Artificial Commutation Circuit with Choke Charging of the Commutating Capacitor

A. I. Zaitsev, B. A. Lapin

(Presented by the scientific seminar of the Electromechanical Faculty)

For turning off thyristors operating in direct-current circuits, capacitor commutation circuits have become the most widespread. A condition for the effective operation of such circuits over a wide range of load variation on a thyristor converter is the independence of the time interval provided to the thyristor for recovery of its control properties from the load current. In circuits with capacitive turn-off, in order to satisfy this condition it is necessary that the magnitude of the commutating pulse increase as the load current increases (see Fig. 4). For this purpose, in the pulse modulator shown in Fig. 1, a choke, Dr, is connected in series with the load; it serves to draw power from the load circuit into the commutation circuit.

Fig. 1

A feature of the operation of such a circuit is that the minimum voltage across the capacitor, corresponding to small loads, is equal to the supply-source voltage. As the load is increased, an increment of voltage proportional to the load current is added to this voltage. It should be noted that this voltage increment is added to the capacitor voltage with a delay within one commutation period. Therefore such a turn-off circuit can be used when a thyristor converter operates into an inductive load, in which the current reaches its steady-state value over several commutation periods.

A possible field of application for thyristor converters with this commutation circuit is the regulation of excitation of electric machines, control of electric-car drives and traction motors of electric locomotives, regulated inverters, etc.

The commutation process in the circuit of Fig. 1 can be divided into four stages. During the first stage, which begins after thyristor \(T_2\) is switched on, resonant recharging of the commutating capacitor takes place through the circuit \(C_1T_1T_2L_1\) (interval \(t_2\)—\(t_3\) in Fig. 2).

Fig. 2

The second stage is characterized by an increase of the current in the \(L_1 C_1\) circuit in the reverse direction (through \(D_1\)) from 0 to \(I_n\) (interval \(t_3—t_4\)). By the same amount, respectively, the anode current \(I_a\) of thyristor \(T_1\) decreases. When \(I_a=0\), the thyristor turns off and, under the action of the voltage \(U_2\), is biased in the reverse direction (Fig. 2, graph 3).

Fig. 3

During the time interval \(t_4—t_5\), corresponding to the third stage of operation of the circuit, the capacitance \(C_1\) discharges through the load. By assumption, the load has an inductive character; therefore, during the time interval \(t_4—t_5\), the current through the capacitor may be regarded as constant in magnitude, and a linear law of variation of the voltage \(U_c\) may be adopted.

The time provided to thyristor \(T_1\) for recovery of its control properties is indicated in graph 3 by \(\Delta t\).

The fourth stage of operation of the circuit \((t_5—t_6)\) begins when capacitor \(C_1\) has charged in the initial direction up to the supply-source voltage \(E\). From this moment there occurs a decrease of the current in the circuit \(C_1 L_1 D_1 L_{\mathrm{dr}}\) from \(i=I_n\) to 0, accompanied by a corresponding increase of the current through the bypass diode \(D_2\), which serves to create a continuous-current mode in the load. During this stage, all the energy stored in the inductances \(L_1\) and \(L_{\mathrm{dr}}\) is transferred to the commutating capacitance. The final voltage to which the capacitance is charged by the end of the fourth stage is the initial voltage for the first stage of the next commutation cycle.

This voltage can be found with the aid of the equivalent circuit for the fourth stage of commutation, which can be composed on the basis of the circuit of Fig. 1, taking into account that from the instant \(t_5\) the voltage on diode \(D_2\) becomes equal to zero (Fig. 3).

Solving the differential equation

\[ \frac{d^2 U_c}{dt^2} + \frac{r_4}{(L_1+L_{\mathrm{dr}})} \frac{dU_c}{dt} + \frac{1}{(L_1+L_{\mathrm{dr}})C_1}U_c = \frac{1}{(L_1+L_{\mathrm{dr}})C_1}E, \]

which describes the circuit of Fig. 3, with the initial conditions \(U_c(0)=E\), \(i(0)=I_n\), one can find the peak voltage on the capacitor:

\[ U_1 = E + k_4 I_n \sqrt{\frac{L_1+L_{\mathrm{dr}}}{C_1}}, \tag{1} \]

where

\[ k_4 = e^{-\frac{b_4 T_4}{4}}. \]

Here \(b_4, T_4\) are the damping coefficient and the period of the natural oscillations of the circuit in Fig. 3.

The voltage \(U_1\) is the initial voltage during the resonant recharging of the capacitor in the first stage of the next commutation cycle. Owing to losses in the \(L_1 C_1\) circuit, after recharging of the capacitance it will decrease to a value equal to

\[ U_2 = k_1\left(E + k_4 I_n \sqrt{\frac{L_1+L_{\mathrm{dr}}}{C_1}}\right), \tag{2} \]

where

\[ k_1=e^{-\frac{b_1T_1}{2}}, \]

\(b_1, T_1\) are the damping coefficient and the period of the natural oscillations of the \(C_1L_1\) circuit.

