ON THE BREAKDOWN OF TRANSFORMER OIL UNDER AN OBLIQUE VOLTAGE WAVE

V. F. Panin

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

Studies of the electric strength of insulation under switching overvoltages began in the 1930s–1940s [1, 2]. However, the study of electric strength under actions of a switching character remains topical, since with the transition to extra-high-voltage systems the insulation levels are determined by internal overvoltages.

Works [2–8] are devoted to the study of the electric strength of transformer oil—the most widespread insulation of high-voltage apparatus—under waves of switching duration. These works cover the principal durations of switching actions, \(10^{-5} \div 10^{-3}\) sec, and clarify certain questions concerning the behavior of transformer insulation under long impulse actions. For example, according to [3], the strength in the region of \(10^{-3}\) sec is 40% higher than at industrial frequency. In view of the small volume of investigations and the different methodological approaches to them by various authors, by the present time the relations of strength under lightning and switching actions in large gaps on waves of different polarity have still not been sufficiently studied. The dependences of volt-second characteristics on the shape of the applied voltage have not been studied. There are no systematic data on determining the magnitudes of the standard deviation of discharge voltages.

In studying the questions indicated above, there are grounds to consider the rate of rise of the voltage across the gap, or the steepness of the impulse front, together with the duration of the voltage action, as one of the most important factors determining its electric strength.

On the basis of the foregoing, investigations of the electric strength of large gaps in transformer oil as a function of impulse steepness are of interest. As the gap under investigation it is appropriate to use the “point–plane” electrode system, as one of the most characteristic.

Apparatus and experimental procedure

Figure 1 presents the schematic diagram of the experiment. The voltage source was an impulse-voltage generator for

3000 kV with discharge capacitance \(C_p = 7200\) pF, GIN-3000. In the first stage of the investigations, adjustment of the impulse-front duration was carried out within the range \(5 \cdot 10^{-7} \div 4 \cdot 10^{-4}\) sec by changing the value of the front resistance \(R_f\) and the resistance \(R_d\) introduced into the gaps of each of the 10 stages of GIN-3000, at a constant shaping capacitance \(C_f = 500\) pF. Measurements were made with a 1 m diameter sphere gap, using OK-19M2 and DESO-1 oscillographs and capacitive

Fig. 1. Schematic electrical circuit used in the experiments. \(R_d\)—damping resistance of GIN-3000; \(C_p\)—discharge capacitance of GIN-3000; \(R_f\)—front resistance; \(C_f\)—shaping capacitance; IO—test object; DN1—capacitive voltage divider; DN2—ohmic voltage divider.

and ohmic voltage dividers. The oil under study had a strength in a standard breakdown cell of 36–40 kV. Breakdown occurred on the front of an oblique impulse at 75–85% of its amplitude, in the time range \(4 \cdot 10^{-7} \div 3 \cdot 10^{-4}\) sec. According to Tepler’s recommendations [9], the pause between two successive discharges was about 2 min.

In repeated experiments, changes were adopted that made it possible to use one divider—a capacitive one; to produce breakdown at 50–60% of the impulse-amplitude value; and to exclude discharges outside the region of the gap under investigation. For the latter purpose, an oil-filled bushing for an impulse voltage of 1 million volts was designed and manufactured.

In the experimental results, the mean breakdown voltages and prebreakdown times from 20–30 measurements were used.

The standard deviation \(\sigma\), the limits of probable scatter \(F\), and the error in determining the mean values of the breakdown voltages \(\delta_i\) were determined by the method given in [10, 11].

Experimental results

Figure 2 presents the volt-second characteristics (Fig. 2,a), the dependences of the mean breakdown voltages \(U_p\) (Fig. 2,b) and the standard deviation \(\sigma\) (Fig. 2,c) on the steepness of the impulse front \(A\) for gaps of 5, 15, and 25 cm with positive polarity of the point. For the time range studied, each volt-second characteristic has three regions of variation of the breakdown voltages. The data

Fig. 2. Volt-second characteristics (a), dependences of the mean discharge voltages \(U_p\) on the steepness \(A\) of the impulse front (b), and the dependence of the standard deviation of the discharge voltages \(\sigma\) on the steepness \(A\) of the impulse front (c) for a “point–plane” gap in transformer oil. Points of positive polarity.

