DISK ESG WITH AN INCREASED NUMBER OF CONDUCTOR CONVEYORS

V. V. PATSEVICH

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

The most promising from the standpoint of specific energy indicators are disk ESGs with an increased number of conveyors when the latter are connected in cascade \[1, 2\]. The operating principle and fundamentals of the design of an ESG with a cascade connection of conveyors, the schematic diagram of which is shown in Fig. 1, are described in \[3, 4\]. The main structural elements of the generator are:

1) a rotating rotor, consisting of separate conductor conveyors, appropriately fastened and insulated from one another;

2) a stationary stator, consisting of separate plates connected to a voltage divider and ensuring a uniform distribution of the potentials of the rotor conveyors, as well as uniformity of the electric field in the generator;

3) an excitation system, consisting of an excitation source connected to one of the stator plates, and a grounded brush that imparts charge to the conveyors when in direct contact with them or by means of a corona discharge;

Fig. 1. Schematic diagram of an ESG with a cascade connection of conductor conveyors.

4) a high-voltage system, consisting of a stator plate connected to a brush that removes charge from the conveyors, and to the generator load.

The current of such a generator is determined by the magnitude of the charge carried by a conveyor during one revolution of the rotor, which in turn can be defined as the difference between the charge carried by the conveyor to the high-voltage system and the charge remaining on the conveyor when it returns from the high-voltage system to the excitation system.

The magnitude of the charge carried by the conveyor to the high-voltage system is usually determined [3] as the charge of a capacitor consisting of the stator excitation plate and the conveyor at the moment when the latter is disconnected from the grounded brush.

To determine the magnitude of the charge remaining on the conveyor, in [3] the concept is introduced of the minimum capacitance of the conveyor in the high-voltage system with respect to ground, which subsequently came to be called the parasitic capacitance of the generator. The concept of parasitic capacitance is also used for the analysis and calculation of electrostatic generators in [4, 6].

In this case the magnitude of the short-circuit current is taken to be

\[ I_{\mathrm{kz}} = 2mnC_1U_{\mathrm{v}}, \tag{1} \]

and the equation of the external characteristic, in the absence of corona and insulation losses, takes the form

\[ I_{\mathrm{n}} = I_{\mathrm{kz}}\left(1-\frac{C_3}{C_1U_{\mathrm{v}}}U_{\mathrm{n}}\right) = I_{\mathrm{kz}}\left(1-\frac{U_{\mathrm{n}}}{U_{\mathrm{xx}}}\right). \tag{2} \]

Here \(2m\) is the number of rotor conveyors,
\(n\) is the number of rotor revolutions per second,
\(C_1\) is the maximum capacitance between a conveyor and the stator excitation plate,
\(C_3\) is the minimum capacitance of the conveyor in the high-voltage system,
\(U_{\mathrm{v}}\) is the excitation voltage,
\(I_{\mathrm{n}}\) and \(U_{\mathrm{n}}\) are the load current and voltage,
\[ U_{\mathrm{xx}}=\frac{C_1U_{\mathrm{v}}}{C_3} \]
is the theoretical value of the generator no-load voltage.

The study of generators of this type on the basis of electrostatic equations that relate the magnitudes of the potentials and charges of a system of conducting bodies through potential coefficients is the subject of [7]. However, in these studies the intermediate stator plates \([1 \div (n-1)]\) (Fig. 1), which ensure a uniform distribution of the potentials of the rotor conveyors and substantially affect the magnitude of the generator voltage and current, were not taken into account in the generator. In the presence of plates \([1 \div (n-1)]\), investigation and calculation on the basis of equations with potential coefficients are considerably complicated, since it is necessary to calculate the charge of the plates, which depends on many factors, including the position of these plates relative to the casing (in Fig. 1 the casing is not shown).

The study of generators is simplified if one uses electrostatic equations with partial capacitances under the conditions—usually encountered in real generators—of a small gap between the conveyors and the stator plates and of a uniform distribution of the potentials of the stator plates. In this case the largest values will be those of the partial capacitance \(C_1\) between a conveyor and the stator plate opposite it, and the partial capacitance \(C_2\) between neighboring conveyors. The magnitudes of the remaining partial capacitances of the conveyors, in accordance with their definition [8], will be considerably smaller than \(C_1\) and \(C_2\), and their influence may be neglected in a first approximation.