This voltage is the initial voltage for the second stage (interval \(t_3\)--\(t_4\)). Its duration \(t'\) depends on the load current and is determined by the following equation:

\[ I_{\mathrm{n}}=U_2\sqrt{\frac{C_1}{L_1}}\cdot e^{-b_2t'}\cdot \sin \omega_1t'. \tag{3} \]

The voltage on the capacitor at the end of the second stage is equal to

\[ U_3=U_2e^{-b_2t'}\cos \omega_1t'. \tag{4} \]

The possible range of variation of the time \(t'\) in equalities (3), (4) is equal to \(T_1/4\). Taking into account that, for circuits with small damping, the change in the quantity \(e^{-b_2t'}\) over the time interval from \(t'=0\) to \(t'=T_1/4\) is insignificant, the factor \(e^{-b_2t'}\) in expressions (3) and (4) may be regarded as constant and equal to

\[ k_2=e^{-b_2t'}. \]

Then, from equations (3) and (4), one can find the voltage on the capacitor at the end of the second stage:

\[ U_3=k_2U_2\sqrt{1-\frac{1}{(k_2)^2}\left(\frac{I_{\mathrm{n}}}{U_2}\right)^2\frac{L_1}{C_1}}. \tag{5} \]

Fig. 4.
Labels in the figure: \(u_k\), \(U_3\), \(E\), \(I_{\mathrm{n}1}>I_{\mathrm{n}2}>I_{\mathrm{n}3}\), \(\Delta t\), \(t_4\), \(t_5\), \(t\).

The third stage of operation of the commutation circuit is characterized by reverse biasing of the thyristor and by the linear discharge of the commutating capacitance. The waveform of the voltage at the cathode of thyristor \(T_1\) is shown in Fig. 4. As follows from this figure, the duration of reverse biasing of the thyristor, \(\Delta t\), is equal to:

\[ \Delta t=\frac{U_3}{I_{\mathrm{n}}}\cdot C_1 \tag{6} \]

Substituting into (6) the value of \(U_3\) from (5) and (2), we obtain:

\[ \Delta t= \sqrt{ \left[ \left(k_1k_2\frac{E}{I_{\mathrm{n}}}\right)^2 C_1^2 + 2k_4(k_1k_2)^2\frac{E}{I_{\mathrm{n}}} \sqrt{\frac{L_1+L_{\mathrm{dr}}}{C_1}}\,C_1^2 \right] + \left[ (k_1k_2k_4)^2(L_1+L_{\mathrm{dr}})C_1-L_1C_1 \right] } \tag{7} \]

As follows from expression (7), when the load current is increased, the time \(\Delta t\) provided to the thyristor for restoration of its control properties tends to a constant value:

\[ \Delta t_c=\lim_{I_n\to\infty}\Delta t= \sqrt{(k_1k_2k_4)^2(L_1-L_{\mathrm{dr}})C_1-L_1C_1} \tag{8} \]

When the condition \(\Delta t_c>t_{\mathrm{rest}}\) is satisfied, the commutation circuit with choke charging of the commutating capacitance will ensure turn-off of thyristor \(T_1\) at any load current.

It should be noted that, when the circuit is calculated according to the condition \(\Delta t_c>t_{\mathrm{rest}}\), in the case of a large value of \(t_{\mathrm{rest}}\) the capacitor will be charged to high voltages, which is not always acceptable. In this case the parameters of the circuit \(L_1\), \(C_1\), \(L_{\mathrm{dr}}\) can be determined by specifying the voltage and current in equation (1) and the value of \(\Delta t\) in expression (7). As a third condition one may take the period of natural oscillations of the circuit \(L_1C_1\):

\[ T_1 \cong 2\pi\sqrt{C_1L_1} \]

To illustrate the quality of operation of the described artificial commutation circuit, Fig. 5 gives the calculated and experimental dependences \(\Delta t=f(I_n)\). From the curves it is seen that, as the load current increases, the value of \(\Delta t\) decreases very slowly. The value of this interval decreases much more rapidly in the usual commutation circuit with the same value of the commutating capacitance (dashed curve).

Fig. 5.

The use of choke charging makes it possible to reduce considerably the size of the commutating capacitor. Owing to this, the lower threshold of voltage regulation at the load is reduced, which ultimately increases the regulation range.

Conclusions

1. In an artificial commutation circuit with choke charging of the commutating capacitor, the reliability of turn-off is increased due to automatic stabilization, as a function of load current, of the time interval provided to the thyristor for restoration of its control properties.

1. Choke charging of the commutating capacitor makes it possible to significantly reduce the value of its capacitance and thereby increase the control range of the thyristor converter.

2. The use of choke charging of the commutating capacitance makes it possible, in principle, to create commutation circuits capable of turning off a power thyristor at any load current.

3. An experimental comparison of various artificial commutation circuits showed that, in terms of commutation reliability and overload capacity, the developed circuit surpasses the circuits described in the literature.