ON A CURRENT SWITCHING SCHEME FOR GENERATING HIGH-ENERGY MAGNETIC FIELDS

V. V. IVASHIN, A. I. BLUDOV, V. L. GROMOK

The generation of powerful magnetic fields in electrophysical installations of various types, for example in elementary-particle accelerators, requires powerful switching devices possessing valve properties. In works [1, 2, 3] it was proposed that such devices be made of the ion-mechanical type. Very promising is the use, in devices of this type, of induction-dynamic drives, which make it possible to create fast-acting contact apparatuses for currents up to 100 kA and more at voltages of 10–15 kV, with contact closing and opening times of \(3 \div 5 \cdot 10^{-3}\) sec [3]. The design of a device using induction-dynamic drives proves to be simple and reliable in operation. However, induction-dynamic drives usually require comparatively powerful pulsed power supplies, the introduction of which into the switching device considerably complicates it.

In the present work, one of the possible electrical circuits of an arcless ion-mechanical switching device with an induction-dynamic contact drive is considered. The pulsed power supply of the drives is provided in this case by the energy of the circuit being switched, which makes it possible to substantially simplify the basic circuit of the device as a whole and to increase the reliability of its operation. Naturally, the use of individual auxiliary elements is not maximally effective, but on the whole the device proves to be the most advanced among known devices of this type.

Principle of Operation

The basic electrical circuit of switching device 1, when supplying inductive load 2 from energy source 3, is shown in Fig. 1. Suppose that in the electromagnet \(L_M\), from energy source 3, for example from a powerful capacitor bank, a high-energy magnetic field is produced. The discharge of the capacitor bank into the inductance \(L_M\) is oscillatory in character, and switching device 1 must ensure that only the first half-wave of current, the maximum in amplitude, passes through the load \(L_M\).

For this purpose it is sufficient, at the required instant of time \(t_0\), to open valve \(B_1\). The capacitor bank of energy source 1 begins to discharge through valve \(B_1\) into the load inductance \(L_M\) and paral-

...the load circuit with the coil \(L_1\) of the induction-dynamic drive for closing the contacts \(K\). When a current flows through \(L_1\), whose magnitude and waveform are determined by the parameters \(C_1, L_6, r_1\), the contacts close, and the current from valve \(B_1\), under the action of the drop in voltage across the valve and across the resistance \(r_2\), is transferred during the time \(t_2—t_3\) into the circuit with the contacts \(K\). The saturable reactor, whose inductance \(L_3\) in the saturated state is small, delays the rise of current in the contacts when they touch for the time \(t_1—t_2\). The inductance \(L_6\) and the capacitance \(C_1\) limit the voltage, as well as the amplitude and duration of the current flowing through the drive \(L_1\), to an admissible and necessary value.

Fig. 1. Circuit diagram of ion-mechanical switching of large currents

Fig. 2 shows the curve of the current \(i_3\), commutated by the contacts \(K\), the curve of the current \(i_2\), commutated by the valve \(B_1\), and the curve of the current \(i_1\), passing through the coil of the closing drive \(L_1\).

The disconnection process begins at the instant \(t_4\) by opening valve \(B_2\) \((3 \div 5)\cdot 10^{-3}\) sec before the load current [Figs. 2 and 4] passes through zero. The capacitance \(C_2\) is then discharged through the circuit \(L_3\)—contacts \(K\); the current in valve \(B_2\) rapidly rises to the value of the current in the inductive load, while in the contacts \(K\) it decreases to the value of the remagnetization current of the saturable reactor. The saturable reactor holds the current in the contacts at the zero level for the time interval \(t_5—t_p\) until they open. After the sign of the voltage on the capacitance \(C_2\) changes, the valve is opened by the control circuit and the current from \(B_2\) during the time \(t_7—t_8\) is transferred to \(B_1\). During the time \(t_4—t_9\), while the current passes through valve \(B_2\) and then through valve \(B_1\), the de-energized contacts have time to open to the required gap, capable of withstanding the voltage of the disconnected circuit.

The coil \(L_4\) of the induction-dynamic drive for opening the contacts is connected, as follows from Fig. 2, in series with the capacitance ...

