Streaming Electrification of C₆₀ Fullerene Doped Insulating Liquids for Power Transformers Applications

Abstract

Long-term and fault-free operation of power transformers depends on the electrical strength of the insulation system and effective heat dissipation. Forced circulation of the insulating liquid is used to increase the cooling capacity. A negative effect of such a solution is the creation of the phenomenon of streaming electrification, which in unfavorable conditions may lead to damage to the insulating system of the transformer. This paper presents results of research confirming the possibility of using fullerene C₆₀ to reduce the phenomenon of streaming electrification generated by the flow of liquid dielectrics. The volume charge density q_w was used as a material indicator to determine the electrostatic charging tendency (ECT) of nanofluids. This parameter was determined from the Abedian-Sonin electrification model on the basis of electrification current measurements and selected physicochemical and electrical properties of the liquid. The electrification current was measured in a flow system with an aluminum pipe of 4 mm diameter and 400 mm length. All measurements were carried out at a temperature of 20 °C. The influence of flow velocity (from 0.34 m/s to 1.75 m/s) and C₆₀ concentration (25 mg/L, 50 mg/L, 100 mg/L, 200 mg/L and 350 mg/L) was analyzed on the electrification of fresh and aged Trafo En mineral oil, as well as Midel 1204 natural ester and Midel 7131 synthetic ester. The density, kinematic viscosity, dielectric constant, and conductivity were also determined. A negative effect of the C₆₀ doping on the electrostatic properties of fresh mineral oil was demonstrated. For other liquids, fullerene C₆₀ can be used as an inhibitor of the streaming electrification process. Based on the analysis of the q_w parameter, the optimum concentration of C₆₀ (from 100 mg/L to 200 mg/L) resulting in the highest reduction of the electrification phenomenon in nanofluids was identified.

1. Introduction

1.1. Insulating Liquids for Power Transformers

Power transformers are a key component of the electricity system, as the continuity of electricity supply to industrial plants, public facilities, and individual consumers depends on their reliability. Interruptions in electricity supply caused by failures of these devices generate huge economic losses in various sectors of the economy. Repairing or replacing a transformer is a logistically complex, time-consuming, and resource-intensive undertaking [1,2,3,4]. Experimental studies and post-failure analyses indicate that the service life of transformers depends mainly on the technical condition of their insulation system. During the long-term operation of a transformer, its insulation system degrades as a result of ageing processes whose rate is determined by temperature, the presence of oxygen and moisture [5,6,7,8]. Economic considerations and good physicochemical and electrical properties have made most transformers filled with mineral oils. The widespread use of these liquids is also determined by well mastered technologies for their production, as well as many years of operational and diagnostic experience [9,10,11,12,13]. Environmental aspects and stringent fire safety regulations have contributed to the increasing popularity of natural and synthetic esters [14,15,16,17,18,19,20]. In recent years, there has been increasing interest in the power sector in the possibility of using nanotechnology solutions [21], through the use of nanoparticles to improve the electrical and thermal performance of fluids used in power transformers [22,23,24,25,26,27,28]. The first scientists to define the concept of nanofluids were Choi and Eastman [29]. They used this term to describe colloidal suspensions in which the dispersion medium is a liquid and the dispersed particles are nanomaterials. In their work, they proposed the concept of using nanofluids as more efficient heat carriers compared to conventional thermally conductive fluids. Based on theoretical analyses, the authors have shown that the use of metal oxides improves the thermal conductivity of the base fluid.

