Streaming Electriﬁcation of C 60 Fullerene Doped Insulating Liquids for Power Transformers Applications

: 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 C 60 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 C 60 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 C 60 doping on the electrostatic properties of fresh mineral oil was demonstrated. For other liquids, fullerene C 60 can be used as an inhibitor of the streaming electriﬁcation process. Based on the analysis of the q w pArameter, the optimum concentration of C 60 (from 100 mg/L to 200 mg/L) resulting in the highest reduction of the electriﬁcation phenomenon in nanoﬂuids was identiﬁed.


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.

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 (Fe 3 O 4 ) 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 (U 50 ) of positive and negative lightning impulse (PLI-BDV and NLI-BDV) and AC breakdown voltage (AC-BDV) of fullerene modified C 60 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 C 60 nanostructures (150 mg/L) increase the breakdown voltage U 50 of transformer oil by 7.5% and 8.3%, respectively, when a positive and negative lightning impulse is applied. At C 60 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 C 60 concentration. The AC breakdown voltage of the nanofluid at C 60 concentration (200 mg/L) is 18% higher compared to the base fluid. Therefore, the optimum concentration of C 60 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 C 60 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 C 60 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 C 60 and 300 mg/L Gr, respectively. It was also found that fullerene C 60 reduces the incomplete discharges in the ester nanofluid, while the addition of Gr increases the intensity of this phenomenon.

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 Al 2 O 3 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 C 60 fullerene (100 mg/L) and TiO 2 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 (Fe 2 O 3 ) and titanium dioxide (TiO 2 ) on the thermal properties and electrical strength of the ester liquid. The presence of Fe 2 O 3 was shown to increase the thermal conductivity of the base fluid by 12%, while theTiO 2 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%.

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 C 60 to reduce the phenomenon of streaming electrification of mineral oil. The study involved preparing 20 oil samples with different fullerene C 60 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 C 60 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 C 60 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 C 60 . For this purpose, three sets of seven samples each were prepared with modified C 60 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 C 60 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 TiO 2 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 TiO 2 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.

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 C 60 to reduce the phenomenon of streaming electrification in insulating liquids. The optimum concentration of the C 60 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 C 60 content were analyzed. Significantly different electrostatic properties of fresh and aged mineral oil were demonstrated due to doping with fullerene C 60 . 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 C 60 content. From an ECT point of view, the optimal concentration of C 60 in nanofluids should be between 100 mg/L and 200 mg/L.

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 cm 2 /kg of oil, air-0.15 L/h). Fullerene C 60 (CAS#99685-96-8, 99.95%) produced by PlasmaChem GmbH (Berlin, Germany) played the role of nanomodifier. The base liquid after addition of C 60 (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].

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 Tables 1-4. Table 1. Properties of C 60 fullerene doped fresh Trafo En mineral oil (20 • C).   Table 3. Properties of C 60 fullerene doped Midel 1204 natural ester (20 • C).  Table 4. Properties of C 60 fullerene doped Midel 7131 synthetic ester (20 • C).

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). (1) 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; ε 0 , 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.
where I∞ is the electrification current for infinite pipe length; qw, volume charge density on the phase border; R, pipe radius; v, average liquid velocity; Re, Reynolds number; τw, shearing stress; λ, Debye length; νk, 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; Dm, molecular diffusion coefficient; ε0, vacuum electric permittivity; εr, dielectric constant of liquid; A/C, constant (A = 11.7; C = 3); T, liquid temperature; and S, Schmidt number (S = νk/Dm). 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.

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  Tables 1-4, 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 C 60 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 C 60 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].

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 (νk) 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 Tables 1-4, 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 (εr) of the insulating liquid contributes to improving the stress distribution in the insulating system, thus increasing its electrical strength [44].  For aged Trafo En oil, the conductivity decreases non-linearly from 16.1 pS/m to 13.2 pS/m with increasing C 60 concentration (Figure 2b). Based on the results obtained, a positive effect of C 60 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 C 60 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 C 60 contents and then studied the basic physicochemical and electrical properties. A beneficial effect of C 60 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 C 60 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 C 60 content (Figure 3a). 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).     For comparison, the current characteristics of fluids modified with fullerene C 60 at a concentration of 50 mg/L are summarized in Figure 4b. A significant effect of C 60 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 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).    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 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 The study also observed a close relationship between conductivity and electrification current with increasing C 60 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 C 60 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.

Streaming Electrification Studies on Nanofluids
For comparative purposes, the results of the electrification current and volume charge density q w for individual C 60 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/m 3 ) and highest (0.09 C/m 3 ) q w values occur at C 60 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/m 3 to 0.11 C/m 3 . The highest q w value (0.53 C/m 3 ) is found in the pure natural ester Midel 1204, while the lowest (0.19 C/m 3 ) is found in the 350 mg/L modified ester C 60 . The nanomodified synthetic ester Midel 7131 exhibits the lowest (0.32 C/m 3 ) and highest (0.39 C/m 3 ) q w values at C 60 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 C 60 concentration between 100 mg/L and 200 mg/L. significantly on the physicochemical properties of the solid and liquid phases. The charge qw 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 qw for individual C60 concentrations in the nanofluids are summarized as bar graphs (Figure 7a,b). According to the model assumptions, the charge qw arising in the electric double layer depends solely on the physicochemical properties of the solid and the liquid. Therefore, the parameter qw 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/m 3

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 C 60 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 C 60 does not affect the density and dielectric constant, but causes a slight increase in kinematic viscosity. Conductivity significantly depends on the concentration of C 60 in the nanofluids. The speed of the fluid flow significantly determines the generation of electrostatic charges. The use of C 60 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 C 60 concentration. Based on the pArameter q w , the optimum concentration of C 60 (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 C 60 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 C 60 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 (Fe 3 O 4 , Fe 2 O 3 , SiC), semiconductive (TiO 2 , ZnO, CuO, Cu 2 O) and insulators (Al 2 O 3 , SiO 2 , BN) nanoparticles on the electrostatic properties of insulating liquids.