$C_2$, which provides artificial de-energizing of the contacts. With such switching-on, the drive coil receives the necessary power from capacitance $C_2$ directly at the moment of switching-off. This substantially simplifies the circuit of the switching device itself and the control unit of the device, since it is not necessary to generate a signal for controlling the power-supply system of the opening drive. At the same time, the consequent introduction of the drive coil $L_4$, which consumes a great deal of energy, in series with capacitance $C_2$ increases the size of the capacitor bank $C_2$ and, as a consequence, increases the dimensions of the saturable reactor.

Fig. 2. Currents in the circuit during closing

Selection of the parameters of the elements operating during contact closing

For normal operation of the device under arc-free contact closing, two conditions must be satisfied:

1. The coil $L_1$ of the closing drive must receive sufficient power to ensure closing of the contacts within $(3 \div 5)\cdot 10^{-3}$ sec from the moment valve $B_1$ is opened.

2. After the contacts are closed, the main load current must flow not through valve $B_1$, but through the contacts.

The induction-dynamic drive can be characterized by the maximum magnetomotive force $F_{m3}$ of coil $L_1$, the rate of rise of the magnetomotive force $\dfrac{dF_{m3}}{dt}$, and the magnetic conductance $G$ of coil $L_1$. The concept of the rate of rise of the magnetomotive force can be replaced by the rise time $t_1$ of the magnetomotive force $F_{m3}$ to its nominal value. To ensure sufficient insulation of coil $L_1$, the maximum permissible voltage $U_{L_1}$ on the closing-drive coil is usually known.

In the general case, for the force developed by an electrodynamic drive, one may write [4]:

\[ f = i_1 \cdot i_2 \cdot \frac{dM}{dx}, \]

where

$i_1$ — current in the drive coil;
$i_2$ — current induced in the metal disk,

\[ \frac{dM}{dt} \]

is the derivative of the mutual-inductance coefficient with respect to the distance between the disk and the coil.

Figure 3 shows the characteristic form of the current through coil \(L_1\). The speed of response is affected practically only by the first current pulse, since the second, negative half-wave has a substantially smaller amplitude, and the derivative of the mutual inductance becomes small during the second current half-wave.

Let us derive approximate relations between the necessary parameters of the first pulse and the parameters of the circuit \(L_1\), \(C_1\), \(L_b\), \(r_1\). For the maximum value of the voltage on the drive coil \(L_1\), one may write

\[ U'_{L_1}=L_1 \cdot I_m \omega_1, \tag{1} \]

Fig. 3. Current pulse in the closing-drive coil

where

\[ I_m \text{ is the current amplitude without allowance for damping,} \]

\[ \omega_1 \simeq \frac{\pi}{2t_1} \text{ is the angular frequency without allowance for damping.} \]

Damping in the circuit affects mainly the current amplitude. Taking into account the decrease in current due to damping, for \(L_1\) we have:

\[ L_1=\frac{U_{L_1}' \cdot e^{-bt}\cdot 2t_1}{I_{mз}\cdot \pi}. \tag{2} \]

Expressing the amplitude value of the current \(I_{mз}\) through the magnetomotive force and taking into account that

\[ L_1=W_1^2 \cdot G, \tag{3} \]

where

\[ W_1 \]

is the number of turns of the closing-drive coil, after transformation we obtain:

\[ L_1=\frac{4t_1^2\cdot U_{L_1}^{\prime\,2}\cdot e^{-2bt}}{F_{mз}^2\cdot G\cdot \pi^2}. \tag{4} \]

If the maximum voltage at the power source is \(U^0\), then

\[ L_b=\frac{L_1\left(U_0-U_{L_1}\right)}{U_{L_1}}, \tag{5} \]

\[ C_1=\frac{4t_1^2}{\pi^2\left(L_b+L_1\right)}. \tag{6} \]

The resistance \(r_1\) is determined by the permissible overvoltages on the capacitance \(C_1\). At \(r_1=0\), the capacitance is charged to twice the voltage of the power source. In the case of the critical process, when

\[ r_1=2\sqrt{\frac{L_1+L_b}{C}}, \]

the capacitor is charged to the voltage of the power supply. In the critical mode the resistance has a strong influence on the current amplitude in the circuit, and the efficiency of the drive power-supply circuit is substantially reduced. In many cases it is rational to choose the resistance \(r_1\) from the condition

\[ e^{-\frac{r_1}{2(L_b+L_1)}\cdot t_1}\simeq 0.5, \]

which leads to small, up to \(20\%\), overvoltages on the capacitor, while the operation of the circuit proves sufficiently effective.

