STUDY OF THE COMMUTATION OF AN ESG WITH CASCADED CONNECTION OF TRANSPORTERS

A. M. Kuptsov, V. V. Patsevich

(Presented by the scientific seminar of the Department of Theoretical Foundations of Electrical Engineering)

In calculating the short-circuit characteristic \(I_{\text{sc}} = f(U_{\text{в}})\), which is one of the principal characteristics of an ESG, those moments of generator operation are usually considered when the transporters are disconnected from the brushes of the excitation system and of the high-voltage system \([1, 2, 3]\). The difference between the charges carried by the transporters from the excitation system to the high-voltage system and in the reverse direction per unit time is taken to be equal to the average value of the generator current. The magnitudes of these charges are determined on the basis of the equations of electrostatics: either from the values of the maximum capacitance in the excitation system and the minimum capacitance in the high-voltage system \([1]\), or by solving the system of Maxwell equations with potential coefficients \([2]\) and with partial capacitances \([3]\).

The validity of such an approach to determining the generator current is justified by the fact that the electric field of an ESG satisfies the condition of quasistationarity and that the rapidly occurring processes associated with commutation are completed by the moment the transporters are disconnected from the brushes. However, this justification has not yet had convincing proof, and a number of works point to the need to study the ESG not as a quasistatic system, but as an electrodynamic system on the basis of the equations of electrodynamics \([4, 5]\).

Below are presented the results of a study of certain processes accompanying commutation in an ESG, obtained by oscillographing the current in a single-disk model of a generator in the short-circuit mode, with the aim of showing the possibility of studying this type of ESG as a quasistatic system and confirming in them the presence of the effect of natural recharging.

Oscillographing was carried out for two interchangeable rotors with oscillographs C 1—13 and 2KO/721. Rotor No. 1 had 60 transporters of cylindrical shape with diameter \(d = 10\) mm. Rotor No. 2 had 60 transporters of complex configuration, in which, with equality of the distances between the parts of the transporters protruding to the outer surface of the rotor, the distance between neighboring transporters in the body of the rotor was different. In this case the partial capacitance between any of the transporters and the stator was practically identical, while the partial capacitances between neighboring transporters were different. Both rotors had an outside diameter \(D = 490\) mm; the transporters were embedded in a dielectric—cold-curing epoxy resin.

To eliminate the effect of the nonuniform distribution of the potential over the stator on the processes accompanying commutation when the stator is made of a poorly conducting material [6], the experiments were carried out with a conduction excitation circuit. With such a circuit, a uniform distribution of the potential over the stator corresponds to equality of the latter to zero, and the stator made of a poorly conducting material can be replaced by a conducting one. It should be noted here that a subsequent comparison of current oscillograms for a metallic stator and for a stator made of a poorly conducting material showed the presence of a certain qualitative difference in the processes accompanying commutation in these generators.

However, with other conditions being equal, the duration of the commutation process in both cases is characterized by a quantity of the same order, and the values of the average generator current turn out to be approximately equal.

Figure 1 shows the measuring circuit of the generator, where the generator is shown schematically. The upper part of the generator with respect to the axial line will be analogous to that shown below. Oscillograms of the currents $i_1$, $i_3$ for rotor No. 1 with wide brushes, simultaneously overlapping three conveyors, are presented in Fig. 2 ($a$, $b$, respectively). Here the distance between the corresponding pulses is proportional to the time $T$ during which the rotor turns through the angle $\dfrac{\pi}{m}$, where $2m$ is the number of rotor conveyors. In the course of the study, oscillography was carried out of the currents in the excitation circuit; the oscillograms of these are analogous to the corresponding oscillograms of the currents of the discharge system and are therefore not given here.

Fig. 1. Oscillography and measurement circuit

Directly from the oscillograms it is evident that both the charging process and the discharging process of the transporter occur over a time considerably shorter than the time \(T\).

Photographing the commutation zone also established that the burning time of the spark, which always precedes the establishment of contact between the brush and the transporter, is also considerably less than the time \(T\). To determine the main factors influencing the shape of the current pulses, oscillograms were taken when a lumped inductance was switched into the circuit and when lumped capacitances were connected to the stator and to the discharge brush. For rotor No. 1 and a narrow brush touching one transporter at a time, the oscillogram of the charging component of the current \(i_3\) in the presence of inductance is shown in Fig. 2в, and with capacitance connected to the stator in Fig. 2г. These oscillograms show that the pulse shape is determined to a considerable degree by the magnitude of the lumped parameters of the transporter charging and discharging circuits. The average value of the current, determined from the ammeter readings, in all cases with the same brushes (wide or narrow), remains practically constant; moreover, with narrow brushes it is somewhat greater than with wide ones. From the constancy of the average current of the circuit it follows that the magnitude of the charge imparted to the transporter during the charging period and given up during the discharging period remains constant in all cases.