\(1, 2, 3\)—dependences for \(S = 5, 15, 25\ \mathrm{cm}\), respectively; \(4, 5, 6\)—discharge voltages at 50 Hz for \(S = 5, 15, 25\ \mathrm{cm}\).

for these regions are shown in Table 1, where \(S\) is the length of the gaps, \(t\) is the time limits for the regions of each gap, and \(K_i\) is the impulse coefficient for the regions of variation of \(U_p\). As is seen from Table 1 and Fig. 2a, for the second region, as the duration of the applied voltage increases, a substantial strengthening of the gap takes place: the impulse coefficient \(K_i\) increases from \(2 \div 3\) to \(3 \div 4\).

When considering the dependences of the mean breakdown voltages \(U_p\) on the steepnesses \(A\), shown in Fig. 2b, it is found that the steepnesses corresponding to a change in the character of the dependence \(U_p=f(A)\) are the same for all the investigated gaps. The region of minimum electric strength corresponds to a front steepness \(A=100\) kV/µsec; the region of maximum strength, to a steepness \(A=15\) kV/µsec.

For the dependence of the standard deviation \(\sigma\) on the steepness \(A\), a maximum at \(\sigma=13\text{–}20\%\) is characteristic (Fig. 2c); this value of the standard deviation corresponds to the greatest value of the limits of probable scatter \(F\), up to 80%, and to the maximum error in determining the mean breakdown voltages \(\delta_i\) (16%).

Figure 3 presents the results of an investigation of the strength of 15- and 13-cm gaps for both polarities of the point, for steepnesses \(A=0.685 \div 2200\) kV/µsec. For positive polarity the same results were obtained as in Fig. 2: the minimum strength of the gaps occurs at a steepness \(A=200\) kV/µsec; the maximum strength, at a front steepness \(A=30\) kV/µsec (Fig. 3b). The shift of the dependence \(U_p=f(A)\) toward greater steepnesses and breakdown voltages is evidently due to the breakdown of the 15- and 13-cm gaps in another region of the impulse front than the breakdown of 5–25-cm gaps.

The course of the dependence of the standard deviation \(\sigma\) on the steepness \(A\) (Fig. 3b) is analogous to the dependence \(\sigma=f(A)\) shown in Fig. 2b. The maximum \(\sigma\) (up to 10%) occurs at steepnesses \(A=60 \div 100\) kV/µsec.

For the dependence of the breakdown voltages \(U_p\) on the time \(t\) and steepness \(A\) of the applied voltage (Fig. 3a, b), with negative polarity of the point, a continuous decrease of \(U_p\) with decreasing \(A\) or increasing \(t\) is characteristic. For all the measurement and processing results, the standard deviation \(\sigma\) did not exceed 8.6%.

As is seen from Fig. 2b, for steepnesses \(A=1000 \div 150\) kV/µsec the strength with a positive point is less than the strength with a negative point by 10–15%. In the region of steepnesses \(A=100 \div 10\) kV/µsec, however, the strength with a positive point exceeds the strength with a negative point by 50–80%. At \(A<10\) kV/µsec there is a slight (up to 10%) excess of strength for negative polarity.

Discussion of Results

The different character of the volt-second characteristics for waves of the standard type and waves with an exponential front, established in [3] (Fig. 3a, curves 1, 5, 6) for negative polarity, is confirmed. According to [3], the strength of transformer oil in the time range \(10^{-4} \div 10^{-3}\) sec exceeds the strength at industrial frequency by 40–50%.

With respect to the volt-second characteristics for positive polarity of the point, the results of the present work did not confirm the data of [3]: in [3] no noticeable difference was found in the volt-second characteristics for positive and negative points.

With respect to the ratio of strengths under lightning and switching influences, the results of the work cannot be compared with the data of (4–6), since in the latter the strength under lightning influences was determined by a 50% breakdown on a \(1/50\)-µsec wave.

Fig. 3. Volt-second characteristics (a), dependences \(U = f(A)\) (b), dependences \(\delta = f(A)\) (c) for a “point—plane” gap in transformer oil. 1, 3 and 2, 4—dependences for the point of negative and positive polarities, respectively. 1, 2 and 3, 4—for \(S = 15\) cm and 13 cm, respectively. 5, 6—volt-second characteristics of a 76 mm rod gap in transformer oil for a wave with a long exponential front and \(1/50\ \mu\)sec, of negative polarity according to [3]. 7—discharge voltage of a 15 cm “point—plane” gap in transformer oil at 50 Hz. \(K\)—impulse coefficient, only for curves 1, 5, 6.

