Some Results of a Study of Rod-Type ESGs

A. F. Kalganov, V. V. Patsevich

(Presented by the scientific seminar of the ESG Problem Laboratory at TPI)

The development of power engineering in the near future is closely connected with the development of technology for the production, transmission, and use of high and extra-high direct-current voltage electrical energy. This presupposes the creation of both power and low-power sources of high and extra-high direct-current voltage. The latter are needed for testing basic power equipment and for conducting scientific research connected with the development and operation of this equipment. At present, sources of high direct-current voltage are also beginning to appear as elements of technological equipment (for example, in electron-ion technology).

Among the various sources of high direct-current voltage, a special place is occupied by so-called electrostatic generators, which operate on the principle of converting mechanical energy into electrical energy when charges (charged bodies or particles) are moved by mechanical forces against the action of the forces of an electric field [1]. Their special place is determined by the fact that, in accordance with their principle of operation, they are the most adapted to the direct production of extra-high direct-current voltage and theoretically can be made for power ratings with specific parameters better than the specific parameters of other sources. On the other hand, the practical problem of creating powerful ESGs has still not found a satisfactory solution. At present, only the belt ESG and the rotor ESG with a dielectric conveyor (ESGD) can be regarded as well-developed types of generators. With the former, voltages of millions of volts are obtained, but with currents of only hundreds of microamperes. The latter develop up to 750 kV, but their power does not exceed several kilowatts, and according to forecasts no more than one or two tens of kilowatts are expected [2].

The situation that has arisen is explained by the fact that, although theoretical and experimental data do make it possible to formulate the basic requirements that an energetically efficient ESG must satisfy, methods for simultaneously and fully satisfying these requirements have not yet been developed. This is connected not only with technological difficulties encountered by ESG developers, but also with the fact that, despite the apparent simplicity of the ESG principle of operation, many processes and phenomena accompanying the functioning of an ESG are still not fully understood or revealed.

From the analysis of published results of ESG studies summarized in [1], and from the results of our initial work [3], it followed that the optimal solution of the problem should be sought along the path of developing an ESG

with rod-type charge carriers, located in the dielectric body of the rotor (ESGS). As calculations showed, with a sufficiently large number of carrier rods, the specific “surface” power of an ESGS approaches the specific “surface” power of an ESGD under comparable conditions [4]. At the same time, owing to the use of concentrated commutation, it becomes possible to double the active surface by employing a double stator, which is already substantial from the standpoint of increasing the specific “volumetric” power. Finally, for the same reasons an ESGS proves to be the most suitable for a multidisk design, and this is the determining factor in solving the problem of increasing the active surface per unit volume.

Analogous considerations in the most generalized form were expressed by Prof. Felici in 1960 [2]. In this, the development of commutation systems was posed as the principal task. It is obvious that the solution of this problem will be more effective if it is associated with the study of the phenomena accompanying the operation of ESGS.

The investigations of ESGS carried out at TPI included the development of a method for calculating the linear sections of the characteristics of generators with contact commutation, verification of this method on experimental ESGS specimens operating both in a free atmosphere and in compressed gas, oscillographic studies of processes in various ESGS circuits, photographic and visual recording of luminous processes in the commutation zones and in the rotor—stator gap, experimental investigation of ESGS characteristics in deep-saturation modes, modeling of electric fields in the ESGS electrode system, and so on.

It was shown that, for calculating ESGS characteristics, a method based on the use of electrostatic equations with partial capacitances is quite applicable [5]. The application of this method on the basis of the method of electrostatic analogy proved highly fruitful [6]. The calculations according to [6] agree with the experimental data [7] with high accuracy. From the calculations and experiments performed it became clear that rod-type ESGs are characterized by a phenomenon analogous to the phenomenon of additional natural self-excitation in ESGDs [8], called, as applied to ESGS, natural recharging [7].

Subsequently it was shown [9] that in an ESGS, as in an ESGD, the phenomenon of double natural charge transfer occurs. Its essence is as follows. Under certain conditions, the electric field in the discharge system changes direction, and energy conversion will then occur both during the forward motion of the carrier (from the charging system to the discharge system) and during its reverse motion. As a result, the maximum power of the generator increases, in the limit, by a factor of two owing to the corresponding increase in the generator current, without forced recharging of the carrier in the high-voltage system.

With high electric strength of the dielectric body of the ESGS rotor, an electric discharge arises in the rotor—stator gas gap if the field strength in the gap, proportional to the charge of the carriers, exceeds the electric strength of the medium. The presence of a dielectric coating on the carriers leads to the fact that, in the process of discharge burning, between the gaps carrier—dielectric surface and dielectric surface—stator, there will occur a redistribution of the electric-field strength due to deposition of charges on the dielectric surface. For a constant value of the carrier charge, the electric-field strength in the gap will decrease,

since part of this charge will be “bound” by the charge deposited on the surface of the dielectric. In the steady-state regime, the magnitude of the “bound” charge will be equal to the difference between the actual charge of the carrier and the “free” charge corresponding to the maximum value of the electric-field strength in the gap at the dielectric surface.

