APPROXIMATE ESTIMATION OF PARAMETERS OF IMPULSE OVERVOLTAGES MOST DANGEROUS FOR HIGH-VOLTAGE INSULATION¹

I. I. Kalyatskii, V. F. Panin

(Presented by the scientific seminar of the Scientific-Research Institute of High Voltages)

Let us note at once that, in essence, we are dealing with overvoltages of non-lightning origin. Indeed, lightning overvoltages are characterized by steepnesses greater than the critical ones—from hundreds to thousands of kV/µsec.

Critical steepnesses belong to the region of internal, or, more precisely, switching overvoltages, located between lightning overvoltages and power-frequency overvoltages.

Modern means for limiting overvoltages make it possible, with a high probability determined by the reliability requirements of insulation operation, to prevent internal overvoltages above a certain level, according to which high-voltage insulation is coordinated. Table 1 gives the permissible multiples of internal overvoltages for systems of the higher classes [2], where \(K = \dfrac{U_{\text{п}}}{U_{\phi}}\), \(U_{\text{п}}\) is the greatest amplitude of internal overvoltages, and \(U_{\phi}\) is the greatest phase operating voltage. These multiples are established without taking into account the anomalous reduction of the impulse strength of insulating media in the region of critical steepness [3–5]. The indicated reduction in impulse strength must be taken into account, since, in insulation coordination, overvoltages with a multiple lower than the permissible one but with a steepness in the critical region may cause a decrease in the reliability of insulation operation.

Let us make an approximate estimate of the permissible multiples of overvoltages, taking into account the reduction of the impulse strength of insulating media in the region of critical steepness.

1. The levels of air insulation under internal overvoltages with the design multiple \(K\) are established according to the level of insulation strength at a voltage of 50 Hz. The relation between the design multiple of internal (including switching) overvoltages and the parameters of the distribution of breakdown voltages of insulation at 50 Hz \((U_{50}; \sigma_{50})\) may be expressed by the relation

\[ \frac{U_{50}\left(1-\dfrac{3\sigma_{50}}{100}\right)}{K_{\text{з}}} = K \cdot U_{\phi}, \tag{1} \]

where \(K_{\text{s}}\) is the safety factor.

For overvoltages with steepnesses close to the critical one, one may write

\[ \frac{K_{\text{v}}\cdot U_{50}\left[1-\frac{3\sigma_{\text{k}}}{100}\right]}{K_{\text{s}}} =K'\cdot U_{\text{ph}}, \tag{2} \]

where \(K_{\text{v}}\cdot U_{50}\); \(\sigma_{\text{k}}\) are the parameters of the distribution of breakdown voltages in the region of critical steepness,
\(K_{\text{v}}\) is the impulse factor in the region of critical steepness,

Table 1

Calculated multiples of internal overvoltages for high-voltage systems

Table 2

Approximate values of the coefficient \(K_{\text{v}}\) for air insulation of the highest voltage classes

\(K'\) is the permissible multiple of overvoltages with steepness close to \(a_{\text{cr}}\).

From (1) and (2) we obtain

\[ K'=K_{\text{v}}\cdot \frac{100-3\sigma_{\text{k}}}{100-3\sigma_{50}}\cdot K . \tag{3} \]

The values of \(K_{\text{v}}\) (Table 2) for different voltage classes were approximately determined from the data of [6] and [7, 8] (for rod–plane gaps), summarized in [9].

The mean value of the impulse coefficient \(K_{\text{v}}\) for air gaps is about 0.76; according to systematic measurements [10], in the region of critical steepness it is about 8%, while \(\sigma_{50}=2\div 3\%\), according to [6]. Let \(\sigma_{50}=3\%\). Then

\[ K'\simeq 0.635K . \tag{4} \]

Thus, for air (external) insulation, overvoltages with a steepness close to the critical one and with a multiple \(K_{\text{op}}\) in the interval \(0.635K\div K\) may be dangerous, i.e., the dangerous multiples are

\[ K_{\text{op}}=(0.817\pm 0.182)K . \tag{5} \]

According to (5), the amplitudes of dangerous overvoltages are determined as

\[ U_{\text{op}}=(0.817\pm 0.182)\cdot K\cdot U_{\text{ph}},\ \text{kV}. \tag{6} \]

For 220-kV systems, for example,

\[ U_{\text{op}}=(0.817\pm 0.182)\cdot 3\cdot \frac{220\cdot \sqrt{2}}{\sqrt{3}}\cdot 1.15\ (\text{kV}) =505\pm 112\ (\text{kV}). \]

II. Estimation of the permissible multiples \(K'\) of overvoltages with critical steepness for solid insulation was carried out on the basis of the following propositions.

a) the estimate of the reduction in strength in the region of \(\alpha_{\mathrm{cr}}\) was made relative to the strength level at steepnesses of the impulse voltage corresponding to the limit of the maximum durations of switching overvoltages \((10^{-1} \div 10^{-2}\ \mathrm{kV}/\mu\mathrm{s})\);

b) since samples made of model materials were used in the measurements, which, owing to inhomogeneities, produce an increased scatter of discharge voltages, a transition was made from the value of the standard deviation obtained in experiments with model dielectrics to the value of the standard deviation characteristic of solid insulation used in actual high-voltage structures.