On this basis it may be assumed that the duration of the current pulses, for sufficiently large values of capacitances and inductances in the load circuit, does not depend on the duration of the commutation time and, consequently, also on the burning time of the spark, which may be shorter than the pulse duration. The maximum possible burning time of the spark is determined by the advance time of the spark relative to the instant of direct contact between the brush and the transporter \((t_1)\). The magnitude \(t_1\) may vary within considerable limits when changing

Fig. 2. Typical oscillograms of currents for rotor No. 1: \(a, б\)—\(i_1, i_2\), respectively; \(в\)—\(i_3\) with inductance; \(г\)—\(i_3\) with capacitance.

the excitation voltage, increasing as the latter increased. It was established that the distance between the front of the charging pulse and the additional pulse appearing on the decay of the charging pulse (Fig. 2c) or after its end, on the oscillogram, is proportional to the value \(t_1\). Consequently, the establishment of metallic contact is accompanied by the appearance of an additional pulse. The small magnitude of the additional pulse indicates that the main commutation process ends during the spark-burning time, which is most often less than the pulse duration and considerably less than the value \(T\). This is also confirmed by the fact that, when direct contact is eliminated and commutation is carried out only through a spark, the average current value decreases only slightly.

Thus, the results set forth above make it possible to conclude, first, that by the moment when the conveyor is disconnected from the brush, in both the charging and discharging systems, a quasi-static state occurs. Second, the commutation process proceeds with practically unchanged partial capacitances and can, with a sufficiently high degree of accuracy, be calculated from equivalent circuits with lumped parameters.

Of definite interest is also the fact that the current in the load circuit \(i_3 = i_1 + i_2\) is, in essence, the charging current, and not the discharge current, of the conveyor in the load system. During discharge of the conveyor, the conveyor–stator capacitance is short-circuited, and the currents \(i_1\) and \(i_2\), having opposite directions with wide brushes, in sum give a value equal to zero; with narrow brushes, \(i_1 > i_2\). It may be noted here that the presence of a compensation current in the conveyor–stator circuit during the commutation period in the discharge system occurs also with a poorly conducting stator, both in the short-circuit mode and under load. In investigating the causes that, with narrow brushes, produce the inequality of the currents \(i_1\) and \(i_2\) and the appearance of an additional pulse at the moment when direct contact is established between the brush and the conveyor, oscillography was carried out according to the circuit of Fig. 1 in the presence of an additional brush in the form of a point, shown in Fig. 1 by a dashed line. By changing the distance between the additional brush and the rubbing narrow brush, the value of the time \(t_1\) was varied over a wide range at constant excitation voltage. If \(t_1 < T\), then the character of the pulse remained the same as in Fig. 2c.

Fig. 3. Typical oscillograms for rotor No. 2: a) for \(T < t_1 < 2T\), b) for \(2T < t_1 < 3T\)

If \(t_1 > T\) was established, then the polarity of the pulse changed to the opposite one. This fact well confirms the explanation of the phenomenon of natural recharging given in [3]. Indeed, if \(t_1 < T\), then by the moment of connection of the conveyor with the rubbing brush the following after it

in the course of rotation of the rotor the conveyor has already commutated through a spark and has been recharged under the influence of the following conveyor through the resistance of the spark. Under the influence of the recharged conveyor, the conveyor that has connected to the brush gives up the charge of opposite sign acquired by it earlier during commutation through a spark and, for certain ratios of the partial capacitances, may even acquire a charge of the same sign as it had before commutation through the spark. A current pulse of opposite sign will appear in the load circuit, natural recharging is eliminated, and the mean value of the current turns out to be smaller than for \(t_1<T\), being approximately equal to the mean value of the current with wide brushes.

Finally, the presence of natural recharging is well confirmed by oscillograms of the current \(i_1\) for rotor No. 2 at \(T<t_1<2T\) (Fig. 3a), and at \(2T<t_1<3T\) (Fig. 3b).

The oscillograms of the currents \(i_1\) and \(i_3\) for rotor No. 2 with one narrow brush will be similar to those given above (Fig. 3a, b), differing from the latter by the absence of additional recharging pulses. The difference in the current values from individual conveyors for rotor No. 2 is due only to the difference in the partial capacitances between neighboring conveyors and is in complete agreement with the concepts of natural recharging in generators of this type.

Thus, experiments with a conducting stator provide the most vivid evidence in favor of the possibility of calculating the generator current from electrical equivalent circuits with lumped parameters, and have made it possible to confirm clearly the presence of the effect of natural recharging in generators of this type.

LITERATURE

1. A. F. Ioffe. ZhTF, No. 9, 1939.
2. S. A. Babkovskii. ZhTF, vol. 10, Nos. 1–7, 1940, p. 1404.
3. V. V. Patsevich. Dissertation, Tomsk, 1964.
4. L. S. Polotovskii. High-Voltage DC Capacitive Machines, Moscow, GEI, 1960.
5. V. I. Levitov, A. G. Lyapin. Electrostatic Generators with a Rigid Rotor, Part 1, Moscow, TsNIPIrbozelektroprom, 1963.
6. N. Zh. Filis. French patent, class H02n, No. 1,397,294.