Study on Power Frequency Breakdown Characteristics of Nano-TiO₂ Modified Transformer Oil under Severe Cold Conditions

Abstract

With 45# transformer oil as the base fluid, different concentrations of TiO₂ nanomodified transformer oil were prepared via the thermal oscillation method. Nanomodified transformer oil with a concentration of 0.01 g/L was selected for evaluation via the breakdown test. Then, 0.01 g/L nanomodified transformer oil and ordinary 45# transformer oil were subjected to the variable control of different moisture contents and different temperatures, and breakdown tests under different types of electrodes were performed within the temperature range of −30 °C to 30 °C. The test results showed the following: Under severe cold conditions, the improvement effect of the breakdown voltage in different temperature ranges was different. Within the temperature range of −30 °C to −10 °C, the enhancement effect could reach 13% to 15%. Within the temperature range of −10 °C to 0 °C, the enhancement effect could reach 8% to 9%. Within the temperature range of 0 °C to 30 °C, the enhancement effect could reach 18% to 21%. Compared with the test results at high water contents, the improvement in the breakdown voltage amplitude of transformer oil by nanomaterials was more obvious at low water contents. In addition, nanomaterials could reduce the dispersion of the breakdown voltage to make the breakdown voltage more stable. Lastly, COMSOL was used to simulate the polarization process of nanoparticles under a uniform electric field and the influence of the trajectory of charged particles in the oil to further analyze the mechanism of the influence of nanoparticles in oil on the breakdown voltage of the oil gap. The simulation results showed that, when the particles were accelerated by the electric field, they moved irregularly. After adding nanoparticles, the charged particles were adsorbed by the nanoparticles when passing through the nanoparticles, which reduced the migration rate of charged particles in the oil. The breakdown voltage of the oil gap increased.

1. Introduction

As it is the core equipment for power transmission and crucial for the safe and stable operation of the power system, transformers play a vital role. With the commissioning of multiple ultrahigh-voltage transmission lines in our country, the threat posed by transformer failures is expected to increase [1,2,3]. The safe operation of transformers largely depends on the reliability and stability of their insulation. The insulation performance of transformer oil directly determines whether these devices can operate safely and stably [4,5]. Therefore, researching transformer oils with excellent electrical properties is of great significance in improving the safety level of transformers [6,7,8,9].

Nanoparticles exhibit excellent surface and volume effects, making nanotechnology one of the hot topics in the field of insulating materials and the most promising direction for improving the performance of insulating materials [10]. The so-called nanofluid usually refers to stable suspensions formed by dispersing nanoparticles with a particle size that is less than 100 nm into a base liquid via certain dispersion methods.

Compared with traditional transformer oil, nanofluids have advantages such as high thermal conductivity, good stability, and reduced equipment wear. Research on nanofluids in recent years has also shown that the addition of nanomaterials can effectively improve the insulation properties of transformer oil [11,12,13,14]. Some scholars have conducted experimental and simulation analyses on the mechanism of nanomaterials, enhancing the breakdown voltage of transformer oil and proposing a series of theoretical models, including the fast electron capture model, potential well model, and shallow trap model. The fast electron capture model suggests that conductive nanoparticles can adsorb fast electrons due to their own characteristics and convert them into slower negative charges, thereby reducing the rate of streamer head development and slowing down the movement rate of positive and negative charges, while weakening the electric field intensity of the streamer head [15]. The potential well model suggests that, under the action of an applied electric field, charges are generated on both sides of the nanoparticle’s surface due to polarization, distorting the original electric field. This distortion forms a “potential well” near the particle, which can capture free electrons generated during the streamer development process [16,17,18]. The shallow trap model suggests that nanoparticles increase the density of shallow traps, impeding the movement of free electrons in transformer oil, thereby improving the breakdown performance of transformer oil modified with nanoparticles [19,20,21]. The shallow trap model effectively avoids the limitation of the relaxation time, influencing electron capture in the fast electron capture model while also compensating for the limitation of only considering individual nanoparticles in the potential well model, thereby allowing for a wider range of applications. In recent years, research on TiO₂ nanoparticles has also revealed that TiO₂ nanoparticles can absorb dissolved water in the oil to form a water film, reducing the probability of water molecules forming small bridges [22].

