OSCILLOGRAPHIC STUDY OF THE POTENTIAL DISTRIBUTION ALONG THE ROTOR IN AN ESG

A. M. Kuptsov, V. V. Patsevich

(Presented by the scientific seminar of the Department of TOE and the RESG Department of the YaF Research Institute)

One of the basic conditions for obtaining maximum useful power in electrostatic generators (ESG) is the creation of a uniform electric field in the working volume. In the general case, the character of the field can be judged from the distribution of potentials along the rotor. The most favorable, from this point of view, is, naturally, a uniform distribution.

To equalize the potentials along the rotor in industrial ESGs, a linear distribution of potentials is created along the stator [1], using weakly conducting coatings, which was first proposed as early as the 1930s by Academician A. F. Ioffe. Glass is most often used for these purposes.

It should be noted that proper attention has not been given to consideration of the question of the distribution of potentials along the rotor, which makes it possible to obtain rather extensive information about the character of the electric field in the working volume. The results presented in [3] for calculating the distribution of potentials along the rotor through partial capacitances on the basis of the electrostatic-analogy method were obtained with a number of assumptions and are not analyzed in this work.

The purpose of the present work is, on the basis of experimental results obtained on a pilot model of an ESG, to study the character of the distribution of potentials along the rotor and to establish the connection of this distribution with other physical processes.

Method of Investigation

The method of investigation, first described in [4], was based on measuring the potential of one of the rotor carriers during operation of the generator by means of a specially made capacitive divider. As it rotates, over one full revolution of the rotor the carrier successively occupies the position of all carriers, changing its potential from the value corresponding to the voltage of the excitation brush to the load voltage and back. Thus, the law of variation of the potential of any one of the carriers over one revolution of the rotor gives a complete picture of the distribution of the potentials of the carriers during operation of the generator in any mode. To record the law of potential distribution along the rotor, an electronic oscilloscope 2KO/721 was used, whose vertical deflection plates, together with the parasitic capacitances of the shunting resistance and the lead wire, formed the capacitance of the low-voltage arm of the divider.

A special air capacitor served as the high-voltage arms of the divider; its rotating plate was located directly on the insulating shaft of the rotor in such a way that the capacitance of the capacitor, whose second stationary plate was mounted on the stator, remained constant during rotation of the rotor.

The carrier was connected to the rotating plate of the capacitor by a conductor laid in the dielectric of the rotor. To change the division factor of the capacitive divider, the capacitance of the air capacitor could be varied by changing the distance between the plates. The divider was calibrated using the voltage of an external high-voltage source with a voltage frequency of 50 Hz, close to the frequency of the signal being measured. At the same time it was established that the measuring circuit does not introduce any significant distortions of the calibration signal.

The investigations were carried out on an operating ESG model in an air atmosphere. The generator rotor was a disk based on a cold-curing epoxy-resin compound, with U-shaped carrier conductors. The outer diameter of the rotor was 494 mm. The number of carriers was 474. The rotor speed was 1000 rpm.

Distribution of Carrier Potentials with a Metallic Stator

Experiments with a conducting stator were carried out primarily in order to refine the technique on an operating generator model, since in this case the law of distribution of carrier potentials can be calculated, for example, by the method set forth in [3], and can also be obtained from the results of a qualitative consideration of the field pattern in the working volume. In addition, these experiments are of independent interest in the study of the phenomenon of natural recharging, whose results are considered separately.

Refinement of the technique was performed at low excitation voltages, at which noticeable leakage of charges from the carriers during current measurements was absent.

The oscillogram of the distribution of carrier potentials for the induction excitation circuit with brushes touching only one carrier (narrow brushes) has the form shown in Fig. 1a.

Here the carrier, at the moment of connection with the excitation brush, has a potential equal in magnitude to the excitation voltage. When disconnected from the excitation brush, its potential rises sharply, remaining practically constant in the interval between the inductors. When approaching the discharge brush, the carrier potential decreases, taking a value equal to zero upon connection with the brush. After disconnection from the charging brush, the carrier potential becomes negative.

If, during generator operation, brushes are used that cover at least five carriers (wide brushes), the potential of a carrier moving toward the discharge system practically does not exceed the value \(U_{\mathrm{v}}\), and during reverse motion (toward the excitation system) its potential is approximately equal to zero.

Comparison of the experimental curve of the potential distribution with the distribution law obtained by calculation according to the relations derived in [3] gives fairly good agreement.

Figure 1. Oscillograms of the potential distribution at \(U_{\mathrm{v}} < U_{\mathrm{k}}\)

Potential Distribution of Carriers

under Forced Assignment of Potentials on the Stator

A stator with forced potential distribution can be made in two forms: in the form of metallic plates—sectors connected to an active divider, and in the form of weakly conducting surfaces. In the first case, with careful construction of the divider, it is simplest to obtain a controlled potential distribution along the stator. Therefore, the potential distribution of the carriers was first considered for a stator made of metallic sectors connected to an active divider, and then for a glass stator. Moreover, if the value of the excitation voltage corresponding to the bend point of the characteristics \(I_{\mathrm{kz}} = f(U_{\mathrm{v}})\) is denoted by \(2U_{\mathrm{k}}\), then oscillograms of the potential distribution at \(U_{\mathrm{v}} < U_{\mathrm{k}}\) and \(U_{\mathrm{v}} > U_{\mathrm{k}}\) have a somewhat different character.

a) The excitation voltage is less than the critical voltage.

