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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, an in-depth analysis of the percolation phenomenon for square matrices with dimensions from L = 50 to 600 for a sample number of 5 × 104 was performed using Monte Carlo computer simulations. The percolation threshold value was defined as the number of conductive nodes remaining in the matrix before drawing the node interrupting the last percolation channel, in connection with the overall count of nodes within the matrix. The distributions of percolation threshold values were found to be normal distributions. The dependencies of the expected value (mean) of the percolation threshold and the standard deviation of the dimensions of the matrix were determined. It was established that the standard deviation decreased with the increase in matrix dimensions, ranging from 0.0262253 for a matrix with L = 50 to 0.0044160 for L = 600, which is almost six-fold lower. The mean value of the percolation threshold was practically constant and amounted to approximately 0.5927. The analysis involved not only the spatial distributions of nodes interrupting the percolation channels but also the overall patterns of node interruption in the matrix. The distributions revealed an edge phenomenon within the matrices, characterized by the maximum concentration of nodes interrupting the final percolation channel occurring at the center of the matrix. As they approached the edge of the matrix, their concentration decreased. It was established that increasing the dimensions of the matrix slowed down the rate of decrease in the number of nodes towards the edge. In doing so, the area in which values close to the maximum occurred was expanded. Based on the approximation of the experimental results, formulas were determined describing the spatial distributions of the nodes interrupting the last percolation channel and the values of the standard deviation from the matrix dimensions. The relationships obtained showed that with increasing matrix dimensions, the edge phenomenon should gradually disappear, and the percolation threshold standard deviation values caused by it will tend towards zero. [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]

The paper presents studies of the site percolation phenomenon for square matrixes with dimensions L = 55, 101 and 151 using the Monte Carlo computer simulation method. The number of iterations for each matrix was 5 × 106. An in-depth analysis of the test results using the metrological approach consisting of determining the uncertainty of estimating the results of iterations with statistical methods was performed. It was established that the statistical distribution of the percolation threshold value is a normal distribution. The coefficients of determination for the simulation results in approximations of the percolation threshold using the normal distribution for the number of iterations 5 × 106 are 0.9984, 0.9990 and 0.9993 for matrixes with dimensions 55, 101 and 151, respectively. The average value of the percolation threshold for relatively small numbers of iterations varies in a small range. For large numbers of iterations, this value stabilises and practically does not depend on the dimensions of the matrix. The value of the standard deviation of the percolation threshold for small numbers of iterations also fluctuates to a small extent. For a large number of iterations, the standard deviation values reach a steady state. Along with the increase in the dimensions of the matrix, there is a clear decrease in the value of the standard deviation. Its value is about 0.0243, about 0.01 and about 0.012 for matrixes with dimensions 55, 101 and 151 for the number of iterations 5 × 106. The mean values of the percolation threshold and the uncertainty of its determination are (0.5927046 ± 1.1 × 10−5), (0.5927072 ± 7.13 × 10−6) and (0.5927135 ± 5.33 × 10−6), respectively. It was found that the application of the metrological approach to the analysis of the percolation phenomenon simulation results allowed for the development of a new method of optimizing the determination and reducing the uncertainty of the percolation threshold estimation. It consists in selecting the dimensions of the matrix and the number of iterations in order to obtain the assumed uncertainty in determining the percolation threshold. Such a procedure can be used to simulate the percolation phenomenon and to estimate the value of the percolation threshold and its uncertainty in matrices with other matrix shapes than square ones. [ABSTRACT FROM AUTHOR]

The article presents an oil moistening method, identical to the oil moistening in power transformers. Moistening took place through the migration of moisture from the moistened pressboard to the brand new oil. The AC electrical parameters (admittance, phase shift angle, permittivity, loss tangent and conductivity) of the brand new and moistened insulating oil were tested. All measured parameters were found to be affected by the oil moistening. The greatest changes were observed in the loss tangent and conductivity. Moisturization increases the value of tanδ at a frequency of 10−4 Hz from about 20 to about 70. With an increase in frequency to about 400–1000 Hz, a minimum is observed, the position of which depends on the temperature. Its value for moistened oil is about six times lower than for brand new oil. This moisturizing increased the activation energy of the conductivity from 0.466 ± 0.0265 eV to 0.890 ± 0.0115 eV. This is likely due to the acceleration of water molecules diffusion from the pressboard into the oil with increasing temperatures. The observed changes in the oil parameters caused by moistening should be taken into account while analyzing the power transformers insulation condition using the FDS method. [ABSTRACT FROM AUTHOR]