In order to enhance the insulation and thermal conductivity performance of transformer oil, researchers from both domestic and international spheres have conducted experiments using various types of nanoparticles. These nanoparticles can be classified into three categories: conductive nanoparticles (Fe₂O₃, Fe₃O₄, and SiC), semiconductor nanoparticles (TiO₂), and insulating nanoparticles (Al₂O₃, SiO₂, BN, and AlN) [23]. Abundant studies have shown that an external magnetic field significantly affects the stability and insulation properties of nanomagnetic fluids, making nanomagnetic fluids that are prepared with nanoparticles such as Fe₃O₄ unsuitable for transformers [24,25,26,27]. AlN-based nanotransformer oil can effectively improve the thermal conductivity, positive polarity lightning impulse breakdown voltage, and partial discharge inception voltage of transformer oil. Compared to regular oil, it can increase these properties by 7%, 50%, and 20%, respectively, with the most outstanding positive polarity lightning impulse breakdown characteristics observed when the nanoparticle concentration is 0.127% [28,29]. For plant-oil-based BN nanofluids, the breakdown strength at 63.2% probability and 5% probability increases by 30% and 33%, respectively, when the mass fraction of BN nanoparticles is 0.05 wt.% [30]. Adding Al₂O₃ to mineral oil can significantly improve the alternating current breakdown voltage under high-moisture conditions and reduce dielectric loss [31]. Furthermore, Al₂O₃ nanofluids can slow down the aging of insulating oil and paperboard, with the insulation properties of aged nanofluids improved compared to pure oil and oil-immersed paperboards [32]. For SiO₂-nanomodified transformer oil, the addition of SiO₂ nanoparticles does not effectively enhance insulation properties when the moisture content is low. However, with higher moisture contents, it can significantly increase the breakdown field strength [33], and SiO₂ nanoparticles can effectively improve the insulation properties of aged transformer oil [34]. Sima and Wang et al. conducted experiments to verify that Fe₃O₄, TiO₂, and Al₂O₃ nanoparticles all have an enhancing effect on the breakdown voltage of transformer oil. Additionally, there exists an optimal mass concentration for each nanoparticle, i.e., 0.03 g/L, 0.01 g/L, and 0.02 g/L, respectively. It can be observed that TiO₂ nanotransformer oil has the smallest optimal mass concentration, indicating that using the least amount of TiO₂ nanoparticles can greatly reduce the breakdown voltage, thus reducing economic costs in practical applications. Furthermore, among the three types of nanoparticles, TiO₂ nanoparticles exhibit the highest relative dielectric constant [35,36].

TiO₂, a white inorganic material, is an n-type wide bandgap semiconductor that exists in two stable forms, rutile and anatase, at room temperature. Due to its excellent properties, such as enhanced surface charge carrier density and improved charge transport, TiO₂ has been a focus of research in the field of insulating materials. Semiconductor TiO₂ nanoparticles can increase the alternating current breakdown voltage of transformer oil. By modifying the microstructure and dispersion of TiO₂ nanoparticles, the thermal aging resistance and resistance to the water degradation of transformer oil can be significantly improved [37]. Additionally, TiO₂ nanoparticles can effectively suppress the streamer development length of oil-immersed paperboards under positive lightning impulse conditions, reduce the streamer propagation velocity, and accelerate streamer dissipation velocity [38]. Wang Lei studied the influence of 10 nm spherical TiO₂ nanoparticles, 5 nm spherical TiO₂ nanoparticles, and 5 nm rod-shaped TiO₂ nanoparticles on the AC breakdown voltage of transformer oil. The results showed that the addition of 10 nm spherical TiO₂ nanoparticles had the most significant effect on increasing the AC breakdown voltage, with an improvement of 111.9% [39]. Currently, research on nanomodified transformer oil in domestic and international studies primarily focuses on normal and high-temperature environments, while the insulation properties of nanomodified transformer oil under extremely cold conditions remain to be investigated.

Due to adverse environmental and weather factors in the northern part of China during winter, the performance of transformer oil is greatly affected. The influence of temperature on transformer oil cannot be ignored, as both high and low temperatures can cause significant fluctuations in breakdown voltage [40,41,42]. Low temperatures not only affect the breakdown voltage of transformer oil but also have a significant impact on other parameters, such as electrical conductivity and relative permittivity, apart from the breakdown voltage [43,44,45]. The most direct effect is a decrease in breakdown voltage, which leads to transformer failures and potentially disastrous consequences for substations and the entire power system [46,47]. Under specific conditions, while low temperatures certainly have a significant impact on the performance of transformer oil, ultimately, the key factor is the water content in the oil. Water tends to precipitate at 0 °C and solidifies into ice below 0 °C. In the oil, water exists in the form of tiny ice crystals. In theory, when the oil is contaminated with impurities, the electric field distribution in the oil is affected, leading to a significant decrease in breakdown voltage [48,49,50].

In order to investigate the applicability of nanomodified transformer oil under extremely cold conditions, 45# transformer oil was selected as the base liquid in this study. Spherical anatase TiO₂ nanoparticles were added to the base oil to prepare nanomodified transformer oil. Breakdown tests were conducted under different water content, temperature conditions, and electric field types to investigate the breakdown characteristics of TiO₂ nanomodified transformer oil. Furthermore, the polarization process of nanoparticles in a uniform electric field and the influence of charged particle trajectories in oil were simulated using COMSOL. The impact of polarized nanoparticles on the trajectories of charged particles in oil was investigated, aiming to further validate the mechanism of how nanoparticles in oil affect the breakdown voltage of oil gaps.

