Frequency Characteristic of the Capacitance and Dielectric Loss Angle of GRShS Cable Insulation

I. G. Galeev

(Presented by the scientific seminar of the Electromechanical Faculty)

Flexible cables of the GRShS type are used to supply the electric motor of mobile mining machines with industrial-frequency current. At the same time, remote control and protective grounding can be carried out through special conductors.

Recently, flexible cables have begun to be used for transmitting high-frequency currents. Thus, for example, in remote control of a mining combine by means of an explosion-proof magnetic starter PMV-1358, it was proposed to organize telephone communication between the operator and the loading point over the same cable [1]. Remote control of face mechanisms is proposed to be carried out through the power conductors of a flexible cable by means of high-frequency currents [2; 3].

Cables intended for transmitting high-frequency currents are characterized by active resistance, inductance, capacitance, and also by insulation conductance.

The possibility of transmitting a high-frequency signal over a cable without distortion and with permissible attenuation is determined by the frequency characteristic of the primary parameters of the cable. These parameters are determined by the cable design, the materials from which it is made, and the current frequency.

GRShS cables were not intended for transmitting high-frequency currents, and therefore the literature contains no data characterizing the primary parameters of these cables.

To calculate the working capacitance of a cable in communication engineering, the formula proposed by V. I. Kuleshov [4] is used,

\[ C=\frac{\lambda \varepsilon 10^{-6}}{36 \ln \frac{2a}{d}} \, \psi , \tag{1} \]

where \(C\) is the working capacitance of a pair of cable conductors, F/km;
\(a\) is the distance between the centers of the conductors, mm;
\(d\) is the conductor diameter, mm;
\(\lambda\) is the lay coefficient;
\(\varepsilon\) is the dielectric permittivity;
\(\psi\) is a correction factor characterizing the distance of the conductors from the grounded sheath (for a considerable distance \(\psi = 1\)).

This formula was derived by means of potential coefficients for a symmetrical four-conductor communication cable with a grounded lead sheath, without taking account of the proximity effect.

In this case the equivalent circuit has the form shown in Fig. 1. Since the conductors of the communication cable are arranged symmetrically with respect to the grounded sheath and to one another, the partial capacitances are

\[ C_{13}=C_{14}=C_{23}=C_{24} \quad \text{and} \quad C_{11}=C_{22}=C_{33}=C_{44}, \]

which considerably simplifies the calculation.

The construction of GRShS cables is shown in Fig. 2, and the dimensions of the various types are given in Table 1. As is seen from Fig. 2, the conductors

Fig. 1. Circuit of the partial capacitances within a quad.

Fig. 2. Construction of four-conductor cables of the GRShS type (M1:1 cable GRShS 3×50+1×10).
1—grounding conductor; 2—hose; 3—conductor insulation made of rubberized yarn in one layer; 4—rubber conductor insulation; 5—current-carrying conductor; 6—rubber core.

of the cable, relative to the earth, the grounding conductor, and to one another, are arranged asymmetrically, and therefore the equivalent circuit will have the form shown in Fig. 3. In this case

\[ C_{14}=C_{24} \quad \text{and} \quad C_{13}=C_{23}. \]

As is seen from Figs. 2 and 3, GRShS cables differ in construction from communication cables; therefore formula (1) cannot be used to determine the operating capacitance of GRShS cables. This is confirmed by experiments that have been carried out.

The number of partial capacitances may be determined from the following expression

\[ N=\frac{n}{2}(n+1)-1, \tag{2} \]

where \(n\) is the number of conductors in the cable.

Fig. 3. Circuit of the partial capacitances of four-conductor GRShS cables.

The partial capacitances of the cable conductors with respect to earth, in comparison with the partial capacitances between conductors, have an insignificant value. Therefore, in calculating the operating capacitance of the cable by partial-

Table 1

Structural dimensions of GRShS and GRShSN cables

Dimensions in mm

capacitances of the conductors relative to earth may be neglected. In that case the circuit shown in Fig. 3 can be transformed into the circuit shown in Fig. 4, and, if it is taken into account that

\[ C_{13}=C_{23} \qquad \text{and} \qquad C_{14}=C_{24}, \]

then the operating capacitance between conductors \(A\) and \(B\) can be expressed through the partial capacitances as follows:

\[ C_{AB}=C_{12}+\frac{C_{14}C_{24}}{C_{14}+C_{24}}+\frac{C_{13}C_{23}}{C_{13}+C_{23}} =C_{12}+\frac{C_{14}+C_{13}}{2}. \tag{3} \]

This formula corresponds to the equivalent circuit of partial capacitances shown in Fig. 5, i.e., the operating capacitance of the cable for conductors \(A\) and \(B\) does not depend on the partial capacitance \(C_{34}\). This is explained by the equality of the partial capacitances \(C_{13}=C_{23}\) and \(C_{14}=C_{24}\), i.e., by the symmetry of the cable with respect to the transverse axis “3—4,” as a result of which the potentials of points 3—4 will be identical.

Fig. 4. Transformed circuit of the partial capacitances of four-conductor GRShS cables.

Fig. 5. Circuit of partial capacitances corresponding to formula 3.

