Precise Measurements of the Temperature-Frequency Dependence of the Conductivity of Cellulose—Insulating Oil—Water Nanoparticles Composite

Abstract

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.

Precise Measurements of the Temperature Influence on the Complex Permittivity of Power Transformers Moistened Paper-Oil Insulation

“…For the analysis of the obtained results, the model of alternating and direct current hopping conductivity was used, which was developed on the basis of the quantum mechanical electron tunneling phenomenon. The results of the direct and alternating current conductivity tests of the composite of cellulose, insulating liquid and water nanoparticles perfectly agree with this model [49,52,[58][59][60][61].…”

“…Formula (10) includes the conductivity σ, which is a function of temperature, ω and ε 0 , the values of which do not depend on temperature. As established in [49], the position of σ curves in the double logarithmic coordinates is affected simultaneously by the temperature dependence of conductivity and the temperature dependence of the relaxation time of conductivity. Both these factors are determined by the same activation energy, the mean value of which equals ∆W στ ≈ (0.894 ± 0.0134) eV [49].…”

“…As established in [49], the position of σ curves in the double logarithmic coordinates is affected simultaneously by the temperature dependence of conductivity and the temperature dependence of the relaxation time of conductivity. Both these factors are determined by the same activation energy, the mean value of which equals ∆W στ ≈ (0.894 ± 0.0134) eV [49]. Formula (10) shows that the activation energies of the imaginary permittivity component value and its relaxation time are identical to the corresponding activation energies for conductivity.…”

“…To produce the samples tested in this work, a method of moistening was used, as close as possible to the natural moistening of pressboard in transformers [49]. The process of sample preparation was carried out in the following way.…”

“…This is contrary to all the experimental results known so far, which in the ultra-low frequency range shows a certain limit of conductivity, equal to DC conductivity. In the paper [49], it was experimentally established that in the ultra-low frequency region, the AC conductivity exactly equals the DC conductivity of moistened oil-impregnated insulating pressboard.…”