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The aim of this study was to determine the frequency–temperature dependence of the AC conductivity and relaxation times in humid electrical pressboard used in the insulation of power transformers, impregnated with the innovative NYTRO® BIO 300X bio-oil produced from plant raw materials. Tests were carried out for a composite of cellulose–bio-oil–water nanodroplets with a moisture content of 0.6% by weight to 5% by weight in the frequency range from 10−4 Hz to 5·103 Hz. The measurement temperatures ranged from 20 °C to 70 °C. The current conductivity in percolation channels in cellulose–bio insulating oil–water nanodroplets nanocomposites was analyzed. In such nanocomposites, DC conduction takes place via electron tunneling between the potential wells formed by the water nanodroplets. It was found that the value of the percolation channel resistance is lowest in the case of a regular arrangement of the nanodroplets. As disorder increases, characterized by an increase in the standard deviation value, the percolation channel resistance increases. It was found that the experimental values of the activation energy of the conductivity and the relaxation time of the composite of cellulose–bio-oil–water nanodroplets are the same within the limits of uncertainty and do not depend on the moisture content. The value of the generalized activation energy is ΔE ≈ (1.026 ± 0.0160) eV and is constant over the frequency and temperature ranges investigated. This study shows that in the lowest frequency region, the conductivity value does not depend on frequency. As the frequency increases further, the relaxation time decreases; so, the effect of moisture on the conductivity value decreases. The dependence of the DC conductivity on the moisture content was determined. For low moisture contents, the DC conductivity is practically constant. With a further increase in water content, there is a sharp increase in DC conductivity. Such curves are characteristic of the dependence of the DC conductivity of composites and nanocomposites on the content of the conducting phase. A percolation threshold value of xc ≈ (1.4 ± 0.3)% by weight was determined from the intersection of flat and steeply sloping sections. The frequency dependence of the values of the relative relaxation times was determined for composites with moisture contents from 0.6% by weight to 5% by weight for a measurement temperature of 60 °C. The highest relative values of the relaxation time τref occur for direct current and for the lowest frequencies close to 10−4 Hz. As the frequency increases further, the relaxation time decreases. The derivatives d(logτref)/d(logf) were calculated, from the analysis of which it was determined that there are three stages of relaxation time decrease in the nanocomposites studied. The first occurs in the frequency region from 10−4 Hz to about 3·10−1 Hz, and the second from about 3·10−1 Hz to about 1.5·101 Hz. The beginning of the third stage is at a frequency of about 1.5·101 Hz. The end of this stage is above the upper range of the Frequency Domain Spectroscopy (FDS) meter, which is 5·103 Hz. It has been established that the nanodroplets are in the cellulose and not in the bio-oil. The occurrence of three stages on the frequency dependence of the relaxation time can be explained when the fibrous structure of the cellulose is taken into account. Nanodroplets, found in micelles, microfibrils and in the fibers of which cellulose is composed, can have varying distances between nanodroplets, determined by the dimensions of these cellulose components. [ABSTRACT FROM AUTHOR]