1.2. Dielectric Breakdown Strength of Nanoliquids

Breakdown voltage is the basic criterion for assessing the technical condition of the liquid insulation of power transformers. The presence of moisture, gases, and solid impurities significantly deteriorates the electrical strength of the insulating liquid. Segal et al. [30] were the first scientists to confirm the possibility of using magnetic nanostructures (Fe₃O₄) to improve the electrical insulating properties of mineral oil. It has been demonstrated that the developed nanofluid retains its stability and initial magnetic susceptibility even after thermal ageing. A higher electrical strength of nanofluids was demonstrated compared to conventional insulating oil. Sima et al. [31] determined the 50% breakdown voltage (U₅₀) of positive and negative lightning impulse (PLI-BDV and NLI-BDV) and AC breakdown voltage (AC-BDV) of fullerene modified C₆₀ mineral oil (50 mg/L, 100 mg/L, 150 mg/L, 200 mg/L, 250 mg/L, and 300 mg/L). The authors demonstrated a high dependence of the dielectric strength of insulating oil on the nanoparticle content. It is proven that C₆₀ nanostructures (150 mg/L) increase the breakdown voltage U₅₀ of transformer oil by 7.5% and 8.3%, respectively, when a positive and negative lightning impulse is applied. At C₆₀ concentration (200 mg/L), NLI-BDV of mineral oil increased by 9.3%, while it decreased by 1.2% at PLI-BDV. The results showed that AC-BDV first gradually increases and then decreases with increasing C₆₀ concentration. The AC breakdown voltage of the nanofluid at C₆₀ concentration (200 mg/L) is 18% higher compared to the base fluid. Therefore, the optimum concentration of C₆₀ in oil is between 150 mg/L and 200 mg/L. Khelifa et al. [32] analysed the effect of concentration (100 mg/L, 200 mg/L, 300 mg/L, 400 mg/L, and 500 mg/L) of graphene nanoparticles (Gr) and C₆₀ on the change in AC breakdown voltage of Midel 7131 synthetic ester. The study of AC breakdown voltage (BDV) was conducted at different electrode distances (from 0.1 mm to 2 mm). A 28.7% increase in AC breakdown voltage was obtained at a concentration of 400 mg/L C₆₀ and a distance between electrodes of 0.5 mm. For the graphene-added liquid, AC-BDV increased by 24.4% at a concentration of 400 mg/L and an interelectrode gap of 0.7 mm. At 2 mm distance, the maximum improvement was 12.6% and 16.6% for 400 mg/L C₆₀ and 300 mg/L Gr, respectively. It was also found that fullerene C₆₀ reduces the incomplete discharges in the ester nanofluid, while the addition of Gr increases the intensity of this phenomenon.

1.3. Thermal Properties of Nanomodified Dielectric Liquids

An important aspect of operating power transformers is ensuring that heat is effectively dissipated from the inside of the transformer. A new generation of nanomodified insulating liquids could help make this process more efficient. Choi et al. [33] determined the thermal properties of mineral oil modified with Al₂O₃ and AlN nanostructures. The study showed that a volume proportion of AlN of 0.5% increases the thermal conductivity of transformer oil by 8%, while the total heat transfer coefficient increases by 20%. Based on a natural convection test using a prototype transformer, an increase in cooling efficiency was observed when nanofluids were used. Dombek et al. [34] investigated the effect of C₆₀ fullerene (100 mg/L) and TiO₂ titanium dioxide (820 mg/L) doping on the thermal properties of Nytro Draco mineral oil, Midel 7131 synthetic ester and Envirotemp FR3 natural ester. The tests were based on measurements of thermal conductivity, specific heat, thermal expansion, kinematic viscosity and density at temperatures from 25 °C to 80 °C. Using Grashof, Prandtl and Nusselt number analysis, the cooling efficiency of power transformers with pure and modified insulating fluids was compared. Modification of liquids with widely used nanoparticles to improve dielectric properties has been shown to have no adverse effect on thermal properties. Olmo et al. [35,36] determined the cooling efficiency of a prototype transformer using nanomodified natural ester. The authors determined the effect of the addition of maghemite (Fe₂O₃) and titanium dioxide (TiO₂) on the thermal properties and electrical strength of the ester liquid. The presence of Fe₂O₃ was shown to increase the thermal conductivity of the base fluid by 12%, while theTiO₂ content decreased it by 3.9%. The optimal concentration of nanostructures of maghemite and titanium dioxide nanostructures in nano-liquids (500 mg/L), resulting in an increase in their electrical strength by 33.2%.

