ELECTRICAL BREAKDOWN OF LIQUID DIELECTRICS IN OBLIQUE-ANGLE WAVES

V. Ya. Ushakov

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

For the study of discharge phenomena in liquids, modern electron-optical equipment has for the first time been used—an image-converter camera possessing a high speed of time sweep and multiple light amplification [1]. The simultaneous use of an image-converter camera for obtaining space-time pictures of a discharge in liquids and of a two-beam oscilloscope for recording discharge currents and voltage across the gap made it possible to obtain new data on the development of pulsed discharge in liquids. The high technical capabilities of the image-converter camera made it possible to investigate the development of a discharge in liquids on waves of the standard type (1.5/70 μsec) without artificial retardation of the discharge*) and on oblique-angle waves over a wide range of steepnesses (0.4 kV/μsec–450 kV/μsec). The present article sets forth the results of investigations of the breakdown of liquids on oblique-angle voltage waves (breakdown on an exponentially rising front of the voltage wave) and proposes a computational-experimental method for obtaining volt-second characteristics of certain liquid dielectrics.

In the experiments the following were used: transformer oil with a strength of 45–50 kV in the standard breakdown apparatus, ethyl alcohol (technical grade), and distilled water ($\rho = 3 \cdot 10^5$ ohm cm). Breakdown of the liquids was carried out in a rod–plane electrode system (R–P) at positive ($+$ R–P) and negative ($-$ R $+$ P) pulse polarities. The interelectrode distance was 20–165 mm. The circuit and methodology of the experiments are given in [2].

Development of Discharge Processes in Time

On the basis of the experiments performed, by averaging a large number of image-converter records, diagrams were compiled for pulsed breakdown of transformer oil and ethyl alcohol—characteristic representatives of nonpolar and polar liquids. Figure 1, a presents a diagram of the development of a discharge in oil on a positive oblique-angle wave with a steepness $(A)$ equal to 4 kV/μsec and an interelectrode distance $(S)$ equal to 2 cm.

) The results of these investigations are set forth in the article by I. S. Stekolnikov and V. Ya. Ushakov, “Investigation of Discharge Phenomena in Liquids,” accepted for publication in the Journal of Technical Physics*.

Fig. 1. Diagram of discharge development in transformer oil under positive oblique voltage waves at \(A = 4\ \mathrm{kV/\mu s}\) (a) and \(A = 400\ \mathrm{kV/\mu s}\) (b), with \(S = 2\ \mathrm{cm}\).

1 — glow of the leader channel; 2 — flashes of the leader channel; 3 — final jump; 4 — main channel; 5 — arc.

As the potential of the rod is increased, ionization processes begin near it from a certain instant, suppressed for some time by recombination of electrons with ions and by capture of electrons by molecules of the medium. When the potential of the rod reaches a critical value, ionization begins to prevail over recombination, and an intense ionization process spreads from the rod toward the plane. In the case considered, the progressive development of ionization begins at \(U = 72\) kV. At this point a glow \(1\) appears near the rod, which is drawn out into a leader channel. In the course of development the leader channel glows continuously \(1\), and against the background of this glow bright flashes \(2\) are visible along the entire length of the channel; these correspond to short-time (fractions of a \(\mu\)sec) current pulses. The flashes of the leader channel and the current pulses follow at time intervals of \(\approx 1.5\ \mu\)sec. The velocity of motion of the leader increases smoothly from \((1.5 \div 1.6)\cdot 10^{5}\) cm/sec near the rod to \((4.5 \div 5)\cdot 10^{5}\) cm/sec near the plane, and the intervals between flashes decrease to \(0.6 \div 0.8\ \mu\)sec. When the leader traverses about \(90\)—\(95\%\) of the interelectrode distance, the field between its head and the plane approaches a uniform field, and breakdown of the remaining part of the gap occurs by a jump which, by analogy with a similar phenomenon in a long spark, may be called the “final jump” \(3\). At the instant when the leader closes the gap, its channel flashes brightly \(4\), the voltage across the gap is cut off, and an arc \(5\) is established in the gap. Investigations of the transitional stage of the discharge from leader to arc at an oscillograph sweep speed of \(\approx 6\cdot 10^{6}\) cm/sec did not make it possible to determine the rate of development of this process. This means that its velocity exceeds \((5 \div 10)\times 10^{8}\) cm/sec. It may be assumed that when the leader channel touches the plane, closure of the gap occurs at a velocity close to the velocity of propagation of an electromagnetic wave.

