ON THE METHOD FOR GENERATING AND RECORDING IMPULSE VOLTAGES CORRESPONDING TO SWITCHING-DURATION OVERVOLTAGES

I. I. Kalyatskii, V. F. Panin

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

Along with the tendency toward a reduction in existing insulation levels, caused by the growing requirements for economy in transmission lines and substations and by the successes achieved in protecting them against lightning overvoltages, interest in internal overvoltages of high-voltage systems has sharply increased, since insulation levels at voltages above 220 kV are determined by switching overvoltages, and the question arises of reducing insulation levels in 110–220 kV networks.

In this connection, it becomes necessary to reproduce switching effects—as at one time the need arose to simulate lightning overvoltages—for the study of high-voltage insulation, the testing of high-voltage apparatus subjected to switching effects, and so forth.

In [1], on the basis of an analysis of studies by various authors, it is shown that the insulation of high-voltage networks and apparatus during switching operations is subjected to the combined action of power-frequency or dc voltage and impulses of damped high-frequency oscillations of a definite form. The oscillation frequencies in switching waves are estimated by domestic and foreign authors [2–6] as lying in the range 0.15–25 kHz; correspondingly, on the average, the rise time of the voltage of the switching wave to its maximum value \((3 \div 3.2\,U_{\phi})\) may be estimated as \(1.5 \cdot 10^{-3} \div 10^{-5}\) sec.

Attempts are known [1, 5] to reproduce switching waves acting on the test object after a preliminary and with subsequent application of power-frequency voltage and dc voltage, i.e., to reproduce effects equivalent to real ones. However, the idea of combined action has not found wide application in the practice of carrying out investigations and tests, and at present single oscillatory [2, 5, 7] or aperiodic impulses with a front duration up to \(10^{-3}\) sec [8 et al.] are mainly used, without preliminary action of other types of voltage.

Oscillatory impulses are obtained by discharging a capacitance through an inductance into another capacitance [1], and also by means of a special device—an internal-overvoltage generator, GVP [5], which is associated with known difficulties: as is seen from [1, 5], obtaining high-voltage oscillatory impulses with frequencies up to 25–0.15 kHz is possib-

but only with the use of powerful high-voltage capacitor banks and reactors; and, in the case of an HVP, a cascade of transformers with a relatively complex synchronization system is required.

These difficulties are largely eliminated by using, for reproducing switching effects, aperiodic pulses with a front duration of \(10^{-3}\) sec and longer, obtained from an ordinary impulse generator with an \(RC\) shaping circuit. Single applications of an aperiodic wave on the front with the indicated duration basically cover the entire range of switching effects and reproduce, with sufficient equivalence, the operating conditions of insulation under switching overvoltages.

It should be noted that in many investigations of the strength of long air gaps, oblique-front voltage waves are used (an aperiodic wave with an elongated front). The results of studies of the strength of air insulation on a wave whose front duration was regulated by changing the parameters of the shaping circuit \(R, C\) [8] were reflected in the IEC recommendations.

In connection with the foregoing, questions of using the existing impulse generators of high-voltage test laboratories to obtain voltage waves reproducing switching effects are of interest. In this case, a considerable increase is expected in the operating time of large impulse generators, which, as for other high-voltage test installations, is very small.

Voltage impulses up to 1500 kV with a front up to 500 μsec were reproduced in the high-voltage laboratory of the Tomsk Polytechnic Institute using a ten-stage suspended-type impulse-voltage generator rated at 3 million volts—GIN-3 [9].

The generator capacitance in the shot \(C_p\) was 7200 pF; the charging resistance of one stage of the GIN, \(R_{\mathrm{st}} = 1.2\) MΩ. The capacitance of the screen mounted at the high-voltage end of the GIN-3 was about 370 pF. The capacitance of the air capacitor \(C_\phi\), whose electrode was a metal plane measuring \(5 \times 5\) m at a distance of 2.5 m from the grounded wall, was 400 pF. The total shaping capacitance, including, in addition to \(C_\phi\), the capacitance of the ohmic voltage divider and connecting buses, was about 500 pF.

The ohmic voltage divider (VD), with resistance \(R_{\mathrm{VD}} = 1250\) kΩ, was made using a polyethylene tube of 54 mm diameter filled with a 70% solution of pure glycerin in distilled water; the electrodes were carbon. According to [10, 11], the base and the high-voltage end of the divider were shielded by metal rings 2 m in diameter, which contributed to some equalization of the capacitive current along its length.

