SEMICONDUCTOR DC COLLECTOR

E. F. OBERGAN, A. I. SKOROSPELKIN

Recommended by the seminar of the departments of electrical machines
and general electrical engineering

In connection with the development of semiconductor technology, work has advanced on the creation of circuits for contactless current commutation in electrical machines.

This article considers a semiconductor collector developed by us, using thyristors, which makes it possible to rotate the magnetic field of direct current in electrical machines.

Figure 1 presents the basic electrical circuit of the semiconductor DC collector.

Designations in the circuit:

Fig. 1. Basic electrical circuit of the semiconductor DC collector.

$W_s$ — one section of the excitation winding;
$B$ — controlled valve;
$C$ — commutating capacitor;
$D_1$ — blocking diode;
$D_2$ — rectifier diode;
$U_B$ — excitation voltage;
$U_d$ — voltage of the additional direct-current source;
$i_B$ — excitation current in one parallel branch of the winding;
$I$ — excitation current in the common circuit;
$r$ — resistance of the $RC$ circuit.

Rotation of the axis of the excitation magnetic flux in space, with the excitation winding stationary, is achieved by successively shifting the points at which $U_B$ is connected to the excitation winding. This is provided by the successive switching on and off of valves connected to diametrically located terminals of the excitation winding and to opposite-polarity buses of the excitation voltage.

Since the valve collector is a symmetrical ring circuit, we shall carry out a detailed analysis of the operating process of switching $U_B$ from one pair of terminals of the excitation winding to another, adjacent pair of terminals, according to the circuit of Fig. 2.

At the instant of time $t_1 = 0$, valves $B_1$ and $B_2$ are switched on. The magnitude of the current flowing through the excitation winding is equal to:

\[ I_B = 2i_B = \frac{U}{R}; \tag{1} \]

where $R$ is the total resistance of the excitation winding.

Fig. 2. Electrical circuit of two operating collector cells during commutation.

At the instant of time \(t_2\), a control pulse arrives from the control device at valves \(B_3\) and \(B_4\), which thereby open. For some time the current \(I_{\mathrm{v}}\) will flow through valves \(B_1\), \(B_2\), \(B_3\), and \(B_4\). After valves \(B_1\) and \(B_2\) are extinguished, the current \(I_{\mathrm{v}}\) will flow through valves \(B_3\) and \(B_4\), i.e., the points of application of \(U_{\mathrm{v}}\) to the excitation winding will be shifted by the angle

\[ \chi=\frac{2\pi}{n}, \]

where \(n\) is the number of terminals of the excitation winding.

A widely used method of extinguishing open valves is the use of internal sources of commutating e.m.f., in which static capacitors operating in a recharge mode are used. Connecting charged capacitors “\(C\)” directly to the open controlled valves leads in practice to instantaneous commutation, since the discharge circuit \(C—B_1—B_3\) is almost completely devoid of inductance. The slight inductance of the connecting wires and of the anode–cathode transitions of the valves may be neglected.

At the same time, each type of controlled valve has, by its construction, a specified time for restoration of its control properties. Therefore the criterion for commutation stability is the inequality

\[ t_{\mathrm{p}} > t_{\mathrm{v}}, \tag{2} \]

where

\[ t_{\mathrm{p}} \]

is the time during which reverse voltage is applied to the valve, or the capacitor discharge time;

\[ t_{\mathrm{v}} \]

is the recovery time of the control properties of the valve.

To ensure this inequality, a resistance \(r\) has been introduced into the capacitor circuit, and blocking diodes \(D_1\) have also been included, preventing the discharge of the capacitor into the short-circuited section of the excitation winding.

Let us consider the process of extinguishing an open valve using as an example the commutation of current from valve \(B_1\) to valve \(B_3\).

Before the control pulse is applied to valve \(B_3\), the current \(I_{\mathrm{v}}\) passes through the open valve \(B_1\), diode \(D_1\), and enters the excitation winding through terminal 1. In this case the polarity of the voltage on the plates of capacitor \(C\) corresponds to the polarity of the voltage drop on section \(W_s\) of the excitation winding.

From the moment the control pulse is applied to valve \(B_3\), the current \(I_{\mathrm{v}}\) passes simultaneously through valves \(B_1\) and \(B_3\), diodes \(D_1\) and \(D_3\), and enters the excitation winding through terminals 1 and 3. Since the potential difference between points 1 and 3 is zero, section \(W_s\) is short-circuited, and the external voltage applied to the capacitor becomes zero. The positively charged plate of capacitor \(C\) is then connected to the anode of valve \(B_1\), and the negatively charged plate to the cathode of \(B_1\). A negative voltage is applied to valve \(B_1\), under the action of which its control properties are restored.