The leader from the negative rod has a greater brightness of glow, is less branched, and the pauses between flashes of the channel amount to \(\approx 1\ \mu\)sec. In other respects the development of the negative discharge is analogous to that described above.

With an increase in the steepness \(A\), the average velocity of motion of the leader increases, and the intervals between flashes of the channel decrease. At \(A = 400\) kV/\(\mu\)sec (Fig. 1, b) they are equal to \(0.05 \div 0.06\ \mu\)sec; for the negative leader at \(A = 400\) kV/\(\mu\)sec they are indistinguishable.

On oscillograms of the discharge in ethyl alcohol at \(A \leq 10 \div 15\) kV/\(\mu\)sec, the discontinuous character of the leader motion attracts attention. Fig. 2, a shows a diagram of the development of the discharge in alcohol in the \(+C\)—\(P\) gap at \(A = 0.4\) kV/\(\mu\)sec and \(S = 5\) cm. At the instant when the voltage across the gap reaches a value of \(\approx 20\) kV, a glow of almost spherical form \(1\) is observed near the rod. Then, after a pause of \(1\ \mu\)sec, the glow appears again in the form of the embryo of a leader channel. The subsequent elongation of the channel occurs by jumps. The leader consists of a channel \(2\) and a head \((1a)\). On fast sweeps it is seen (see the inset in Fig. 2, a) that during the jumps the leader head advances into the depth of the gap over \(0.12 \div 0.13\ \mu\)sec \((t_{1} - t'_{1})\) at a velocity of \(\approx 1\cdot 10^{6}\) cm/sec, while the channel glows during this time. The left boundary of the channel is sharply outlined \(2\) and gradually passes into a diffuse glow \(2a\) of decreasing brightness. During pauses of duration \(0.9\)—\(1.1\ \mu\)sec, no glow is recorded in the gap. As the leader moves toward the plane, the pauses between jumps are shortened to \(0.5\)—\(0.7\ \mu\)sec, and the effective velocity of motion of the head of the leader channel increases from \((6 \div 5)\cdot 10^{4}\) cm/sec to \(1.5\cdot 10^{5}\) cm/sec. The final stage of the discharge is analogous to that described above for transformer oil.

Fig. 2. Schemes of discharge development in ethyl alcohol on positive oblique voltage waves with a slope \(A = 0.4\ \mathrm{kV/\mu s}\) (a) and \(A = 400\ \mathrm{kV/\mu s}\) (b), and \(S = 5\ \mathrm{cm}\).
\(1\)—first visible glow in the gap; \(1a\)—head of the leader channel; \(2\)—leader channel; \(2a\)—diffuse glow of the channel; \(3\)—final jump; \(4\)—main channel; \(5\)—arc.

With an increase of \(A\) to \(\simeq 10\) kV/μsec, the time of motion of the leader head during a push increases, while the duration of the pauses between pushes is correspondingly shortened. At \(A > 10\text{–}15\) kV/μsec the pauses are indistinguishable (Fig. 2, б).

The development of the discharge in alcohol in the \(-C+P\) system and in distilled water in the \(+C-P\) system [2] is in many respects similar to that for alcohol in the \(+C-P\) system. The time sweep of the negative leader in water, even at small \(A\), is a uniformly luminous triangle. The discharge pattern is similar to that shown in Fig. 2, б.