The maximum possible distance of the VD from the GIN-3 is 3 m; the distance of the GIN-3 from the air capacitor is 5.5 m.

Figure 1 (a, b) presents a sketch of the mutual arrangement of the elements and the electrical circuit of the test installation, reduced to a single-stage generator.

Lengthening the impulse front by the usual method—by increasing \(R_\phi\)—gave the results shown in Fig. 2 (a, b, c, d). It is evident from the figure that the waves with an elongated front obtained in this way are unacceptable for insulation tests requiring the use of impulses with a long oblique front, since the smooth exponential rise of the voltage is preceded by a rapid rise of it to a value of 20% or more of the impulse amplitude value—ne-

Fig. 1. Sketch of the relative arrangement of the elements (a) and the electrical circuit of the test setup, reduced to a single-stage impulse-voltage generator (b).

1—assembly of the IVG-3; 2—test object; 3—front resistance—\(R_{\phi}\); 4—front capacitance; 5—voltage divider—DN; 6—oscilloscope in a shielding cabin; 7—measuring sphere gap; \(C_{p}\)—capacitance of the IVG during the impulse; \(S\)—spark gap; \(L_{\Sigma}\)—parasitic inductance of the discharge circuit of the IVG; \(R_{\mathrm{dg}}\)—total damping resistance of the IVG; \(C_{\Gamma}\)—resulting parasitic capacitance of the elements of the IVG discharge circuit to ground; \(R_{0}\)—resulting discharge resistance of the IVG, excluding \(R_{\mathrm{DN}}\); \(C_{\mathrm{p}}\) and \(C'_{\mathrm{p}}\)—parasitic capacitances of the IVG to the divider and to the elements of the shaping circuit; \(C_{\mathrm{D}}\)—capacitance of the voltage divider; \(R_{\mathrm{DN}}\)—resistance of the voltage divider; \(C_{\mathrm{pl}}\)—capacitance of the phenomenon plates.

which is a preliminary potential step. In our case the step was already clearly indicated at \(R_{\phi}=10\) kohm.

Similar results were obtained in [12]. In Fig. 3 (\(a, b\)) are shown a sketch and the electrical circuit of the installation used in the cited work, with designations corresponding to Fig. 1.

Fig. 2. Oscillograms of voltage impulses with an extended front, obtained from the GIN-3 when switching in \(R_{\phi}\) of various magnitudes: \(U_{\text{charge}}=90\) kV, \(R_{\text{dn}}=500\) kohm.

\(a\) — \(R_{\phi}=0;\ C_{\phi}+C_{\text{d}}=500\) pF, \(U_m=900\) kV;
\(b\) — \(R_{\phi}=75\) kohm; \(C_{\phi}+C_{\text{d}}=500\) pF, \(U_m=810\) kV;
\(v\) — \(R_{\phi}=500\) kohm; \(C_{\phi}+C_{\text{d}}=500\) pF, \(U_m=405\) kV;
\(g\) — \(R_{\phi}=\infty:\ C_{\text{d}}=100\) pF, \(U_m=210\) kV.

In Fig. 4 (\(a, b, v, g\)) are presented oscillograms of chopped waves with an extended front, obtained on this installation at various \(R_{\phi}\). On oscillograms \(b, g\) the preliminary step amounts to 54%, while for oscillograms \(a, v\) it is 28% of the impulse amplitude. In [12] the presence of the step is explained by a certain “lifting” of the impulse above the zero line due to interference on the low-voltage electrode of the capacitive divider, with the assumption that the test object is acted upon by a high-voltage impulse with an exponential front, without a step.

Meanwhile, analysis of the actual electrical circuits of both installations, taking into account the parasitic capacitances between the impulse-voltage generator and the shaping-measuring devices, gives grounds to assert that the preliminary step on the front of the impulses considered is also present in the high-voltage wave acting on the object.

Indeed, all elements of the impulse-voltage generator—capacitors, resistances, spheres, etc.—during discharge form a single spiral, each element of which has a certain capacitance. We shall restrict the consideration, as elements of the spiral, to the stages of the impulse-voltage generator and shall denote the capacitance between any stage of the impulse-voltage generator and the voltage divider by \(C_i'\), and the capacitance between a stage of the impulse-voltage generator and the shaping elements by \(C_i\), where \(i=1 \div n\);

Fig. 3. Sketch (a) and electrical circuit of the installation (b) [12].
7a — damping resistance — $R_t$,
7b — discharge resistance — $R_p$.