2. Experiment

2.1. Sample Preparation

2.1.1. Preparation of the TiO₂ Nanomodified Transformer Oil Sample

In this study, 45# transformer oil was chosen as the pure oil for the experiments; for the preparation of nanomodified transformer oil, 45# transformer oil was also selected as the base fluid. The morphology of the chosen TiO₂ nanomaterials was unprocessed anatase-type nanoparticles, presenting as white powder-like solid particles. On the microscale, the particle size of the nanoparticles was approximately 20 nm. In order to obtain a nanomodified transformer oil with good stability, the oil sample preparation process involved heating and mechanical dispersion, with oscillation dispersion performed using an automated oscillation instrument. To achieve good stability of the nanomodified transformer oil, the nanomaterials were first dissolved in a portion of the base fluid during the oil preparation process, followed by thorough dispersion, before being mixed with the remaining base fluid for secondary dispersion. The experiments were conducted at an ambient temperature of 20 °C and a humidity of 32% RH. Four different concentrations of TiO₂-nanomodified transformer oil samples were prepared, namely, 0.0048 g/L, 0.01 g/L, 0.09 g/L, and 0.2 g/L. The physical pictures of the four samples are shown in Figure 1.

2.1.2. Preparation of Oil Samples with Different Moisture Contents and Temperatures

The solubility of water in oil is commonly expressed as the weight of water per liter of oil. The concentration of solute in parts per million (ppm) represents the percentage of solute mass in relation to the total solution mass, which is also known as the concentration in parts per million.

The prepared nanomodified transformer oil and 45# pure oil were dried for 72 h, and then placed in a constant-temperature and -humidity chamber. The temperature was set at 20 °C, and different moisture contents of the oil samples were prepared by varying the humidity inside the chamber using the moisture absorption method. After multiple repeated experiments and measurements, the moisture content in all oil samples was ultimately controlled at three different levels: 26 ppm, 61 ppm, and 85 ppm. However, due to experimental errors, it was not possible to precisely control the moisture content of the oil samples at the exact levels mentioned above every time. Therefore, the moisture content of the samples produced in each experiment could only be controlled within a range of ±1 ppm. Temperature control was achieved using a programmable constant temperature and humidity chamber. Each temperature control cycle lasted for at least 15 h. According to the experimental requirements, the temperature of all oil samples was controlled at seven different levels: −30 °C, −20 °C, −10 °C, 0 °C, 10 °C, 20 °C, and 30 °C. The actual temperature measurements were within a range of ±1.2 °C, accounting for errors in temperature measurements.

2.2. Experimental Platform Building

The transformer oil breakdown test platform used the OTS100 AF insulating oil withstand voltage tester produced by Megger. Its internal principle is shown in Figure 2. The external power frequency uses an AC power supply. The electrode’s end is connected to a high-voltage bushing. One end is connected to the oil cup. The maximum breakdown voltage is 100 kV. The oil cup is placed on the insulation platform.

The electrode is a copper electrode, the distance between the electrodes is adjustable, and the shape of the electrode can be replaced. There are spherical cap electrodes, spherical electrodes, and flat plate electrodes for test selection. The side view is shown in Figure 3. The diameter of the ball cap electrode used is 3.5 cm, the diameter of the flat electrode is 1.5 cm, and the diameter of the spherical electrode is 1 cm. The physical image of the oil cup and electrode used in the test is shown in Figure 4.

2.3. Test Method and Procedure

The breakdown voltage of transformer oil is one of the important parameters used to measure its electrical resistance performance, and it is also the most important tests in this study. In the experiment, the breakdown of pure oil and transformer oil with added nanomaterials is conducted separately. The experimental operation adopts the method of controlling variables, testing the oil samples with different water contents and different temperatures.

Since the uniform electric field represented by the plate-to-plate electrode is overly idealized and does not meet the requirements of practical applications, this study focuses on comparing the breakdown characteristics between a pair of spherical cap electrodes and the sphere-to-plate electrode. All breakdown tests were conducted in accordance with international standard IEC60156. The experimental procedures were as follows:

• Select the type of electrode and adjust the electrode spacing to the standard distance of 2.5 mm.
• Pour the test oil sample quickly into the oil cup, adjust the position of the magnetic stirring rod on the inner wall of the oil cup, and close the top cover of the oil cup and the electrostatic shielding cover.
• Select the test standard and set the frequency to 61.8 Hz for alternating current. Gradually increase the voltage with a step size of 2 kV/s until breakdown occurs in the oil gap.
• Allow the sample to stand for 2 min. During this resting time, stir the oil sample using the magnetic stirring rod. Repeat the breakdown test 12 times and take the average value.