The most interesting results of the experiments performed are the following: a) the leader character of the breakdown of liquids; b) the push-like character of the leader motion in polar liquids at small \(A\), and its change to continuous motion at \(A \geq 10 \div 15\) kV/μsec; c) the dependence of the velocity and character of the discharge processes in liquids on their physicochemical properties.

Calling the cord-like channel developing from the electrode of large curvature the leader, let us note some differences between this process and the leader process in air. As is known [3], in air, ahead of the leader channel, an ionization zone propagates in the form of a leader corona, resembling the primary impulse corona. The leader corona, already at the early stages of discharge development, bridges the greater part of the interelectrode gap.

In liquids, at \(S = 2 \div 16.5\) cm, neither the primary corona nor the leader corona was recorded, although experiments showed that the apparatus used makes it possible to register a corona in air through a discharge chamber made of organic glass and filled with distilled water. It is also difficult to suppose that the glow of the ionization zone in liquids corresponds to the red or infrared region of the spectrum, in which the sensitivity of the image-converter tube is minimal (an EOP with an antimony–cesium photocathode). The data obtained show that ionization in liquid and gaseous media proceeds differently because of substantial differences in the conditions of its development in these media: a) the small mean free path of electrons in liquids \((\lambda_{\text{liq}} \simeq 0.001\,\lambda_{\text{air}})\); b) significant dissociation of liquid molecules, etc. Probably, ionization in liquids occurs only in the immediate vicinity of the head of the leader channel. It should be assumed that in liquids—media denser than air—the ionization zone has a high concentration of charge carriers. This enables it, even at small dimensions, to generate per unit time such a number of charge carriers as maintains the high conductivity of the leader channel.

As already noted above, in polar liquids at \(A \leq 8\text{–}15\) kV/μsec the leader channel advances in a push-like manner. It may be expected that the formation, near the head of the leader channel, of a space charge of the same sign as the sign of the leader lowers the field strength \(E\) at the head of the channel and stops its advance into the gap. The glow of the leader channel in the pauses weakens considerably; however, the conductivity of the channel remains sufficiently high, and the electrode potential is carried to the head of the leader channel. At high field strengths at the boundary of the ionization zone, the ionization front moves toward the plane, which is equivalent to the removal of the space charge from the head of the leader channel. The increase of \(E\) at the head of the channel occurs owing to this removal of charge from the head and its partial neutralization, as well as because of the increase in the electrode potential as the amplitude of the voltage wave rises. At large \(A\), the field strength at the head during the pause is restored more rapidly to the critical value, and for a greater interval of time its magnitude remains sufficient for

maintaining ionization from the head of the leader channel. This explains the shortening of the pauses between leader steps and the increase in the effective velocity of motion of the channel head with increasing \(A\). When the stepwise motion of the leader changes to continuous motion in alcohol for \(+C-P\) and \(-C+P\), and in water for \(+C-P\), the rate of increase of the velocity with increasing steepness slows down.

In oil, where the trajectory of motion of the head of the leader channel is continuous even at small \(A\), no such phenomenon is observed. Although in oil the phenomenology of the discharge differs somewhat from that described for polar liquids, the conversion of the portion of the interelectrode gap covered by ionization into a well-conducting channel is probably carried out in the same way as in polar liquids.

The differences in the phenomenology and in the rate of development of the discharge for positive and negative polarities of the rods, in polar and nonpolar liquids, are due mainly to differences in the conditions for the formation and propagation of space charge in front of the head of the leader channel. Thus, for example, the pronounced polarity effect in water, whose molecules are subject to considerable dissociation, can be explained by the fact that, because of recombination of electrons with \(H^+\) ions, in front of the heads of positive and negative leaders there is concentrated a space charge consisting mainly of \(OH^-\) ions. The space charge increases the field strength at the head of the positive leader and promotes its development. The action of this charge on the negative leader, however, is the opposite. Similar considerations were expressed earlier in [4]. In those liquids in which molecular dissociation is insignificant, the polarity effect is less pronounced.