The aim of this study was to perform precision measurements of the frequency-temperature dependences of the loss angle tangent of the liquid-solid composite with the FDS Dirana meter. The composite consisted of heavily moistered oil-impregnated pressboard. The moisturization of the pressboard occurred in a manner as close as possible to the process of wetting the insulation in power transformers to a moisture content of (5.0 ± 0.2) wt. %. This value of moisture content was chosen because exceeding this value can lead to transformer failure. The measuring temperature range was from 293.15 K (20 °C) to 333.15 K (60 °C), with a step of 8 K. The measuring frequency range was 0.0001 Hz to 5000 Hz. It was observed that the shape of the frequency dependence of the loss angle tangent for a moisture content of 5.0 wt. % does not depend on the value of the measuring temperature. An increase in temperature leads to a shift of the waveforms into the higher frequency region. This is associated with a decrease in the relaxation time, and its value depends on the activation energy. It was found that a good fit of the waveforms, simulated by Dirana, to the actual tgδ waveforms obtained at temperatures between 293.15 K (20 °C) and 333.15 K (60 °C) requires the introduction of temperatures, higher than the actual insulation temperatures, into the program. It was found that estimating the moisture content for different temperatures using Dirana soft-ware for insulating an oil-impregnated pressboard produced large discrepancies from the actual content. Better results were obtained after an adjustment requiring manual temperature correction towards higher, compared to measured, temperatures. The moisture content estimated after correction by the Dirana meter ranges from of 4.5 wt. % to 5.7 wt. % and increases almost linearly with increasing measuring temperature. The average moisture content estimated by the Dirana meter for all measuring temperatures is 5.1 wt. % and is close to the actual content (5.0 ± 0.2) wt. %. The uncertainty of the estimate is ±0.43 wt. % and is more than twice as high as the true value. [ABSTRACT FROM AUTHOR]

In this study, the conductivity and permittivity of electrical pressboard—insulating liquid—water composites were investigated, and the electrical properties of the composites and water were analysed comparatively. Mineral oil and synthetic ester were used as insulating liquids. It was found that the presence of water caused an increase in the permeability of the composite in the frequency range below 100 Hz. The value of static permittivity determined by water in the content of 5 wt. % was approximately 15. To obtain this value caused by liquid water, its volume should be approximately five (oil) and four times (ester) higher than its actual content, respectively. The determined values of the activation energy of the DC conductivity of the composites were several times higher than the values of the activation energy of the conductivity of the liquid water. The experimental values of the dielectric relaxation times were many orders of magnitude higher than the dielectric relaxation times of water. This means that the experimental results obtained for the dielectric permittivity, the activation energy of conductivity and the dielectric relaxation times for moisture electrical pressboard impregnated by mineral oil or synthetic ester exclude the possibility of the presence of liquid water in the composites. It was found that the conductivity of the composites increased exponentially with increasing water content. Such dependencies are characteristic of hopping conductivity, caused by the quantum phenomenon of electron tunnelling between nanometre-sized potential wells. As the increase in conductivity is determined by the presence of water in the composites, therefore, the nanometre potential wells were single-water molecules or nanodrops. [ABSTRACT FROM AUTHOR]

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Self-ordered arrays of Ni, Ni(50)Pd(50), and Ni(78)Pd(22) nanowires were synthesized by simultaneous electrochemical deposition of Ni and Pd components into porous templates of anodic aluminum oxide using alternating current. This paper is focused on the interplay of structure and chemical composition of Ni and Ni–Pd bicomponent nanowires arrays and the peculiarities of its magnetic anisotropy. [ABSTRACT FROM AUTHOR]

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The reference characteristics of complex permittivity of the transformers insulation solid component were determined for use in the precise diagnostics of the power transformers insulation state. The solid component is a composite of cellulose, insulating oil and water nanoparticles. Measurements were made in the frequency range from 10−4 Hz to 5000 Hz at temperatures from 293.15 to 333.15 K. Uncertainty of temperature measurements was less than ±0.01 K. Pressboard impregnated with insulating oil with a water content of (5.0 ± 0.2) by weight moistened in a manner maximally similar to the moistening process in power transformers was investigated. It was found that there are two stages of changes in permittivity and imaginary permittivity components, occurring for low and high frequency. As the temperature increases, the frequency dependencies of the permittivity and imaginary permittivity component shifts to the higher frequency region. This phenomenon is related to the change of relaxation time with the increase in temperature. The values of relaxation time activation energies of the permittivity ΔWτε′ ≈ (0.827 ± 0.0094) eV and the imaginary permittivity component ΔWτε″ = 0.883 eV were determined. It was found that Cole-Cole charts for the first stage are asymmetric and similar to those described by the Dawidson–Cole relaxation. For stage two, the charts are arc-shaped, corresponding to the Cole-Cole relaxation. It has been established that in the moistened pressboard impregnated with insulating oil, there is an additional polarization mechanism associated with the occurrence of water in the form of nanodrops and the tunneling of electrons between them. [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]

This study investigates the frequency–temperature relations between the phase angle φ and admittance Y for composites of cellulose, synthetic ester, and water nanoparticles. We determined the activation energy value for the relaxation time of a phase shift angle ΔWφ ≈ (0.783 ± 0.0744) eV, which was related to the shift of φ(f) waveforms in higher frequency area with increasing temperature. We found that the position of admittance frequency waveforms in double logarithmic coordinates was simultaneously influenced by the temperature dependence of admittance and its relaxation time. Activation energy values for the relaxation time of admittance ΔWτ ≈ (0.796 ± 0.0139) eV and the activation energy value of admittance ∆WY ≈ (0.800 ± 0.0162) eV were determined. It was found that all three activation energy values were identical and their average was ΔW ≈ (0.793 ± 0.0453) eV. Impregnation with synthetic ester resulted in a decrease of activation energy by 0.26 eV compared to the impregnation with insulating oil. This was related to higher dielectric permittivity of the synthetic ester. [ABSTRACT FROM AUTHOR]