It is important to note that this study only focuses on the breakdown tests of oil samples with a nanoparticle concentration of 0.01 g/L. This choice is based on multiple preliminary breakdown tests conducted on oil samples with four different concentrations, which revealed that the oil sample with a concentration of 0.01 g/L exhibited the highest absolute breakdown voltage.

3. Experimental Results and Analysis

3.1. Effect of Temperature on the Breakdown Voltage of Nanomodified Transformer Oil

Firstly, several samples of nanofluids with a water content of 26 ppm and a nanofluid concentration of 0.01 g/L were prepared. For comparison, several samples of pure oil with a water content of 26 ppm were also prepared. Breakdown tests were conducted at six different temperatures ranging from −30 °C to 20 °C. Additionally, tests were performed on nanofluid samples with a water content of 85 ppm. The results at low water content are shown in Figure 5, where the absolute values of the breakdown voltages for pure oil and nanofluid varied with temperature. The minimum value was observed at 0 °C, where the breakdown voltages of both types of oil were the closest. Within the temperature range of −30 to 30 °C, the breakdown voltage of nanofluid was significantly higher than that of pure oil.

Results of the breakdown tests on high-water-content pure oil and nanofluid are illustrated in Figure 6. Compared with Figure 5, it can be observed that the breakdown voltage of the oil samples was lower, reaching its minimum value at 0 °C. Within the temperature range of −10 to 0 °C, for the high-water-content oil samples, the rate of increase in breakdown voltage relative to decreasing temperatures was significantly lower compared to the low-water-content oil samples.

The breakdown voltages of the two oil samples under AC voltage varied with temperature. When the temperature exceeded 0 °C, the breakdown voltage increased with temperature, with a relatively slow rate of increase between 0 °C and 10 °C, and the fastest rate of increase was observed beyond 10 °C. On the other hand, when the temperature was below 0 °C, the breakdown voltage increased with decreasing temperature, with the slowest rate of increase between −10 and 0 °C and a slightly faster rate of increase below −10 °C. Nevertheless, the rate of increase remained lower than that above 10 °C. The overall trend of this curve resembled a “V” or “U” shape, with the minimum value still occurring at 0 °C.

This phenomenon occurs because, at higher temperatures, moisture exists in oil primarily in the form of dissolved water, which has no significant impact on the breakdown voltage. As the solubility decreases with decreasing temperatures, the moisture gradually precipitates and exists in the form of suspended water in the oil. Around 0 °C, the suspension of water in the oil reaches its maximum. This suspended water causes the distortion of the electric field, and, under the influence of the electric field, the suspended water droplets elongate and deform, forming conductive bridges in an orderly arrangement. Consequently, the breakdown voltage of the oil gap is significantly reduced. As the temperature continues to decrease, the suspended water particles undergo solidification and transform into ice crystals. At this stage, moisture in the form of impurities affects the breakdown voltage of the oil gap. The ice particles cannot be elongated by the electric field, and their dielectric constant is similar to that of insulating oil. This results in the weakened distortion of the electric field. Additionally, as the temperature decreases, the viscosity of the oil increases, causing hindrance to the formation of conductive bridges. Therefore, the breakdown voltage increases below 0 °C as the temperature decreases. This phenomenon can be explained by the “bridge theory”.

From the graph, it is evident that the breakdown voltage of the nanofluid is consistently higher than that of the pure oil, with the most significant improvement observed at temperatures above 10 °C. Calculations using Equation (1) yielded the following results: When the temperature was above 10 °C, the addition of nanomaterials to the transformer oil led to an increase in the breakdown voltage by 18% to 21%. When the temperature was below −10 °C, the breakdown voltage could be enhanced by 13% to 15%. Within the temperature range of −10 °C to 0 °C, the increase in breakdown voltage was relatively smaller, ranging from 8% to 9%, as determined by conducting multiple experiments and calculations.

$$W=\frac{U_{NP}-U_{MO}}{U_{NP}}\times 100\%$$

(1)

In the equation, $W$ represents the percentage increase in the breakdown voltage of the nanofluid compared to that of the pure oil, $U_{NP}$ represents the breakdown voltage of the nanofluid in kilovolts (kV), and $U_{MO}$ represents the breakdown voltage of the pure oil in kilovolts (kV).

3.2. Effect of Water Content on the Breakdown Characteristics of Oil in the Nanotransformer

In accordance with Faraday’s law, the moisture content in transformer oil can be represented by Equation (2).

$$S=\frac{Q}{10.772{\rho }_{MO}}$$

(2)

In the equation, $S$ represents the moisture content in transformer oil (ppm), $Q$ represents the electrolysis charge (mc), and ${\rho }_{MO}$ represents the density of the transformer oil at standard temperature and pressure (kg/m³).

