INVESTIGATION OF THYRISTOR FORCED-COMMUTATION DEVICES ON AN ANALOG COMPUTER

V. A. Beinarovich, A. E. Deev, L. S. Udut, V. S. Fadeev

(Presented by the scientific and technical seminar of the NII AEM)

Forced-commutation devices for thyristors (FCDs) are the principal elements determining the operating reliability, dynamic properties, energy characteristics, weight, and dimensions of power thyristor reversible pulse-width converters. Of the large number of known FCDs, in our opinion the best capabilities are offered by an FCD with independent charging of the commutating capacitor and a diode-inductive reset circuit, the equivalent circuit of which is shown in Fig. 1.

Fig. 1.

Such FCDs have a number of advantages. The charging and discharging of the commutating capacitor in these FCDs is carried out through separate charge-discharge circuits independently of the load-current magnitude, down to no-load operation of the converter, when the load current is zero. In such FCDs there is an automatic increase in the commutating voltage \(U_c\) on the commutating capacitor \(C_k\) as the load current increases, due to the voltage increment produced by the reactor \(L_k\), which makes it possible to substantially increase the short-term overloads of the converter. Energy losses during the commutation process are reduced, since the energy of the capacitor \(C_k\) not used for commutation of the power current is returned to the capacitor owing to the oscillatory process in the circuit \(C_k L_k\) and the presence of the recharge circuit \(C_k L_p\), bypassing the power source, the supply circuits, and the load.

In this FCD, only an additional charge of the commutating capacitor is drawn from the power source in order to cover energy losses in the commutating and recharge circuits. In the forced-commutation device under consideration there is no possibility of failure of

commutation due to the occurrence of a through current through the commutating thyristor and the charging circuit, since in the charging circuit of the forced-commutation device a thyristor is used rather than a diode, with turn-on synchronization delayed relative to the commutating thyristor; furthermore, a blocking circuit is used which prevents the passage of a triggering pulse to turn on the commutating thyristor until the commutating capacitor \(C_k\) has been charged to a preset voltage. Forced-commutation devices built according to the circuit of Fig. 1 make it possible, by means of a pulse transformer, to transform the commutating voltage simultaneously in several commutated thyristor circuits that are galvanically isolated from one another. Another advantage of such forced-commutation devices is that they are supplied from the same source as the motor supply, i.e., no separate power supply is required. This is because the forced-commutation device under consideration does not use the phenomenon of “pumping” from the power source in order to raise the commutating voltage, which would considerably increase the preparation time of the forced-commutation device for operation.

A method for determining the optimal parameters of a forced-commutation device can be developed on the basis of studies of the influence of the magnitudes of the parameters of the forced-commutation device on the electromagnetic processes in the circuit, the commutation properties, and the energy and dynamic indices of the forced-commutation device.

During operation of a forced-commutation device, owing to the switching of the valves, the electrical circuit changes, and it is convenient to consider the electromagnetic processes over time intervals during which the circuit does not change, while the initial conditions are determined by the final values of the quantities in the preceding interval.

When the forced-commutation device is initially switched on, the commutating capacitor \(C_k\) is charged from the power source \(E\) through switch T2 (Fig. 1). The differential equations of the process have the form

\[ \left. \begin{aligned} E &= U_c + L_3 \frac{di_3}{dt} + i_3 r_3,\\ i_3 &= i_c = - C_k \frac{dU_c}{dt} \end{aligned} \right\}. \tag{1} \]

After the charging of the capacitor \(C_k\) is completed, at the instant of commutation switch T1 is closed, the capacitor \(C_k\) discharges through the commutating choke \(L_k\), and the process will be described by the differential equations

\[ \left. \begin{aligned} U_c &= L_k \frac{di_k}{dt} + i_k r_k,\\ i_k &= - C_k \frac{dU_c}{dt} \end{aligned} \right\}. \tag{2} \]

When switch T2 is switched on again, the capacitor \(C_k\) is recharged with simultaneous topping-up of its charge from the power source. The differential equations of the process in this time interval have the form

\[ \left. \begin{aligned} E &= U_c + L_3 \frac{di_3}{dt} + i_3 r_3,\\ U_c &= L_p \frac{di_p}{dt} + i_p r_p,\\ i_3 + i_p &= - C_k \frac{dU_c}{dt} \end{aligned} \right\}. \tag{3} \]

The recharging process ends faster than the process of additional charging from the power source, and when the recharging current decreases to zero, the process is again described by the differential equations (1).