1.4. Streaming Electrification of Nano-Based Insulating Liquids

In recent years, intensive work has been carried out on the possibility of using nanomaterials as an inhibitor of the electrification process of liquid dielectrics. Aksamit and Zmarzły [37] proposed the use of fullerene C₆₀ to reduce the phenomenon of streaming electrification of mineral oil. The study involved preparing 20 oil samples with different fullerene C₆₀ contents (from 0 mg/L to 512 mg/L) and then determining the effect of the dopant on the generation of electrification current. Measurements were carried out using a wireless measuring system with a rotating electrometer. A metal measuring disc with a diameter of 120 mm was used for tests, with the speed adjusted from 0 rpm to 400 rpm. It was found that the rotational speed of the disc and the variable content of fullerene C₆₀ in the mineral oil significantly affected the sign, value and course of the electrification current. The authors observed that the lowest electrification current values were recorded with C₆₀ contents ranging from 100 mg/L to 200 mg/L. Aksamit et al. [38] also conducted a comparative electrification analysis of fresh and aged mineral oil doped with fullerene C₆₀. For this purpose, three sets of seven samples each were prepared with modified C₆₀ ranging from 0 mg/L to 300 mg/L. The first set of samples was fresh oil, while the other two were aged 24 and 96 h, respectively. Electrification tests were carried out in a system with a rotating disc whose diameter was 120 mm and whose speed ranged from 0 rpm to 150 rpm. A reduction in streaming electrification of 30% to 90% was achieved, depending on the disc speed, ageing time, and weight content of carbon nanostructures. The authors suggest that the optimum concentration of C₆₀ in fresh or aged mineral oil resulting in the highest reduction in electrocution current is about 100 mg/L. Amalanathan et al. [39] presented stream electrification studies of natural ester Midel 1215 with TiO₂ nanostructures, cetyl trimethyl ammonium bromide (CTAB) surfactant and anti-static additive 1,2,3-benzotriazoles (BTA). The tests were carried out in a rotating system using a 6 mm thick disc with diameters of 30 mm, 40 mm, and 50 mm, whose rotational speed ranged from 0 to 600 rpm. The disc was covered on both sides with 0.5 mm or 1.5 mm thick pressboard. The liquid temperature ranged from 30 °C to 100 °C. The obtained results show that the electrification current increases with an increase in the thickness of the pressboard, the diameter and speed of the disc, as well as the temperature of the insulating liquid. The natural ester modified with TiO₂ and CTAB was found to exhibit higher susceptibility to stream electrification compared to the base liquid. The addition of BTA has a significant effect on reducing the electrification current. Based on the analysis of the electrification model, it was shown that the ion mobility, laminar sublayer thickness and shear stress in nanofluids and ester liquids are similar. However, a decrease in Debye length and relaxation time is evident, indicating a higher value of the electrification current in the ester modified with additives.

1.5. Purpose and Scope of the Research

The author’s previous research work concerned determining the optimum composition of oil-ester mixtures in the aspect of retrofilling transformers. A small amount of mineral oil (up to 20%) has been shown to effectively reduce the ECT of natural and synthetic esters [40,41,42]. This paper presents the research results indicating the possibility of using fullerene C₆₀ to reduce the phenomenon of streaming electrification in insulating liquids. The optimum concentration of the C₆₀ additive in the nanofluids was determined from the volume charge density q_w results. This parameter was determined from the Abedian-Sonin electrification model based on measurements of electrification current and density, kinematic viscosity, dielectric constant and conductivity. The electrification current was measured in a flow system with an aluminum measuring pipe. The effects of flow velocity and C₆₀ content were analyzed. Significantly different electrostatic properties of fresh and aged mineral oil were demonstrated due to doping with fullerene C₆₀. In the first case (fresh Trafo En) the effect is unfavorable, while in the second case (aged Trafo En) a significant reduction of the electrification phenomenon is observed. The nanomodified ester liquids also show a high dependence of electrification on C₆₀ content. From an ECT point of view, the optimal concentration of C₆₀ in nanofluids should be between 100 mg/L and 200 mg/L.