Three different moisture levels (26 ppm, 61 ppm, and 85 ppm) of nanoparticle oil samples and the corresponding pure oil samples with the same moisture content were selected to conduct breakdown experiments. The aim was to compare and analyze the enhancement effect of TiO₂ nanoparticles on the breakdown voltage of oil samples under different moisture levels.

The experimental results of pure oil at various water contents are shown in Figure 7, with the overall variation trend of the curve exhibiting a “U” shape. From the figure, it can be observed that, for any given temperature, the breakdown voltage of oil samples with low water contents was higher than that of samples with high water contents, and the minimum breakdown voltage occurred at 0 °C. For oil samples with high water contents, the rate of increase in breakdown voltage was slower for temperatures ranging from −10 °C to 10 °C compared to samples with low water contents, while the rate of increase in breakdown voltage was faster for temperatures below −10 °C in samples with high water contents.

The experimental results of nanofluid at different water contents are shown in Figure 8. Numerically, the breakdown voltage was higher than that of pure oil, with the maximum value occurring at 30 °C at approximately 75 kV. Through comparison with Figure 7, it can be observed that, when the temperature was above 0 °C, the enhancement of the breakdown voltage by the nanomaterial in transformer oil was more significant. However, when the water content in the oil was high, the improvement effect of the nanoparticle on the breakdown voltage was limited, and the enhancement magnitude was relatively small.

The experimental results of the two oil samples are summarized in Figure 9, which shows that the breakdown voltage of nanofluid was higher than that of pure oil at different water contents. Starting from −10 °C, as the temperature decreased, and the impact of the nanomaterial on the breakdown voltage of transformer oil became more significant, with a more pronounced enhancement. Within the temperature range of 0 °C to 30 °C, the enhancement of the breakdown voltage of transformer oil by the nanomaterial became increasingly apparent with the increase in temperature.

It can be observed that the water content in transformer oil had a significant impact on its breakdown voltage. As the temperature decreased, the breakdown voltage showed a decreasing trend followed by an increasing trend, with an overall curve variation resembling a “U” shape. When the water content in the oil was 26 ppm, the minimum breakdown voltage for both types of oil occurred at 0 °C. At this point, the lowest breakdown voltage for pure oil was 19.9 kV, while the breakdown voltage for nanoparticle fluid was 21.3 kV, resulting in an increase of 7.03% in breakdown voltage. When the water content in the oil was 61 ppm and 85 ppm, the lowest breakdown voltage did not exceed 10 kV. Compared to pure oil, the nanoparticle fluid exhibited an increase of 9.80% and 8.99% with respect to breakdown voltage, respectively.

Compared to oil samples with low water contents, when the water content was relatively high, within the experimental temperature range, TiO₂-nanomodified transformer oil exhibited a smaller magnitude of enhancement in breakdown voltage compared to pure oil but a higher percentage increase.

In addition, it can be observed that nanoparticles had a certain enhancing effect on the breakdown voltage of transformer oil. The breakdown process of transformer oil under the action of power frequency AC electric field can be regarded as the development process of streamer in the oil. The influence of nanoparticles on electron migration weakens the electron collision ionization process. On the one hand, the role of shallow traps accelerates the escape of electrons from the ionization region. When free electrons migrate at high speed, they are prone to ionization due to collisions with liquid molecules. The addition of nanoparticles introduces a large number of shallow traps, which capture free electrons and make them more likely to jump between adjacent traps, prompting electrons to escape from the ionization region. The escaped electrons are either neutralized or form negative ions, thereby weakening the repeated collision ionization process caused by electrons in the ionization region and suppressing the initiation of electron avalanche [51]. On the other hand, the polarizing trapping effect of nanoparticles reduces the number of electrons in the ionization region. Under the action of an external electric field, nanoparticles undergo polarization, and the positively charged region induced on the surface of nanoparticles captures high-speed moving electrons, forming negatively charged nanoparticles with slow movement speed. In this way, while reducing the electric field intensity in the oil, it also slows down the movement rate of positive and negative charges, thereby increasing the breakdown voltage and breakdown time.

3.3. Effect of Electric Field Type on the Breakdown Voltage of Transformer Oil

In this experiment, a pair of spherical cap electrodes was used to simulate a slightly non-uniform electric field, while a sphere-to-plate electrode was used to simulate an uneven electric field. Breakdown tests were conducted on the two types of oil samples with low water contents.

The experimental results of nanofluids at low water contents are shown in Figure 10. From the figure, it can be observed that there was a clear difference in the test results between the two electrodes, and the breakdown voltage under the slightly non-uniform electric field was higher than that under the uneven electric field. This is because the fault breakdown in transformer oil is more likely to occur in situations with a less uniform electric field.