Calculation of currents and voltages in the circuit during closing

After an approximate determination of all parameters, the current curves in the drive coil and the voltage on the capacitor \(C_1\) during closing of the circuit can be constructed from exact formulas.

\[ i=\frac{U_{c0}}{\omega_0 L}\cdot e^{-bt}\sin\omega_0 t, \tag{7} \]

\[ U_{c_1}=-U_{c0}+U_{c0}e^{-bt}\left(\cos\omega_0 t+\frac{b}{\omega_0}\cdot\sin\omega_0 t\right), \tag{8} \]

where

\[ U_{c0}\text{ is the voltage on the charged capacitor,} \]
\[ \omega_0\text{ is the angular frequency of the switching circuit,} \]
\[ b\text{ is its time constant.} \]

At the end of the main pulse, when the current in valve \(B_1\) and, consequently, in the load reaches zero, the capacitor \(C_1\) is charged to the recharge voltage of the capacitor \(C\), \(U_{\mathrm{st}}\). When valve \(B_1\) is blocked at \(t_0\), the capacitor \(C_1\) begins to discharge through the circuit \(L_1—C_1—L_b—r_1—L_M\). In the closing-drive coil \(L_1\) there arises a current pulse described by the equation:

\[ i=\frac{U_{\mathrm{st}}}{\omega_0' L_{\mathrm{eq}}}\cdot e^{-b't}\sin\omega_0 t, \tag{9} \]

where

\[ L_{\mathrm{eq}}=L_1+L_b+L_M, \]

\[ b'=\frac{r_1}{2L_{\mathrm{eq}}};\qquad \omega_0=\sqrt{\frac{1}{L_{\mathrm{eq}}C_1}-(b')^2}. \]

This current, analogously to the current at the beginning of the pulse, causes electrodynamic forces to arise in the closing drive.

The magnitude of the current in the coil is thereby substantially reduced, since the considerable inductance \(L_M\) is included in the discharge circuit. The force arising in the drive during the flow of the discharge current of the capacitor \(C_2\) must be insufficient to effect the closing of the contacts \(K\).

At the instant \(t_2\), current commutation begins from the circuit with valve \(B_1\) into the circuit with the contacts. Solving, by the operational method, the voltage equation for the circuit with the contacts and valve \(B_1\) gives the following approximate equation for the current in valve \(B_1\):

\[ i_2=\frac{\lambda_1}{\delta}(1-e^{-\delta t})+\frac{\lambda_2}{\omega}\sin\omega t+\frac{\lambda_3}{\omega^2}(1-\cos\omega t)+ \]

\[ +I_2 e^{-\delta t}+\frac{a_3}{\delta}(1-e^{-\delta t}), \tag{10} \]

where

\[ \lambda_1 = \frac{a_1 \cos \psi + a_2 \sin \psi}{1+\dfrac{\omega^2}{\delta^2}} - \frac{\omega \delta (a_2 \cos \psi - a_1 \sin \psi)}{\omega^2+\delta^2}; \]

\[ \lambda_2 = \left( \frac{a_1 \cos \psi + a_2 \sin \psi}{1+\dfrac{\omega^2}{\delta^2}} \right) \frac{\omega^2}{\delta^2} + \frac{\omega \delta (a_2 \cos \psi - a_1 \sin \psi)}{\omega^2+\delta^2}; \]

\[ \lambda_3 = - \left( \frac{a_1 \cos \psi + a_2 \sin \psi}{1+\dfrac{\omega^2}{\delta^2}} \right) \frac{\omega^2}{\delta^2} + \frac{\omega^3 (a_2 \cos \psi - a_1 \sin \psi)}{\omega^2+\delta^2}; \]

\[ a_1=\frac{\omega L_3 I_m}{L_3+L_2}; \qquad a_2=\frac{I_m r_3}{L_3+L_2}; \qquad a_3=-\frac{U}{L_3+L_2}; \]

\[ \delta=\frac{r_3+r_2}{L_3+L_2}; \]

\(\psi\) is the phase-shift angle of the main current relative to the current in the valve,

\[ \psi=\arcsin \frac{I_2}{I_m}; \]

\(I_m\) is the maximum commutated current;
\(U\) is the burning voltage of the valve.

The resistance \(r_2\), on which the remagnetization time of the choke \(D\) depends, should not be very small, so that the voltage across it is sufficient for remagnetization of the choke in a time not less than \(1\ \mu\text{s}\).