Since the analytical solution of equations (1), (2), (3) and the selection, on the basis of the solution results, of the parameters of the TFC device by analyzing the influence of the parameters on the commutation properties of the TFC device present great difficulties, the solution of these equations and the analysis of the influence of the parameters on the commutation processes are carried out with the aid of an analog computer.

In constructing the electronic model of the TFC device, assumptions were adopted concerning the ideality of the valves: the resistance of a valve in the forward direction is equal to zero, the reverse current of a valve is not taken into account, and commutation of the valves takes place instantaneously. Such assumptions are generally accepted and facilitate modeling without introducing a significant error.

For convenience of modeling, let us represent the differential equations (1) for the charging circuit in the form of a system of two equations [1]

\[ \begin{aligned} E &= U_c + L_3 \frac{di_3}{dt} + i_3 \cdot r_3,\\ U_c &= \frac{1}{C}\int i_3 \cdot dt . \end{aligned} \tag{4} \]

Introducing the scale factors of current \(m_i\), voltage \(m_u\), and time \(m_t\), we obtain from (4) the machine equations

\[ \begin{aligned} \frac{dU_{Mi_3}}{dt_M} &= E_M \frac{m_{i_3}}{m_u \cdot m_t \cdot L_3} - U_{Mi_3}\frac{r_3}{m_t \cdot L_3} - U_{cM},\\ U_{cM} &= \frac{m_u}{m_{i_3}\cdot m_t \cdot C_k} \int U_{Mi_3}\cdot dt_M . \end{aligned} \tag{5} \]

The block diagram of the model according to equations (5) is shown in Fig. 2 with three computing amplifiers \(1, 2, 5\). The model parameters are determined from the relations

\[ R_{21}C_{11}=R_{31}C_{11}=\frac{m_u\cdot m_t\cdot L_3}{m_{i_3}}; \qquad R_{11}C_{11}=\frac{m_t L_3}{r_3}; \]

\[ R_{22}C_{12}=\frac{C_k\cdot m_{i_3}\cdot m_t}{m_u}. \tag{6} \]

The differential equations for setting up the model of the commutating and recharging circuits have the form

\[ U_c=L_{\mathrm{k}}\frac{di_{\mathrm{k}}}{dt}+i_{\mathrm{k}}\cdot r_{\mathrm{k}}; \tag{7} \]

\[ U_c=L_{\mathrm{p}}\frac{di_{\mathrm{p}}}{dt}+i_{\mathrm{p}}\cdot r_{\mathrm{p}}. \tag{8} \]

Introducing the scale factors, we obtain the machine equations

\[ \frac{dU_{Mi_{\mathrm{k}}}}{dt_M} = U_{cM}\frac{m_{i_{\mathrm{k}}}}{m_u\cdot m_t\cdot L_{\mathrm{k}}} - U_{Mi_{\mathrm{k}}}\frac{r_{\mathrm{k}}}{m_t\cdot L_{\mathrm{k}}}; \tag{9} \]

\[ \frac{dU_{Mi_{\mathrm{p}}}}{dt_M} = U_{cM}\frac{m_{i_{\mathrm{p}}}}{m_u\cdot m_t\cdot L_{\mathrm{p}}} - U_{Mi_{\mathrm{p}}}\frac{r_{\mathrm{p}}}{m_t\cdot L_{\mathrm{p}}}. \tag{10} \]

Fig. 2.

The structural diagram of the model of equation (9) is shown in Fig. 2 by integrating amplifier 3 and inverter 4. The model parameters are determined from the relations

\[ R_{15} C_{15} = \frac{m_u \cdot m_t \cdot L_k}{m_{i_k}}, \qquad R_{25} C_{15} = \frac{m_t \cdot L_k}{r_k}. \tag{11} \]

The structural diagram of the model of equation (10) in Fig. 2 contains integrating amplifier 7 and inverter 9; the model parameters are determined from the relations

\[ R_{14} C_{14} = \frac{m_u \cdot m_t \cdot L_p}{m_{i_p}}, \qquad R_{24} C_{14} = \frac{m_t \cdot L_p}{r_p}. \tag{12} \]

The process of switching on the commutating thyristor T1 is simulated by normally closed contacts 4P, 5P, and the switching on of the charging thyristor T2 by normally open contacts 1P, 2P, 3P of the switching device P. Diodes D1–D5 make it possible to take into account the nonlinearities of the actual circuit associated with the one-way conductivity of the valves. To account for the load current in the model (Fig. 2), amplifier 11 is used, and to account for the load current increasing with time, integrating amplifier 15 is used.

