UDC 621.316.3

ON A METHOD FOR SWITCHING THE CURRENT OF AN INDUCTIVE LOAD FROM ONE GROUP OF VALVES TO ANOTHER

V. V. IVASHIN, E. G. FURMAN

When exciting accelerator electromagnets in installations for thermonuclear research, it becomes necessary to obtain a magnetic cycle with a complex law of variation in time. In oscillatory \(LC\) circuits such fields are obtained by artificial switching of the current of the inductive load from the discharge circuit of the storage capacitor into the recharge circuit, or by disconnecting the inductive load from the storage device with subsequent short-circuiting, etc. [1, 2]. In this case it is necessary to provide conditions for the normal operation of controlled switching devices with respect to the rate of rise of current and the recovery time of their control properties.

In [1, 2], individual circuits of commutating capacitances in high-power \(LC\) circuits were considered for forming in them currents of triangular, sinusoidal, and trapezoidal shape. In such circuits, to provide artificial turn-off of each of the controlled devices in the \(LC\) circuit, an additional controlled device is required.

In the present work a circuit using a multiwinding transformer is considered, suitable for capacitances for artificial switching of several switching devices simultaneously, including cases in which these devices have no common points at the anodes and cathodes. Such a solution increases the reliability of operation of the circuit as a whole by reducing the total number of controlled devices and eliminating certain emergency modes. It is expedient to make the transformer with premagnetization and to select its parameters taking into account saturation of the magnetic core and a number of specific features of the circuit operation.

Let us consider the operation of the circuit using as an example the switching of devices in a circuit with the formation, in an inductance \(L\), of triangular current pulses (Fig. 1). The storage capacitor \(C\), through thyristors \(T_1, T_1^{i}\) and diodes \(D_1, D_1^{i}\), is connected to the electromagnet \(L\). In series with the diodes are connected the secondary windings of the commutating transformers \(Tr_1, Tr_2\), whose primary windings are connected in series and, through thyristor \(T_2\), are connected to the commutating capacitor \(C_1\). The magnetic cores of the transformers are premagnetized by the current of the electromagnet \(L\), flowing through the windings \(W_3\). Capacitor \(C_1\) has a recharge circuit consisting of diode \(D_2\) and inductance \(L_1\). The essence of forming triangular current pulses consists in an artificial stepwise ...

the transfer of the circuit from the mode corresponding to the angle $\omega t_k$ to the mode corresponding to the angle $\pi-\omega t_k$ (Fig. 1b). For this it is necessary to turn off thyristors $T_1$, $T_1^1$ and turn on diodes $D_1$, $D_1^1$. By the instant $t_1$ the electromagnet current is closed through the circuit: capacitor $C$, thyristor $T_1$, demagnetizing winding $W_3$ of transformer $\mathrm{Tr}_1$, electromagnet $L$, demagnetizing winding $W_3$ of transformer $\mathrm{Tr}_2$, thyristor $T_1^1$. In this case the magnetic state of the transformers is characterized by point $A$ in Fig. 3. The storage capacitor $C$ and the commutating capacitor $C_1$ are charged, respectively, to the voltages $U_2$ and $U_1$. At the instant of time $t_1$ thyristor $T_2$ is turned on and the commutating capacitor $C_1$ is connected to the primary windings of transformers $\mathrm{Tr}_1$ and $\mathrm{Tr}_2$. Under the action of the voltage induced in the secondary windings $W_2$, over time the current in diodes $D_1$ and $D_1^1$ begins to increase, while the current of thyristors $T_1$ and $T_1^1$ decreases so that the sum of the currents $i_T$ and $i_D$ of both branches during the commutation time $t_\gamma$ in Fig. 2 is equal to the current of the inductive load

\[ t_\gamma=\frac{I_m\cdot L_k}{U_{W_2}-U_2}, \tag{1} \]

where $U_{w_2}$ is the voltage induced in the secondary winding of the commutating transformer; $L_k$ is the equivalent inductance of the discharge circuit of capacitance $C$, taking into account the referred inductances of the secondary circuits with diodes, thyristors, and capacitor $C_1$.

Fig. 1. Circuit for supplying an electromagnet with triangular current pulses.