As indicated above, during the commutation period the potentials of points 1 and 3 are equal to one another when the current \(I_{\mathrm{v}}\) flows. However, before valve \(B_3\) is switched on, a direct current \(i_{\mathrm{v}}\) flows through section \(W_s\). Consequently, during the commutation period section \(W_s\), owing to the energy of the magnetic field stored in it, will generate reactive power; in this case the polarity of the voltage at points 1 and 3 will be

of the reverse polarity of the voltage drop across section \(W_s\) when current \(i_{\mathrm{в}}\) flows through it. This reactive power is negative with respect to the power developed in the field winding by the current \(I_{\mathrm{в}}\). To eliminate pulsations of the current \(I_{\mathrm{в}}\) in the field winding, the capacitance of the capacitor \(C\) should be chosen so that the recharge time of \(C\) is equal to the time required for the current \(i_{\mathrm{в}}\) to become established in section \(W_s\) after valve \(B_1\) is blocked. If, in doing so, the upper limit of the valve switching frequency is restricted, then the capacitance \(C\) need be chosen only from condition (2); and, for compensating the reactive resistance of the sections \(W_s\) during commutation, as well as for compensating the reactive power of the field winding caused by pulsation of the field current, it is advisable to use the recommendations given by the theory of valve inverters.

If all taps of the field winding are connected to a multiphase rectifier, then the reactive power of the commutating sections and the reactive power of the field winding are transformed into an additional direct-current source, which can be connected to the main direct-current source—the excitation source. Thus, the reactive power of the field winding becomes active and is returned to the supply-source circuit of the scheme. The described operating mode is shown graphically in Fig. 3. At the instant of time \((\pi-\varphi)\), energy from the excitation circuit is transferred to the field winding, while at the instant \(\varphi\) the energy stored in the reactive elements of the field winding is transferred to the additional direct-current circuit \(U_{\mathrm{д}}\). Consequently, operation of the scheme can occur for any \(\cos\varphi\) from 1 to 0, and for \(\varphi > \dfrac{\pi}{2}\) the field winding passes into generator mode, and in this case energy is transferred from the source \(U_{\mathrm{д}}\) to the source \(U_{\mathrm{в}}\).

Fig. 3. Curves of energy relationships in the direct-current circuits \(U_{\mathrm{в}}\) and \(U_{\mathrm{д}}\).

If

\(P_{\mathrm{v}}\) is the average value of the power consumed from the source \(U_{\mathrm{v}}\),

\(P_{\mathrm{d}}\) is the average value of the power delivered by the excitation winding to the circuit \(U_{\mathrm{d}}\),

\(S\) is the apparent power of the load,

then, assuming that the current \(I_{\mathrm{v}}\) and the voltage \(U_{\mathrm{v}}\) in the excitation winding vary sinusoidally with time (considering the first harmonic), one may write [4]:

\[ P'_{\mathrm{v}}=\frac{P_{\mathrm{v}}}{S};\qquad P'_{\mathrm{d}}=\frac{P_{\mathrm{d}}}{S}, \tag{3} \]

\[ i_{\mathrm{v}}=\sqrt{2}\,I_{\mathrm{v}}\sin(\omega t-\varphi), \tag{4} \]

\[ U_{\mathrm{v}}=\sqrt{2}\,U_{\mathrm{v}}\cdot \sin \omega t, \tag{5} \]

\[ P_{\mathrm{v}}=i_{\mathrm{v}}U_{\mathrm{v}}\,[\cos\varphi-\cos(\omega t-\varphi)], \]

\[ P'_{\mathrm{v}} = \frac{1}{IU}\cdot \frac{2}{T} \int_{\frac{1}{2\pi}\varphi}^{\frac{1}{2}} P_{\mathrm{v}}\,dt = \cos\varphi+\frac{1}{\pi}(\sin\varphi-\varphi\cos\varphi), \tag{7} \]

\[ P'_{\mathrm{d}} = \frac{1}{I\cdot U}\cdot \left| \frac{2}{T} \int_{0}^{\frac{1}{2\pi}\varphi} P_{\mathrm{v}}\,dt \right| = \frac{1}{\pi}(\sin\varphi-\varphi\cos\varphi). \tag{8} \]

As is evident from the expressions obtained, the power delivered by the excitation winding to the additional direct-current circuit depends on the magnitude of \(\cos\varphi\). At the same time, the circuits of the direct-current sources are unbalanced, and the degree of unbalance also depends on \(\cos\varphi\). If the direct-current source \(U_{\mathrm{v}}\) has no reverse conductance, then the minimum \(\cos\varphi\) of the excitation winding must be greater than a certain critical value, at which the current of the source \(U_{\mathrm{v}}\) will fall to zero.