The electronic model of the FCD makes it possible to investigate the pattern of transient processes in a wide variety of operating modes and to evaluate the influence of the FCD parameters on its commutation and dynamic properties.

As a result of investigating the influence of changes in the parameters of the charging and recharging circuits, the dependences shown in Fig. 3 were obtained for the relative amplitude voltage \(U_c\) on the commutating capacitor \(C_k\) as a function of the ratio \(\frac{L_3}{L_p}\), for different but equal figures of merit of the charging and recharging circuits \(Q\), and in the absence of load current \((I_n = 0)\). Considering these dependences, one can conclude that, in order to eliminate the “build-up” of the commutating voltage above \(2E\) at no load, it is necessary to choose the ratio \(\frac{L_3}{L_p}\),

Fig. 3.

equal to 15–20 when the quality factor of the circuits is \(Q=15\text{–}20\). The magnitude of the inductance of the charging choke must be chosen from the condition that, over a time equal to the commutation period, the oscillatory charging of the commutating capacitor \(C_k\) from the power source \(E\) is completely completed.

Neglecting losses in the commutating circuit, the relationship between the parameters \(L_k\) and \(C_k\), ensuring forced commutation of the power thyristor, for constant values of the maximum voltage on the capacitor \(U_{c\max}\), the maximum load current \(I_{\max}\), and the recovery time of the thyristor blocking properties \(t_v\), can be written with sufficient accuracy for practical calculations in the following form [2]:

\[ L_k=\frac{U_{c\max}\cdot t_v^2}{2C_k\left[U_{c\max}-E-\frac{I_{\max}\cdot t_v}{C_k}\right]}. \tag{13} \]

Figure 4 shows the relationship between the parameters \(L_k\) and \(C_k\), plotted according to equation (13) for certain values of the other quantities. From Fig. 4 it is seen that the parameters \(L_k C_k\) that ensure commutation can be varied over wide limits. However, the choice of the parameters of the commutating circuit \(L_k C_k\) must be made taking into account the

Fig. 4.

overload capability of the converter, that is, to ensure the required automatic increase of the commutating voltage as the load current increases. For this purpose, the dependencies of the ratio of the voltage amplitude \(U_c\) on the commutating capacitor \(C_k\) to the supply-source voltage \(E\) as a function of the relative value of the load current were calculated and investigated on the analog computer, for various ratios

\[ \frac{L_k}{C_k}, \]

defined by expression (13) of Fig. 4. The form of such dependencies is shown in Fig. 5 by solid lines. In the same Fig. 5, the dashed lines, for the same ratios

\[ \frac{L_k}{C_k}, \]

show the dependencies of the magnitude of the commutating voltage required for switching off various values of load current, calculated by formula (14), obtained from (13)

Fig. 5.

\[ U_c=\frac{2L_k C_k\left(E+\dfrac{I_n\cdot t_B}{C_k}\right)}{2L_k C_k-t_B^2}. \tag{14} \]

It is evident from Fig. 5 that, as the ratio

\[ \frac{L_k}{C_k} \]

increases, the commutating voltage on capacitor \(C_k\) increases due to the voltage increment from the load current. In the investigations it was determined that the optimum ratio

\[ \frac{L_k}{C_k} \]

is equal to 26. At smaller values of the ratio

\[ \frac{L_k}{C_k}, \]

the voltage increment from the load current is small, and the forced-commutation device does not ensure switching off of the specified maximum load current. At ratios

\[ \frac{L_k}{C_k} \]

greater than 26, an excessive increase in the commutation voltage is observed, which leads to the necessity of using capacitors and thyristors with increased operating voltage and causes an increase in commutation losses.

The electronic model of the forced-commutation device makes it possible to investigate the dynamic properties of the FCD. To this end, a load current increasing with time is introduced into the model by means of amplifier 15, and the rate of rise of the commutating voltage on capacitor \(C_k\) is then determined. Thus, it is possible to determine the permissible rate of rise of the load current at which commutation failure will not occur.

Modeling the FCD makes it possible to assess the influence of the parameters on the commutation properties of the FCD and to determine the permissible rates of rise of the load current.

REFERENCES

1. V. I. Stulnikov, E. V. Kolchev. Modeling of Semiconductor Converters. Kiev, “Tekhnika,” 1971.

2. V. A. Beinarovich, L. S. Udut, V. S. Fadeev, N. G. Volkov. On the calculation of the parameters of a forced-commutation unit. Proceedings of the VII Scientific and Technical Conference. Static Converters in Electric Drives and Automation. Tomsk, TTU Publishing House, 1971.