 60060 standard, and the breakdown voltage with 1% probability risk (i.e., the lowest possible breakdown voltage) was also estimated. The experimental results showed that these NPs improved the LI-BDV of both synthetic and natural ester liquids and an optimal concentration of NPs can be determined. Statistical analysis was also performed to check the compliance of the experimental results with the most common probability distributions, normal and Weibull distributions.

**INDEX TERMS** U₅₀% breakdown voltage, nanofluids, natural ester, synthetic ester, statistical analysis, Weibull distribution, normal distribution.

## I. INTRODUCTION

Natural and synthetic esters are increasingly used in oil-filled apparatus, especially in high voltage (HV) transformers, to replace the commonly used mineral oil (MO). As well as some of their interesting properties from an environmental point of view, such as biodegradability and non-toxicity [1]–[4], these insulating liquids have a high flash point and low sensitivity to water content. These characteristics qualify them for use in devices installed near urban areas. However, the dielectric withstand of these esters is less good than that of MO [5]. In addition, their viscosity is 3 to 4 times higher than that of MO, which constitutes a disadvantage for heat transfer

The associate editor coordinating the review of this manuscript and approving it for publication was Nagarajan Raghavan <sup>1)</sup>.

and thus for the cooling of power transformers. To solve this problem, one of the solutions would be the addition of specific nanoparticles (NPs) to the esters. Indeed, the addition of some NPs considerably improve the thermal properties of liquids; nanofluids (NFs) are commonly used for cooling of various devices and systems [6]–[8]. However, according to recent studies, the addition of some NPs also enhances the AC breakdown voltage (AC-BDV) of insulating liquids and especially that of MO-based Fe₃O₄ nanofluids [9]. In the case of esters, the AC-BDV can also be improved, but to a lesser degree than that of MO [10], [11].

Nanofluids thus appear to be potential substitutes for MO, since they fulfill two of the essential properties for use in HV devices and in particular in power transformers, namely efficient heat transfer and good dielectric performances.

<footnote n="1">¹AMPERE Laboratory, CNRS UMR 5005, École Centrale de Lyon, University of Lyon, 69134 Ecully, France</footnote>

<footnote n="2">²Department of Electrical Engineering, Faculty of Energy Engineering, Aswan University, Aswan 81528, Egypt</footnote>

<footnote n="3">³Department of Electrical Engineering, College of Engineering, King Saud University, Riyadh 11421, Saudi Arabia</footnote>
Note that, due to the oxidation concern, the use of natural esters is limited to sealed oil-filled apparatus such as sealed rectifier transformers, tap-changers and power transformers up to 550 kV as those produced by General Electric [12]. Large sealed transformers are rare and very expensive. However, despite this limitation for natural esters, the higher permissible moisture content of both natural and synthetic esters makes the moisture resulting from thermal aging of paper insulation readily absorbed by ester liquids, which slows the paper aging process by keeping the paper drier and helps extend the life of the transformer. In addition, ester liquids have higher electrical permittivity than mineral oils which is an advantage in terms of electrical field distribution in insulating system of a power transformer.

Oil-filled devices and their components, including the insulating oils, must also withstand certain constraints including lightning over-voltages. These constitute key performance indicators of insulating materials, in particular in insulations based on liquids and liquid-paper for HV applications.

To this end, some investigations have taken place into the LI-BDV of NFs [13]–[20]. It has been reported that, in a divergent electric field (point-plane electrode configuration); Fe₃O₄ NPs significantly increased the positive LI-BDV of MO [13]. The same results were found for the negative LI-BDV; however, the improvement is less important than for the positive polarity [13], [14]. The polarity effect will not be observed in uniform or quasi-uniform electric fields because of the symmetry of electrode configuration.

The aim of this work is to study the LI-BDV of natural ester (NE) and synthetic ester (SE) liquid-based NFs in a sphere-to-sphere electrode configuration (i.e., in a quasi-uniform electric field), using the same NPs as in previous work in AC [10], [11]. The main objective of this study is to compare the dielectric withstand in lightning impulse voltages to those measured in AC in our previous work, under the same experimental conditions and for the same nanofluids. Weibull and normal statistical analyses are performed to verify the compliance of the experimental findings with one or both of these probabilistic laws. The interest of such study is, among other things, the prediction of failures of nanofluids-filled apparatus in the event of lightning overvoltages and therefore the protection of HV equipment.

## II. EXPERIMENTAL TECHNIQUE

MIDEL 7131 SE and MIDEL 1204 NE are chosen as the base liquids in this study; their main characteristic parameters are given in Table 1. The NPs used for preparing nanofluid samples are (1) insulating NPs of Al₂O₃ and SiO₂ of 50 nm size; and (2) magnetic NPs of Fe₃O₄ of 50 nm size. These were supplied by Sigma-Aldrich. Their distribution, composition, shape and size as well as the techniques used for their characterization were described in previous works [9], [10].