When the carrier is connected to the high-voltage brush, its charge, bound to the charge on the rotor surface, will be redistributed between the carrier and the inductor. In the gap between the dielectric surface and the stator, an electric field of the opposite direction will appear. The charge redistributed onto the inductor will be delivered to the load during the return stroke of the carrier, when work is performed against the forces of the electric field acting not on the charges of the carriers, but on the charges of opposite sign of the dielectric coating of the carriers. As the magnitude of the charge of the carriers increases (for example, when the excitation voltage is increased), the “bound” charge will increase and, accordingly, so will the magnitude of the electric-field strength in the region of the return stroke of the carrier. With complete symmetry of the charging and discharging systems, the value of the ratio of load current to excitation voltage does not change when the “bound” charge appears. It is obvious that an increase in the generator current due to redistribution of the bound charge is possible only when, in the field produced by it in the region of the return stroke of the carrier, the field strength is less than the electric strength of the medium. When the critical gradients are also reached in the region of the return stroke of the carriers, an electric discharge arises there as well, which limits the magnitude of the charge on the dielectric surface transferred from the load system to the excitation system. Thus, the generator current reaches its maximum value.

Using Gauss’s theorem for suitably chosen surfaces enclosing the carriers and the rotor dielectric, one can determine the magnitude of the maximum charge transferred by one carrier in one revolution of the rotor with one pair of poles:

\[ Q_m=\frac{1}{m}\varepsilon_0\left(\oint \overline{E}_1\,d\overline{s}-\oint \overline{E}_2\,d\overline{s}\right) =\frac{1}{m}\varepsilon_0\left(E_{1n}\cdot S_1+E_{2n}\cdot S_2\right), \]

where \(\overline{E}_1\) and \(\overline{E}_2\) are the vectors of the electric-field strength in the gas gap in the region of the forward and return stroke of the carriers, respectively;

\(E_{1n}\) and \(E_{2n}\) are the maximum mean values of the normal components of the fields \(\overline{E}_1\) and \(\overline{E}_2\);

\(m\) is one half of the number of rotor carriers.

In the case of complete symmetry of the generator,

\[ E_{1n}=E_{2n}=E_n. \]

Assuming, as a first approximation, that

\[ S_1=S_2=\frac{1}{2}S, \]

where \(S\) is the total active surface of the rotor, we obtain the following expression for the maximum load current:

\[ I_{\mathrm{н}m}=2mnQ_m=2n\varepsilon_0E_n\cdot S=2I'_{\mathrm{н}m}, \tag{1} \]

where \(n\) is the number of rotor revolutions per second, and

\[ I'_{\mathrm{н}m}=n\cdot\varepsilon_0E_nS \]

is the maximum load current in the absence of double transfer.

At present, the physics of a gas discharge in a gas gap bounded by a dielectric has not yet been sufficiently studied. However, the available data on this question show that the magnitude of the maximum field strength may be taken as equal to the magnitude of the breakdown gradients in a uniform field for the corresponding gaps between metallic electrodes [10, 11]. Then the maximum value of the generator current, determined from (1), may be regarded, with a certain approximation, as the physical limit for a generator with a specified gap size and with the selected composition and pressure of the gas filling the rotor–stator gap.

The decisive influence of the magnitude of the electric-field strength in the rotor–stator gap on the maximum generator current has been confirmed experimentally on a single-disk generator with a glass stator in tests of several rotors of identical overall dimensions, but differing in the number and diameter of the transporters, their mutual arrangement, and the depth at which the transporters were embedded in the rotor body. In tests of the generator in air, the following results, in particular, were obtained. The minimum value of the generator current remained approximately the same, equal to \(100 \div 110\ \mu\mathrm{A}\), when the number of transporters was reduced from 330 to 36 with a simultaneous increase in the thickness of the dielectric coating from \(0.8\ \mathrm{mm}\) to \(3.5\ \mathrm{mm}\). With a small number of transporters and a constant rotor–stator gap equal to \(0.2\ \mathrm{mm}\), reducing the thickness of the dielectric coating from \(3.5\ \mathrm{mm}\) to \(0.5\ \mathrm{mm}\) led to a decrease in the maximum current by more than a factor of two. As the number of transporters increased, the change in current with changing thickness of the dielectric coating decreased. With an increase in the rotor–stator gap from \(0.2\ \mathrm{mm}\) to \(1.5\ \mathrm{mm}\), the maximum current decreased from \(100\)—\(110\ \mu\mathrm{A}\) to \(40 \div 50\ \mu\mathrm{A}\), which corresponds to a decrease in \(E_n\) from \(60\ \mathrm{kV/cm}\) to \(22\ \mathrm{kV/cm}\). The magnitude of the excitation voltage at which the maximum current was reached increased from \(4 \div 5\ \mathrm{kV}\) (at the minimum values of the air gap and dielectric-coating thickness and the maximum number of transporters) to \(20 \div 30\ \mathrm{kV}\) (at the maximum gaps and dielectric-coating thickness and the maximum number of transporters).

