*3.4. Partial Discharge*

In Figure 10, the change in apparent charge is depicted versus the applied AC voltage, while the PDIV and the value of apparent charge at the PDIV for each sample are presented in Table 7. It is evident that all the samples in question have similar behavior until about the level of 3 kV. Above this voltage level, only the paper impregnated to sNF demonstrates a stable resistance to PD activity for the whole range of AC stress, with the accumulation of apparent charge at the level of 5.5 kV (highest applied voltage) being improved by 97.5 and 95.8% in comparison to the corresponding one of the paper impregnated to base oil and iNF, respectively. Papers impregnated to sNF and iNF samples demonstrate improved resistance to PD appearance by 92 and 44% with respect to the paper impregnated to the matrix.

**Figure 10.** Change of the apparent charge as a function of the applied voltage for the three samples under investigation.

**Table 7.** PDIV and apparent charge at the PDIV.


Figure 11 depicts the PD pulses related to the papers impregnated to sNF (Figure 11a) and iNF (Figure 11b) at the highest applied voltage. In the case of iNF impregnated insulating paper, the multiple pulses of irregular form indicate the presence of voids in the vicinity of the NF.

**Figure 11.** Waveforms of PD pulses at 5.5 kV applied voltage: (**a**) Paper impregnated to sNF; (**b**) Paper impregnated to iNF.

#### **4. Discussion**

Taking into account the U50% values from Table 5 according to Weibull distribution, the mean AC dielectric strength for a gap of 2.5 mm is 24.9 kV·mm−1, 25.9 kV·mm−1, and 28.9 kV·mm−<sup>1</sup> for base, iNF, and sNF samples, respectively. This finding could be attributed to the fact that the addition of semi-conducting SiC NPs for the selected weight fraction can lead to the delay of streamer propagation, by trapping and de-trapping the fast electrons at the tip of the streamer in shallow traps [27,28,32,38].

In an effort to explain the effect of the two types of NPs on BDV of the oil, Sima et al. [28] proposed a theory according to which the addition of NPs in the matrix results in change of the main electrodynamics in the dielectric liquid, regardless of their electrical properties. If considerable divergence exists in conductivity or permittivity between NP and base oil, then induced or polarized charges are generated at the interface between NP and matrix. These charges result in the production of a potential well that can trap the fast electrons at the tip of the streamer in shallow traps and slow down its propagation. As for the SiC NPs, they are characterized by much higher conductivity than that ofthe base oil, and due to their characterization as semi-conductors, charge induction involves also positive holes apart from electrons. These redistributed charges on the surface of SiC NPs produce a potential well, which is given by the formula [28] for the electric field direction (θ = 0) and the opposite one (θ = π):

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

where <sup>σ</sup>1, <sup>σ</sup><sup>2</sup> are the conductivities of matrix and NPs in S·m<sup>−</sup>1, respectively, R is the radius of NP in m, *<sup>E</sup>*<sup>0</sup> is the mean dielectric strength of the NF in V·m−<sup>1</sup> and r is the distance from the NP's surface in m.

On the other hand, surface charges, known as bound charges, are formed at the surface of dielectric alumina NPs, due to polarization under the influence of an external electric field *E*0. This mechanism incorporates displacement and turning-direction polarizations. The displacement polarizations are generated very quickly in only 10−<sup>15</sup> to 10−<sup>12</sup> s, while turning-direction polarizations in time ranging from 10−<sup>10</sup> s to 10−<sup>2</sup> s [28]. Therefore, they can also produce a potential well, which is given by:

$$q\_{A\to 3} = \begin{cases} \frac{\varepsilon\_2 - \varepsilon\_1}{2\varepsilon\_1 + \varepsilon\_2} R^3 E\_0 \frac{1}{r^2}, & \theta = 0, \ r \ge R \\\\ -\frac{\varepsilon\_2 - \varepsilon\_1}{2\varepsilon\_1 + \varepsilon\_2} R^3 E\_0 \frac{1}{r^2}, & \theta = \pi, \ r \ge R \end{cases} \tag{4}$$

where <sup>ε</sup>1, <sup>ε</sup><sup>2</sup> are the permittivities of matrix and NPs in F·m<sup>−</sup>1, respectively.

