A Scheme for Accumulating Energy in a Single-Phase Inductive Load from a Three-Phase Pulse Generator

G. A. Sipailov, K. A. Khorkov, A. V. Loos

(Presented by the scientific seminar of the Department of Electrical Machines and General Electrical Engineering.)

The transfer of large energies, measured in tens of millions of joules, over times measured in tens of milliseconds, as well as the accumulation of energy in inductance coils, can be carried out most effectively with the aid of pulse generators. Previously, schemes were considered for the transfer and accumulation of energy in a single-phase inductive load from a single-phase pulse generator or from two phases of a three-phase generator [1]. Since three-phase pulse generators have now found wide application, it is of undoubted interest to investigate the possibilities of using all phases of the generator in the process of energy transfer and accumulation.

One possible method of operation of a three-phase pulse generator into a single-phase load is to connect the generator phases according to a half-wave rectification scheme of successively alternating positive half-waves of line e.m.f.s, analogous to the scheme of three-phase full-wave rectification. It should be noted, however, that the analogy concerns only the external appearance of the schemes, whereas the essence of their operation is different. Operation of the scheme in the mode of half-wave rectification of successively alternating half-waves of line e.m.f.s makes it possible to use, instead of valves, ion-mechanical fast-acting switching devices, which gives the scheme new positive qualities.

It is known that in the scheme of three-phase full-wave rectification, switching of the load from one phase to another is carried out at the moment when the e.m.f.s of the phases being switched are equal; moreover, the current is transferred from the phase whose e.m.f. is decreasing in amplitude to the phase whose e.m.f. is increasing. In this case the line e.m.f. of the two phases that take over the current is close to its maximum, and the current has a purely periodic character. When this scheme is used for rectifying large currents, a large number of valves is required and, in addition, a special circuit for uniform distribution of the load among the valve elements [4]. In a number of cases, for example, when supplying the electromagnets of thermonuclear devices, when accumulating energy in an inductance coil, etc., where the condition of a smooth rise of current is not obligatory, the power-supply scheme can be substantially simplified and thereby the reliability of its operation increased and its cost substantially reduced.

The described scheme of half-wave rectification of three-phase current consists of a three-phase pulse generator, six ion-mechani-

... mechanical fast-acting controlled devices [2, 3] and an inductive load or an inductive energy storage device. Ion-mechanical contact devices make it possible to switch on and switch off various branches of a circuit in any sequence and can pass currents of hundreds of kiloamperes, at voltages of 10–20 kV, which many times exceeds the capabilities of existing valves.

The essence of the operation of the circuit is as follows. The load is connected to the positive half-waves of the generator line e.m.f. (the process of energy storage) and is short-circuited for the duration of the negative half-waves of the e.m.f. (the period of maintaining the stored energy). In contrast to a single-phase generator, where the interval between storage cycles is 180 electrical degrees, i.e., the storage time is equal to the time of maintaining the stored energy, in the case of a three-phase surge generator it is possible to use the positive half-waves of the line e.m.f. of different pairs of phases, following one another every 60 electrical degrees (Fig. 2). The energy-maintenance time is reduced by a factor of 3, which is of exceptionally great importance for increasing the efficiency and productivity of the installation.

The load is switched on each time at the instant when the line e.m.f. passes through zero, which makes it possible to use the aperiodic component of the sudden short-circuit current, increasing the current amplitude almost twofold.

Operating Process of the Circuit

The basic circuit for connecting a three-phase surge generator to an inductive load is shown in Fig. 1. In the initial state only one contact device out of six is closed, for example, K-5. At the instant when the line e.m.f., for example, of phases \(A\) and \(B\), passes through zero, device K-1 is closed (Fig. 2). The polarity of the half-wave of the e.m.f. of these phases, after the load is switched on, is taken as positive. The equivalent supertransient inductance of two

Fig. 1. Basic circuit for connecting the generator to the load.

Fig. 2. Curves of e.m.f. and currents of the load and generator.

therefore, the series-connected generator phases \(L_{\mathrm{g}}\) may, over the course of one emf period, be regarded with sufficient accuracy as unchanged. Then the current flowing through the generator phases and through the load is determined by the solution of the equation

\[ E_{BA}\sin \omega t=(L_{\mathrm{g}}+L_{\mathrm{n}})\frac{di}{dt}+i(r_{\mathrm{g}}+r_{\mathrm{n}}). \tag{1} \]

At the instant \(t_1\), when the load current reaches a maximum, apparatus K-2 is closed. The load is thereby short-circuited, and the energy accumulated in the inductance is preserved during the time interval from \(t_1\) to \(t_4\). The decay of the load current in this period is determined by the time constant of the short-circuited circuit: “load—contacts K-2 and K-5.” The generator then enters a short-circuit mode. Because of the change in polarity of the emf \(E_{BA}\), the generator current rapidly decreases to zero. At the instant when the generator current passes through zero, the circuit is opened by apparatus K-1. In the time interval after K-2 is closed, the generator and load currents are determined from the equations

\[ E_{BA}\sin \omega t=L_{\mathrm{g}}\frac{di_{\mathrm{g}}}{dt}+i_{\mathrm{g}}r_{\mathrm{g}}, \tag{2} \]

\[ 0=L_{\mathrm{n}}\frac{di_{\mathrm{n}}}{dt}+i_{\mathrm{n}}r_{\mathrm{n}}. \tag{3} \]