The breakdown voltage (BDV) tests were executed under negative lightning impulse, on a test cell of 500 ml volume containing two brass spherical electrodes of 12.5 mm

<table><caption>TABLE 1. Physicochemical properties of synthetic MIDEL 7131 and Natural MIDEL 1204 Ester Liquids.</caption><thead><tr><td>Property</td><td>MIDEL 7131</td><td>MIDEL 1204</td></tr></thead><tbody><tr><td>Density at 20 °C (kg/dm³)</td><td>0.97</td><td>0.92</td></tr><tr><td>Kinematic viscosity at 40 °C (cSt)</td><td>29</td><td>37</td></tr><tr><td>Pour point (°C)</td><td>-56</td><td>-31</td></tr><tr><td>Flash point (°C)</td><td>260</td><td>> 315</td></tr><tr><td>Fire point (°C)</td><td>316</td><td>> 350</td></tr><tr><td>Total acid number (mg KOH/g)</td><td>< 0.03</td><td>> 0.04</td></tr><tr><td>Water content (ppm)</td><td>300</td><td>100</td></tr><tr><td>Dissipation factor at 90 °C</td><td>0.8 %</td><td>0.9 %</td></tr></tbody></table>

diameter with the electrode gap being 2.50 ± 0.05 mm. All measurements were performed under continuous stirring. The lightning impulse (LI) voltage was supplied by a 1 MV - 40 kJ - 1.2/50 µs Marx generator (Haefely type) connected to a dedicated capacitive divider; note that only three stages of the generator were used for a maximum voltage of 300 kV. The U₅₀% breakdown voltage is determined by the up-and-down method according to IEC 60060 ed3 2010-09.

The method involves performing first some preliminary tests to determine the proper voltage from which one starts the series of measurements. Once this voltage has been determined, a series of 24 measurements is started by increasing by 3 kV if there is no breakdown or by decreasing by 3 kV in the event of breakdown and so on; 24 readings are taken to be sufficient for statistical analysis of Weibull and normal distributions.

Note that most researchers use the step-by-step method following IEC 60897 standard. However, some studies also used the up-and-down method [21].

## III. EXPERIMENTAL RESULTS: STATISTICAL ANALYSIS

This section presents the results of U₅₀% LI-BDV measurements of NFs' samples and their compliance with the normal and Weibull distribution laws [22], [23]. These probabilistic distributions are the most used to analyze the BDV of dielectrics. The interest in such analyses for the design and maintenance of power apparatus as well as for improving the predictability of insulation performance has been outlined in previous work [10]. Note that in this study one uses the 2-parameter Weibull distribution assuming the location parameter equal to 0 instead 3-parameter Weibull distribution.

Two hypothesis tests are applied to verify to which probabilistic law the experimental data complies, namely the Shapiro-Wilk test [23] and the Anderson-Darling test [24]. The details of the methods of application of these tests and computation of the related parameters have been described elsewhere [25]. The significance level α to which the p-values are compared in order to decide whether or not the experimental results comply with the statistical distribution is taken to be 5%. Recall that for the p-values less than or equal to α, the null hypothesis is rejected and, consequently, the data of the sample do not belong to the law of statistical distribution considered. Smaller p-values provide stronger evidence against the null hypothesis. Larger values for the Anderson-Darling statistic indicate that the data do not follow a Weibull distribution.
<figure><img src="image_2.png" /><figcaption>**FIGURE 1.** Weibull distribution of the LI breakdown voltages of SE/Al₂O₃ nanofluid.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**FIGURE 2.** Weibull distribution of the LI breakdown voltages of SE/SiO₂ nanofluid.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**FIGURE 3.** Weibull distribution of the LI breakdown voltages of SE/Fe₃O₄ nanofluid.</figcaption></figure>

## A. WEIBULL DISTRIBUTION

### 1) SYNTHETIC ESTER LIQUID – BASED NANOFLUIDS

Figures 1 to 3 depict the Weibull LI-BDV plots of SE-based Fe₃O₄, Al₂O₃ and SiO₂ NFs with different concentrations of NPs. Beside each figure are given the main parameters characterizing the Weibull distribution, namely the shape parameter representing the slope of the line, the scale parameter related to the scattering of the data and indicating the degree of failure, the Anderson–Darling (AD) and the *p*-values.

