A Simple Circuit for Pulse Feeding of a Converter of Electromagnetic Energy into Kinetic Energy

V. V. Ivashin, I. M. Churkin

(Presented by the scientific seminar of the departments of electrical machines and general electrical engineering)

Pulsed magnetic fields are widely used both in the technology of physical experiments, where a large circle of engineers is engaged in producing them, and in the creation of installations where electromagnetic energy is converted by pulses into kinetic energy of motion—electromagnetic launchers, hammers, fast-acting electromagnetic drives of switching apparatus, etc.

Recently, alongside electromagnetic systems, induction-dynamic and electrodynamic systems have been receiving ever broader development and application. In such systems, the volume occupied by the magnetic field is formed with the aid of the magnetizing forces of windings, which may be made in the form of short-circuited plates of conducting material, rings, etc. Such systems make it possible to use magnetic fields whose intensity is considerably higher than the saturation of ferromagnets, which determines an energy-conversion time measured by a quantity on the order of \((0.5 \div 10)\cdot 10^{-3}\) sec.

Capacitor banks capable of developing the powers required for creating the converter’s magnetic field are widely used in the supply circuits of such converters. These powers exceed the powers of the supply network by tens of times.

A typical, widely used pulse-feeding circuit, using the example of an induction-dynamic converter, is shown in Fig. 1. The main energy storage element—the capacitance \(C_{\text{н}}\)—is charged from a power source, for example a rectifier, through the limiting charging choke \(L_{\text{з}}\). When the switching device \(T_1\) is fired, the capacitor \(C_{\text{н}}\) discharges into the winding \(L_{\text{н}}\) and is short-circuited by the diode \(D\) when a positive voltage arises across it. The closing of the current

Fig. 1. Typical feeding circuit of a pulsed induction-dynamic converter with short-circuiting.

short-circuiting the load at its maximum value eliminates recharging of the capacitance \(C_{\mathrm{n}}\) to a voltage of opposite polarity and provides improved conditions in the load for conversion of energy into kinetic energy [1, 2].

In such circuits the amount of energy transferred from the capacitor \(C_{\mathrm{n}}\) to the load can be regulated mainly by changing the voltage across the capacitance, which requires a controlled rectifier. Artificial turn-off of thyristor \(T_1\) is possible with the aid of circuits widely used in pulse-width voltage regulation [3], but all of them require the obligatory use of controlled switching devices.

Fig. 2. Power-supply circuit with partial discharge of the capacitance

Figure 2 shows a circuit that we investigated and used to supply a powerful induction-dynamic energy converter. The circuit makes it possible, over a wide range, to regulate the turn-off instant of thyristor \(T_1\) without additional controlled devices, which substantially increases the reliability of the power-supply and control circuits.

In a number of cases, regulation of the thyristor turn-off instant is required in order to improve the energy-conversion process. When thyristor \(T_1\) is turned on, the capacitance \(C_{\mathrm{n}}\) begins to discharge into the load \(L_{\mathrm{n}}\). Through the inductance \(L_{\mathrm{k}}\), an oscillatory charging of the commutating capacitance \(C_{\mathrm{k}}\) takes place. The parameters \(L_{\mathrm{k}}\) and \(C_{\mathrm{k}}\) are chosen so that the voltage \(u_{\mathrm{k}}\) across the capacitance \(C_{\mathrm{k}}\) (Fig. 2) at some instant \(t_{\mathrm{k}}\) becomes greater than the voltage \(u_{\mathrm{cn}}\) of the partially discharged capacitance \(C_{\mathrm{n}}\) (Fig. 3). Diode \(D_2\) opens at the instant \(t_{\mathrm{k}}\), and the saturation choke \(D N\) begins to be remagnetized under the action of the voltage difference across the capacitances \(C_{\mathrm{k}}\) and \(C_{\mathrm{n}}\). By the instant \(t_2\) it becomes saturated, its inductance decreases, and thyristor \(T_1\) is de-energized and turns off by the discharge current of the capacitance \(C_{\mathrm{k}}\). When the capacitance \(C_{\mathrm{k}}\) is discharged to zero, it is short-circuited by diode \(D_1\). The unipolar operating mode of the capacitors \(C_{\mathrm{n}}\) and \(C_{\mathrm{k}}\) with respect to voltage makes it possible to use high-energy pulse or electrolytic capacitors. The instants at which diode \(D_1\) opens and thyristor \(T_1\) turns off can be regulated over a wide range by changing the values of the inductance \(L_{\mathrm{k}}\) or the capacitance \(C_{\mathrm{k}}\).