2. Materials and Methods

2.1. Preparation of Nanoliquids

Insulating nanofluid samples with a volume of 1000 mL were prepared based on Trafo En mineral oil produced by Orlen Oil (Kraków, Poland), Midel 1204 natural ester and Midel 7131 synthetic ester produced by M&I Materials (Manchester, UK). Accelerated thermal ageing of mineral oil was carried out according to IEC 1125 standard (Method C: 164 h, 120 °C, copper catalyst—1144 cm²/kg of oil, air—0.15 L/h). Fullerene C₆₀ (CAS#99685-96-8, 99.95%) produced by PlasmaChem GmbH (Berlin, Germany) played the role of nano-modifier. The base liquid after addition of C₆₀ (25 mg/L, 50 mg/L, 100 mg/L, 200 mg/L and 350 mg/L) was mechanically stirred (72 h, 25 °C, 1100 rpm) and then sonicated (5 h, 60 °C, 20 kHz). The prepared samples were degassed in a vacuum chamber (24 h, 60 °C, 0.1 kPa) and then seasoned in tightly closed bottles for seven days in the absence of light. After this time, fully stable mixtures could be obtained [34].

2.2. Measurement of Physicochemical and Electrical Properties

The density of the liquid was determined with a glass areometer (ISO 3675 Standard). The liquid kinematic viscosity was measured with a Brookfield DV-II+Pro viscometer (ISO 2555 Standard). The conductivity was determined from liquid resistivity measurements with an MR0-4c meter, while the dielectric constant was determined from liquid capacitance measurements with a Hioki 3522-50 LCR HiTester meter (IEC 60247 Standard). Selected physicochemical and electrical properties of the nanomodified insulating liquids are presented in

Table 1. Properties of C₆₀ fullerene doped fresh Trafo En mineral oil (20 °C).

C60 (mg/L)	ρ (kg/m3)	νk (m2/s)	σ (S/m)	εr (−)
0	871	2.26 × 10−5	6.06 × 10−13	2.21
25	871	2.27 × 10−5	1.21 × 10−12	2.19
50	871	2.28 × 10−5	1.35 × 10−12	2.28
100	871	2.29 × 10−5	1.04 × 10−12	2.22
200	871	2.31 × 10−5	1.52 × 10−12	2.18
350	871	2.32 × 10−5	2.18 × 10−12	2.27

,

Table 2. Properties of C₆₀ fullerene doped aged Trafo En mineral oil (20 °C).

C60 (mg/L)	ρ (kg/m3)	νk (m2/s)	σ (S/m)	εr (−)
0	870	2.41 × 10−5	1.61 × 10−11	2.23
25	870	2.42 × 10−5	1.39 × 10−11	2.27
50	870	2.44 × 10−5	1.37 × 10−11	2.25
100	870	2.45 × 10−5	1.35 × 10−11	2.29
200	870	2.46 × 10−5	1.33 × 10−11	2.26
350	870	2.47 × 10−5	1.32 × 10−11	2.21

,

Table 3. Properties of C₆₀ fullerene doped Midel 1204 natural ester (20 °C).

C60 (mg/L)	ρ (kg/m3)	νk (m2/s)	σ (S/m)	εr (−)
0	918	8.45 × 10−5	8.26 × 10−12	3.16
25	918	8.49 × 10−5	4.08 × 10−11	3.20
50	918	8.54 × 10−5	2.07 × 10−11	3.17
100	918	8.59 × 10−5	1.91 × 10−11	3.19
200	918	8.63 × 10−5	1.53 × 10−11	3.21
350	918	8.68 × 10−5	2.34 × 10−11	3.18

and

Table 4. Properties of C₆₀ fullerene doped Midel 7131 synthetic ester (20 °C).