<table><caption>**TABLE 2.** Hypothesis test of compliance with Weibull distribution of the average LI-BDV of SE-based nanofluids.</caption><thead><tr><th>Sample</th><th>p-value</th><th>Conformity to Weibull distribution</th></tr></thead><tbody><tr><td>Pure SE</td><td>0.069</td><td>Accepted</td></tr><tr><td>SE/Fe<sub>3</sub>O<sub>4</sub> (0.05 g/L)</td><td>0.183</td><td>Accepted</td></tr><tr><td>SE/Fe<sub>3</sub>O<sub>4</sub> (0.2 g/L)</td><td>0.214</td><td>Accepted</td></tr><tr><td>SE/Fe<sub>3</sub>O<sub>4</sub> (0.3 g/L)</td><td>0.056</td><td>Accepted</td></tr><tr><td>SE/Fe<sub>3</sub>O<sub>4</sub> (0.4 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>SE/Al<sub>2</sub>O<sub>3</sub> (0.05 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>SE/Al<sub>2</sub>O<sub>3</sub> (0.2 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>SE/Al<sub>2</sub>O<sub>3</sub> (0.3 g/L)</td><td>0.022</td><td>Rejected</td></tr><tr><td>SE/Al<sub>2</sub>O<sub>3</sub> (0.4 g/L)</td><td>0.033</td><td>Rejected</td></tr><tr><td>SE/ SiO<sub>2</sub> (0.05 g/L)</td><td>&lt;0.010</td><td>Rejected</td></tr><tr><td>SE/ SiO<sub>2</sub> (0.2 g/L)</td><td>&lt;0.010</td><td>Rejected</td></tr><tr><td>SE/ SiO<sub>2</sub> (0.3 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>SE/ SiO<sub>2</sub> (0.4 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr></tbody></table>

<table><caption>**TABLE 3.** U₅₀% LI-BDV of SE-Based Nanofluids.</caption><thead><tr><th></th><th>SE</th><th>Fe<sub>3</sub>O<sub>4</sub></th><th>Al<sub>2</sub>O<sub>3</sub></th><th>SiO<sub>2</sub></th></tr></thead><tbody><tr><td></td><td colspan="4" style="text-align: center;">SE / 0.05 (g/L) NF</td></tr><tr><td>BDV (kV)</td><td>126.06</td><td>158.29</td><td>138.55</td><td>131.89</td></tr><tr><td>Increment (%)</td><td></td><td>25.57</td><td>9.91</td><td>4.62</td></tr><tr><td></td><td colspan="4" style="text-align: center;">SE / 0.2 (g/L) NF</td></tr><tr><td>BDV (kV)</td><td>126.06</td><td>156.53</td><td>131.32</td><td>144.63</td></tr><tr><td>Increment (%)</td><td></td><td>24.17</td><td>4.17</td><td>14.73</td></tr><tr><td></td><td colspan="4" style="text-align: center;">SE / 0.3 (g/L) NF</td></tr><tr><td>BDV (kV)</td><td>126.06</td><td>143.35</td><td>149.15</td><td>153.69</td></tr><tr><td>Increment (%)</td><td></td><td>13.72</td><td>18.32</td><td>21.84</td></tr><tr><td></td><td colspan="4" style="text-align: center;">SE / 0.4 (g/L) NF</td></tr><tr><td>BDV (kV)</td><td>126.06</td><td>134.09</td><td>140.58</td><td>130.47</td></tr><tr><td>Increment (%)</td><td></td><td>6.37</td><td>11.52</td><td>3.50</td></tr></tbody></table>

The *p*-values and compliance of experimental data with the Weibull distribution are summarized in Table 2. It appears that the experimental results generally comply with this probabilistic distribution law, apart from SE with Al₂O₃ at concentrations of 0.3 g/L and 0.4 g/L, and SE with SiO₂ at concentrations of 0.05 g/L and 0.2 g/L.

Table 3 summarizes the U₅₀% values of LI-BDV. It is noted that the tested NPs improve the LI-BDV of SE. The best improvements are approximately 25.6% with Fe₃O₄ at a concentration of 0.05 g/L; 18.3% with Al₂O₃ at a concentration of 0.3 g/L; and 22% of SiO₂ at a concentration of 0.3 g/L. It is also noticed from Table 3, the existence of an optimal concentration for each type of NPs, in the investigated concentrations range.

Among the interesting and useful parameters from a practical viewpoint, in particular for the design of insulating components, is the LI-BDV at 1% cumulative probability, this being the lowest possible BDV. Table 4 summarizes the LI-BDV at 1% probability for investigated NFs. It can be observed that for each type of NP, the 1% values of LI-BDV increase up to an optimal concentration corresponding to the highest value and then decrease.

