**3. Results**

Figure 3 shows the AC BDV of both measured nanofluids versus the concentration of nanoparticles as compared with the mean BDV for the natural ester matrix oil which is 64.5 kV.

**Figure 3.** Mean AC breakdown voltage (BDV) versus nanoparticles concentration (colNF and silica NF).

As it is obvious from Figure 3, for the nanofluid with oleate-coated colloidal MIONs (colNF), the BDV increases as the concentration of nanoparticles increases until the 0.012% *w*/*w* concentration, at which point it reaches its maximum value of 77.8 kV, while at higher concentrations the BDV decreases sharply. However, colNF exhibits higher BDV than natural ester oil only at 0.008% *w*/*w* and 0.012% *w*/*w* concentrations.

As regards the BDV of nanofluid with SiO2, nanoparticles (silica NF–sNF) exhibit similar behavior to the colNFs in terms of increasing nanoparticle concentration, although it always remains lower than the BDV of natural ester oil. The maximum BDV value of 59.7 kV is achieved at 0.02% *<sup>w</sup>*/*<sup>w</sup>*. Any further addition of silica nanoparticles results in an instant drop of the BDV.

Table 1 gives the probabilities 50%, 10%, and 1% for the three dielectric liquids, as well as their standard deviation. In addition, to enable a comparison, in Table 1 the results from two other nanofluids are given, i.e., the probabilities 50% and 10% for TiO2 0.007% *w*/*w* in ester oil [14] and SiO2 0.02% *w*/*w* in mineral oil [19].


**Table 1.** Breakdown voltage probabilities.

According to Table 1, the two nanofluids show differences not only in the mean value of BDV but also in standard deviation. The BDV values of sNF are more scattered at all ranges of concentrations and standard deviation varies from 9.5 kV up to 14.1 kV. The standard deviation of colNF is also large for a nanoparticle concentration of 0.008% or less, but above this value it declines sharply.

As it is known, the low probabilities of breakdown voltage play a pivotal role in designing electrical apparatus such as transformers [9]. The results from Table 1 show that the colNF appeared

with the highest value of V1% BDV which is 62.1 kV, while for natural ester oil the value is 37.6 kV and for sNF the value is 21.7 kV. This can be attributed to its extremely low standard deviation.

#### *The Impact of Nanoparticles on Dielectric Behavior of Insulating Oil*

A considerable amount of research has already been carried out to date to explain the enhanced dielectric behavior of nanofluids [12,20–25]. In [20,21], these are attributed to the capability of nanoparticles to trap electrons. This happens due to inductive charging for the conductive nanoparticles and by means of polarization for the non- and semi-conductive nanoparticles.

When an external electric field, *E*0, is applied to the gap, the electrical charges of a conductive nanoparticle are redistributed inversely along the direction of the electric field within a relaxation time, τ*r*. The relaxation time is expressed as follows [22]:

$$
\pi\_r = \frac{2\varepsilon\_1 + \varepsilon\_2}{2\sigma\_1 + \sigma\_2} \tag{1}
$$

where, ε**1** and ε2 are the permittivity of transformer oil and nanoparticle, respectively and σ1 and σ2 are the conductivities of transformer oil and nanoparticle respectively. Conductive NPs, such as Fe3O4 or ZnO, have a very small relaxation time of the order of 10−11–10−<sup>14</sup> s [20] as can be seen in Table 2. Non-conductive NPs on the other hand have large relaxation times. However, bound charges are formed on their surface due to polarization. Electronic and ionic displacement polarizations are generated very quickly in 10−<sup>15</sup> s to 10−<sup>12</sup> s. It should be noted that conductive NPs with large dielectric permittivity contain both induced and polarized charges on their surface.

**Table 2.** Relaxation time of indicative nanoparticles adapted from Hwang et al. [20].


The potential well due to the redistributed charges on the surface of conductive nanoparticles is given for the direction of the applied field (θ = 0) and for the opposite direction (θ = π) by [22]:

$$q\_{cNP} = \begin{cases} \frac{\sigma\_2 - \sigma\_1}{2\sigma\_1 + \sigma\_2} R^3 E\_0 \frac{1}{r^2} \, \{\theta = 0, \ r \ge R\\ -\frac{\sigma\_2 - \sigma\_1}{2\sigma\_1 + \sigma\_2} R^3 E\_0 \frac{1}{r^2} \, \{\theta = \pi, \ r \ge R\end{cases} \tag{2}$$

where, σ1 and σ2 are the conductivities of transformer oil and nanoparticles respectively, *R* is the radius of nanoparticle, *E*0 is the applied field, and r the distance from nanoparticles surface.