The study determines the frequency–temperature dependence of the conductivity of a moist solid insulation component of power transformers, impregnated with the innovative bio-oil NYTRO® BIO 300X, manufactured from plant-based raw materials. The research was conducted for six moisture levels ranging from 0.6% to 5% by weight, within a frequency range from 10−4 Hz to 5 · 103 Hz and measurement temperatures from 20 °C to 70 °C, with a 10 °C step. The conduction model for both DC and AC, based on the quantum mechanical phenomenon of electron tunneling between water nanodroplets, was used to analyze the obtained results. It was determined that the frequency dependence of the conductivity of pressboard-bio-oil-moisture composites is influenced by two factors as follows: the activation energy of conductivity and the activation energy of relaxation time. For each moisture content, 16 values of the activation energy of the relaxation time and 16 values of the activation energy of conductivity were determined. It was found that the values of activation energy of conductivity and relaxation time are equal and independent of moisture content, frequency, and temperature. Based on 192 residual activation energy values, the mean generalized activation energy value for the relaxation time and conductivity was calculated with high precision, resulting in ΔE ≈ (1.02627 ± 0.01606) eV. The uncertainty of its determination was only ±1.6%. This indicates that electron tunneling from the first nanodroplet to the second, causing AC conductivity, and their return from the second nanodroplet to the first, determining the relaxation time, occur between the same energy states belonging to the water nanodroplets located in the pressboard impregnated with bio-oil. For each moisture content, the curves obtained for different measurement temperatures were recalculated to a reference temperature of 20 °C using the generalized activation energy. It was found that the shifted curves obtained for different temperatures perfectly overlap. Increased moisture content shifts the recalculated curves toward higher conductivity values. It was established that for all moisture contents in the lowest frequency range, conductivity is constant (DC conductivity). A further increase in frequency causes a rapid rise in conductivity. The increasing period can be divided into two stages. The first stage occurs up to about 100 Hz–101 Hz, depending on the moisture content. In the second stage, the rate of conductivity increase is higher, and its value depends on moisture content. The lower the moisture content, the faster the conductivity increases. Recalculation using the generalized activation energy eliminated the effect of temperature on the curves. It was found that the shapes of the recalculated curves and their position relative to the coordinates depend only on the moisture content in the composite. The equality of the activation energy of the relaxation time and conductivity established in the study, as well as their independence from frequency and moisture content in the pressboard impregnated with NYTRO® BIO 300X bio-oil, allows for recalculating the curves of electrical parameters determined at any operating temperatures of the transformer to a reference temperature, for example, 20 °C. Comparing the curve obtained for the transformer, recalculated to the reference temperature, with reference curves determined by us in the laboratory for different moisture contents, will allow for the precise determination of the moisture content of the solid insulation component impregnated with NYTRO® BIO 300X bio-oil. This will contribute to the early detection of approaching critical moisture content, threatening catastrophic transformer failure. [ABSTRACT FROM AUTHOR]

This paper presents the results of the study of the direct current (DC) and alternating current (AC) electrical properties of an electrical pressboard–bio-insulating oil–water composite in a wide range of water content and temperatures used in electric power transformers. These parameters allow the level of insulation reliability to be determined after many years of operation of power transformers. To analyse the experimental results, a model of the DC and AC conductivities of nanocomposites based on the quantum-mechanical phenomenon of electron tunnelling was used. It was found that in a low-frequency region, the conductivities of AC and DC and their activation energy are equal. The relaxation times of AC conductivity and permittivity are also equal. It was found that the dependence of the DC conductivity on the distance between water molecules is an exponential function. On the basis of the model of conductivity by electron tunnelling between potential wells, the average number of water molecules in a nanodroplet, located in a composite of electrical pressboard–bio-insulating oil–moisture was determined to be (126 ± 20). It was found that the measured dependencies of DC and AC conductivity, permeability and dielectric relaxation times are consistent with the results of computer simulations performed on the basis of the model. This study showed that the composite of pressboard impregnated with bio-oil spontaneously transforms through water absorption into a pressboard–bio-oil–water nanocomposite. These will serve as the basis for the application of actual conductivity and dielectric relaxation mechanisms to improve the accuracy of moisture estimation in the solid component of power transformer insulation carried out on the basis of measurements of DC and AC properties. This will improve the operational safety of the transformers, minimise the occurrence of transformer failure and the associated environmental pollution. [ABSTRACT FROM AUTHOR]