Earlier investigations of discharge in polar and nonpolar liquids [5] showed that more polar liquids have lower electric strength. Later [6], for direct and alternating voltage at small \(S\) (about \(1\) mm), the dependence of \(E_{\mathrm{br}}\) on \(\varepsilon\) was found for 30 liquids. The dependence has the form

\[ \lg E_{\mathrm{br}}=-k\cdot \varepsilon+c. \tag{1} \]

For pulse voltages we have established the dependence of \(E_{\mathrm{br}}\) and of the mean discharge velocity \((V_{\mathrm{av}})\) on \(\varepsilon\). The velocities of development of the leader process in liquids with larger \(\varepsilon\) are higher, and \(E_{\mathrm{br}}\) is lower. The exception is distilled water in the electrode system \(-C+P\).

At large \(A\), the retarding action of the space charge decreases; therefore the differences in the conditions of its formation and neutralization in different liquids are only weakly reflected in the velocity of leader development. At \(A=400\ \mathrm{kV}/\mu\mathrm{sec}\), the values of \(V_{\mathrm{av}}\) for different liquids are close. The dependences of \(V_{\mathrm{av}}\) and \(E_{\mathrm{br}}\) of liquids on \(\varepsilon\) are most clearly manifested when the discharge develops on the tail of the wave, when its amplitude is close to the 50% discharge value. Figure 3 shows the dependences of \(E_{\mathrm{br}}\) (curve 1) and \(V_{\mathrm{av}}\) (curve 2) on \(\varepsilon\) for five liquids. Breakdown of the liquids was carried out in the electrode system \(+C-P\) at \(S=5\) cm. The voltage wave had the form \(1.5/70\ \mu\mathrm{sec}\). The dependence of \(V_{\mathrm{av}}\) on \(\varepsilon\) may be represented by the equation

\[ \lg V_{\mathrm{av}}=0.151\cdot \varepsilon+5.07. \tag{2} \]

The dependence of \(E_{\mathrm{br}}\) on \(\varepsilon\) in the range of variation of \(\varepsilon\) from 2 to 16 (as was the case in [6]) may be represented by an equation of the type

\[ \lg E_{\mathrm{br}}=-k_{1}\cdot \varepsilon+c_{1}, \tag{3} \]

but the values of the coefficients \(k_{1}\) and \(c_{1}\) differ from \(k\) and \(c\) in (1). Over the whole range of variation of \(\varepsilon\) from 2.3 to 80, the dependence of \(E_{\mathrm{br}}\) on \(\varepsilon\) is equ—

… by equation (3). It is difficult, of course, to imagine that the entire set of factors affecting the development of the discharge process is reducible to the dielectric constant of the medium. Nevertheless, the dependences obtained by us and in [6] cannot be attributed to pure chance. If it is assumed that in an electric field in polar—

Fig. 3. Dependence of the breakdown field strength (1) and of the average discharge-development velocity (2) on the dielectric constant of the medium.

—liquids, bridges of dipoles may form, then, according to quantum-mechanical calculations [7, 8], the conditions for electron motion will be considerably facilitated. In this case the conditions for discharge development are also facilitated.

A definite role in the development of a discharge in liquids (especially in polar ones) may be played by internal microfields [9].

On the calculation of volt-second characteristics

In connection with the development of questions concerning the practical use of the energy of a spark discharge [10] and the coordination of insulation of apparatus for high and ultrahigh voltages [11], the study of the impulse electric strength of liquid dielectrics under the application to them of an exponentially rising voltage (oblique waves) has acquired particular importance. It therefore appears necessary to develop a simplified method for obtaining the volt-second characteristics of liquids, which would reduce the laborious work of experimentally recording volt-second characteristics. The empirical equations of volt-second characteristics [12, 13] and the methods for recalculating volt-second characteristics for one voltage-wave shape into waves of another shape, considered in [3], are applicable only to air insulation.