After K-1 is opened, in the time interval from \(t_2\) to \(t_3\), the generator operates at no load. At the instant \(t_3\), when the emf \(E_{CB}\) passes through zero, K-4 is closed; this corresponds to the regime of a sudden two-phase short circuit of the generator. The generator current begins to increase rapidly; in apparatus K-5 the generator and load currents are oppositely directed. At the instant when the generator current reaches a value equal to the load current, apparatus K-5 is de-energized and opens, which corresponds to connecting the load to the emf \(E_{CB}\) of positive direction. Under the action of this emf the load current

Fig. 3. Oscillogram of the solution of the equations on the MNB-1 for \(L_{\mathrm{n}}=1.25L_{\mathrm{g}}\), with

\[ \frac{r_{\mathrm{g}}}{\omega L_{\mathrm{g}}}=\frac{r_{\mathrm{n}}}{\omega L_{\mathrm{n}}}=0.05. \]

begins to increase rapidly; meanwhile, in apparatus K-5 the generator and load currents are oppositely directed. At the instant when the generator current reaches a value equal to the load current, apparatus K-5 is de-energized and opens, which corresponds to connecting the load to the emf \(E_{CB}\) of positive direction. Under the action of this emf the load current

additionally increases and, consequently, an additional transfer of energy from the generator to the load takes place. At the moment \(t_5\), the load current reaches a maximum, and the load is again short-circuited (by apparatus K-3), which creates conditions for conserving energy in the circuit: “load—contacts K-3 and K-4.” The generator current again decreases and, at the moment when it passes through zero, is switched off by apparatus K-2. Thereafter the process proceeds analogously to that described above. In the limit, in the load one can obtain a current equal to the surge current of a two-phase short circuit, independently of the magnitude of the load inductance. By means of the described circuit, a significant part of the kinetic energy of the rotating rotor can be transferred to the load.

Although the solution of equations (1–3) presents no difficulty, the calculation of the currents in the individual nodes of the circuit for all operating cycles of the circuit is difficult, since it is associated with computing a large number of initial conditions for each subsequent stage of the circuit operation from the results of the solution for the preceding stage. Therefore, the operation of the circuit was investigated with the aid of an MNB-1 analog computer, using a special programming device carrying out all the necessary switchings in the mathematical model. This made it possible to obtain a complete picture of the operation of the circuit and to carry out the necessary investigations.

Table 1

The results of processing the obtained oscillograms (Fig. 3), with the aim of investigating the rate of accumulation and the magnitude of the accumulated energy for different load inductances, are presented in Table 1, where \(n\) is the number of positive half-waves of the line voltages for which the load must be switched on in order to obtain in the load a current equal to \(0.9 I_{\mathrm{u}}\);

\(I_{\mathrm{u}}\) is the surge current of a sudden two-phase short circuit at the generator terminals;

\(Q_1\) is the energy that the generator transfers to the load for \(L_{\mathrm{n}} = L_{\mathrm{g}}\) in one pulse.

Figure 2 presents the calculated curves of variation of currents and voltages in the branches of the circuit for the case \(L_{\mathrm{n}} = 1.25 L_{\mathrm{g}}\) with

\[ \frac{r_{\mathrm{n}}}{\omega L_{\mathrm{n}}} = \frac{r_{\mathrm{g}}}{\omega L_{\mathrm{g}}} = 0.05 . \]

In the same figure, the dashed line shows the current curve when the circuit operates in the mode of three-phase two-half-period rectification, calculated by the method of [6]. The calculations show that, in order to reach one and the same current, for example \(0.9 I_{\mathrm{u}}\), the principle of operation of the circuit described requires a time interval 1.3 times smaller. In addition, the copper losses in the stator winding of the generator decrease sharply (by more than a factor of 2), which is due to the replacement of continuous current by pulsed current.

To increase the efficiency of the circuit still further, an auxiliary capacitor bank may be connected in parallel with the load [5]. In this case, the share of energy transferred during each positive half-wave of the emf is considerably increased. This leads to a reduction in the time required to attain the same values of energy in the load as in the circuit without capacitance. For example, an auxiliary capacitor bank designed for an energy amounting to about

5% of the energy delivered to the load leads to a reduction of the accumulation time by approximately a factor of 2. In addition, the capacitor bank considerably facilitates the operation of the contact apparatus when the short-circuit is cleared—the uncharged capacitor bank takes up the commutation currents.

REFERENCES

1. V. V. Ivashin, A. V. Loos, G. A. Sipailov, K. A. Khorykov. A circuit for increasing the energy and the rate of its transfer from a surge generator to an inductive load. Izvestiya TPI, vol. 139, 1965.

2. V. V. Ivashin, G. A. Sipailov. Author’s Certificate No. 156200. Bulletin No. 15, 1963.

3. V. V. Ivashin, G. A. Sipailov. Arc-free interruption of large currents. Elektromekhanika, No. 9, 1964.

4. E. G. Komar, M. A. Gashev. Power-supply system for the electromagnet of the synchrophasotron of the Joint Institute for Nuclear Research. Elektrichestvo, No. 1, 1960.

5. G. A. Sipailov, K. A. Khorykov. On the joint operation of a surge generator and a capacitor bank into an inductive load. Izvestiya TPI, vol. 132, 1965.

6. A. V. Posse. Justification of replacing a rectifier by an equivalent generator for calculating transient processes. Izvestiya AN SSSR, Energetika i transport, No. 4, 1965.