The polarity effect established in [4–6] for the steepnesses of the voltages used, \(A = 0.1 \div 3\) kV/μsec and about 300 kV/μsec, is in agreement with the results of the present work.

The possibility that the strength of a gap in transformer oil is exceeded for positive polarity of the point is seen in the results of [7]. Tetschner [7] established that for gaps in transformer oil, under pulsating impulse voltages with a front steepness of about \(30 \div 40\) kV/μsec, the time of discharge formation from a positive point is significantly greater than from a negative one. It follows from this that, when two waves of the same steepness but of different polarity are applied to the gap, the breakdown voltage for the positive wave will be higher.

In the available works [3–8], no systematic analysis is given of the standard deviation \(\sigma\) as a function of the voltage steepness \(A\); however, the average limits of \(\sigma\) in the cited works are determined as \(4\)—\(12\%\), which corresponds to the data of the present work.

Use of the adopted method in the breakdown of large gaps in transformer oil made it possible to establish the following characteristic dependences:

a) the presence of strengthening of interelectrode gaps in transformer oil at impulse steepnesses of \(10 \div 100\) kV/μsec for positive polarity of the point;

b) the presence of a maximum scatter of breakdown voltages for steepnesses of \(40 \div 80\) kV/μsec with a positive point;

c) a continuous decrease in strength with decreasing voltage steepness for a negative point.

The data obtained can be explained on the basis of ideas about the stage of discharge formation as a leader process, developed for large air gaps [12, 13] and for transformer oil [14, 15]. According to [12], the right branch of the U-shaped volt-second characteristic of a long air gap is due to an excessive space charge introduced into the gap by the impulse corona and by the leader corona, and reducing the gradients in the near-electrode region. The region of the minimum of the volt-second characteristic is explained by the relatively small magnitude of the space charge introduced into the gap at large voltage steepnesses and, consequently, by less shielding of the electrodes.

In transformer oil, ionization events similar to the primary corona and the leader corona in large air gaps have not been recorded [14]; however, this does not exclude the possibility of the discharge-formation process proceeding by similar ionization events, much more localized because of the greater density of the liquid.

With such a consideration of predischarge processes in transformer oil, the right branch of the dependence \(U_p = f(A)\) can be explained by the inertia of the development of the first ionization event (of the type of the primary corona in air) and of the leader.

The left branch of the dependence of breakdown voltages on steepness is apparently caused by the introduction into the near-electrode zone of the gap of an increasingly larger space charge.

A larger charge more effectively counteracts the advance of the leader channel toward the opposite electrode. Possible fluctuations in the magnitude of the space charge probably have a maximum at steepnesses \(A \div 40 \div 80\) kV/μsec, which may account for the great instability of breakdown voltages at these steepnesses.

The repeated decrease of breakdown voltages for steepnesses \(A = 20 \div 30\) kV/μsec (by a factor of \(3 \div 5\) when the rate of voltage rise is several-

…kilovolts per second) may be regarded as a consequence of secondary processes, for example, the formation of bridges from inclusions that are constantly present in liquids of technical purity.

An explanation of the monotonic decrease of breakdown voltages with decreasing steepness for negative point polarity is possible by using the indications available in the literature [16] concerning the different mode of advance of the discharge channel for different point polarities.

Conclusions

It has been established that the impulse strength of gaps of length 5–25 cm with “point–plane” electrodes in transformer oil under the action of an oblique voltage wave is characterized by the following:

1. The presence of a minimum in the breakdown voltages for steepnesses of about 100 kV/μsec and an increase in the mean breakdown voltages in the region of steepness 100–10 kV/μsec (up to 30–50%) for positive point polarity.

2. A continuous decrease in the strength of the gaps with decreasing impulse steepness from 2200 kV/μsec to 0.685 kV/μsec for negative point polarity.

3. A 50–80% excess of the breakdown voltages of the gaps with a positive point over the breakdown voltages of gaps with a negative point for steepnesses of 100–10 kV/μsec.

4. A 2–3-fold excess of the strength in the region of lightning effects (\(10^{-6}\) sec) over the strength in the region of switching overvoltages (\(10^{-4}\) sec).

5. A high instability of the breakdown voltages for steepnesses of 40–80 kV/μsec (scatter up to 40–80%).

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