C60 (mg/L)	ρ (kg/m3)	νk (m2/s)	σ (S/m)	εr (−)
0	968	7.47 × 10−5	8.77 × 10−12	3.19
25	968	7.51 × 10−5	2.52 × 10−11	3.17
50	968	7.55 × 10−5	2.98 × 10−11	3.24
100	968	7.59 × 10−5	3.02 × 10−11	3.22
200	968	7.63 × 10−5	2.08 × 10−11	3.17
350	968	7.67 × 10−5	1.92 × 10−11	3.21

.

2.3. Streaming Electrification Mathematical Model and Measurements

Streaming electrification closely depends on electrokinetic phenomena occurring in the electrical double layer at the solid-liquid interface. The process of electrification of an insulating liquid in a flow system is described by the Abedian-Sonin model [43]. The ECT of liquid dielectrics is determined from the volume charge density q_w, which is determined using Formulas (1) and (2). The Reynolds number (3), shear stress (4) and laminar sublayer thickness (5) are parameters that synthesise the influence of hydrodynamic flow conditions and the physicochemical properties of the fluid on the generation of electrification current. The Debye length (6) describes the charge distribution in the laminar sublayer. This parameter is determined based on the dielectric constant, conductivity and molecular diffusion coefficient of the liquid (7).

$$\frac{I_{\infty }}{q_w\pi R^{2}v}=Re\frac{{\tau }_w{\lambda }^2}{\rho v^2{R}^2}\left[1-\frac{\frac{\delta }{\lambda }}{\sinh \left(\frac{\delta }{\lambda }\right)}\right]+\frac{\frac{\delta }{\lambda }}{\sinh \left(\frac{\delta }{\lambda }\right)}\left[\frac{2{\lambda }^2}{1+R\frac{\delta }{2{\lambda }^2}}\right]$$

(1)

$$I=I_{\infty }\left[1-{\mathrm{e}}^{-\frac{l}{L}}\right]$$

(2)

$$Re=\frac{2Rv}{{\upsilon }_k}$$

(3)

$${\tau }_w=\frac{8\rho v}{Re}$$

(4)

$$\delta =\frac{A{\upsilon }_k}{S^{\frac{1}{C}}{\left(\frac{{\tau }_w}{\rho }\right)}^{0.5}}$$

(5)

$$\lambda =\sqrt{\frac{D_m{\epsilon }_0{\epsilon }_r}{\sigma }}$$

(6)

$$D_m=\frac{3.93\times {10}^{-14}·T}{{\upsilon }_k\rho }$$

(7)

where I_∞ is the electrification current for infinite pipe length; q_w, volume charge density on the phase border; R, pipe radius; v, average liquid velocity; Re, Reynolds number; τ_w, shearing stress; λ, Debye length; ν_k, liquid kinematic viscosity; ρ, liquid density; δ, laminar sublayer thickness; I, electrification current for any pipe length; L, characteristic length of the pipe; l, length of the pipe; D_m, molecular diffusion coefficient; ε₀, vacuum electric permittivity; ε_r, dielectric constant of liquid; A/C, constant (A = 11.7; C = 3); T, liquid temperature; and S, Schmidt number (S = ν_k/D_m).

Figure 1 shows a flow system for studying the phenomenon of streaming electrification of insulating liquids. The measuring system consists of a hermetic upper container with liquid (1) equipped with a heater (2), a solenoid valve (3) and a pipe (4). The lower container (5) was placed on Teflon insulators in a Faraday cage (6). The electrostatic charges generated by the fluid flow are transferred to an isolated measuring vessel, from where their leakage to earth is measured with a Keysight B2981A electrometer (7). Acquisition, transmission and recording of measurement data is performed using software supplied by the meter manufacturer (8). The liquid flow velocity (0.34–1.75 m/s) was determined by varying the nitrogen pressure (9) in the upper tank. The temperature (20 °C) and flow time (120 s) of the liquid were set using regulators mounted in an electrical control box (10). After the measurement was completed, the liquid was pumped from the lower tank to the upper tank using a pump (11). An aluminum pipe with a diameter of 4 mm and a length of 400 mm was used for the measurements. The point on the current characteristic was the average of 240 values obtained in five measurement series, each lasting 120 s. Error bars were determined using the mean electrification current, standard deviation and significance level α = 0.05.

