ON THE ELECTRICAL STRENGTH OF SOLID DIELECTRICS OVER A WIDE RANGE OF RATES OF RISE OF IMPULSE VOLTAGE

V. F. PANIN

(Presented by the scientific seminar of the Department of High-Voltage Engineering)

Introduction

Under the established standards for protecting high-voltage insulation against lightning overvoltages, the indices of impulse strength of insulating structures are the 50% discharge voltage and the volt-second characteristics obtained using standard impulses of 1.5/40 (1/50) μsec. The results of measurements of the electrical strength of solid dielectrics under standard impulses, carried out by many researchers, have served as the basis for designing high-voltage apparatus with solid insulation, with coordination for atmospheric overvoltages.

Improvement in the characteristics of lightning arresters has made it possible to reduce the levels of solid insulation. However, in order to realize this possibility, it is necessary to study the behavior of insulation under nonstandard impulse voltages, which mainly include switching overvoltages. The latter are distinguished by a great variety of forms. The frequencies of oscillations during switching lie within the range \(10^2\)—\(10^5\) Hz; accordingly, understandable difficulties arise in the systematic study of the electrical strength of solid insulation under the action of switching waveforms, especially in studying its strength in large interelectrode gaps.

In formulating studies of the strength of solid insulation in the region of action of switching overvoltages, it is necessary to resolve the question: variation of which parameters characterizing the form of the impulse voltage has the greatest influence on the discharge process in a solid dielectric and, consequently, on its electrical strength.

An analysis of the space-time patterns and quantitative characteristics of discharge in air and liquids according to data [1–5 and others], taking into account known analogies in the development of discharge in air and solid dielectrics [6, 7–9], has shown that, for solid dielectrics, as for air and liquids, the parameter determining the features of discharge development under impulses of different form is the rate of rise of the voltage.

This conclusion made it possible to infer that, for systematic investigations of the behavior of solid insulation under conditions of switching overvoltages, it is expedient to study its electrical strength on oblique-front voltage waves with steepnesses corresponding to the range of steepnesses of real overvoltages: \(10^3 \div 10^{-2}\) kV/μsec.

Research Methodology

In accordance with the foregoing considerations in the study of the electrical strength of solid insulation in the region of action of a switching waveform, the following research procedure was adopted: measurement of the mean breakdown voltages and of the standard deviations of the breakdown voltage from the mean value during breakdown of solid dielectrics on the front of an exponential impulse (the impulse steepness was varied within the range \(1.4 \cdot 10^{3}—10^{-2}\ \text{kV}/\mu\text{s}\)); followed by a comparative analysis of the obtained and literature data.

The apparatus and the method for processing the results are described in [10, 11]. The electrical strength was investigated for specimens made of model dielectrics: crystalline (ice) and amorphous (bitumen), in typical discharge gaps “point—plane” of length \(10 \div 15\ \text{mm}\) for both polarities of the point, and “sphere—plane” of length \(10\ \text{mm}\) for positive polarity of the spherical electrode.

The ice specimens were prepared according to the procedure adopted in [12]; the bitumen specimens were prepared by pouring bitumen, melted and then cooled to \(112^\circ\text{C}\), into brass molds at an ambient-air temperature of \(18 \div 26^\circ\text{C}\) and atmospheric pressure.

Results and Discussion

In Fig. 1 (curve 1) the dependences of the mean breakdown voltages \(U_p\) on the impulse steepness \(a_{\text{avg}}\) are presented for ice specimens in the “P—plane” gap, \(15\ \text{mm}\). A characteristic feature of the dependence \(U_p(a_{\text{avg}}\)

Fig. 1. Dependence of the breakdown voltage \(U_p\) on the steepness \(a_{\text{avg}}\) of a positive oblique-front wave for ice specimens: 1 — for mean values, 2 — for values \(U_{\text{avg}} - 2\sigma\), 3 — for values \(U_{\text{avg}} - 3\sigma\).

is an anomalous decrease of the mean breakdown voltages in the steepness region of about \(30\ \text{kV}/\mu\text{s}\). At this steepness the mean breakdown voltages were approximately equal to the breakdown voltages at steepnesses ...

slope $\sim 10^{-2}$ kV/μsec, corresponding to the maximum duration of switching overvoltages.

Another characteristic feature of the electrical strength of ice specimens is the considerable increase in the scatter of discharge voltages in the region of slopes of about 30 kV/μsec. Figure 2 shows the dependence of the standard deviation $\sigma$ on the voltage slope for ice specimens. As follows from Fig. 2, the value of $\sigma$ in the region of a slope of 30 kV/μsec exceeds the scatter at other slopes by a factor of 1.5–2.5. The decrease in the mean discharge voltages and the increased scatter

Fig. 2. Dependence of the standard deviation $\sigma$ on slope for ice specimens.

of the results in the region of slope $a \simeq 30$ kV/μsec cause a significant decrease in the levels $U_{\mathrm{av}} - 2\sigma$ and $U_{\mathrm{av}} - 3\sigma$, which in practice characterize the withstand voltages of insulation structures, Fig. 1 (curves 2 and 3), where $U_{\mathrm{av}}$ is the mean discharge voltage.