Fig. 4. Oscillograms of chopped voltage waves with a prolonged front for various values of $R_\phi$ and distances between the impulse-voltage generator and the voltage divider [12].
Calibration frequency $10^5$ Hz (a, b) and $10^6$ Hz (c, d);
a, b — $R_\phi = 8$ kΩ; c, d — $R_\phi = 20$ kΩ;
a, c — 4 m; b, d — 1.8 m.

\(n\) is the number of stages. When the first stage of the impulse-voltage generator operates, a voltage appears on the divider

\[ U_1 = U_0 \frac{c_1 + c'_1}{c_1 + C_{\mathrm{d}} + c'_1 + C_{\mathrm{f}}}, \tag{1} \]

where \(U_0 \simeq U_{\text{charging}} = U\) of the stage and under the condition that, for the buses connecting the divider, the test object, and the shaping elements, it may be assumed that

\[ R_{\mathrm{b}} = 0,\qquad L_{\mathrm{b}} = 0, \tag{2} \]

\[ C_{\mathrm{IO}} \ll C_{\mathrm{d}} \text{ and } C_{\mathrm{f}}, \tag{3} \]

where \(C_{\mathrm{IO}}\) is the capacitance of the test object (IO).

When the \(i\)-th stage operates, the following is added to the potential of the divider, the front capacitance, and the IO:

\[ U_i = U_0 \frac{c_i + c'_i}{c_i + C_{\mathrm{d}} + c'_i + C_{\mathrm{f}}}. \tag{4} \]

After the last stage has operated, there is on the divider, the front capacitance, and the IO a potential equal to the sum of the potentials induced by all stages:

\[ U_{\mathrm{d}} = U_0 \sum_{i=1}^{i=n} \frac{c_i + c'_i}{c_i + C_{\mathrm{d}} + c'_i + C_{\mathrm{f}}}. \tag{5} \]

For the single-stage equivalent circuit of the impulse-voltage generator (Fig. 1, b) we have

\[ \sum_{i=1}^{i=n} (c_i + c'_i) = C_{\mathrm{p}} + C'_{\mathrm{p}} = C_{\mathrm{p0}}, \tag{6} \]

since

\[ c_i + c'_i \simeq c_{i+1} + c'_{i+1}, \tag{7} \]

where \(C_{\mathrm{p}}\) and \(C'_{\mathrm{p}}\) are the stray capacitances of the impulse-voltage generator to the divider and to the elements of the shaping circuit, respectively, reduced to a single-stage circuit.

\(C_{\mathrm{p0}}\) is the total stray capacitance of the impulse-voltage generator to the shaping-measuring device. Then

\[ U_{\mathrm{d}} = U_0 \frac{C_{\mathrm{p0}}}{c_i + C_{\mathrm{d}} + c'_i + C_{\mathrm{f}}}. \tag{8} \]

As is evident, \(U_{\mathrm{d}}\) is greater the larger \(C_{\mathrm{p0}}\) is, i.e., ultimately, the closer the impulse-voltage generator is to the shaping-measuring device. The latter is clearly illustrated by the oscillograms presented in Fig. 4. The share of \(U_{\mathrm{d}}\) in the pulse amplitude increases from 28%, when the divider is moved 4 m away from the impulse-voltage generator, to 54% when it is moved 1.8 m away.

According to (8), \(U_{\mathrm{d}}\) can be negligibly small if

\[ c_i + C_{\mathrm{f}} + c'_i + C_{\mathrm{d}} \gg C_{\mathrm{p0}}, \]

but provided condition (2) is fulfilled.

In [12], \(C_{\mathrm{f}} = 4600\) pF, and \(C_{\mathrm{p0}}\) may be estimated at \(100 \div 200\) pF. However, in the circuit under consideration (Fig. 3, b), a damping resistance \(R_{\mathrm{t}} = 15\) kΩ was inserted between \(C_{\mathrm{f}}\) and \(C_{\mathrm{d}}\), which prevented the establishment on the divider and on the test object of a small potential corresponding to the value of \(C_{\mathrm{f}}\) in expression (8).