3. Results

3.1. The Study on Physicochemical and Electrical Properties of Nanofluids

The effectiveness of heat dissipation from the inside of a transformer significantly depends on the used cooling system and on the physicochemical properties of the insulating fluids, of which density (ρ) and kinematic viscosity (ν_k) play a decisive role. To ensure the best possible convection and circulation, dielectric fluids should have low values of both parameters. Based on the analysis of the data in Table 1, Table 2, Table 3 and Table 4, there was no effect of accelerated thermal ageing on the density of Trafo En mineral oil. The density of Midel 1204 natural ester and Midel 7131 synthetic ester is 5.4% and 11.2% higher, respectively compared to fresh insulating oil. The kinematic viscosity of Trafo En mineral oil increases by 7% due to accelerated heat ageing. The process of doping the liquid with fullerene C₆₀ does not cause any change in density, but causes a 3% increase in kinematic viscosity. A wide range of studies confirming the positive effect of C₆₀ nanostructures on the thermal conductivity, specific heat and thermal expansion of Nytro Draco mineral oil, Envirotemp FR3 natural ester and MIdel 7131 synthetic ester are presented in [34].

The insulating system of a transformer is usually a combination of solid and liquid dielectric in series, parallel and series-parallel configurations. The higher dielectric constant (ε_r) of the insulating liquid contributes to improving the stress distribution in the insulating system, thus increasing its electrical strength [44]. Fresh and aged Trafo En mineral oil have similar values ε_r, 2.21 and 2.23, respectively. For Midel 1204 natural ester and Midel 7131 synthetic ester, the ε_r values are 3.16 and 3.19. No significant effect of C₆₀ addition on the change of dielectric constant of nanofluids is observed. Chen et al. [45] presented results confirming the minimal dependence of ε_r on the concentration of C₆₀ carbon nanostructures in mineral oil. In contrast to the previously considered physicochemical properties (ρ, ν_k, ε_r), the conductivity (σ) shows a strong dependence on the C₆₀ concentration in nanofluids. The conductivity of fresh Trafo En oil (Figure 2a) is 0.6 pS/m and deteriorates significantly with increasing C₆₀ doping. The course of the function is non-linear and is characterised by two extremes, at a C₆₀ content of 50 mg/L (1.35 pS/m) and 100 mg/L (1.04 pS/m). A further increase in the proportion of C₆₀ in the nanofluid is accompanied by a linear increase in conductivity to 2.18 pS/m.

For aged Trafo En oil, the conductivity decreases non-linearly from 16.1 pS/m to 13.2 pS/m with increasing C₆₀ concentration (Figure 2b). Based on the results obtained, a positive effect of C₆₀ carbon nanostructures on the physicochemical and electrical properties of aged mineral oil was demonstrated. Zmarzły and Dobry [46] conducted research on the possibility of using C₆₀ additive as an inhibitor of ageing processes occurring in electrical insulating oils. The authors carried out an accelerated thermal ageing process of mineral oil with different C₆₀ contents and then studied the basic physicochemical and electrical properties. A beneficial effect of C₆₀ on the reduction of water absorption in oil, dielectric loss factor and AC breakdown voltage has been demonstrated. No effect of carbon nanostructures was found on the acid number and dielectric constant. A slight reduction in resistivity was observed. According to the authors, the optimum concentration of fullerene C₆₀ in mineral oil should be between 100 mg/L and 200 mg/L.