Analysis of the circuit and selection of its parameters

In calculating the circuit it is necessary to determine the values of the inductance \(L_{\mathrm{k}}\), the capacitance \(C_{\mathrm{k}}\), and the flux linkage of the saturation choke \(D N\) that ensure the specified turn-off instant of the thyristor, for known values of the capacitance \(C_{\mathrm{n}}\), the maximum voltage at its terminals \(U_m\), and also of the nonlinear active-inductive load \(L_{\mathrm{n}}\). Solving the problem in general form involves considerable difficulties, since the exact law

Fig. 3. Equivalent circuit of the charging circuit (a) and current and voltage curves in the power-supply circuit (b)

the variation of the parameters of the active-inductive load, determined by the nonlinear character of the energy conversion, is usually unknown. A comparatively simple and, in many practical cases, sufficiently accurate solution of this problem is obtained by approximating the voltage on the capacitance \(C_{\mathrm{n}}\) by a cosine function

\[ u_{C_{\mathrm{n}}}=U_m\cos\omega t, \tag{1} \]

where \(\omega\) is the natural frequency of the \(C_{\mathrm{n}}L_{\mathrm{n}}\) circuit.

Such an assumption is justified by the fact that the energy transferred from the capacitance \(C_{\mathrm{n}}\) into the \(L_k C_k\) circuit is considerably less than the total energy of the storage capacitor \(C_{\mathrm{n}}\), while the inductance \(L_{\mathrm{n}}\) changes little during the charging time of the capacitance \(C_k\), by no more than \(5 \div 10\%\). The charge of the capacitance \(C_k\) usually satisfies well the condition of oscillatory behavior; therefore, in addition, the active resistances of this circuit may be neglected, and the equation of the charging process will have the form

\[ u_{L_k}+u_{C_k}=U_m\cos\omega t, \tag{2} \]

where \(u_{L_k}\) and \(u_{C_k}\) are the voltage drops across the inductance \(L_k\) and the capacitance \(C_k\).

The parameters of the switching circuit for a given frequency \(\omega_0\) are chosen from the condition of ensuring the voltage difference \(\Delta U_k\) and acceptable values of capacitance and inductance.

It follows from the principle of operation of the circuit that the energy of the capacitance \(C_k\) is usefully employed in the conversion process, whereas the energy of the inductance \(L_k\) is dissipated as heat; therefore preference should be given to large values of capacitance. From (2) one can determine the voltage on the capacitance \(C_k\) and the current of its charge

\[ u_{C_k}=U_m\,\frac{\omega_0^2}{\omega^2-\omega_0^2}\left(\cos\omega_0 t-\cos\omega t\right), \tag{3} \]

\[ i_{C_k}=U_m\frac{\omega_0^2 C_k}{\omega^2-\omega_0^2}\left(\omega\sin\omega t-\omega_0\sin\omega_0 t\right), \tag{4} \]

where \(\omega_0\) is the frequency of the \(L_k C_k\) circuit.

Figure 3 shows the nature of the variation of the voltage \(u_{C_k}\) for different values of \(\omega_0\). From the simultaneous solution of (1) and (3), one can obtain an equation relating the frequency \(\omega_0\) and the instant \(t_k\):

\[ \cos \omega t_k - n \cos \omega_0 t_k = 0, \]

where

\[ n=\frac{\omega_0}{\omega}. \]

With a known \(t_k\), it is not difficult to determine from it the corresponding value of \(\omega_0\), and then to choose the parameters \(L_k\) and \(C_k\).