Figures 3 and 4 present the measurement results for bitumen specimens. As can be seen, for bitumen as well the characteristic features are a significant decrease in the mean discharge voltages and an increased scatter of the results in the region of slopes of about 30 kV/μsec. As in the case of ice, in the region of a slope of 30 kV/μsec the voltage levels $U_{\mathrm{av}} - 2\sigma$ and $U_{\mathrm{av}} - 3\sigma$ are significantly lower than the corresponding levels in the region of slope $10^{-2}$ kV/μsec.

An analogous effect of a decrease in impulse strength in the region of a slope of 30 kV/μsec was also established for specimens of ice and bitumen when tested in a weakly nonuniform field, with positive polarity of the spherical electrode. With negative polarity of the point, the indicated effect was observed in the case of bitumen. For the dependences of the discharge voltage of ice specimens on slope with negative polarity of the point, a monotonic decrease in discharge voltage with decreasing wave slope is characteristic.

Fig. 3. Same as in Fig. 1, but for bitumen specimens.

Fig. 4. Same as in Fig. 2, but for bitumen specimens.

It was of interest to compare the results obtained with data from previously published works on the breakdown of solid dielectrics under oblique-front voltage waves. A comparative analysis of the obtained and literature data showed that solid dielectrics with different physicochemical properties, when broken down in discharge gaps of different lengths and with electrodes of different shapes, are characterized by anomalously low discharge voltages in the region of a steepness of \(30\ \mathrm{kV/\mu s}\), which will hereafter be defined as critical. Some results of the comparative evaluation are given in Table 1, according to data from [12—14].

It is important to note that an analogous conclusion—on the existence of critical steepnesses—has also been drawn with respect to gaseous (air) and liquid (transformer oil) insulating media [15].

In earlier published works [16, 17], the presence of a minimum in the volt-second characteristics of solid dielectrics was associated with polarization processes, which play a significant role in impulse breakdown of solid dielectrics in a weakly nonuniform field.

In the case of breakdown of solid dielectrics in a sharply nonuniform field, space polarization charges apparently also exert a certain influence on the dielectric strength level at different rates of voltage rise. In this case, however, long before breakdown an ionization process begins, accompanied by the formation of ionization space charges.

For gaps in air with a sharply nonuniform field, direct measurements have established [5] that the strength level of the gap is unambiguously related to the magnitude of the excess space charge introduced into the gap by the discharge process, with the minimum of the space charge corresponding to the minimum discharge voltage.

Analogies drawn in the literature between the development of discharge in solid dielectrics and in air [6, 7÷9], in liquid and in air [4, 18, 19], give grounds to suppose that the discharge voltages of solid dielectrics at different rates of voltage rise are likewise determined by different magnitudes of ionization space charges introduced into the gap by the discharge process.

It is interesting to note that the influence of ionization space charges on the electrical strength of solid dielectrics is analogous to the influence of polarization space charges. This is evidenced by the coincidence of the steepness of minimum strength for specimens broken down in weakly and sharply nonuniform fields (Figs. 1, 3, Table 1).

The coincidence of the critical rates of voltage rise for solid dielectrics deserves attention, irrespective of the physicochemical properties of the dielectric, the length of the interelectrode gap, and the shape of the electrodes. This fact can be interpreted on the basis of concepts concerning the kinetics of discharge in long air gaps, using the analogies noted above.

According to [20], the anomalous decrease in the discharge voltages of long air gaps at voltage rise times of \(100÷300\ \mu\mathrm{s}\) is caused by the coincidence of the propagation velocities of the external field in the gap and of the drift of the space charge, which leads to an increase in the resultant field and to a reduction in the strength of the gap. On the other hand, according to [15], the minimum strength of air gaps occurs at one and the same, critical, voltage steepness (about \(7\ \mathrm{kV/\mu s}\)). If it is taken into account that the propagation velocity of the external field in a dielectric is determined by the rate of voltage rise between the electrodes, then the foregoing leads to the following conclusion: the decrease in the strength of gaps of different lengths and with electrodes

of different shape at one and the same critical steepness is due to the constancy of the drift velocity of the space charge in the given medium. Differences in the physicochemical properties of solid dielectrics apparently cannot substantially affect the drift velocity of the space charge, and the decisive factor in this case is the belonging of the dielectric to one of the aggregate states of insulating media.