In appearance, the oscillograms of the potential distribution practically do not differ from the oscillograms with a conducting stator when the generator operates with wide brushes under identical conditions with a conduction excitation circuit. If the excitation circuit is changed to an induction one, then the potential of the carrier connected to the excitation brush is equal to 0 and, upon further displacement toward the discharge system, increases linearly to \(U_{\mathrm{v}}\). When connected to the discharge brush, the carrier potential falls to 0, and upon displacement toward the excitation system it changes linearly, analogously to the change in the stator potentials.

When the generator operates with a glass stator in the steady state (7–10 minutes after a change in the operating mode or in \(U_{\mathrm{v}}\)) with a conduction excitation circuit, the law of distribution of the carrier potentials becomes the same as when operating with conducting or sector stators. Oscillograms with an induction excitation circuit are analogous in appearance to those shown in Fig. 1, б. It should be noted that in the potential-distribution curve for sector and weakly conducting stators there are small pulsations, the number of which is equal to the total number of carriers. For a sector stator the pulsations are somewhat larger because of the discrete structure of the stator itself and are proportional to the number of stator elements.

Fig. 2. Oscillograms of the potential distribution for \(U_{\mathrm{v}} > U_{\mathrm{k}}\)

b) The excitation voltage is greater than the critical value. An oscillogram of the potential distribution with a sector stator (conduction excitation circuit) with wide brushes is shown in Fig. 2a. In contrast to the oscillograms for \(U_{\mathrm{v}} < U_{\mathrm{k}}\), here, after the carrier leaves the excitation system, the carrier potential decreases somewhat, rising again as it approaches the discharge system. However, as the carrier approaches the discharge brush, its potential is lower than \(U_{\mathrm{v}}\).

An oscillogram of the distribution with an induction excitation circuit is shown in Fig. 2b. If the excitation source is now short-circuited, the potentials of the carriers do not assume a zero value, as was the case at low \(U_{\mathrm{v}}\). The oscillogram of the potential distribution in this case is similar to that shown in Fig. 2c. The polarity of the carrier potentials with short-circuited \(U_{\mathrm{v}}\) is always opposite in sign to the carrier potentials in the preceding operating mode.

When the sector stator is replaced by glass, the law of potential distribution along the rotor is somewhat more complex, but the principal regularities of the change in steady-state operation are analogous to those described for the sector stator.

Potential Distribution Along the Rotor with a Dielectric Stator

The potential distribution of carriers in a generator with a stator made of organic glass, and also during operation of the generator with the inductors alone, was considered. The law of potential distribution with an organic-glass stator is random in character, changes when the stator is touched by grounded objects, and also changes with time; it is predominantly sharply nonuniform.

The nonuniformity of the potential distribution is greater the higher the applied excitation voltage. This is characteristic of both conduction and induction excitation circuits. During operation of the generator with the inductors alone, an oscillogram of the potential distribution of the carriers (wide brushes, conduction excitation circuit) is presented in Fig. 2г at an excitation voltage somewhat greater than \(U_k\).

The potential of a carrier connected to the excitation brush is equal to the potential of that brush. When moving toward the discharge system, its potential rises sharply, considerably exceeding \(U_v\), and has a maximum in the gap between the inductors. In the discharge system, the carrier immediately before commutation has a potential close in magnitude to \(U_v\).

When moving toward the excitation system, the potential of the carriers is zero for \(U_v<U_k\), while for \(U_v>U_k\) it is nonzero and is greater (in absolute value) the larger \(U_v\) is.

Discussion of the Results

The experimental data obtained on the potential distribution of the carriers along the rotor for \(U_v<U_k\) agree fairly well with the qualitative consideration of the character of the potential distribution on the basis of the electrostatic-analogy method.

Consideration of the character of the potential distribution of the carriers for \(U_v<U_k\) and \(U_v>U_k\) shows that these regimes must differ substantially in the physical processes accompanying operation of the generator, despite the fact that up to \(U<2U_k\) the linearity of the short-circuit characteristic is preserved. By an approximate estimate, the magnitude of the average value of the normal component of the electric-field intensity in the rotor–stator gap (with metallic, sector, and weakly conducting stators) for \(U_v\approx U_k\) is found to be \(E_{\text{n. av.}}=18\div20\ \text{kV/cm}\).

Taking into account that the maximum value of the electric-field intensity in the gap will be greater than the average, it is natural to suppose that for \(U_v>U_k\) critical gradients arise in the gap, causing increased ionization of the gas.