Note that the U₅₀% value of LI-BDV of pure SE of 126.06 kV is more than twice the mean value of 60 kV of the BDV measured under AC-BDV.
<table><caption>TABLE 4. LI-BDV at 1% cumulative probability of SE-based nanofluids (from weibull distribution).</caption><thead><tr><th rowspan="2"></th><th rowspan="2">SE</th><th colspan="6">Breakdown voltage probability (%)</th></tr><tr><th>0.05 g/L</th><th>0.2 g/L</th><th>0.3 g/L</th><th>0.4 g/L</th><th>Increment (%)</th><th>Increment (%)</th></tr></thead><tbody><tr><td rowspan="4">1%</td><td colspan="6">Fe<sub>3</sub>O<sub>4</sub> Nanoparticles</td></tr><tr><td>108.1</td><td>144.8</td><td>34.0</td><td>141.2</td><td>30.6</td><td>125.7</td><td>16.3</td><td>104.9</td><td>-3.0</td></tr><tr><td colspan="6">Al<sub>2</sub>O<sub>3</sub> Nanoparticles</td></tr><tr><td>108.1</td><td>121.6</td><td>12.5</td><td>106.4</td><td>-1.6</td><td>132.0</td><td>22.1</td><td>112.7</td><td>4.3</td></tr><tr><td></td><td colspan="6">SiO<sub>2</sub> Nanoparticles</td></tr><tr><td></td><td>108.1</td><td>100.1</td><td>-7.4</td><td>122.1</td><td>13.0</td><td>137.8</td><td>27.5</td><td>101.1</td><td>-6.5</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>FIGURE 4. Weibull distribution of the LI breakdown voltages of NE/Al₂O₃ nanofluid.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIGURE 5. Weibull distribution of the LI breakdown voltages of NE/SiO₂ nanofluid.</figcaption></figure>

## 2) NATURAL ESTER LIQUID – BASED NANOFLUIDS

Figures 4 to 6 show the Weibull plots of the LI-BDV of NE-based Fe₃O₄, Al₂O₃ and SiO₂ nanofluids. The characteristic parameters of these curves are indicated beside each figure. Table 5 summarizes the *p*-values and compliance of experimental data with the Weibull distribution for investigated NFs. It should be noted that the experimental data generally follow the Weibull distribution with the exception

<figure><img src="image_7.png" /><figcaption>FIGURE 6. Weibull distribution of the LI breakdown voltages of NE/Fe₃O₄ nanofluid.</figcaption></figure>

<table><caption>TABLE 5. Hypothesis test of compliance with weibull distribution of the average LI-BDV of NE-based nanofluids.</caption><thead><tr><th>Sample</th><th>p-value</th><th>Conformity to Weibull distribution</th></tr></thead><tbody><tr><td>Pure NE</td><td>0.145</td><td>Accepted</td></tr><tr><td>NE/Fe<sub>3</sub>O<sub>4</sub> (0.05 g/L)</td><td>0.025</td><td>Rejected</td></tr><tr><td>NE/Fe<sub>3</sub>O<sub>4</sub> (0.2 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>NE/Fe<sub>3</sub>O<sub>4</sub> (0.3 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>NE/Fe<sub>3</sub>O<sub>4</sub> (0.4 g/L)</td><td>&lt;0.010</td><td>Rejected</td></tr><tr><td>NE/Al<sub>2</sub>O<sub>3</sub> (0.05 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>NE/Al<sub>2</sub>O<sub>3</sub> (0.2 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>NE/Al<sub>2</sub>O<sub>3</sub> (0.3 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>NE/Al<sub>2</sub>O<sub>3</sub> (0.4 g/L)</td><td>0.128</td><td>Accepted</td></tr><tr><td>NE/SiO<sub>2</sub> (0.05 g/L)</td><td>0.140</td><td>Accepted</td></tr><tr><td>NE/SiO<sub>2</sub> (0.2 g/L)</td><td>0.230</td><td>Accepted</td></tr><tr><td>NE/SiO<sub>2</sub> (0.3 g/L)</td><td>&gt;0.250</td><td>Accepted</td></tr><tr><td>NE/SiO<sub>2</sub> (0.4 g/L)</td><td>0.045</td><td>Rejected</td></tr></tbody></table>

of three mixtures, namely NE/Fe₃O₄ (0.05 g/L), NE/Fe₃O₄ (0.4 g/L) and NE/SiO₂ (0.4 g/L) for which the *p*-values are lower than 5% that is the level of significance chosen for the tests.

It should first be noted that *U*₅₀% of the LI-BDV value of pure NE is also almost twice that of the mean value of the AC-BDV (i.e., 129.34 kV against 68.77 kV). However, it is observed that the NPs under consideration improve the LI-BDV of NE (Table 6); and for each type of NPs, there exists, in the range of the studied concentrations, an optimal concentration giving the highest value of *U*₅₀% LI-BDV. The best improvements are approximately 7.5% with Fe₃O₄ at a concentration of 0.2 g/L; 16.8% with Al₂O₃ at a concentration of 0.05 g/L; and 13% of SiO₂ at a concentration of 0.2 g/L.