As has already been noted, it is considered [2] that the principal task in developing rod-type ESGs is to solve the problem of commutation. At the same time, no very deep experimental or theoretical studies of commutation in generators of this type have been carried out. In this connection, a seemingly quite obvious fact was accepted on faith: that the flow of current in the load is caused by the transfer of charge from the transporter to the collector (the high-voltage inductor), to which the load is connected, during the period when the brush is connected to the transporter through a gas discharge or metallic contact. This proposition was taken as an axiom and served as the starting point for most studies concerned with commutation in rod-type ESGs.

An oscillographic study of the currents in the generator [12] made it possible to establish that the law governing the variation of the load current for inductors spanning three or more transporters, and brushes located approximately in the middle part of the inductors, is on the whole independent of the commutation conditions (brush width, their construction, spark, corona, or contact commutation). The establishment of metallic contact, or contact through a spark or corona, between the transporter and a brush connected to the inductor is accompanied mainly only by the flow of current in the “transporter—brush—inductor” circuit; the law governing its variation is analogous to the law of current variation in a short circuit between

plates of the charged capacitor. In this case, energy is released in the discharge circuit

\[ W < \frac{1}{2} Q U_{\mathrm{v}}, \]

where \(Q\) is the magnitude of the charge carried by the conveyor during one cycle of generator operation;
\(U_{\mathrm{v}}\) is the excitation voltage.

If no special measures are taken, this energy is released in the discharge channel between the brush and the conveyor, causing destruction of the brush and of the collector part of the rotor. To reduce the destructive action of these discharges, it is necessary, on the one hand, to reduce the amount of energy released and, on the other, to distribute this energy over the discharge circuit. To reduce the energy released in this process, it is necessary to reduce the excitation voltage and the magnitude of the charge carried by one conveyor, for example by increasing the number of conveyors. Distribution of the energy can be achieved by connecting a resistance into the discharge circuit. In addition, the service life and reliability of the commutating systems will depend to a considerable degree on the design features of their implementation.

The investigations carried out showed that ESGs with rods placed in a dielectric possess the same positive properties associated with the presence of the phenomena of natural recharging and double natural transfer as do ESDs. Moreover, an ESG of this kind is, in a certain sense, simultaneously also a generator with a dielectric conveyor, since during the return stroke of the conveyor the carried charge is located on the dielectric surface of the rotor. At the same time, the potential advantages of concentrated commutation are fully retained here, making it possible to achieve higher specific energy indices in a multidisk design, and favorable possibilities are created for using new media (for example, liquid dielectrics [13, 14]) if they are successfully applied in other types of ESG.

REFERENCES

1. High-Voltage Testing Equipment and Measurements. Edited by Prof. A. A. Vorob’ev, GEI, 1960.

2. Application of Electric-Field Forces in Industry and Agriculture. Edited by V. I. Levitov and A. G. Lyapin, VNIIEM Publishing House, pp. 11–17, 1964.

3. A. A. Vorob’ev, A. F. Kalganov, Yu. A. Korzennikov, V. V. Patsevich, V. P. Shcherbinin. Electron accelerators (Proceedings of the IV Interuniversity Conference on Electron Accelerators), Vysshaya shkola Publishing House, pp. 9–14, 1964.

4. A. F. Kalganov, V. V. Patsevich. Izv. vuzov, “Elektromekhanika,” 1963, No. 8, 917.

5. Yu. A. Korzennikov, V. V. Patsevich, Yu. N. Sivkov. Electron Accelerators. Atomizdat, pp. 16–21, 1966.

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8. N. J. Felici, E. Gartner. Rev. Gén. Electr., 62, No. 2/No. 3, 1953.

9. A. M. Kuptsov, V. V. Patsevich. Izv. TPI, 191: 75, 1968.

10. B. N. Kanon’in. ZhTF, 9, No. 10, 1939.

11. A. V. Dmitriev. ZhTF, 33, No. 9, 1963.

12. A. M. Kuptsov, V. V. Patsevich. “Elektrichestvo,” No. 7, 1968.

13. N. J. Felici. French patents No. 1430401 of 24.01.66 and No. 1431070 of 31.01.66.

14. “Electr. Rev.,” 164, No. 5, 159, 1969.