On the exterior of a non-conductive nanoparticle, the potential well is given by [22]:

$$\varphi\_{n\text{NP}} = \begin{cases} \frac{\varepsilon\_2 - \varepsilon\_1}{2\varepsilon\_1 + \varepsilon\_2} R^3 E\_0 \frac{1}{r^2} \, \{\theta = 0, \ r \ge R\\ -\frac{\varepsilon\_2 - \varepsilon\_1}{2\varepsilon\_1 + \varepsilon\_2} R^3 E\_0 \frac{1}{r^2} \, \{\theta = \pi, \ r \ge R\end{cases} \tag{3}$$

where, ε1 and ε2 are the permittivity of transformer oil and nanoparticle respectively. Fast moving electrons are captured by the potential well, forming negatively charged nanoparticles. The latter nanoparticles are introduced with slower mobility and charged negatively, as a consequence the streamer speed is reduced which leads to increased breakdown voltage. Equations (4) and (5) give the total amount of charges trapped by a conductive nanoparticle and non-conductive, respectively [22]:

$$Q\_{cNP} = -12\pi\varepsilon\_1 E\_0 R^2 \tag{4}$$

$$Q\_{\rm ncNP} = -12\pi\varepsilon\_1 E\_0 R^2 \frac{\varepsilon\_2}{2\varepsilon\_1 + \varepsilon\_2} \tag{5}$$

Table 3 depicts the conductivity and permittivity of the colMIONs, SiO2, and natural ester oil FR3. As mentioned above, the colMIONs were synthesized in situ, thus their conductivity and permittivity are accurately considered equal to that of a commercial Fe2O3 NP.

Taking into account Equations (3) and (4), as well as the values of Table 3, the potential well of the suspended colMIONs and SiO2 are given as [22]:

$$
\varphi\_{calMON} = 1.25 \cdot E\_0 \cdot \frac{1}{r^2} \cdot 10^{-25} \,\mathrm{[V]}\tag{6}
$$

$$
\rho\_{\rm SiO2} = 1.9 \cdot E\_0 \cdot \frac{1}{r^2} \cdot 10^{-26} \,\mathrm{[V]}\tag{7}
$$

where, *E*0 is the average electric field and r is the distance from the surface of the nanoparticle.


**Table 3.** Breakdown voltage probabilities.

The electric field, *E*0, for colNF is calculated as 31.12 × 10<sup>6</sup> V/m and for sNF as 23.88 × 10<sup>6</sup> V/m considering that the breakdown voltage for colNF and sNF is 77.8 kV and 59.7 kV, respectively, for a gap of 2.5 mm. Substituting these values of electric field *E*0, as well as the values of average nanoparticle diameter *R* from Table 3, into Equations (4) and (5) for the colMIONs and SiO2 NPs, respectively, their saturation charges are:

$$Q\_{\rm calMON} = -0.83 \times 10^{-18} \,\text{C} \quad \text{and} \quad Q\_{\rm SiO\_2} = -0.35 \times 10^{-18} \,\text{C} \tag{8}$$

Accordingly, substituting the above electric field values *E*0 into Equations (6) and (7), the potential well as a function of the distance from the nanoparticles' surface before breakdown occurs is given in Figure 4 for both nanoparticles in question.

**Figure 4.** Potential well distribution of oleate-coated colloidal magnetic iron oxide nanocrystals (colMION) and SiO2 nanoparticles versus the distance from the nanoparticle's surface.

Figure 4 shows the difference in the potential well between colMIONs and sNF and especially near the nanoparticle's surface. The saturation charges of nanoparticles Equation (8) with respect to the potential well of colMIONs (Figure 4), indicate their higher capability to trap electrons generated from ionization or injection in the bulk of dielectric liquid which can affect the streamer early development. The above is an indication of the better dielectric performance of colNF as compared to sNF which is due to the increased potential well of the colNF.

The results from dielectric relaxation spectroscopy study for natural ester oil and colNF 0.012% *w*/*w* at 20 ◦C and 100 ◦C for a frequency range of 10−1–106 Hz are given in Figure 5.

**Figure 5.** Dielectric losses (tanδ) for natural ester oil and colNF 0.012% at 20 ◦C and 100 ◦C.

From Figure 5 it is demonstrated that the dielectric losses (tanδ) are reduced by increasing the frequency and increased by increasing the temperature. A differentiation of the dielectric losses response is monitored at the frequency regime above 20 kHz associated with high frequency relaxations.