Figure 11 shows the breakdown test results of pure oil under two different electrodes. In the breakdown test of pure oil, the difference between the two electrodes was relatively small in terms of the absolute value of the breakdown voltage. Within the experimental temperature range, the breakdown voltage under the slightly non-uniform electric field was slightly higher than that under the uneven electric field. At a temperature of −20 °C, the breakdown voltage under both electrodes was equal, deviating from the expected results. This indicates that the breakdown voltage of pure oil in an uneven electric field exhibits instability. In comparison to Figure 10, it can be inferred that the nanoparticle material enhanced the stability of the breakdown voltage.

Comparing the experimental results of the two oil samples, it can be inferred that the electric field type had an influence on the breakdown voltage of pure oil, but the overall difference was not significant. In the breakdown tests of the two oil samples, the absolute value of the breakdown voltage under the slightly non-uniform electric field was greater than that under the uneven electric field. Comparing the two, it can be observed that transformer oil with the addition of nanoparticle materials had an advantage in a uniform electric field. Additionally, the addition of TiO₂ nanoparticle materials played a stabilizing role in the breakdown voltage of transformer oil, especially under low-temperature conditions.

3.4. Effect of Nanomaterials on the Dispersion of Breakdown Voltage in Transformer Oils

A breakdown experiment was conducted on pure oil and nanoparticle fluids with a water content of 26 ppm.

The error bars of the breakdown voltage of pure oil at different temperatures were obtained by processing the experimental data, as shown in Figure 12. From the figure, it can be observed that the dispersion of the breakdown voltage was large within the temperature range of −30 °C to −10 °C, indicating an unstable breakdown voltage. The dispersion of the breakdown voltage was smaller around 0 °C due to its minimal absolute value. As the temperature continued to increase, the dispersion of the breakdown voltage of pure oil started to increase again, indicating a significant influence of temperature variation on the stability of the breakdown voltage of the oil sample.

The summary of the breakdown test data for nanofluid is shown in Figure 13. Compared to Figure 12, it can be observed that, within the experimental temperature range, the dispersion of the breakdown voltage for the nanofluid was significantly smaller than that of pure oil. Furthermore, as the temperature increased above 20 °C, the dispersion further decreased. This indicates that, at higher temperatures, the nanomaterials still had a noticeable effect on reducing the dispersion of the breakdown voltage in oil gaps.

When the temperature was below 0 °C, the dispersion of the breakdown voltage for the nanofluid was smaller than that of pure oil. When the temperature was above 0 °C, the nanomaterials had less impact on the dispersion of the breakdown voltage in transformer oil compared to below 0 °C, and their effect was not as significant. As both types of oil exhibited the minimum breakdown voltage at 0 °C, the addition of nanomaterials had no noticeable effect on improving the dispersion of the breakdown voltage. On the basis of the analysis, it can be concluded that, within the temperature range of −30 °C to 30 °C, the breakdown voltage values had a large dispersion, while the addition of nanomaterials to transformer oil resulted in a smaller dispersion of the breakdown voltage. From the perspective of practical applications, nanomaterials significantly improve the dispersion of the breakdown voltage in transformer oil.

4. Simulation

The static electric field model was constructed using COMSOL 5.6 finite element simulation software to model the electrodes and oil gaps and subsequently investigate the movement of charged particles under the electric field; moreover, the influence of the added nanoparticles was also examined. On the basis of the simulation results and experimental data analysis, the mechanism of nanomaterials affecting the breakdown voltage in oil gaps was analyzed.

4.1. Two-Dimensional Model of the Electrostatic Field

A model of a spherical cap electrode pair is shown in Figure 14 with a diameter of 3.5 cm and an electrode spacing of 2.5 mm. Similarly, a two-dimensional model of a sphere plate electrode was also constructed, as illustrated in Figure 15. In the construction of the sphere plate electrode model, only the electrodes were changed. The diameter of the spherical electrode was 1 cm, the diameter of the flat electrode was 1.5 cm, and the electrode spacing was also 2.5 mm. Copper was chosen as the electrode material with a conductivity of 5.998 × 10⁷ S/m, a relative permittivity of 1, and a reference resistivity of 1.72 × 10⁻⁸. The insulating medium filled in the model was transformer oil, and its parameters were set according to the parameters of 45# transformer oil.

4.2. Physical Field Control Equations

4.2.1. Electrostatic Field Control Equations

The transient equations of the electrostatic field are as follows:

$$\nabla ·D={\rho }_V$$

(3)

$$E=-\nabla V$$

(4)

The control equations of charge conservation are as follows:

$$\nabla ·\left({\epsilon }_0{\epsilon }_{r}E\right)={\rho }_V$$

(5)

$$D={\epsilon }_0{\epsilon }_{r}E$$

(6)

In these equations, ${\epsilon }_0$ represents the relative permittivity in a vacuum, ${\epsilon }_r$ represents the relative permittivity of the material, $E$ represents the electric field strength, $D$ represents the displacement in the direction of the electric field, and ${\rho }_V$ represents the spatial charge density.