The conductivity of nanofluids prepared on the basis of the natural ester significantly depends on the C₆₀ content (Figure 3a). The lowest value of the parameter σ is characterized by pure Midel 1204 (8.26 pS/m), while the highest (40.8 pS/m) is the liquid containing C₆₀ additive in the amount of 25 mg/L. In the C₆₀ concentration range (50 mg/L to 350 mg/L), the conductivity oscillates between 15.3 pS/m and 23.4 pS/m. Also, for the synthetic ester-based nanofluids, a significant effect of fullerene C₆₀ concentration on the conductivity becomes apparent (Figure 3b). The lowest electrical conductivity (8.77 pS/m) is shown by pure Midel 7131, while at C₆₀ content (100 mg/L) this parameter reaches a maximum value (30.2 pS/m). Above this range, a non-linear decrease in conductivity is observed. For C₆₀ concentrations of 200 mg/L and 350 mg/L the conductivity reaches 20.8 pS/m and 19.2 pS/m, respectively. Yao et al. [47] studied the effect of fullerene C₆₀ doping on the electrical properties of mineral oil and natural ester. The optimum concentration of C₆₀ (100 mg/L) in the ester liquid providing the highest improvement in dielectric loss factor, resistivity and AC breakdown voltage was identified. In the case of mineral oil, the best value of dielectric loss factor and AC breakdown voltage are obtained at 50 mg/L and 200 mg/L, respectively. The addition of C₆₀ affects the deterioration of the resistivity of the insulating oil over the entire doping range.

3.2. Streaming Electrification Studies on Nanofluids

Figure 4a shows the dependence of the electrification current of unmodified insulating liquids on the velocity of flow (from 0.34 m/s to 1.75 m/s) through an aluminum tube of 4 mm diameter and 400 mm length. All measurements were carried out at a temperature of 20 °C. A linear course of the characteristics I = f(v) is observed. Analyzing the results for maximum flow velocity, fresh mineral oil has the lowest susceptibility to electrification (34.8 pA). The accelerated thermal ageing process increases the generation of electrostatic charge in Trafo En oil by almost three times (96.5 pA). The electrification propensity of the natural ester (83.1 pA) is 20% higher than that of the synthetic ester (70.8 pA). For comparison, the current characteristics of fluids modified with fullerene C₆₀ at a concentration of 50 mg/L are summarized in Figure 4b. A significant effect of C₆₀ addition on the intensity of the streaming electrification process in nanofluids was found. The electrification current of fresh Trafo En oil increased by two times (68.8 pA), while it decreased by two times (38.6 pA) for natural Midel 1204 ester. There was also a 23% decrease in the electrification current of the aged Trafo En oil (78.5 pA) and 30% of the synthetic ester Midel 7131 (54.7 pA).

Figure 5a,b and Figure 6a,b show the electrification current characteristics from the concentration of C₆₀ nanoparticles in liquids flowing at 0.34 m/s through the test pipe. A significant dependence of the measured parameter on the C₆₀ content in the nanofluids was demonstrated. Trafo En modified fresh oil has a higher electrification than the base fluid over the entire doping range. The electrification current reaches its maximum value (13.2 pA) at a C₆₀ content of 50 mg/L. In the case of aged Trafo En oil, an increase in the concentration of C₆₀ effectively reduces the phenomenon of streaming electrification. A 59% decrease in electrification current from 19.3 pA to 12.2 pA is observed. Modification of the Midel 1204 ester with fullerene C₆₀ significantly reduces the generation of electrostatic charges. The lowest electrification current value (5.04 pA) is obtained at a C₆₀ concentration of 25 mg/L. The electrification current waveform of the nanomodified Midel 7131 ester resembles a parabola and reaches a minimum value (9.8 pA) at C₆₀ content of 100 mg/L.