The analysis of the LI-BDV at 1% cumulative probability also shows that NPs enhance the LI-BDV. For each type of NPs, the variation in 1% values of LI-BDV with the concentration of NPs displays an optimal concentration corresponding to the highest value and then decreases (Table 7). The best improvement is approximately 17.6% for the three types of NPs, but at different concentrations of NPs: 0.2 g/L with Fe₃O₄, 0.05 g/L with Al₂O₃ and 0.3 g/L with SiO₂.
<table><caption>TABLE 6. U₅₀% LI-BDV of natural ester-Based nanofluids.</caption><thead><tr><th></th><th>NE</th><th>Fe<sub>3</sub>O<sub>4</sub></th><th>Al<sub>2</sub>O<sub>3</sub></th><th>SiO<sub>2</sub></th></tr></thead><tbody><tr><th>BDV (kV)</th><td>NE / 0.05 (g/L) NF</td><td></td><td></td><td></td></tr><tr><th>Increment (%)</th><td>129.34</td><td>132.73</td><td>151.02</td><td>139.37</td></tr><tr><th>BDV (kV)</th><td>NE / 0.2 (g/L) NF</td><td></td><td></td><td></td></tr><tr><th>Increment (%)</th><td>129.34</td><td>139.05</td><td>144.08</td><td>146.28</td></tr><tr><th>BDV (kV)</th><td>NE / 0.3 (g/L) NF</td><td></td><td></td><td></td></tr><tr><th>Increment (%)</th><td>129.34</td><td>123.59</td><td>136.90</td><td>145.43</td></tr><tr><th>BDV (kV)</th><td>NE / 0.4 (g/L) NF</td><td></td><td></td><td></td></tr><tr><th>Increment (%)</th><td>129.34</td><td>118.62</td><td>132.08</td><td>142.09</td></tr></tbody></table>

<table><caption>TABLE 7. LI-BDV at 1% cumulative probability of NE-based nanofluids (from weibull distribution).</caption><thead><tr><th>Breakdown voltage probability (%)</th><th>Breakdown voltage (kV)</th><th>Breakdown voltage (kV)</th><th>Increment (%)</th><th>Breakdown voltage (kV)</th><th>Breakdown voltage (kV)</th><th>Increment (%)</th><th>Breakdown voltage (kV)</th><th>Increment (%)</th></tr></thead><tbody><tr><td rowspan="4">1%</td><td>NE</td><td>0.05 g/L</td><td></td><td>0.2 g/L</td><td>0.3 g/L</td><td></td><td>0.4 g/L</td><td></td></tr><tr><td colspan="8">Fe<sub>3</sub>O<sub>4</sub> Nanoparticles</td></tr><tr><td>103.1</td><td>108.5</td><td>5.2</td><td>121.6</td><td>17.9</td><td>107.1</td><td>3.9</td><td>96.9</td><td>-6.0</td></tr><tr><td colspan="8">Al<sub>2</sub>O<sub>3</sub> Nanoparticles</td></tr><tr><td>103.1</td><td>121.2</td><td>17.6</td><td>118.3</td><td>14.7</td><td>93.1</td><td>-9.7</td><td>107.4</td><td>4.2</td></tr><tr><td colspan="8">SiO<sub>2</sub> Nanoparticles</td></tr><tr><td>103.1</td><td>113.4</td><td>10.0</td><td>117.9</td><td>14.4</td><td>121.2</td><td>17.6</td><td>109.8</td><td>6.5</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>FIGURE 7. LI Histogram of pure SE.</figcaption></figure>

## B. NORMAL DISTRIBUTION

### 1) SYNTHETIC ESTER LIQUID – BASED NANOFLUIDS

The histograms of the distribution of the U₅₀% LI-BDV values of the tested samples and the corresponding skewness and kurtosis are given in Figures 7 to 10. This representation enables to detect possible anomalies in the distribution of the BDV in different ranges of voltages. So, it appears from the computed *p*-values that the experimental findings do not completely comply with the normal distribution. Indeed, the hypothesis tests show that the *p*-values for SE/Al₂O₃ (0.4 g/L), SE/SiO₂ (0.2 g/L) and SE/SiO₂ (0.3 g/L) NF samples are lower than 5% as shown on Table 8.

Regarding the skewness and kurtosis values, they indicate that the SE-based NFs results do not rigorously comply with the normal distribution since they are different

<figure><img src="image_9.png" /><figcaption>FIGURE 8. a. Histogram of LI SE/Al₂O₃. b. Skewness and kurtosis of LI SE/Al₂O₃.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>FIGURE 8. (Continued) a. Histogram of LI SE/Al₂O₃. b. Skewness and kurtosis of LI SE/Al₂O₃.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIGURE 9. a. Histogram of LI SE/SiO₂. b. Skewness and kurtosis of LI SE/SiO₂.</figcaption></figure>

from 0 and 3, respectively; the coefficients of skewness and kurtosis of the normal distribution have to be respectively 0 and 3. The experimental findings deviate somewhat from the normal distribution since the skewness values vary between -1.2 and +0.6. In addition, the highest value of the kurtosis is less than 1.4; thus the distribution is slightly
<figure><img src="image_12.png" /><figcaption>**FIGURE 9.** (Continued) a. Histogram of LI SE/SiO₂. b. Skewness and kurtosis of LI SE/SiO₂.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**FIGURE 10.** a. Histogram of LI SE/Fe₃O₄. b. Skewness and kurtosis of LI SE/Fe₃O₄.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**FIGURE 10.** (Continued) a. Histogram of LI SE/Fe₃O₄. b. Skewness and kurtosis of LI SE/Fe₃O₄.</figcaption></figure>

platykurtic [25]. Note that the skewness and kurtosis values are computed using the statistical package - Statistical Package for the Social Sciences (SPSS) [26].