MATHEMATICAL ANALYSIS OF THE COMMUTATION PROCESS

In the analysis we shall make the following assumptions:

1. Commutation of current from an opened valve to the valve opened by the triggering pulse occurs instantaneously.

2. The internal resistance of the direct-current sources \(U_{\mathrm{v}}\) and \(U_{\mathrm{d}}\) is equal to zero.

We shall analyze the commutation process by considering two time intervals, depending on the combination of switched-on valves:

a) the time interval \(\alpha\), when the valves \(B_1;\ D_1;\ B_3;\ D_3;\ B_2;\ D_2;\ B_1;\ D_1\) conduct current;

b) the time interval \(\beta\), when the valves \(B_3;\ D_3;\ B_4;\ D_4\) conduct current.

a) Time interval \(\alpha\).

Before the control pulse is applied to valve \(B_3\), the current \(I_{\mathrm{v}}\) in the field winding is

\[ I_{\mathrm{v}}=\frac{U_{\mathrm{v}}}{R}, \]

where \(R\) is the ohmic resistance of the field winding. This equality indicates that at the end of the interval \(\alpha\) the transient process ends with the established value of the current \(I_{\mathrm{v}}\).

After the control pulse is applied to valve \(B_3\), at the instant \(t(0)\), the current \(I_{\mathrm{v}}\) that had been flowing through valve \(B_1\) begins to flow also through valve \(B_3\). In this case, assuming the conductances of the valves to be identical, the current \(I_{\mathrm{v}}\) will be divided equally between them.

The magnitude of the current \(I_{\mathrm{v}}\) will then change as a result of the change in the ohmic resistance of the field winding by the amount

\[ \frac{R-\Delta R}{R}, \]

where \(\Delta R=2r_s\) is the resistance of two short-circuited sections \(W_s\) of the field winding, and will be equal to

\[ I_{\mathrm{v}x}=I_{\mathrm{v}}+\Delta I_{\mathrm{v}0}\left(1-e^{-\frac{t}{\tau_1}}\right); \tag{9} \]

where

\[ \Delta I_{\mathrm{v}0}=U_{\mathrm{v}}\cdot\frac{\Delta R}{R(R-\Delta R)}. \tag{10} \]

\[ \tau_1=\frac{L-2L_s}{R-2r_s} \]

is the time constant of the field winding with two short-circuited sections.

\[ \tau_1=\frac{L/n}{R/n}=\frac{L}{R}. \tag{11} \]

Simultaneously with this process, the process of discharging capacitor \(C\) through the circuit \(C—B_1—B_3—r\) will take place, as well as the process of the current in section \(W_s\) decaying to zero. Neglecting the resistances of the open valves \(B_1\) and \(B_3\), we can write the value of the voltage across the capacitor plates during the discharge process as

\[ U_c=U_s e^{-\frac{t}{\tau_2}}; \tag{12} \]

where

\(U_s\) is the voltage drop across the resistance of section \(W_s\) before the control pulse is applied to valve \(B_3\);

\[ \tau_2=r\cdot C \tag{13} \]

is the time constant of the circuit.

The current in section \(W_s\) will decrease according to an exponential law. Since in the time interval \(\alpha\) under consideration valve \(B_1\) is open, section \(W_s\) is short-circuited through the circuit of the additional source \(U_{\mathrm{d}}\). The value of the current will then be

\[ i'_{\mathrm{v}}=i_{\mathrm{v}}e^{-\frac{t}{\tau_3}}, \tag{14} \]

where

\[ i_{\mathrm{v}}=\frac{I_{\mathrm{v}}}{2} \]

is the magnitude of the current in the parallel branch of the field winding before the start of commutation;

\[ \tau_3=\frac{L_s}{r_s} \]

is the time constant of section \(W_s\) of the field winding,

\[ \tau_3=\frac{L_s\cdot n}{r_s\cdot n}=\frac{L}{r}=\tau_1 . \]

To eliminate the influence of the reactive emf of section \(W_s\), which participates in the commutation process, on the common circuit of the field winding, it is expedient that by the end of the time interval \(\alpha\) the current in section \(W_s\) should fall to 0. According to the given law of variation of the current \(i'_B\), it will become equal to zero only after an infinitely long time. In practice, at values

\[ \frac{i'_B}{i_B}=0.01\div 0.005 \]

the process of dissipation of the reactive energy of the short-circuited section \(W_s\) may be regarded as completed.

Consequently, in order to satisfy the condition

\[ i'_B(\alpha)=0 \]

it is necessary that the time of energy dissipation in section \(W_s\) be no greater than the recovery time of the control properties of valve \(B_1\), i.e., it is expedient to satisfy the inequality

\[ \frac{t_B}{\tau_1}>5 . \tag{15} \]

Fulfillment of this condition depends on the quality of the selected controlled valves. If it is impossible to satisfy this inequality, compensation of the influence of the reactive energy of the commutating section is effected by an additional source \(U_d\).