It is easy to see that, in the breakdown of liquids on oblique waves whose form is described by the equation \(U=A\cdot t\), the discharge voltage can be represented as the sum of two components

\[ U = U_{\text{n.l.}} + \frac{A\cdot S}{v_{\text{av}}}, \tag{4} \]

where \(U_{\text{n.l.}}\) is the voltage at which leader development begins, \(A\) is the wave steepness, \(v_{\text{av}}\) is the average velocity of leader development, and \(S\) is the magnitude of the interelectrode distance. The second term in (4) is the increase in voltage during the time of leader development from the rod to the plane.

Experiments showed that \(V_{\text{av}}\) depends on \(A\) and does not depend on \(S\), which follows directly from the leader mechanism of breakdown of liquids in a nonuniform field.

The beginning of the leader process depends on the field strength at the electrode surface, and should also depend on \(A\) because of the inertia of the ionization processes. If the point of a high-voltage electrode sharpened into a cone is taken as a sphere of radius \(r\), then \(E\) at the surface of such a sphere is determined by the expression [14]

\[ E = 0.9 \cdot \frac{U}{S}\cdot \frac{S+r}{\varepsilon\cdot r}. \]

For \(r \ll S\), \(E \simeq \dfrac{U}{r}\), i.e., with small error it may be assumed that the field strength at the electrode surface does not depend on the interelectrode distance. Obviously, the voltage \(U_{\text{n.l.}}\) also should not depend on \(S\) when \(S \gg r\). The experiments confirmed this supposi-

Table 1

tion. The voltage \(U_{\text{n.l.}}\) was determined from oscillograms and image-converter records when they were recorded synchronously. In addition, the results were checked by comparing current oscillograms with oscillograms-

... of the voltage maximum, since the moment of appearance of the leader is marked on the oscillogram by a current pulse. Describing mathematically the experimentally found dependences \(U_{n.l.}=f(A)\) and \(V_{\mathrm{avg}}=f(A)\) and substituting the expressions obtained into (4), we obtain a formula relating the discharge voltage to the steepness and the magnitude of the interelectrode distance. In general form the formula is written as

\[ U=\alpha(\lg A)^2+\beta\lg A+\gamma+S\cdot\delta\cdot A^{\lambda-z(\lg)^\varphi} \tag{5} \]

The values of the coefficients are given in Table 1.

In Table 1, in the “Notes” column, the limits of variation of \(A\) are indicated for which the coefficients given are applicable. In formula (5), \(A\) is the steepness of the voltage wave (kV), \(S\) is the interelectrode distance (cm), and \(U\) is the discharge voltage (kV). A comparison of the volt-second characteristics calculated by formula (5) with experimental ones obtained by different authors indicates their good agreement at \(S=0.5\text{--}5\) cm. At smaller \(S\), the discrepancies reach substantial values. Probably, at \(S<0.4\div0.5\) cm, \(U_{n.l.}\) depends on \(S\) and becomes noticeably smaller than \(U_{n.l.}\) for larger \(S\).

Conclusions

1. During electrical breakdown of liquids on oblique waves, a leader process develops that differs from the leader process in air.

2. The nature of the discharge process depends on the type of liquid, the polarity, and the steepness of the voltage wave.

3. More polar liquids have lower electric strength; the discharge in them develops at a higher velocity.

4. The role of the physicochemical properties of liquids in the development of the discharge process decreases as the voltage exposure is reduced (the steepness is increased).

5. The experiments carried out made it possible to derive formulas for calculating the volt-second characteristics of transformer oil, ethyl alcohol, and distilled water in the electrode systems \(+C-P\) and \(-C+P\) for \(S=0.5\text{--}5\) cm and \(A=0.4\div600\) kV/microsec.

6. The calculation method can be extended to other liquids, interelectrode distances, and electrode systems after carrying out relatively simple experiments.

References

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