## 2) NATURAL ESTER LIQUID – BASED NANOFLUIDS

Figures 11 to 14 depict the histograms of the distribution of BDV of the tested samples and the corresponding skewness and kurtosis. By applying the hypothesis test and

<table><caption>**TABLE 8.** Hypothesis test of compliance with normal distribution of the average LI-BDV of SE-based nanofluids.</caption><thead><tr><th>Sample</th><th>p-value</th><th>Conformity to normal distribution</th></tr></thead><tbody><tr><td>Pure SE</td><td>0.151</td><td>Accepted</td></tr><tr><td>SE/Fe<sub>3</sub>O<sub>4</sub> (0.05 g/L)</td><td>0.149</td><td>Accepted</td></tr><tr><td>SE/Fe<sub>3</sub>O<sub>4</sub> (0.2 g/L)</td><td>0.563</td><td>Accepted</td></tr><tr><td>SE/Fe<sub>3</sub>O<sub>4</sub> (0.3 g/L)</td><td>0.234</td><td>Accepted</td></tr><tr><td>SE/Fe<sub>3</sub>O<sub>4</sub> (0.4 g/L)</td><td>0.234</td><td>Accepted</td></tr><tr><td>SE/Al<sub>2</sub>O<sub>3</sub> (0.05 g/L)</td><td>0.513</td><td>Accepted</td></tr><tr><td>SE/Al<sub>2</sub>O<sub>3</sub> (0.2 g/L)</td><td>0.831</td><td>Accepted</td></tr><tr><td>SE/Al<sub>2</sub>O<sub>3</sub> (0.3 g/L)</td><td>0.054</td><td>Accepted</td></tr><tr><td>SE/Al<sub>2</sub>O<sub>3</sub> (0.4 g/L)</td><td>0.032</td><td>Rejected</td></tr><tr><td>SE/SiO<sub>2</sub> (0.05 g/L)</td><td>0.051</td><td>Accepted</td></tr><tr><td>SE/SiO<sub>2</sub> (0.2 g/L)</td><td>0.039</td><td>Rejected</td></tr><tr><td>SE/SiO<sub>2</sub> (0.3 g/L)</td><td>0.024</td><td>Rejected</td></tr><tr><td>SE/SiO<sub>2</sub> (0.4 g/L)</td><td>0.285</td><td>Accepted</td></tr></tbody></table>

<figure><img src="image_15.png" /><figcaption>**FIGURE 11.** LI Histogram of pure NE.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**FIGURE 12.** a. Histogram of LI NE/Al₂O₃. b. Skewness and kurtosis of LI NE/Al₂O₃.</figcaption></figure>

by computing the *p*-values, it is noticed that all experimental data comply with the normal distribution except pure NE, as shown on Table 9.

Note, even if the *p*-values indicated that the distribution of experimental results of all NFs obeys that normal law, the skewness values are not null and the kurtosis scores vary between -0.8 and +0.8. This indicates that the distribution of experimental results slightly deviates from the normal law.
<figure><img src="image_17.png" /><figcaption>**FIGURE 12.** (Continued) a. Histogram of LI NE/Al₂O₃. b. Skewness and kurtosis of LI NE/Al₂O₃.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**FIGURE 13.** a. Histogram of LI NE/SiO₂. b. Skewness and kurtosis of LI NE/SiO₂.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**FIGURE 13.** (Continued) a. Histogram of LI NE/SiO₂. b. Skewness and kurtosis of LI NE/SiO₂.</figcaption></figure>

Note that most of the standard deviations are less than 7%, except NE/Al₂O₃ at a concentration of 0.3 g/L in which case it is of about 10.8%.

<figure><img src="image_20.png" /><figcaption>**FIGURE 14.** a. Histogram of LI NE/Fe₃O₄. b. Skewness and kurtosis of LI NE/Fe₃O₄.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**FIGURE 14.** (Continued) a. Histogram of LI NE/Fe₃O₄. b. Skewness and kurtosis of LI NE/Fe₃O₄.</figcaption></figure>