4.2.2. Particle Tracking Control Equations for Fluid Flow

The equations describing the forces exerted on particles and their motion velocities are as follows:

$$\frac{\mathrm{d}\left(m_{p}v\right)}{\mathrm{d}\mathrm{t}}=F_t$$

(7)

$$v=v_c-2(n·v_c)n$$

(8)

In these equations, $m_p$ represents the particle mass, $v$ represents the particle velocity, $v_c$ denotes the velocity upon impact with the wall, and $n$ represents the unit vector in the normal direction of the interface between the two media.

Charged particles in an electric field experience the force exerted by the electric field, which can be mathematically expressed as follows:

$$F_e=eZE$$

(9)

The value of $e$ is 1.602 × 10⁻¹⁹; $Z$ is the number of charges (dimensionless).

The configuration of particle interactions describes the interactions between different charged particles and between charged particles and nanoscale particles. This is expressed by the following descriptive equation:

$$F=\frac{e^2}{4\pi {\epsilon }_0}{\sum }_{j=1}^{N}Z{Z}_j\frac{r-r_j}{{\left|r-r_j\right|}^3}$$

(10)

In the equation, $r_j$ represents the position vector of the j-th particle, and $F$ represents the interaction force between any particle and the $j$-th particle.

5. Simulation Results and Analysis

5.1. Simulation Results of a Pair of Spherical Cap Electrodes

The motion trajectories and release characteristics of particles in pure oil under a pair of spherical cap electrodes were obtained, as shown in Figure 16. During the actual breakdown process, electrons were emitted from the cathode, leading to the presence of free charged particles in the oil. From the figure, it can be observed that the trajectories of the charged particles under the electrostatic field were irregular. By carrying out multiple comparisons of simulation results, it was observed that the motion of the charged particles under the influence of the electric field was irregular. Initially, the charged particles were accelerated under the electric field, and then they underwent irregular motion in subsequent stages. Due to the non-uniform distribution of the electric field’s strength, the motion velocity of the charged particles was also different.

Similarly, under the aforementioned simulation conditions, an attempt was made to introduce nanoparticles. However, since the simulation software cannot simulate actual TiO₂ nanomaterials, neutral solid particles without charge were used to simulate them while keeping other conditions unchanged. The simulation result of the motion trajectories of charged particles after adsorption by nanoparticles in the transformer oil can be observed in Figure 17. It can be observed from the simulation results that the addition of nanoparticles led to a decrease in the motion velocity of the charged particles after being adsorbed by the nanoparticles, indirectly reducing the migration rate of the charged particles in the oil. By comparing the two simulation result figures, the impact of nanoparticles on charged particles in the oil can be clearly observed.

The reason why nanoparticles have a certain impact on the motion of charged particles in oil is because their particle size is several orders of magnitude larger than that of the charged particles. The presence of nanoparticles can cause adsorption effects on the charged particles, thereby affecting their motion. The presence of nanoscale particles increases the number of “shallow traps” in the oil, which can capture the charged particles in the oil, thereby reducing the migration rate of the electrons. From the simulation results, it can be observed that the migration rate of charged particles adsorbed by nanoparticles in the oil decreased.

5.2. Simulation Results of the Sphere-to-Plate Electrode

The motion trajectories and release characteristics of particles in pure oil under a sphere plate electrode configuration were obtained, as depicted in Figure 18. From the figure, it can be observed that the motion of charged particles in the oil was influenced by the variation gradient of electric field strength between the two electrodes. The motion state of the charged particles underwent significant changes in this region with the highest field strength variation. At positions further away from the electrode, where the field strength was weaker, the acceleration effect on the charged particles was noticeably reduced. Overall, the charged particles in the oil underwent irregular accelerations under the influence of the non-uniform electric field. Moreover, it can be observed from the figure that, due to the unaffected motion of charged particles by external substances, the density of motion trajectories was higher. This provides a microscopic explanation for oil gap breakdown.

Similarly, by incorporating nanoparticles into the sphere plate electrode simulation model, the obtained simulation results are shown in Figure 19. From the figure, it can be observed that the motion velocity of charged particles significantly decreased after being adsorbed by nanoparticles. Unlike the ball-covered electrode, the potential variation near the sphere plate electrode was larger, resulting in a more non-uniform electric field surrounding it. This led to a higher acceleration of particle motion compared to the ball-covered electrode. However, the simulation results indicate that, under the sphere plate electrode configuration, nanoparticles also played a certain obstructive role in the motion of charged particles, thereby effectively reducing their migration rate.

5.3. Simulation of the Effect of Nanoparticles on Charged Particles

The method of adding nanoparticles to transformer oil can effectively improve the breakdown voltage of transformer oil. Nanoparticles have a larger specific surface area, which leads to adsorption forces between them and the liquid phase medium molecules. In other words, nanoparticles provide “shallow traps” that can effectively capture charged particles in the oil, thereby reducing their migration rate and energy [52,53].