To simplify the analysis of electromagnetic processes in the circuit, let us consider the operation of one commutating unit. From the instant of time $t_2$ (Fig. 2) the commutating capacitor $C_1$ is discharged by the current

\[ i_c(t)=I_m\cdot W_2/W_1+i_\mu, \tag{2} \]

where $i_\mu$ is the transformer magnetizing current. If the insignificant change in the electromagnet current during the discharge of the commutating capacitor is not taken into account and the magnitude of the transformer magnetizing current is neglected, then the reverse voltage applied to the thyristor can be determined as

\[ U_T(t)=U_1\cdot W_2/W_1-U_2+ \left[ \frac{I_m}{C} - \frac{I_m\cdot W_2^2}{W_1^2\cdot C_1} \right](t+t_\gamma). \tag{3} \]

Equating $U_T(t)=0$, we determine the time allotted to the thyristor for recovery of its valve properties (Fig. 2)

\[ t_{\mathrm{v.t.}}= \frac{U_1\cdot W_2/W_1-U_2} {I_m\cdot W_2^2/W_1^2\cdot C_1-I_m/C} -t_\gamma. \tag{4} \]

Under the action of the positive voltage of the commutating capacitor, applied to the primary winding of the transformer, its core during the time \(t_3-t_1\) is remagnetized from \(B_1\) to \(-B_2\). With zero voltage on capacitor \(C_1\), the magnetic state of the core is characterized by point \(D\) in Fig. 3. In the time interval \(t_4-t_3\) the commutating capacitor is recharged, and the transformer core is remagnetized from induction \(-B_2\) to \(+B_m\) (Fig. 3). At time \(t_4\) the transformer core becomes saturated, and thyristor \(T_2\) is turned off.

With symmetrical remagnetization of the transformer core from \(+B_m\) to \(-B_m\) and back from \(-B_m\) to \(+B_m\), the initial and final voltages on the commutating capacitor \(C_2\) are equal, i.e., the energy of the \(LC\) circuit increases during capacitor discharge and decreases during recharge by the amount of energy stored in the commutating capacitor.

Fig. 2. Curves of current and voltages in the circuit during current commutation from thyristor to diode

Fig. 3

If remagnetization of the core is asymmetrical, as shown in Fig. 3, then the induction at point \(A\) of the magnetization curve will be less than the saturation induction, and the initial and final voltages on the commutating capacitor will be different. The final voltage on capacitor \(C_2\) is proportional to the ratio of the change in induction, i.e.,

\[ U_1^{1}=U_1(\Delta B_1+\Delta B)/\Delta B_1. \tag{5} \]

The induction \(B_1\) in the transformer core is chosen from the condition that, when capacitor \(C_1\) is recharged through \(L_1\) and \(D_2\) (Fig. 1), the final voltage on the capacitor is equal to the required value of the voltage on it before commutation. The value of the induction to which the transformer core must be premagnetized can be determined from the condition

\[ B_1=B_m\cdot e^{-b/2}, \tag{6} \]

where \(b\) is the damping coefficient of the recharge circuit \(C_1, L_1, D_2\).

The design parameter determining the dimensions of the transformer will be

\[ W_1\cdot S=\frac{\Psi}{B_1+B}, \tag{7} \]

where \(S\) is the cross section of the steel of the core magnetic circuit, and \(\Psi\) is the transformer flux linkage, equal to

\[ \Psi=\int_{t_1}^{t_3} U_1(t)dt \simeq \frac{I_m \cdot W_1 \cdot t_k^2}{2 \cdot W_2 \cdot C_1}. \tag{8} \]

The structural design calculation of the transformer is carried out according to known methods for calculating pulse transformers, for example [3]. When placing several secondary windings on the transformer, it is necessary to determine the discharge current of capacitance \(C\) from (2) with allowance for this factor, and also to take into account the inductances of all secondary circuits when determining \(t_y\) in (1), etc., according to known relationships. It should be noted that, in the commutation method considered, saturation of the transformers at the instant \(t_4\) prevents overvoltages from arising in the circuit.

Conclusions

1. The considered method of capacitive forced commutation of the current of an inductive load from one group of valves to another through an isolating transformer, using a single commutating capacitor bank, makes it possible to commutate currents simultaneously in a number of groups of devices that have no common anode–cathode points.

2. The basic calculation relationships obtained make it possible to carry out an engineering calculation of the commutating unit.

Literature

1. V. V. Ivashin, G. A. Sipailov. PTE, 1966, No. 5, 151.
2. V. V. Ivashin. Dissertation. Tomsk, 1968.
3. Ya. S. Itskhoki. Pulse Devices. Gosenergoizdat, 1958.