<table><caption>**TABLE 9.** Hypothesis test of compliance with normal distribution of the average LI-BDV of NE-based nanofluids.</caption><thead><tr><th>Sample</th><th>p-value</th><th>Conformity to normal distribution</th></tr></thead><tbody><tr><td>Pure NE</td><td>0.020</td><td>Rejected</td></tr><tr><td>NE/Fe<sub>3</sub>O<sub>4</sub> (0.05 g/L)</td><td>0.333</td><td>Accepted</td></tr><tr><td>NE/Fe<sub>3</sub>O<sub>4</sub> (0.2 g/L)</td><td>0.294</td><td>Accepted</td></tr><tr><td>NE/Fe<sub>3</sub>O<sub>4</sub> (0.3 g/L)</td><td>0.502</td><td>Accepted</td></tr><tr><td>NE/Fe<sub>3</sub>O<sub>4</sub> (0.4 g/L)</td><td>0.182</td><td>Accepted</td></tr><tr><td>NE/Al<sub>2</sub>O<sub>3</sub> (0.05 g/L)</td><td>0.763</td><td>Accepted</td></tr><tr><td>NE/Al<sub>2</sub>O<sub>3</sub> (0.2 g/L)</td><td>0.330</td><td>Accepted</td></tr><tr><td>NE/Al<sub>2</sub>O<sub>3</sub> (0.3 g/L)</td><td>0.730</td><td>Accepted</td></tr><tr><td>NE/Al<sub>2</sub>O<sub>3</sub> (0.4 g/L)</td><td>0.334</td><td>Accepted</td></tr><tr><td>NE/SiO<sub>2</sub> (0.05 g/L)</td><td>0.062</td><td>Accepted</td></tr><tr><td>NE/SiO<sub>2</sub> (0.2 g/L)</td><td>0.119</td><td>Accepted</td></tr><tr><td>NE/SiO<sub>2</sub> (0.3 g/L)</td><td>0.816</td><td>Accepted</td></tr><tr><td>NE/SiO<sub>2</sub> (0.4 g/L)</td><td>0.091</td><td>Accepted</td></tr></tbody></table>

## IV. DISCUSSION

Based on the aforedescribed results,

1) The $U_{50\%}$ value of LI-BDV of pure SE is more than twice that of the mean value of BDV measured under
AC-BDV; (i.e., 126.06 kV against 60 kV) [11]. Similar results are found with NE, where the $U_{50\%}$ of the LI-BDV value of pure NE is also almost twice that of the mean value of the AC-BDV (i.e., 129.34 kV against 68.77 kV) [10].

2) The LI-BDVs of both natural and synthetic esters are enhanced when adding NPs. Note that for each type of NP, there is an optimal concentration that gives the highest value of $U_{50\%}$ LI-BDV for both ester liquids.

For SE, the best improvement of the $U_{50\%}$ value of LI-BDV is obtained with magnetic NPs (Fe₃O₄), as is also the case of the AC-BDV [11]. For the LI-BDV, the value is increased by approximately 25.6% with Fe₃O₄ at a concentration of 0.05 g/L; 22% with SiO₂ at a concentration of 0.3 g/L; and 18.3% with Al₂O₃ at a concentration of 0.3 g/L. The improvement of the AC-BDV is approximately 48% with Fe₃O₄, 32% with SiO₂ and 25% with Al₂O₃; respectively.

For NE, the best improvements of the $U_{50\%}$ value of LI-BDV are approximately 7.5% with Fe₃O₄ at a concentration of 0.2 g/L; 16.8% with Al₂O₃ at a concentration of 0.05 g/L; and 13% of SiO₂ at a concentration of 0.2 g/L [10]. However, under AC, the best improvement of AC-BDV does not exceed 7%, obtained with Fe₃O₄ at a concentration 0.4 g/L. The increase is 6% with Al₂O₃ at a concentration of 0.3 g/L. In some cases, the addition of NPs even reduces the AC-BDV of NE oil. A decrease of 15% is observed with SiO₂ at a concentration of 0.05 g/L [10]. Therefore, SE-based NFs are found to be more advantageous than NE-based NFs.

Based on the *p*-values, it is noticed that, with the exception of SE with Al₂O₃ at concentrations of 0.3 g/L and 0.4 g/L, and SE with SiO₂ at concentrations of 0.05 g/L and 0.2 g/L, the experimental findings with SE-based NFs comply with Weibull's probabilistic law. Similarly, with NE-based nanofluids with the exception of mixtures of NE/Fe₃O₄ (0.05 g/L), NE/Fe₃O₄ (0.4 g/L) and NE/SiO₂ (0.4 g/L).

Regarding the normal law, the hypothesis test and the *p*-values showed that the experimental results of SE-based NFs conform to the normal distribution with the exception of SE/Al₂O₃ (0.4 g/L), SE/SiO₂ (0.2 g/L) and SE/SiO₂ (0.3 g/L) NF samples. Similarly with NE-based NFs, all experimental data complies with the normal distribution except pure NE.

Regarding the processes involved in the presence of NPs, neither the polarity effect nor the development of streamers can be used to explain the experimental results. The experiments were carried out in a quasi-uniform electric field, even if the applied voltage waveform was a negative lightning impulse, due to symmetrical configuration of the electrodes (sphere-to-sphere electrode configuration). However, several mechanisms can be advanced to explain the effect of NPs, as discussed elsewhere [9].