Under the influence of an external electric field, nanomaterials become polarized. The negatively charged particles in the nanoparticles move in a directed manner under the external electric field and accumulate on one side of the nanoparticles. Correspondingly, an equal amount of positive charge appears on the other side, which is distributed on the surface of the nanoparticles as surface charges. This results in one end of the nanoparticles exhibiting positive polarity and the other end exhibiting negative polarity. To study this phenomenon, a modeling approach using COMSOL was employed to simulate the migration process of negatively charged particles in nanoparticles under the influence of an external electric field (Figure 20), as well as the migration process of positively charged particles in nanoparticles under the influence of an external electric field (Figure 21). As time progresses, the trajectory of charged particles evolves from figure (a) to figure (f). The arrows in the figures indicate the direction of the electric field.

Under the action of an electric field, the migration path of charged particles in transformer oil is generally from the negative plate to the positive plate. The polarized nanoparticles, due to the accumulation of surface charges, exhibit an external electric field and have a certain adsorption effect on the negatively charged particles moving in the oil. The simulation results of the time-varying adsorption process are shown in Figure 22. However, due to the limited surface charge of the nanoparticles, the adsorption of negatively charged particles is also limited. When the nanoparticles reach saturation in terms of adsorbing negatively charged particles, the charged particles will escape from the surface of the nanoparticles. Subsequently, under the action of the applied electric field, they continue to move toward the positive plate. From the simulation results, it can be concluded that the nanoparticles were first polarized in the electric field, and then affected the motion trajectory of the charged particles, obstructing the directed motion of the charged particles in the oil.

Nanoparticles are too large for electrons, which suggests that they can only play a certain role in hindering and adsorbing electrons, thereby reducing the density of free electrons in the oil. The charged particle capture model proposed in this study is more suitable for larger-sized positive and negative ions. Due to the extremely microscopic scale of the study, direct observation is not possible. At this stage, the construction of this model remains largely speculative and hypothetical. Therefore, further research is needed to elucidate the specific mechanisms involved.

6. Conclusions

• Low concentrations of nanoparticles can improve the quality of transformer oil, but the enhancement of breakdown voltage is not significant. On the other hand, high concentrations of nanoparticles not only fail to improve the quality of transformer oil but also reduce the breakdown voltage. Analysis of the experimental results revealed that the current stage’s appropriate choice was a concentration of 0.01 g/L of TiO₂ nanoparticles, which could significantly improve the breakdown voltage of transformer oil without significantly compromising its quality.
• The relationship curve between the breakdown voltage absolute value of TiO₂ nanomodified transformer oil and temperature exhibited a “V” or “U” shape. Within the range of −30 °C to 30 °C, the breakdown voltage of the nanofluid was higher than that of pure oil, but the amplitude of improvement compared to pure oil was the smallest around −10 °C to 0 °C. Within the range of 0 °C to 30 °C, the breakdown voltage of the nanofluid increased with temperature, and the amplitude of improvement compared to pure oil also increased. Within the range of −30 °C to 0 °C, the breakdown voltage of the nanofluid increased with decreasing temperature, and the amplitude of improvement compared to pure oil also increased. Within the temperature range of −30 °C to −10 °C, the breakdown voltage could be increased by 13% to 15%; within the range of −10 °C to 0 °C, it could be increased by 8% to 9%; within the range of 0 °C to 30 °C, it could be increased by 18% to 21%.
• The moisture content had a significant impact on the breakdown voltage of TiO₂-nanomodified transformer oil: the higher the moisture content, the lower the breakdown voltage. Regardless of whether the moisture content was high or low, the breakdown voltage of nanofluids was higher than that of pure oil, and the lowest breakdown voltage occurred at 0 °C. Compared to oil samples with low moisture content, when the moisture content is high, within the experimental temperature range, nanofluids exhibited a smaller amplitude of breakdown voltage enhancement compared to pure oil; however, the percentage enhancement was greater.
• Regardless of whether TiO₂ nanomodified transformer oil or pure oil was used, the breakdown voltage under non-uniform electric fields was lower than that under slightly non-uniform electric fields. However, the breakdown voltage of pure oil exhibited instability under non-uniform electric fields, and the dispersion of breakdown voltage could be significantly reduced by adding TiO₂ nanoparticles.
• The simulation results indicated that the addition of nanoparticles led to a certain adsorption effect on charged particles and facilitates their low-rate movement while carrying them. This validates the mechanism of nanomaterials enhancing the breakdown voltage of transformer oil, which is attributed to the hindrance of nanoparticle particles on the directed motion of charged particles in the oil. However, it should be noted that the model in this paper was established on the basis of numerous approximations and assumptions, and further research is needed to validate the specific mechanism.