The study also observed a close relationship between conductivity and electrification current with increasing C₆₀ concentration in mineral oil (σ↗ ⇒ I↗) and ester liquids (σ↗ ⇒ I↘). The reason for this phenomenon may be the different molecular structure of the used dielectric fluids, resulting in, among other things, a different ability to absorb water from the environment. Another issue is the mechanisms of liquid modification with nanoparticles. These factors influence the structure of the electrical double layer, which depends significantly on the physicochemical properties of the solid and liquid phases. The charge q_w arising in this layer directly determines the ECT of the insulating liquids. Chen et al. [45] provided a broad description of the effect of C₆₀ modification mechanisms on the dielectric strength of mineral oil. Vihacencu et al. [48] demonstrated on the basis of model and experimental studies that an increase in conductivity intensifies the electrification process of mineral and synthetic oil. Rajab et al. [49] confirmed this phenomenon by studying the electrification of PFAE (palm fatty acid ester) blends with fresh and operating mineral oil. Studies demonstrate that modification of insulating liquids with nanocomponents leads to mixtures with different physicochemical, thermal and electrical properties. It is therefore necessary to take these phenomena into account when preparing nanodielectrics, which are expected to replace traditional liquid insulation in power transformers in the future.

For comparative purposes, the results of the electrification current and volume charge density q_w for individual C₆₀ concentrations in the nanofluids are summarized as bar graphs (Figure 7a,b). According to the model assumptions, the charge q_w arising in the electric double layer depends solely on the physicochemical properties of the solid and the liquid. Therefore, the parameter q_w can be used as a material constant to determine the ECT of liquid dielectrics [50]. For Trafo En fresh mineral oil, the lowest (0.05 C/m³) and highest (0.09 C/m³) q_w values occur at C₆₀ concentrations of 0 mg/L and 50 mg/L respectively. The aged Trafo En mineral oil is characterized by a decrease in the parameter q_w from 0.17 C/m³ to 0.11 C/m³. The highest q_w value (0.53 C/m³) is found in the pure natural ester Midel 1204, while the lowest (0.19 C/m³) is found in the 350 mg/L modified ester C₆₀. The nanomodified synthetic ester Midel 7131 exhibits the lowest (0.32 C/m³) and highest (0.39 C/m³) q_w values at C₆₀ concentrations of 200 mg/L and 350 mg/L, respectively. Comparing Figure 7a,b, it should be noted that correct assessment of the ECT of insulating liquids requires knowledge of both the electrification current and the physicochemical properties of the insulating liquids. Based on the results of the q_w parameter, it can be assumed that the reduction of nanofluid ECT occurs most effectively at a C₆₀ concentration between 100 mg/L and 200 mg/L.

4. Conclusions

The development of nanotechnology has made it possible to develop a new generation of nanofluids with improved thermal conductivity and electrical strength. The research conducted by the author concerned the possibility of using fullerene C₆₀ as an inhibitor of the process of stream electrification of insulating liquids. The ECT of nanofluids was determined from the volume charge density q_w. This parameter was determined from an electrification model based on measurements of current and physicochemical and electrical parameters. It was shown that the addition of C₆₀ does not affect the density and dielectric constant, but causes a slight increase in kinematic viscosity. Conductivity significantly depends on the concentration of C₆₀ in the nanofluids. The speed of the fluid flow significantly determines the generation of electrostatic charges. The use of C₆₀ increases the electrification of fresh mineral oil, while it reduces this phenomenon in aged mineral oil. Natural and synthetic ester-based nanofluids also show a high dependence of ECT on C₆₀ concentration. Based on the parameter q_w, the optimum concentration of C₆₀ (from 100 mg/L to 200 mg/L) at which the highest reduction of the electrification phenomenon in nanofluids occurs was determined. In this way, it has been demonstrated that in a well-defined doping range, fullerene C₆₀ can act as an inhibitor of the electrification process of insulating liquids. In the long term, it would be beneficial to define ECT of a wider group of nanofluids based on fresh and in-service mineral oils. From the point of view of the operating conditions of transformers, it is worth considering the effect of temperature. The next step of the research should be to determine the C₆₀ doping on the stream electrification of thermally aged natural and synthetic esters. It would also be interesting to investigate the influence of a wider group of conductive (Fe₃O₄, Fe₂O₃, SiC), semiconductive (TiO₂, ZnO, CuO, Cu₂O) and insulators (Al₂O₃, SiO₂, BN) nanoparticles on the electrostatic properties of insulating liquids.