A characteristic quantity necessary for determining the parameters of the saturating choke is the time instant \(t_2\), when the voltage across the commutating capacitance becomes greater than the instantaneous value on the capacitance \(C_n\) by the amount \(\Delta U_k\), necessary to ensure reliable turnoff of thyristor \(T_1\) and its blocking.

\[ \Delta U_k \approx \frac{t_{\mathrm{rec}}}{C_k} I_m \sin \omega t_k , \tag{5} \]

where \(t_{\mathrm{rec}}\) is the recovery time of the control properties of the thyristor. \(\Delta U_k\) can be expressed as

\[ \Delta U_k = u_{C_k}-u_{C_n}. \tag{6} \]

Taking into account expressions (1) and (3), from (6) we obtain

\[ \Delta U_k = U_m\frac{\omega_0^2}{\omega^2-\omega_0^2} \left(\cos\omega_0 t_2-\cos\omega t_2\right) - U_m\cos\omega t_2 , \tag{7} \]

whence, for any values of \(\omega\), \(\omega_0\), and \(\Delta U_k\), it is not difficult to determine \(t_2\).

In general form, the time \(t_2\), for a given value of \(n\), is determined by solving the trigonometric equation:

\[ n^2\cos\omega_0 t_2-\cos\omega t_2 = \frac{\Delta U_k}{U_m}(1-n^2). \]

The flux linkage of the choke required for normal operation of the supply circuit is determined by the value of the hatched area in Fig. 3, enclosed between the line \(u_{C_n}\) and the lines \(u_{C_k}\) constructed from the condition of ensuring the commutation instant at the angle \(\omega t_k\).

\[ \Psi = \int_{t_k}^{t_2}\left[u_{C_k}(t)-u_{C_n}(t)\right]dt = \frac{U_m\omega_0^2}{\omega^2-\omega_0^2} \left[ \frac{1}{\omega_0}\left(\sin\omega_0 t_2-\sin\omega_0 t_k\right) \right. \]

\[ \left. - \frac{1}{\omega}\left(\sin\omega t_2-\sin\omega t_k\right) \right] - \frac{U_m}{\omega}\left(\sin\omega t_2-\sin\omega t_k\right). \tag{8} \]

The saturating choke has the greatest flux linkage at the commutation angle \(0.5\pi\). Taking into account that, in the range of angles \(\omega t_k \approx 0.5\pi\), the cosine function describing the variation of the voltage \(u_{C_n}\) may be replaced by a straight line,

\[ u_{C_n}=-U_m\omega t, \tag{10} \]

the maximum value of the choke flux linkage can be determined by the formula:

\[ \Psi_m=\frac{\Delta u_k^2}{2U_m\omega}. \tag{11} \]

The condition $\omega t_k = 0.5\pi$ corresponds to a circuit solution in which $C_k \to \infty$, $C_n \to \infty$, which in practice can be obtained by connecting a series circuit consisting of a saturating reactor and a diode in parallel with the load. Commutation of the current of thyristor $T_1$ in this case is accomplished by discharging onto it the capacitance $C_n$, recharged to the voltage minus $\Delta u_k$. At $\omega t_k \approx 0.5\pi$, a unipolar mode of operation with respect to the voltage of capacitor $C_n$ is not ensured. Such a mode is ensured when $\omega t_k < \dfrac{\pi}{2}$.

The magnitude of the saturating reactor also decreases as the angle $\omega t_k$ is reduced.

If, by the instant $t_k$, the load inductance has changed substantially as a result of energy conversion in comparison with its initial value, then the approximation of the voltage $u_{Cn}$ by (1) will give a significant error. In this case the flux linkage of the reactor can be determined from the mean values of the currents through the capacitances $C_n$ and $C_k$, determined with allowance for the change in inductance $L_n$, or from oscillograms of the current in the circuit, obtained in an actual installation or on an analog computer.