Solving the system of equations with partial capacitances leads to equations [9] of the form:

\[ I_{\mathrm{kz}} = 2mn a_1 C_1 U_{\mathrm{v}} \tag{3} \]

and

\[ I_{\mathrm{n}} = 2mn\left(a_1 C_1 U_{\mathrm{v}} - a_2 U_{\mathrm{n}}\right) = I_{\mathrm{kz}}\left(1 - \frac{a_2}{a_1} U_{\mathrm{n}}\right) = I_{\mathrm{kz}}\left(1 - \frac{U'_{\mathrm{n}}}{U_{\mathrm{xx}}}\right), \tag{4} \]

where \(a_1\) and \(a_2\) are coefficients depending on the ratio of the partial capacitances \(C_1\) and \(C_2\) and on the number of rotor conveyors. For \(C_2 \ne 0\), which practically always occurs in generators of this type, \(a_1 > 1\) and \(a_2 > 0\). The quantities \(a_1\) and \(a_2\) increase as the ratio \(\frac{C_2}{C_1}\) increases.

The increase in the short-circuit current when \(C_2 \ne 0\) can be physically explained on the basis of the phenomenon of electrostatic induction. As is known, if another charged body is brought near a grounded body, a charge of opposite sign with respect to the charge of the second body appears on the first. When one of two bodies, previously charged with charges of the same sign and located sufficiently close to one another, is grounded, the latter becomes charged with a charge of the opposite sign. In the presence of only two bodies, the magnitude of the induced charge is determined by the capacitance and the potential difference between the bodies. In the presence of several bodies, the magnitude of the discharge of the grounded body will depend in a more complicated way on the magnitudes of the charges and potentials of the bodies and can be calculated by known methods of electrostatics, for example through equations with partial capacitances. As calculations show, in the presence of the partial capacitance \(C_2\), in short-circuit operation, and also under some load, the conveyor, being connected to the load brush, not only gives up the charge it has on it, but also receives a charge of the opposite sign.

Consequently, when \(C_2 \ne 0\), the conveyor in the high-voltage system is not only discharged into the load, but is also recharged. The generator operates with natural recharging of the conveyors in the high-voltage system.

Charging the conveyor with a charge of the opposite sign corresponds to delivering to the load an additional charge of the same sign as that which was on the conveyor before it was grounded, as a result of which the current and power of the generator increase.

It should be noted that the manifestation of natural recharging is not limited to phenomena occurring only in the high-voltage system. In the excitation system, the grounded conveyor, after transferring to ground the charge received in the high-voltage system, is charged again due to the phenomenon of electrostatic induction under the action not only of the excitation inductor, but also of the adjacent charged conveyor 1, which leads to an increase in the charge carried from the excitation system to the load.

Directly from equations (2, 4) it follows that the magnitude of the short-circuit current does not fully determine the power of the generator when it operates into a load. This circumstance is due to the fact that, as the load voltage increases, a decrease in the generator current occurs, caused by the presence of armature reaction.

Quantitatively, the magnitude of the armature reaction can be estimated from the angle of inclination of the external characteristic to the current axis. For a generator in which armature reaction is absent, the current remains constant at any load voltage, and the external characteristic will be parallel to the voltage axis. The no-load voltage of such a generator—

… in the absence of leakage is theoretically equal to infinity at any excitation voltage. In the presence of armature reaction, the angle of inclination of the external characteristic to the current axis is less than \(90^\circ\). For a large armature reaction, the characteristic will be very flat with respect to the current axis, and when the generator operates with such a characteristic into a load, its power will be much less than the theoretically possible value. In this connection, the study of ways of reducing the magnitude of armature reaction in an electrostatic generator is of great importance.

According to equation (4), the magnitude of the armature reaction is determined by the ratio

\[ \frac{a_2}{a_1} = \frac{U_{\mathrm{B}}}{U_{\mathrm{xx}}}. \]

Calculations show that the value of the ratio \(\frac{a_2}{a_1}\) decreases both with a decrease in the ratio \(\frac{C_2}{C_1}\) and with an increase in the number of rotor conveyors \(2m\).

A decrease in the ratio \(\frac{C_2}{C_1}\) can be achieved, in particular, by increasing \(C_1\) while reducing the rotor–stator gap. Since both reducing the rotor–stator gap and increasing the number of rotor conveyors correspond to an increase in the maximum power of the generator [9, 10], in order to reduce armature reaction it is necessary to make maximum use of both possibilities. It should be noted that reducing the rotor–stator gap is also highly desirable from the standpoint of reducing the magnitude of the generator excitation voltage.

