On the Practical Possibility of Transmitting Powerful High-Voltage Pulses over Long Distances
Abstract Generated abstract
The paper examines whether a nomogram developed for estimating the dielectric permittivity of mixtures can also be used, by electrostatic analogy, to estimate the specific conductivity of mixtures of two dielectrics. Transformer oil and powdered Kamensk limestone were tested at several volume fractions, with volume specific conductivity measured by a direct-deflection method at a constant voltage and compared with values calculated from the nomogram using the conductivity ratio of the components. The comparison shows partial agreement, supporting the use of the same nomographic approach as a first approximation for determining mixture conductivity despite the physical difference between permittivity and conductivity.
Full Text
On Determining the Specific Conductivity of a Mixture of Two Dielectrics
T. Yu. Mogilevskaya, V. I. Obukhov
(Presented by the scientific seminar of the Department of Theoretical Foundations of Electrical Engineering)
The dielectric permittivity of a mixture of two dielectrics is determined from a nomogram [1, 2]. On the basis of the principle of electrostatic analogy, we considered it possible to use the same nomogram to determine also the specific conductivity of a mixture [3, 4, 5]. However, the correctness of such a determination of the specific conductivity of a mixture of two dielectrics was not indisputable and required experimental verification.
As the components of the mixture, transformer oil and Kamensk limestone, ground to a fine powder, were taken.
The volume specific conductivity was measured by the direct-deflection method according to the circuit approved by GOST [6].
Transformer oil and mixtures with different contents of limestone and oil were placed in turn in a breakdown vessel (Fig. 1) with two flat electrodes 1 and 2 of diameter \(d = 50\) mm. The distance \(l\) between the electrodes was set by means of micrometric screw 3.
Fig. 1. Breakdown vessel with a micrometric screw for measuring specific conductivity.
When measuring the specific conductivity of limestone, an electrode of diameter \(d = 40\) mm and a guard ring were used. The thickness of the sample in the uniform part of the field was \(l = 27\) mm.
The specific conductivity was determined by the formula:
\[ \gamma_{\text{op}} = \frac{4 C_D l \alpha_{\text{cp}} n}{U \pi d^2}, \tag{1} \]
where \(C_D = 4.5 \cdot 10^{-11}\) A/mm is the dynamic constant of the galvanometer;
\(n\) is the shunt number;
\(\alpha_{\text{cp}}\) is the mean of the galvanometer deflections for different polarities of the supply voltage.
All measurements were carried out at a constant voltage \(U = 1000\) V. The measurement results are given in Table 1.
Table 1
| \(p_1\) | \(a\) | \(a_{\mathrm{avg}}\) | \(n\) | \(l\) | \(\gamma_{\mathrm{exp}}\) | \(k\) | \(\gamma_{\mathrm{calc}}\) | Notes | |
|---|---|---|---|---|---|---|---|---|---|
| % | mm | mm | — | mm | \(10^{-10}\,1/\Omega\cdot\mathrm{m}\) | — | \(10^{-10}\,1/\Omega\cdot\mathrm{m}\) | ||
| Kamensk limestone | 100 | \(-147\) \(+153\) |
150 | 10 | 27 | \(14.5\cdot10^3\) | — | — | \(p_1\)—volume content of limestone in the mixture |
| Transformer oil | 0 | \(-51\) \(+51\) |
51 | 1 | 12 | 0.14 | — | — | \(\dfrac{\gamma_1}{\gamma_2}=1.04\cdot10^5\); \(\gamma_{\mathrm{calc}}=k\gamma_2\) |
| Mixture of limestone powder with transformer oil | 11.1 | \(-47\) \(+49\) |
48 | 10 | 12 | 1.32 | 6 | 0.84 | |
| ” | 20 | \(-56\) \(+59\) |
57.5 | 10 | 12 | 1.58 | 10 | 1.4 | |
| ” | 27.3 | \(-75\) \(+71\) |
73 | 10 | 12 | 2.01 | 24 | 3.36 | |
| ” | 33.3 | \(-77\) \(+85\) |
81 | 10 | 12 | 2.23 | 45 | 6.3 |
The same table gives the calculated values of the specific conductivity of the mixture, obtained with the aid of the nomogram. From the ratio of the specific conductivities of limestone and transformer oil \(\gamma_1/\gamma_2\) and the volume content of limestone in the mixture \((p_1)\), the calculation coefficient \(k\) was determined from the nomogram, making it possible to find the specific conductivity of the mixture as
\[ \gamma_{\mathrm{calc}}=k\gamma_2 . \]
A comparison of the experimental and calculated data shows that the analogy between the dielectric permittivity and the specific conductivity of a substance (despite the physical difference between these quantities) makes it possible, as a first approximation, to use one and the same nomogram for determining them.
LITERATURE
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