The presence of a sufficiently large number of ions in the gap leads to the latter, under the action of the electric field, being deposited on the surface of the rotor dielectric and on the stator. In this case, a current from the excitation source through the stator divider will be superimposed by the current due to the deposited ions. The magnitude and direction of the current from the deposited ions can be judged from the law of potential distribution of the stator sectors for the conduction excitation circuit, when both the high-voltage inductor and the excitation inductor are grounded.

At an excitation voltage of \(6\ \text{kV}\) (wide brushes), the potential of the sectors located midway between the inductors is \(2.5\ \text{kV}\) for the rising branch and \(1.2\ \text{kV}\) for the falling branch. During operation without a stator

with single inductors, the critical gradients appear at lower excitation voltages because of the strong nonuniformity of the electric field in the zone where the carriers leave the region of the inductors (Fig. 2d). Confirmation of the presence of charges on the dielectric surface of the rotor at \(U_{\mathrm{в}} > U_{\mathrm{к}}\) is the appearance of a potential on the carriers during reverse travel, as well as the presence of a potential on the carriers when the excitation source is short-circuited, if before the short circuit \(U_{\mathrm{в}} > U_{\mathrm{к}}\).

The qualitative agreement of the oscillograms of the potential distribution of the carriers with a sector stator and with glass in the established regime indicates that gas ionization in the gap also occurs here. The nonlinearity of the potential distribution is caused by the nonlinear distribution of the potential over the stator due to the current produced by the ions deposited on the glass. An essential fact confirming the presence of charge on the surface of the rotor dielectric is also that, at an excitation voltage \(U_{\mathrm{в}} > 2U_{\mathrm{к}}\), in the rotor–stator gap, in the region of both the high-voltage inductor and the excitation inductor, an intense corona is visible in the dark, spreading over the entire gap as the excitation voltage is further increased.

Potential distribution and natural recharging

According to the explanation of the phenomenon of natural recharging given in [5], this phenomenon occurs with narrow brushes and consists in a certain increase in the generator current due to the influence of neighboring charged carriers. The phenomenon of natural recharging should be absent with wide brushes that simultaneously cover several carriers. With a metallic stator, replacing wide brushes by narrow ones leads, other conditions being equal, to an increase in the potentials of the carriers during their forward travel and to the appearance of a potential of the opposite sign on the carriers during their reverse travel (Fig. 1a).

Fig. 3. Oscillograms of the potential distribution in the absence (a) and presence (b) of natural recharging.

In Fig. 3a are shown oscillograms of the distribution of the potentials of the carriers with a metallic stator, when two wide discharge brushes were installed behind the charging brush, with \(U_{\mathrm{v}} < U_{\mathrm{k}}\). If, all other conditions being equal, the first discharge brush is replaced by a narrow one, the oscillogram assumes the form shown in Fig. 3b. Here the potential of the carrier, after it is disconnected from the first discharge brush, changes its sign to the opposite of that which it had before connection to the brush. The change in sign of the carrier potential is clear evidence of the phenomenon of natural recharging. It may be noted that replacing wide brushes by narrow ones in all other experiments gives the same effect, i.e., the absolute value of the carrier potential increases during both their forward and reverse travel. In this case, for \(U_{\mathrm{v}} > U_{\mathrm{k}}\), the maximum current is reached at smaller values of \(U_{\mathrm{v}}\) and is approximately equal to the maximum current value with wide brushes for conducting, sector, and semiconducting stators. Thus, the appearance of critical electric-field strengths is determined primarily by the magnitude of the carrier charge.

Conclusions

On the basis of the material obtained, the following can be said about the distribution of potentials along the rotor:

1. In all cases, the maximum potential gradients are found in the commutation zones.

2. For dielectric stators, and when the generator operates with a single inductor, the presence of increased potential differences both between the carriers and relative to grounded elements is characteristic, which confirms their lack of promise.

3. The change in the law of distribution of the carrier potentials at increased \(U_{\mathrm{v}}\) is caused by ionization phenomena in the rotor–stator gap.

4. Ionization in the gap occurs at smaller \(U_{\mathrm{v}}\) if the effect of natural recharging appears, which always takes place when the generator operates with narrow brushes.

LITERATURE

1. N. Zh. Felisi. Electrostatic generator with a rotating cylinder and hydrogen insulation. Elektrichestvo, No. 1, 1962.

2. A. F. Ioffe. Electrostatic Generator, ZhTF, vol. IX, 1939.

3. V. D. Ez’kov. On the question of the distribution of potentials along the rotor in an ESG. Izv. TPI, vol. 152, 1966.

4. A. M. Kuntsov. On the question of investigating commutation in rod-type ESGs. Abstracts of papers at the VI Interuniversity Conference on Accelerators, TSU, Tomsk, 1966.

5. V. V. Padeevich. Certain questions of the theory and calculation of ESGs with conductor carriers. Dissertation, Tomsk, 1964.