However, the improvement in the dielectric withstand of esters in the presence of NPs may be due to (1) the fact that the NPs play the role of electron trap sites in the vicinity of the electrodes by reducing the number of electrons

and consequently by raising the initiation threshold voltage of the streamer/discharge resulting in an increase of breakdown voltage; and (2) by reducing the number of electrons moving towards the opposite electrode (in the volume of the liquid), due to accumulation of electrons at the nanoparticle-surrounding liquid interfaces, forming a double layer, and thereby slowing down the development of the discharge leading to breakdown.

In the event that there is an excess of electrons on the surface of the nanoparticles and the double layer is saturated, the excess electrons which arrive later cannot be trapped; they will participate in the development of streamers, thus reducing the breakdown voltage. This may therefore explain the concept of optimal concentration; it is the threshold beyond which the electrons are no longer stopped. Thus, this process explains the concept of electron capture and release.

The improvement of the dielectric strength of esters-based nanofluids can be explained on the base of the influence of NPs on the streamer development as proposed by some authors such as Hwang et al. [27], Du et al. [28] and J. Miao et al. [29]. According to these authors, the NPs in particular the conducting ones, catch electrons in their movement under the effect of the electric field and accumulate them on their surfaces creating a local electric field which will oppose to the external electric field. The nanoparticles will act as “electron traps” inside the nanofluid. It results in a slowdown of the streamer propagation leading to the increase the breakdown voltage. Such a theory has been advanced for magnetic nanoparticles in the presence of lightning impulse voltage [27].

By using thermally stimulated current method (TSC) and pulse electroacoustic technique (PEA) for measuring the charge trap and transportation characteristics in pure transformer oil and transformer oil-TiO₂ based nanofluids submitted to positive impulse voltage, Du et al. [27] observed that electron shallow and trap density and charge decay rate are greatly increased in nanofluids. They concluded that fast electrons may be converted to slow electrons by electron trapping and de-trapping in shallow traps of nanofluids, resulting in an improved breakdown voltage compared to that of pure oil.

## V. CONCLUSION

In this paper, the effects of magnetic (Fe₃O₄) and insulating (Al₂O₃ and SiO₂) NPs on the $U_{50\%}$ negative LI-BDV of natural and synthetic liquids (MIDEL 1204 and MIDEL 7131, respectively) were investigated. It is shown that the NPs improve the LI-BDV of both ester liquids, and that for each type of NP there is an optimal concentration of NP for which the $U_{50\%}$ LI-BDV is the highest. The LI-BDVs of investigated pure esters were found to be approximately twice those of the AC-BDVs.

The performed statistical analysis also showed that the experimental findings generally comply with normal and Weibull probabilistic laws.

The results presented in this work can have several applications such as the prediction of failures of
nanofluids-filled apparatus in the event of lightning overvolt-
ages and therefore the protection of high voltage equipment;
or even in the techniques using repetitive pulse voltages such
as electro-poration and treatment of some fluids, for example.

ACKNOWLEDGMENT

The authors extend their appreciation to RSSU at King Saud
University for their technical support.

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**ABDERRAHMANE BEROUAL** (Fellow, IEEE) is currently a Distinguished Professor at the École Centrale de Lyon, University of Lyon, France. He is also the Head of the High Voltage Group, AMPERE Laboratory – CNRS and a Scientific Expert at the Super Grid Institute. He was also responsible for the Master Research Program in electrical engineering from 2013 to 2015. He is the author/coauthor of more than 470 technical articles, including more than 210 refereed journal

articles, five patents, two books, and six book chapters. He has supervised more than 45 Ph.D. theses. His main research interests include high voltage insulation, outdoor insulation, dielectric materials, long air gaps discharge and lightning, modeling of discharges, and composite materials. He is a Distinguished Visiting Professor of the U.K. Royal Academy of Engineering at Cardiff University and at King Saud University, Saudi Arabia. He was a recipient of the 2016 IEEE T. Dakin Award. From 1994 to 1998, he chaired the International Study Group on Streamer Propagation in Liquids of the IEEE – DEIS. He is a member of many advisory committees of international conferences, Technical Committee of the IEEE CEIDP, UF10 Technical Commission – MT30 of IEC, and an Associate Editor of the IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION.

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**USAMA KHALED** was graduated and received the M.Sc. degree in electrical engineering from Aswan University, Egypt, in 1998 and 2003, respectively, and the Ph.D. degree in electrical engineering from Cairo University, Egypt, and Kyushu University, Japan, through a joint scholarship, in 2010. Since 2000, he has been with the Department of Electrical Power Engineering, Faculty of Energy Engineering, Aswan University, working as a Teaching Assistant, an Assistant

Lecturer, an Assistant Professor, and an Associate Professor. Since 2014, he had been an Assistant Professor at the College of Engineering, King Saud University, where he has been an Associate Professor, since 2018. His research interests include nanodielectric materials, applied electrostatics, and high voltage technologies.

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