From the operating principle of the circuit it follows that, after thyristor $T_1$ is turned off, instead of the capacitance $C_n$ the capacitance $C_k \ll C_n$ is connected into the load circuit; it rapidly discharges and is clamped by diode $D_1$. The energy stored in the capacitance $C_k$ after thyristor $T_1$ is turned off is transferred to the magnetic field and can be usefully employed in energy conversion. The energy stored in the inductance $L_k$ after saturation of the reactor S. R. is dissipated in the active resistances of the windings of the inductance $L_k$ and of the reactor.

For better utilization of the magnetic core of the saturating reactor, it may be premagnetized by the load current, by the capacitance-charging current, or by current from an external source.

The circuit for pulsed production of a magnetic field was tested in the mode of operation into an inductive load with constant and variable inductance with the parameters: $U_m = 400$ volts, $C_n = 30 \cdot 10^{-3}$ F,

Fig. 4. Oscillograms of processes in the power-supply circuit at a commutation angle of $40^\circ$ (a) and $80^\circ$ (b) of the period of the main circuit.

\(C_k = 2 \cdot 10^{-3}\ \mathrm{F}\). The duration of the current pulse in the load was \((10 \div 15)\cdot 10^{-3}\ \mathrm{s}\). The weight of the saturable reactor did not exceed \(3\ \mathrm{kg}\). The amplitude of the current in the \(L_n\) winding was \(1000\ \mathrm{A}\) for constant inductance, and \(720\ \mathrm{A}\) for variable inductance.

The load was made in the form of the inductor of an induction-dynamic energy converter, the weight of whose striker is \(100\ \mathrm{kg}\), and the total weight with the inductor is \(400\ \mathrm{kg}\). The oscillograms in Fig. 4, a, b show the curves of the variation of the voltages on the storage and commutating capacitors and of the load current at a commutation angle of \(\sim 40^\circ\) (a) and \(85^\circ\) (b) of the circuit frequency \(\omega\). The circuit made it possible to regulate over wide limits the energy transferred from the storage capacitor to the load. The maximum striker velocity was \(1.44\ \mathrm{m/s}\) in the oscillogram of Fig. 4, a, and \(2.7\ \mathrm{m/s}\) in the oscillogram of Fig. 4, b. The coefficient of conversion of the energy of the capacitance \(C_n\) into kinetic energy (efficiency) under various operating conditions has the value \((25 \div 30)\%\).

Conclusions

1. The circuit operates with electrolytic capacitors and makes it possible, without the use of additional controlled commutating devices, to commutate the load current during a partial discharge of the storage capacitance. Changing the commutation angle \(\omega t_k\) makes it possible, in a simple manner and over wide limits, to regulate the magnitude of the energy introduced into the load and thus to vary the power of the electromechanical converter.

2. The cost and dimensions of the auxiliary elements of the artificial-commutation circuit—the inductance \(L_k\), the capacitance \(C_k\), and the reactor DN—constitute an insignificant part of the cost and dimensions of the main capacitance \(C_k\), even for current-pulse durations up to \(20 \cdot 10^{-3}\ \mathrm{s}\). For longer current pulses the capability of the circuit is limited by the size of the commutating reactor DN.

3. Application of the circuit is possible in any systems of electromechanical converters (electromagnetic, electrodynamic, induction-dynamic, etc.) when pulsed currents must be passed through the windings.

4. The analysis carried out of the operation of the circuit and the formulas obtained make it possible to determine correctly all the basic parameters of the elements.

LITERATURE

1. Smart D. L. Proc. Instr. Electical Engs., A-106, suppl N 2, 1959.
2. Rogers. Proc. Instr. Electrical Engs., vol 116, N 1, 1969.
3. I. N. Kraitsberg, E. V. Shikht. Pulse methods for regulating direct-current circuits by means of thyristors. Moscow, “Energiya,” 1969.
4. V. V. Ivashin, E. G. Furman. Experimental study of losses in capacitors of type IM-3/100. Proceedings of the Research Institute of Nuclear Physics, issue 1, Moscow, Atomizdat, 1971.