In the same way an expression can be obtained for determining the operating capacitance of the cable with respect to conductors \(AC\) or \(BC\)

\[ C_{AC}=C_{BC}\simeq C_{13}+ \frac{(2C_{12}+C_{14})(C_{13}+C_{34})}{2C_{12}+2C_{13}+C_{34}}. \tag{4} \]

The calculation formula derived from expressions (3), (4) is very complicated and of little use for practical application; therefore it is proposed that calculations of the operating capacitance of GRShS cables be made by formula (5), which gives an accuracy within the manufacturing tolerances for cables of \(\pm 10\%\):

\[ C=\frac{\varepsilon k} {10^{6}\cdot 36 \ln\left(\dfrac{A}{d}+\sqrt{\dfrac{A^{2}}{d^{2}}-1}\right)}, \tag{5} \]

where \(\varepsilon\) is the dielectric permittivity of the cable insulation;
\(A\) is the distance between the centers of the conductors, mm;
\(d\) is the diameter of the working conductor of the cable, mm;
\(k\) is a coefficient taking into account the influence of the grounding conductor, the third working conductor, and the lay of the cable conductors.

Table 2

Change in the dielectric permittivity of different cores of GRShS cables with change in current frequency

Dielectric permittivity of the insulation of different cores of GRShS cables

The values of the dielectric constant for various GRShS cables at frequencies from 50–21000 Hz are given in Table 2. The data presented in this table were obtained by measuring the operating capacitances of GRShS cables and calculating the dielectric constant by formulas.

The distances between conductors are taken from Table 1. According to Fig. 2, \(A = a\) or \(A = b\), depending on between which conductors the operating capacitance is determined.

The values of \(k\) for various types of cables are given in Table 3.

Table 3

Value of the coefficient \(k\) for various GRShS cables

For the purpose of verifying the formulas obtained, measurements were made of the operating capacitances of GRShS cables.

The operating capacitance was measured at the testing station of the Tomsk Cable Plant by the following method. The operating capacitance of the cable was measured with a Schering bridge at a frequency of 800 Hz over the manufacturing length of the cable.

Subsequently, on cable samples in the laboratory of the Department of Cable and Insulation Technology of TPI, the frequency characteristic of the operating capacitance was recorded with an MLE-1 bridge. In this case, only those samples were admitted to testing for recording the frequency characteristic for which the operating capacitance and dielectric loss angle, recalculated per 1 km of length, coincided with or were close to the results of measurements performed on the manufacturing length of the cable at the same frequency. Measurements of the operating capacitance were carried out in all cases according to the circuit shown in Fig. 6.

The measurements on the samples were repeated at intervals of 4 and 12 months. On the basis of these measurements Table 4 was compiled. In parallel with the measurement of operating capacitance, the dielectric loss angle of the cable insulation was determined while varying the current frequency in the range 0.05–20 kHz. Measurements of \(\operatorname{tg}\delta\) were made with an MLE-1 bridge by the generally accepted direct method. The measurement error was \(\pm 0.02 \operatorname{tg}\delta + 0.0005\). According to the results of data processing

Table 4

Change in operating capacitance of GRShS cables with changes in frequency and conductor cross-section

Operating capacitances in \(10^{-9}\ \mathrm{F/km}\) for different pairs of conductors.

measurements, curves were plotted for the dependence of the change in $\operatorname{tg}\delta$ of the insulation of various GRShS cables on frequency (Fig. 7).

The character of the change in the tangent of the dielectric-loss angle of the insulation of GRShS cables is typical for rubber with additions of soot and talc. As is known [5], the inflection points of the curve $\operatorname{tg}\delta = \varphi(f)$ for rubber depend on the content of bound sulfur. The considerable difference in the value of $\operatorname{tg}\delta$ for different cables is explained by the features of the

[Diagram labels: “To bridge”; “To bridge.”]

Fig. 6. Diagram for measuring the working capacitance of four-core GRShS cables.

construction and by the nonuniformity of the composition of the insulation. For hose rubber there is no standard for $\operatorname{tg}\delta$ or for $\varepsilon$. As a result, the state and composition of the insulation elements are not controlled.

Fig. 7. Dependence of the change in $\operatorname{tg}\delta$ of the insulation of various grades of GRShS cables on frequency.
1—GRShS $3 \times 70 + 1 \times 10$; 2—GRShS $3 \times 50 + 1 \times 10$;
3—GRShS $3 \times 35 + 1 \times 10$; 4—GRShS $3 \times 25 + 1 \times 10$; 5—GRShS $3 \times 16 + 1 \times 10$;
6—GRShS $3 \times 10 + 1 \times 6$.

Measurements showed that the working capacitance and the dielectric-loss angle of GRShS cables depend strongly on the manufacturing technology

of manufacture, the quality of the insulating materials, and for different cable specimens vary within comparatively wide limits.

In connection with the use of GRShS cables for transmitting high-frequency currents, it is necessary to establish standards for the magnitude of the dielectric loss angle and the dielectric constant of the core, hose rubber, and insulating materials. In the manufacture of cables, the condition and content of the constituent parts of the rubber insulation, the core, and the hose should be monitored.

REFERENCES

1. Svetlichnyi P. L. Remote control of face machines. Ugletekhizdat, 1956.

2. Galeev I. G. Prospects for remote control of face mechanisms through the power conductors of a flexible rubber cable. Ugol’, No. 11, 1955.

3. Ogorodneichuk I. F. Remote control of mine mechanisms by means of high-frequency currents. Proceedings of the scientific and technical conference. Konotop. Automation of production processes in the coal industry. Ugletekhizdat, 1956.

4. Kuleshov V. N. Theory of communication cables. Svyaz’izdat, 1950.

5. Gorshkov P. I. Fundamentals of high-current cable engineering. Gosenergoizdat, 1940.