Thus, the production of high-voltage waves with a long oblique front in a room of limited dimensions, with a front capacitance comparable to the stray capacitances between the impulse-voltage generator

and by the shaping-measuring devices, is complicated by the fact that, during the operation of the IVG on the object under test, with a rate determined by the parasitic parameters of the IVG \((R_{\mathrm{p}}, L_{\mathrm{p}}, C_{\mathrm{p}})\), a certain potential (8) is established; only after the last stage of the IVG has operated does the voltage on the TO increase at a rate corresponding to the time constant of the shaping circuit \(\tau_{\mathrm{f}} = R_{\mathrm{f}} \cdot C_{\mathrm{f}}\). When \(\tau_{\mathrm{f}} \gg \tau(R_{\mathrm{p}}, L_{\mathrm{p}}, C_{\mathrm{p}})\) and the preliminary potential \(U_{\mathrm{d}}\) is relatively large—15–20% and more—an impermissible distortion of the impulse front occurs.

To eliminate the distortion of the extended front, we undertook experiments on increasing the operating time of the individual stages of the IVG and, consequently, of the entire IVG as a whole; for this purpose the parasitic capacitances of the stages to ground were used. If increased damping resistances are inserted into the stage gaps, then the process of stage operation will be prolonged to a time proportional to the time constant

\[ \tau_i = R_{\mathrm{d}i} \cdot C_{\mathrm{p}i}, \]

where \(C_{\mathrm{p}i}\) is the parasitic capacitance of the \(i\)-th stage.

The IVG operation slowed down in this way will correspond to a preliminary potential \(U_{\mathrm{d}}\) rising to the same extent more slowly on the shaping-measuring devices and on the TO. In Fig. 1b the capacitance \(C_{\mathrm{g}}\) is equivalent to the total parasitic capacitance of the stages, and \(R_{\mathrm{dg}}\) to the sum of the damping resistances of the stages.

When \(\tau_{\mathrm{g}} = R_{\mathrm{dg}} \cdot C_{\mathrm{g}}\), comparable with \(\tau_{\mathrm{f}} = R_{\mathrm{f}} \cdot C_{\mathrm{f}}\), the rate of buildup of \(U_{\mathrm{d}}\) is comparable with the rate of discharge of \(C_{\mathrm{f}}\), which helps eliminate the distortion.

In view of the known difficulties in determining \(C_{\mathrm{p}i}\), adjustment of the IVG to a wave with an oblique front can be carried out by selecting the appropriate \(R_{\mathrm{d}i}\). In doing so it is necessary to take into account that the operating rate of the stages lying closer to the high-voltage end is greater than the operating rate of the more remote stages, owing to the higher voltages on the triggering sphere gaps. Accordingly, larger damping resistances should be inserted in the gaps of the stages near the high-voltage end of the IVG in order to equalize the operating rates of the IVG stages.

Fig. 5. Oscillogram of the front of an oblique-front wave obtained by inserting \(R_{\mathrm{d}i}\) into the stage gaps of the IVG.

In our case (a 10-stage IVG), satisfactory results were obtained by inserting \(R_{\mathrm{d}i}\) in the ratio: \(1:1:2:2:2:2:3:3:3:3\), beginning with the first stage. Figure 5 presents an oscillogram of the front obtained by inserting \(R_{\mathrm{d}i}\) in the indicated ratio \((R_{\mathrm{dg}} = 45\ \text{k}\Omega)\) with \(R_{\mathrm{f}} = 300\ \text{k}\Omega\). As can be seen, distortion of the wave front is practically absent.

It should be noted that, with such “switching” of part of \(R_{\phi}\) into the IVG discharge circuit, the reduction in the utilization factor of the IVG—caused mainly by the limited wave half-period—is comparatively small (Table 1, \(R_{\phi}=0\)).

where \(U_0\) is the charging voltage of the IVG,
\(U_m\) is the impulse amplitude.

Conclusions

1. It is recommended that the unique operating IVGs of high-voltage testing laboratories be used to reproduce switching effects on insulation by means of an aperiodic wave with an oblique front of duration up to \(10^{-3}\) sec and more. This increases the utilization factor of expensive high-voltage equipment.

2. It has been shown that, in order to eliminate distortion of the oblique wave front due to possible strong capacitive couplings between the IVG and the shaping-measuring devices, it is advisable to use damping resistances distributed correspondingly over the stages of the IVG.

Literature

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