Table 1

Values of the critical steepness for solid dielectrics

Note: P.—point, S.—sphere, Pl.—plane.

The assumption of an unambiguous relation between the magnitude of the excess space charge and the discharge voltage of a solid dielectric makes it possible to explain the decrease in the average discharge voltages of the specimens investigated in this work in the region of steepnesses below 10 kV/µsec (Figs. 1, 3).

The formation of a space charge is accompanied by the reverse process: its dissipation [21], or diffusion to the periphery of the specimen under the action of high gradients at its boundaries. The intensity of dissipation must increase as the duration of voltage application increases and as the electrical conductivity of the material rises. In the region where the steepness decreases from \(\sim 10^2\ \mathrm{kV/\mu sec}\) to \(10\ \mathrm{kV/\mu sec}\), the processes leading to an increase in space charges most probably predominate. At steepnesses less than \(10\ \mathrm{kV/\mu sec}\), charge leakage begins to manifest itself, leading to a decrease in its magnitude and, consequently, to a decrease in the breakdown voltage.

For single crystals of rock salt, which are characterized by very low electrical conductivity, no decrease in breakdown voltage at steepnesses less than \(10\ \mathrm{kV/\mu sec}\) has been established [21], which confirms the assumption of the significant influence of electrical conductivity on the conditions for the formation of space charges and their role in electrical breakdown.

When considering the causes of the decrease in the breakdown voltage of dielectrics in the region of low steepnesses, one should take into account the thermal effect of conduction currents, the possibility of which—even for a duration of \(10^{-5}\) sec—is indicated by the experiments of Keller [22] and Fermer [23].

Thus, the results presented make more specific the concepts concerning the regularities in the behavior of solid insulation under the action of overvoltages of a great variety of forms; they indicate the need to take into account the features of discharge under pulses of different forms when setting up studies of strength in the region of switching overvoltages.

The establishment, for solid dielectrics, of a critical voltage steepness characterized by an anomalous decrease in breakdown voltage has made possible a systematic approach to determining the forms of overvoltages most dangerous for solid insulation. The most dangerous overvoltages are pulse actions whose steepness lies in the critical region.

For typical forms of switching overvoltages, which can be reduced to aperiodic, pulsating, and oscillatory pulses, expressions have been obtained that relate the front duration \(\tau_\phi\) of an aperiodic pulse and the frequencies of pulsating and oscillatory pulses \(f_{\cos}\) and \(f_{\sin}\) to the magnitude of the impulse voltage and to the critical steepness \(a_{\mathrm{cr}} = 30\ \mathrm{kV/\mu sec}\):

\[ \tau_\phi = \frac{1.06\,U_a}{a_{\mathrm{cr}}}, \tag{1} \]

\[ f_{\cos} = \frac{0.334\,U_a}{a_{\mathrm{cr}}}, \tag{2} \]

\[ f_{\sin} = \frac{0.212\,U_a}{a_{\mathrm{cr}}}. \tag{3} \]

If, in place of \(U_a\), one substitutes the amplitudes of overvoltages with steepness \(a_{\mathrm{cr}}\) that constitute a danger to insulation, it is possible to obtain the values of the dangerous parameters \(\tau_\phi\), \(f_{\cos}\), and \(f_{\sin}\) for solid insulation at different voltage classes.

Table 2 presents the results of calculating the dangerous parameters, carried out for insulation at nominal voltages of \(110 \div 330\ \mathrm{kV}\).

As is evident from Table 2, the calculated values of the frequencies of pulsations and oscillations of dangerous pulses correspond to the average frequencies of real switching overvoltages (kilohertz to tens of kilohertz).

This gives grounds to believe that the anomalous decrease in the impulse electrical strength of solid dielectrics in the region of critical rates of rise must be taken into account when selecting levels of solid insulation operating under the action of overvoltages with a medium oscillation frequency.

Table 2

Parameters of hazardous overvoltages for solid insulation

Conclusions

1. To study the behavior of solid insulation under the action of overvoltages of various forms, investigations of the electrical strength of solid dielectrics on oblique waves over the range of rates of rise of real overvoltages, $10^3 \div 10^{-2}$ kV/μsec, are advisable.

2. The electrical strength of solid dielectrics in typical discharge gaps is characterized by an anomalous decrease in the mean discharge voltages and an increased scatter of the results in the region of a rate of rise of 30 kV/μsec.

3. The effect of the anomalous decrease in the discharge voltages of solid dielectrics in discharge gaps with a sharply nonuniform field is apparently due to the same role of volume ionization charges that the latter play in the breakdown of long gaps in air and liquids.

4. For solid insulation at voltages of 110–330 kV, switching overvoltages with oscillation frequencies of 9–40 kc/s should be regarded as the most hazardous overvoltages.

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