Studies of the Reliability of Polyethylene Insulation under Pulses

V. F. Vazhov, V. S. Dmitrevsky, R. E. Klein, Yu. B. Fortes

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

Polyethylene insulation has a fairly high electric strength, which makes it very promising for the manufacture of a number of electrical-insulation structures.

It has been shown [1, 2, 3] that under prolonged action of electric voltage there is a noticeable decrease in the electric strength of polyethylene. The main cause producing the decrease in the electric strength of polyethylene is said to be ionization in gas inclusions.

Usually the design and manufacture of insulation are carried out in such a way that, at operating voltage, ionization in gas inclusions does not occur. However, during service the insulation may be subjected to overvoltages considerably exceeding the amplitude of operating voltages. Under overvoltages, appreciable wear of electrical insulation may be observed.

The present work deals with questions concerning the behavior of polyethylene insulation under the action of impulse voltage.

The experiments were carried out on cylindrical specimens with a coaxial electrode system. The form of the specimen is shown in Fig. 1. The coaxial

Fig. 1. System for testing specimens.

system with the specimen was placed in transformer oil. Owing to the adopted shape of the specimens, surface flashover along the specimens was not observed; instead, breakdown of the polyethylene occurred. The dimensions of the specimen were as follows: length 30 mm; outside diameter 84 mm; inside diameter 26 mm (Fig. 1).

The voltage was applied to the specimens from an impulse-voltage generator constructed according to the Arkad’ev—Marx multiplication circuit. The main-

A feature of the circuit of the generator used is the charging of the capacitors through an inductance, which ensures a high pulse repetition rate. The maximum generator voltage is 300 kV; the voltage-pulse frequency is up to 30 Hz; the discharge capacitance of the generator is 12,500 pF.

In the experiments a voltage wave was used that was cut off on the pulse front after 0.18 μsec by an air spark gap.

The amplitude of the voltages in the experiments was 232 kV. The waveform of the pulse voltages is shown in the oscillogram (Fig. 2) and is close

Fig. 2. Oscillogram of the voltage applied to the specimen. Frequency of the superposed calibration oscillations: 10 MHz.

in shape to switching overvoltages. The oscillogram was obtained on an OK-19-2M oscilloscope. The frequency of the calibration oscillations was 10 MHz.

The results of the observations were processed using probability theory [4]. The principal characteristic adopted was the intensity of the probability of failure of a specimen, which was calculated from the formula

\[ \lambda(n)=\frac{\Delta m}{\Delta n\,(M-m)}, \tag{1} \]

where \(\Delta m\) is the number of specimens punctured during the application of \(\Delta n\) pulses; \(M\) is the total number of specimens put on test; \(m\) is the number of specimens punctured by the beginning of the period under consideration.

For the calculation, \(\Delta n\) was taken equal to 50 thousand pulses. Fig. 3 shows the dependence of \(\lambda(n)\) on the number of pulses. Three regions are clearly visible on the curve: 1) the burn-in region, \(n \leq 70\) thousand pulses; 2) the region of random failures, \(70\) thousand pulses \(\leq n \leq 450\) thousand pulses; 3) the aging region, \(n \geq 450\) thousand pulses.

In the burn-in region a sharp decrease in the intensity of failures is observed. During this period the main defects present in the insulation after manufacture are revealed.

The second region—the region of random failures—is characterized by the relative constancy of \(\lambda(n)\) and by its small magnitude.

The third region is characterized by an increase in \(\lambda(n)\) and corresponds to a higher intensity of insulation breakdowns.

Before the samples were subjected to breakdown, all of them underwent X-ray defectoscopy. X-ray defectoscopy showed that large pores up to \(17\) mm in size were present in the samples. Breakdown of the insulation occurred mainly at the locations of pore accumulations. However, there were cases in which samples with greater porosity withstood up to

Fig. 3. Dependence of the probability of sample failure on the number of pulses.