Fig. 2. Schematic diagram of the construction of a disk electrostatic generator.

The results presented have been verified experimentally on a model of a disk electrostatic generator with a cascade connection of conductor conveyors; the basic design scheme is shown in Fig. 2, and the external appearance of the generator in Fig. 3.

The rotor 6 of the generator is made of a compound based on epoxy resin, with conveyors 4 embedded in it. The potential distribution over the stator was accomplished by a semiconducting coating, the possibility of using which was first indicated by A. F. Ioffe [3]. The semiconducting stator coating 5, with metal high-voltage inductors 1 and excitation inductors 7 embedded in it, was made of a compound based on epoxy resin with silicon carbide. Commutation was carried out by a grounded brush mounted in an insulating brush holder 8, and by brush 3 mounted in a metal brush holder 2. Inductors 1 and brush holder 2 simultaneously form a high-voltage conductor, ensuring charge removal from the conveyors under conditions close to those of a Faraday cylinder.

The design of the generator provided for the possibility of using both contact and corona commutation, with an adjustable gap between the brush and the rotor, as well as variation of the gap between the rotor and the stator.

Rotor data: outer diameter \(D_2 = 154\) mm, inner diameter along the conveyors \(D_1 = 96\) mm, rotor disk thickness \(h = 8\) mm, number of conveyors \(2m = 200\).

Fig. 3. Disk ESG with cascade connection of conveyors.

In tests of the generator, \(a_1 = 2.3\) was obtained with a rotor–stator gap of 0.4 mm, and \(a_1 = 3.0\) with a gap of 1.1 mm; in this case the values of \(a_2\) were respectively 0.036 and 0.084.

Along with proving the presence of natural overcharging and the possibility of creating generators with a small value of armature reaction, the experiments showed the possibility of successful operation of an ESG with conductor conveyors under corona commutation.

Despite its simplicity and apparent effectiveness, contact commutation, most often used in ESGs with conductor conveyors, is a serious brake on their practical development. Its main drawback is dusting of the working volume and the resulting sharp decrease in its electrical strength.

The possibility of using corona commutation, already widely employed in ESGs with a dielectric conveyor at powers up to several kilowatts, makes it possible to assess in a new way the practical possibilities of generators of this type.

On the whole, the investigations carried out define more concrete directions for research and design work on creating ESGs with conductor conveyors for high specific ratings (up to \(1\ \text{W}/\text{cm}^3\)) [11].

References

1. Felici U., L’avenir de la génération électrostatique, 102ème colloque du SNRC, Grenoble, 1960.

2. V. V. Patsevich, On the determination of the maximum powers and specific energy indices of certain electrostatic generators, Proceedings of the Fifth Inter-University Conference on Electron Accelerators, 1964, Atomizdat, 1966.

3. A. F. Ioffe, Journal of Technical Physics, 9, No. 23, 2071, 1939.

4. B. M. Gokhberg, A. F. Ioffe, N. M. Reinov, Journal of Technical Physics, 9, No. 23, 2094, 1939.

5. Felici N., J. Phys. et Rad. 9, No. 2, 66, 1948.

6. A. F. Kalganov, Proceedings of Higher Educational Institutions—Electromechanics, No. 4, 20, 1960.

7. S. A. Bobkovskii, Journal of Technical Physics, 10, No. 17, 1404, 1940.

8. L. R. Neiman, P. L. Kalantarov, Theoretical Foundations of Electrical Engineering, Gosenergoizdat, 1959, Part III.

9. Yu. A. Korzennikov, V. V. Patsevich, Yu. N. Sivkov. Calculation of a rod-type electrostatic generator of constant current on the basis of equations with partial capacitances, Proceedings of the Fifth Inter-University Conference on Electron Accelerators, 1964, Atomizdat, 1966.

10. A. F. Kalganov, V. V. Patsevich. Proceedings of Higher Educational Institutions—Electromechanics, No. 8, 917, 1963.

11. A. A. Vorob’ev, A. F. Kalganov, V. A. Lukutin, V. V. Patsevich. On the theory and practice of electrostatic machines, Proceedings of the Fifth Inter-University Conference on Electron Accelerators, 1964, Atomizdat, 1966.