The potential well on each occasion is able to catch the fast-moving electrons and transform them into negatively charged NPs which are moving slowly due to their larger radius. This could lead to the delay of streamer propagation and thus higher required voltage level to bridge the gap.

Substituting the values of conductivity and permittivity of FR3TM, SiC and Al2O3 NPs, as well as the corresponding values of mean dielectric strength and radius of NPs in Equations (3) and (4), the potential well of the colloidal suspensions of SiC and Al2O3 is given as:

$$
\varphi\_{\text{SiC}^{-}(r)} = 3.61 \times 10^{-15} \times \frac{1}{r^2} \text{ [V]} \tag{5}
$$

$$
\varphi\_{A\text{I2O3}}\left(\right) = 1.32 \times 10^{-15} \times \frac{1}{r^2} \left[V\right] \tag{6}
$$

Figure 12 demonstrates the higher potential well of the suspended SiC NPs in the oil, especially while moving closer to their surface. These types of NPs have the ability to capture more free electrons in shallow traps than the alumina NPs. This fact explains their increased dielectric performance. The total amount of charge that can be trapped by each of these two types of NPs is expressed by (7) and (8), respectively:

$$Q\_{\rm SiC} = -12\pi\varepsilon\_1 E\_0 R^2 \tag{7}$$

$$Q\_{A2O3} = -12\pi\varepsilon\_1 E\_0 R^2 \frac{\varepsilon\_2}{2\varepsilon\_1 + \varepsilon\_2} \tag{8}$$

**Figure 12.** Potential well distribution versus the distance from the NPs' surface.

Additionally, with substitution of the corresponding values as indicated above, they give:

$$Q\_{\rm SiC} = -7.71 \times 10^{-17} \,\mathrm{C} \tag{9}$$

$$Q\_{A2O3} = \text{--} 4.18 \times 10^{-17} \text{ C} \tag{10}$$

This means that each SiC and Al2O3 NP could potentially capture approximately 482 and 300 electrons, respectively, until they are saturated. The higher amount of trapped charge carriers in sNF is ought to the higher conductivity of SiC NPs and is a result of the mechanism described above. Streamers propagate in different modes, which are characterized by increasing velocity. Atiya et al. [32] indicated that the operation of NPs as electron traps hinders the first two slow modes, which are applicable under AC voltage.

Unlike AC, higher streamer propagation velocities are applicable under Lightning Impulse Voltage (LIV). Ionization of the oil molecules begins above a threshold value of electric field which includes positive ions and electrons. During positive LIV, the space charge field created by the positive ions increases towards the grounded sphere, facilitating the propagation of positive streamers. Under negative polarity, the electric field towards the grounded sphere is weakened by the space

charge field, hindering the propagation of negative streamers. This explains why negative LI BDV is higher than the positive LI BDV. Both types of NFs demonstrate increased strength under positive and negative LIV, which indicates that the trapping of high mobility electrons at the tip of the streamer in shallow traps results in increased BD performance [2,7,39]. However, the better performance of iNF during positive LIV and its worse performance during negative LIV with respect to sNF could be attributed to the distribution of the space charge field [39,40]. The positive charges induced by the Al2O3 NPs can trap the fast electrons at the tip of the streamer, inhibiting its initiation and propagation towards the grounded sphere electrode. On the other hand, under negative polarity, the addition of Al2O3 NPs increases the electric field towards the grounded sphere, accelerating the propagation of negative streamers.

The improved resistance to PD activity of both NF samples, with respect to the base oil, can be attributed to the formation of the electrical double layer (EDL) between the surface of the NP and the oil [3,7,32]. The addition of these types of NPs can augment the interfacial EDL, which can capture the charge carriers and delay the initiation of PD activity. The better performance of sNF can be interpreted by the greater ability of SiC NPs to trap the charge carriers, foremost the high mobility electrons, and delay the appearance of PD in the vicinity of the liquid, as it was explained above.