In this study, the temperature–frequency dependencies of the pressboard–bio-oil–water nanoparticle composite's fundamental parameters—phase shift angle and admittance—were examined using the Frequency Domain Spectroscopy method. Measurements were conducted in a frequency range of 10−4 Hz to 5 × 103 Hz at temperatures ranging from 293.15 K to 343.15 K, with a step of 10 K. The temperature stabilization accuracy was less than ±0.05 K. A total of 15 Arrhenius plots were determined for various phase shift angle values, from which 15 values and the average activation energy of relaxation time were determined. Similarly, the values of the activation energy of admittance relaxation time and the activation energy of admittance were determined. It was established that all three average values are identical within the bounds of uncertainty. Based on 45 values, a generalized activation energy was determined, with a value of ΔW ≈ (1.032 ± 0.0196) eV. Using the generalized activation energy value, the phase shift angle curves determined for all temperatures were recalculated to a temperature of 293.15 K. It was found that after conversion, all curves perfectly overlap. A similar operation was carried out for the frequency dependencies of admittance. In this case, too, the recalculated dependencies perfectly match. This means that the shape of the frequency dependencies of the phase shift angle and admittance depends solely on the moisture content in the pressboard–bio-oil–water nanodrop composite. The position of the curves in doubly logarithmic coordinates depends only on temperature and is determined by the generalized activation energy Using the generalized activation energy determined in this study will allow for the development of accurate methods for estimating moisture content in cellulose insulation of power transformers containing bio-oil. This will contribute to the detection of critical moisture content, which is about 5% by weight, and to the elimination of the risk, associated with such a high moisture content, of catastrophic failure of power transformers. [ABSTRACT FROM AUTHOR]

In this study, the phenomenon of node percolation was tested using the Monte Carlo computer simulation method for square matrices with dimensions L = 55, 101 and 151. The number of samples for each matrix was 5 × 106. The spatial distributions of the coordinates of the nodes creating the percolation channel were determined, and maps of the density distribution of these nodes were created. It has been established that in matrices with finite dimensions, an edge phenomenon occurs, consisting of a decrease in the concentration of nodes creating a percolation channel as one approaches the edge of the matrix. As the matrix dimensions increase, the intensity of this phenomenon decreases. This expands the area in which values close to the maximum occur. The length distributions of the left and right clusters of non-conducting nodes were determined for the situation when the next randomly selected node connects them and thus reaches the percolation threshold. It was found that clusters whose dimensions are close to half of the matrix dimensions are most likely to occur. The research shows that both the values of the standard deviation of the percolation threshold and the intensity of the edge phenomenon are clearly related to the dimensions of the matrices and decrease as they increase. [ABSTRACT FROM AUTHOR]

This article presents direct σDC and alternating σ(f) current conductivity measurements obtained by the frequency domain spectroscopy (FDS) method on cellulose-transformer oil–water nanoparticle composite with a moisture content of (5.0 ± 0.2)% by weight in a temperature range from 293.15 to 333.15 K with step of 8 K. The uncertainty of temperature maintenance during measurements was below ±0.01 K. The sample was prepared for testing in a manner as close as possible to the cellulose insulation moisturizing process in power transformers. For the analysis of the results obtained, a model of alternating and direct current hopping conductivity was used, based on the quantum phenomenon of electron tunneling between the potential wells and nanodrops of water. It was observed that on the d(logσ)/d(logf)-derived waveforms there was a clear low-frequency maximum, and a tendency to reach the next maximum in the high-frequency area was visible. On this basis it was established that the increase in conductivity takes place in two stages. It was found that the position of σ(f) waveforms in the double logarithmic coordinates is influenced by the temperature dependence both of the conductivity and of the relaxation time of the conductivity. These relationships are described with the appropriate activation energies of the conductivity and relaxation time of conductivity. Based on the analysis of experimental data using Arrhenius diagrams, average values of the activation energy of conductivity ΔWσ ≈ (0.894 ± 0.0134) eV and the relaxation time of conductivity ΔWτσ ≈ (0.869 ± 0.0107) eV were determined. The values were equal within the limits of uncertainty and their mean value was ΔW ≈ (0.881 ± 0.0140) eV. Using the mean value of the activation energy, the frequency dependence of conductivity, obtained at different temperatures, was shifted to 293.15 K. For this purpose, first the waveforms were shifted along the horizontal and then the vertical axis. It was found that after the shift the σ(f) waveforms for the different temperatures overlap perfectly. This means that the shape of the frequency dependence of the conductivity is determined by the moisture content of the pressboard. The position of the waveforms in relation to the coordinates is determined by the temperature relationships of the conductivity and the relaxation time of the conductivity. [ABSTRACT FROM AUTHOR]