If, however, the indicated condition is satisfied, then the calculation of capacitor \(C\) is made only from the condition of ensuring reliable commutation.

b) Time interval \(\beta\)

The time interval \(\beta\) is counted from the moment when the control properties of valve \(B_1\) are restored and the current

\[ \frac{I_B}{2} \]

through it ceases to flow. From this moment the entire current \(I_B\) passes through valve \(B_2\). Splitting into two parallel branches of the field winding, the current

\[ \frac{I_B}{2} \]

will pass through section \(W_s\), which we regard as de-energized by the beginning of the time interval \(\beta\), and through the circuit \(r—C—D_1\). The current through section \(W_s\) will be equal to

\[ -i'_B=\frac{I_B}{2}\left(1-e^{-\frac{t}{\tau_1}}\right), \tag{16} \]

the current through the circuit \(r—C\)

\[ i'_C=\frac{I_B}{2}e^{-\frac{t}{\tau_2}} . \tag{17} \]

The total current in the parallel branch must not change its value and is equal

\[ \frac{I_{\mathrm{v}}}{2}=i'_{\mathrm{v}}+i'_{\mathrm{c}}= \frac{I_{\mathrm{v}}}{2}\left(e^{-\frac{t}{\tau_2}}-e^{-\frac{t}{\tau_1}}\right)+\frac{I_{\mathrm{v}}}{2}, \tag{18} \]

whence

\[ e^{-\frac{t}{\tau_2}}=e^{-\frac{t}{\tau_1}}, \tag{19} \]

\[ \tau_2=\tau_1 . \tag{20} \]

Consequently, from the condition of continuity of the current \(I_{\mathrm{v}}\), the value of the capacitor must be taken equal to

\[ r \cdot C=\frac{L}{R}, \]

\[ C=\frac{L}{R \cdot r}. \tag{21} \]

The value of the capacitance of the capacitor, from the condition of reliable commutation, can be determined if we set

\[ t_{\mathrm{p}}=2t_{\mathrm{v}}, \tag{22} \]

then

\[ \frac{U_{\mathrm{c}}}{U_{\mathrm{s}}}=e^{-\frac{t_{\mathrm{p}}}{\tau_2}}=e^{-\frac{2t_{\mathrm{v}}}{\tau_2}} . \]

The discharge may be considered completed at

\[ \frac{2t_{\mathrm{v}}}{\tau_2}=5, \tag{23} \]

whence

\[ \tau_2=\frac{2t_{\mathrm{v}}}{5}=r \cdot C, \]

\[ C=\frac{2t_{\mathrm{v}}}{5r}. \tag{24} \]

If it is necessary to ensure the maximum upper limit of the switching frequency for the selected type of valves, the capacitance of capacitor \(C\) is chosen according to equality (24).

If it is necessary to ensure minimum pulsations of the current \(I_{\mathrm{v}}\), the capacitance of capacitor \(C\) is chosen from condition (21).

CONCLUSIONS

The developed circuit of the semiconductor collector makes it possible to implement a direct-current or alternating-current electric machine in which the axis of the excitation magnetic field, produced by direct current, can rotate in space over a wide range of speeds, or else turn through a specified angle according to a prescribed law.

The number of winding terminals is determined by the specified permissible percentage of distortion of the magnetic-field shape during rotation and by the maximum value of the field-rotation frequency (the switching frequency of the semiconductor cells).

In this case

\[ f_{\mathrm{n}}=\frac{f_{\mathrm{upr}}}{n}. \]

$f_{\text{p}}$ — field-rotation frequency;
$f_{\text{ctrl}}$ — frequency of the control pulses (cell switching);
$n$ — number of winding terminals.

REFERENCES

1. A. A. Bulgakov. Fundamentals of the Dynamics of Controlled Valve Circuits. Academy of Sciences of the USSR, 1964.

2. F. I. Butaev, E. L. Ettinger. Valve Electric Drive. GEI, 1961.

3. A. S. Vasil’ev, A. E. Slukhatskii. Electronic and Ionic High-Frequency Inverters. GEI, 1951.

4. D. A. Zavalishin, V. F. Shukalov. Valve frequency converters for frequency control of the speed of asynchronous motors. Vestnik elektropromyshlennosti, No. 6, 1961.

5. I. I. Kanter. Theory of operation of multiphase self-controlled inverters with capacitor commutation. Elektrichestvo, No. 3, 1951.

6. M. P. Kostenko. A collector-type alternating-current generator with frequency regulation independent of rotational speed. Elektrichestvo, No. 2, 1948.