The current in the contacts:

\[ i_3=i-i_2=I_m \sin(\omega t+\psi)-i_2. \tag{11} \]

Figure 2 shows the form of the current curve \(i_2\), characteristic for real parameters of commutated circuits.

Selection of parameters and calculation of currents and voltages when the contacts open

The inductance of the opening coil \(L_4\) is selected on the basis of the required operating speed of the apparatus, specified by the value of the maximum magnetomotive force, taking into account the magnitude of the current in the contacts at \(t_4\).

The capacitance \(C_2\) must be sufficiently large so that the amplitude of the discharge current is not less than the current being switched off, and complete transfer of the current into the commutating capacitance \(C_2\) is possible.

The current and voltage in the capacitance \(C_2\) during transfer of the current from the contacts into the capacitance are described by sinusoidal damped functions:

\[ i_4=\frac{U_{c2m}}{\omega'_k L_k} e^{-b_k t}\sin \omega'_k t; \tag{12} \]

\[ U_{c2}=-U_{c2m} e^{-b_k t}\sin(\omega'_k t+\psi_k), \tag{13} \]

where

\(U_{c2m}\) is the voltage on the capacitance \(C_2\) at the initial instant of opening;

\[ \omega'_k=\sqrt{\frac{1}{L_k C_2}-b_k^2}; \qquad L_k=L_4+L_3; \]

\[ b_k=\frac{r_4+r_3}{2L_k};\qquad \psi_k=\operatorname{arc\,tg}\frac{\omega'_k}{b_k}. \]

The current in the contacts at this time decreases according to the formula

\[ i_3 \approx I_4-kt-i_4, \tag{14} \]

where

\[ I_4-kt=i_4+i_3=i \]

is the current in the main circuit.
\(K\) is the derivative of the current at \(t=t_4\),

\[ K=\frac{di}{dt}=\frac{U}{L}. \]

The current in the capacitance \(C_2\) when it is transferred from the capacitance to valve \(B_1\) \((t_7-t_8)\) is determined by

\[ i_4=\frac{I_4L_4+L_2\cdot I_7}{L_4+L_2}\,e^{-bt} \left(\cos\omega_0t-\frac{b}{\omega_0}\sin\omega_0t\right)+ \]

\[ +\frac{I_7r_2-L_2K-U_{c0}}{(L_4+L_2)\omega_0}\,e^{-bt}\sin\omega_0t, \tag{15} \]

where \(U_{c0}\) is the voltage on the capacitance \(C_2\) at the instant \(t_7\). For the current in valve \(B_1\) we write: \(i_2=i-i_4\approx I_7-kt-i_4\). The current in the capacitance \(C_2\) between transfers \((t_5-t_7)\) is determined as

\[ i_4\approx I_5-kt. \tag{16} \]

The voltage on the capacitance in this interval of time is

\[ U_{c2}=\frac{1}{C_2}\int i_4\,dt=\frac{I_5\cdot t}{C_2}-\frac{kt^2}{2C_2}+U_5. \tag{17} \]

Fig. 4. Currents in the circuit during opening.

And on the choke or on the valve:

\[ U_{\text{d}}=U_{B1}=U_{c2}+L_4\frac{di_4}{dt}+i_4r_4= \]

\[ =\frac{I_5\cdot t}{C_2}-\frac{Kt^2}{2C_2}+U_5-L_4K+(I_5-\kappa t)r_4. \tag{18} \]

The entire disconnection process is shown in Fig. 4.

From formulas 17 and 18 one can determine, for the specified parameters, the voltage across the choke from the start of contact motion \(t_k\) to their complete separation \(t_p\), which in turn determines the required flux linkage of the choke, ensuring reversal of the choke magnetization within the required time interval, not less than \(1\ \mu\text{s}\).

REFERENCES

1. V. V. Ivashin, G. A. Sipailov. Arc-free switching of large currents. Elektrotekhnika, No. 9, 1964.

2. V. V. Ivashin. Inventor’s Certificate No. 155206.

3. V. V. Ivashin, A. I. Blyudov. A new high-power switching device. Proceedings of the VI Interuniversity Conference on Electron Accelerators, 1966.

4. V. N. Bondaletov. A method for calculating electromagnetic forces and their work under arbitrary variation of flux linkages, currents, self- and mutual inductances. TVN, Proceedings of MEI, vol. LXIV, 1965.