It is known that the standard deviation of discharge voltages for commonly used solid insulation (for example, compounds based on epoxy resins) lies within the range \(4 \div 10\%\). Assuming that the increased degree of inhomogeneity of the samples used led to approximately a twofold increase in scatter, it was taken that the standard deviation for real solid insulation in the region of critical steepness is about \(16\%\) instead of \(30—32\%\), according to [5].

The value \(K'\), found with allowance for the indicated assumptions, is \(0.75K\).

The multiplicity of dangerous overvoltages is

\[ K_{\mathrm{op}} = (0.875 \pm 0.125)\,K \tag{7} \]

and

\[ U_{\mathrm{op}} = (0.875 \pm 0.125)\,K \cdot U_{\mathrm{f}},\ \mathrm{kV}. \tag{8} \]

III. The permissible multiplicity of overvoltages with critical steepness for liquid insulation was determined by a rough estimate from the data of [3] and is about \(0.8K\).

Accordingly, we have

\[ U_{\mathrm{op}} = (0.9 \pm 0.1)\,K \cdot U_{\mathrm{f}},\ \mathrm{kV}. \tag{9} \]

Table 3 gives the values of dangerous overvoltage levels for insulating structures of the higher voltage classes in various insulating media.

Table 3

Approximate values of dangerous levels of internal overvoltages for structures of higher voltage classes in various insulating media

According to the data of Table 3, using the relations obtained in [1], the front durations and oscillation (pulsation) frequencies of overvoltages with critical steepnesses have been determined (Table 4).

As follows from Table 4, the intervals of dangerous front durations for air, solid, and liquid insulation lie within the ranges \(38.3 \div 182\ \mu\mathrm{s}\), \(9 \div 43.2\ \mu\mathrm{s}\), and \(1.8 \div 8.4\ \mu\mathrm{s}\), respectively. Accordingly, dangerous

Table 4

Parameters of overvoltages with dangerous and critical steepness

frequencies lie within the limits \(9.25 \div 1.24\) kHz, \(39 \div 5.2\) kHz, and \(198 \div 26.5\) kHz.

The established frequencies fall within the range of possible frequencies of oscillations of switching overvoltages and, consequently, there is reason to believe that high-voltage insulation has reduced operational reliability in the region of high and medium overvoltage frequencies.

Table 4 gives the values of \(\tau_{\phi}\) and \(f\) at which the lowest breakdown gradients are expected. Reduced breakdown gradients should also be expected at other steepnesses close to the critical one. For air insulation, the dangerous steepnesses are determined by the interval \(\sim 20—1\) kV/μsec, which for insulation of the 220 kV class, for example, corresponds to an interval of dangerous front durations of \(\sim 13—260\) μsec and an interval of dangerous frequencies of \(\sim 14—0.4\) kHz.

A similar estimate of the intervals of dangerous parameters can also be made for solid and liquid insulation.

LITERATURE

1. I. I. Kalyatskii, V. F. Panin. On a method for determining the parameters of impulse overvoltages most dangerous for insulation (present collection).

2. A. A. Akopyan, A. V. Panov, V. V. Shmanovich, A. I. Yaroshenko. VEP, No. 2, 1962.

3. V. F. Panin. Izv. TPI, vol. 139, 1965.

4. A. A. Vorob’ev, I. I. Kalyatskii, V. F. Panin. Izv. TPI, vol. 152, 1960.

5. V. F. Panin. Izv. TPI, vol. 159 (in press).

6. G. N. Aleksandrov, V. E. Kizevetter, V. M. Rusakova, A. N. Tushnov. Elektrichestvo, No. 5, 1962.

7. I. S. Stekol’nikov, E. N. Brago, E. M. Bazelyan. ZhTF, 32, issue 8, 1962.

8. H. Takeshita, Y. Miyake, T. Oikawa, Y. Kamata. Hitachi Rev., 11, No. 5, 1962.

9. Edited by V. S. Komel’kov. Discharge Voltages of Long Air Gaps and Insulators, 1961—1963. Academy of Sciences of the USSR, INI, Moscow, 1964.

10. E. M. Bazelyan. Dissertation, Moscow, 1964.

1. See [1]. ↩