2 million pulses. It was observed that breakdown occurs at the pore locations if the pores are situated near the inner electrode, i.e., in the region of higher field strength. The field strength in the pores of the insulation, irrespective of their location, greatly exceeded the breakdown value. Consequently, the conditions for the development of ionization processes in the pores were created during the course of testing. Taking into account that breakdown of polyethylene did not always occur at porous locations, it must be stated that failure of the samples was caused not only by ionization processes in the pores.

It becomes necessary to estimate the confidence interval for a statistical characteristic so that, with a specified confidence probability (reliability), it can be asserted that the true value of the desired characteristic lies within the limits of such an interval. For this it is necessary to determine the total operating time.

\[ T_{\mathrm{н}}=\sum_{i=1}^{N} t_i, \tag{2} \]

where \(T_{\mathrm{н}} = 12092000\) pulses, \(t_i\) is the operating time of the \(i\)-th element.

In the present case the exponential law of reliability is applicable. On the basis of this law, the quantity \(2T_{\mathrm{н}}\lambda(n)\) is distributed according to the \(\chi^2\) law.

If the tests are terminated after the \(m\)-th failure, then with reliability \(\alpha\) it may be asserted that \(2T_{\mathrm{н}}\lambda(n)\) lies within the limits

\[ \chi^2_{\frac{1-\alpha}{2}}(2n) > 2T_{\mathrm{н}}\lambda(n) > \chi^2_{\frac{1+\alpha}{2}}(2n), \tag{3} \]

where \(X^2_{\frac{1-\alpha}{2}}(2n)\) and \(X^2_{\frac{1+\alpha}{2}}(2n)\) are determined according to [4]

\[ \frac{1}{2T_{\mathrm{n}}}X^2_{\frac{1-\alpha}{2}}(2n)>\lambda(n)> \frac{1}{2T_{\mathrm{n}}}X^2_{\frac{1+\alpha}{2}}(2n). \tag{4} \]

With confidence \(\alpha=0.9\),

\[ 2\cdot 10^{-6}>\lambda(n)>5\cdot 10^{-7}. \]

The one-sided interval for finding \(\lambda(n)\) with confidence \(\alpha\) is determined as:

\[ \lambda(n)\leqslant \frac{X^2_{1-\alpha}(2n)}{2T_{\mathrm{n}}}, \tag{5} \]

\[ \lambda(n)\leqslant 1.75\cdot 10^{-6}\ \frac{1}{\text{imp}}. \]

From this it is not difficult to calculate, for the period of random failures, the mathematical expectation of the number of pulses of operation of the specimen,

\[ \bar n\leqslant \frac{1}{\lambda(n)}, \tag{6} \]

\[ \bar n\leqslant 573000\ \text{imp}. \]

If a product of this type has a great length (for example, a cable with polyethylene insulation), then it may be regarded as consisting of a large number of identical elements. Taking the probabilistic characteristics for each element to be unchanged, we find

\[ \lambda(n)_{\mathrm{cab}}\leqslant \frac{L}{e}\lambda(n). \tag{7} \]

For cable insulation of this type, in a calculation per \(1\ \text{km}\) of cable one may obtain for the period of random failures

\[ \lambda(n)_{\mathrm{cab}}\leqslant \frac{10^5}{3}\cdot 1.75\cdot 10^{-6} =0.0583\ \frac{1}{\text{imp}}. \]

On the basis of the work carried out, the following conclusions may be drawn:

1. Under multi-pulse voltage action on polyethylene insulation, three regions of the probability of insulation failure have been revealed.

2. The use of polyethylene insulation is recommended only after conditioning, which in the specimens studied amounted to 70 thousand pulses.

REFERENCES

1. G. P. Delektorskii. On certain regularities of breakdown of polyethylene insulation. Elektrichestvo, No. 11, 1961.

2. J. Mason. Breakdown of dielectrics as a result of internal discharges. The Proc. IEE, Part I, issue 98, p. 44, 1951.

3. S. Whitehead. Breakdown of Solid Dielectrics. Gosenergoizdat, Leningrad, 1957.