APPLICATION OF A SEMICONDUCTOR COMMUTATOR IN A CONTACTLESS ELECTRIC-MACHINE AMPLIFIER AND AN ALTERNATING-CURRENT CONVERTER

E. F. OBERTAN

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

It is known that the best technical and economic characteristics are possessed by an alternating-current electric drive with frequency regulation of the speed of rotation of the actuator motor. As the source of alternating current of adjustable frequency feeding the actuator motor, such systems use various electric-machine and electronic converters, whose widespread application is limited because of the disadvantages inherent in each of the known devices.

The development of semiconductor technology now makes it possible to consider, in practical terms, the problem of creating a combined electronic–electric-machine alternating-current converter of adjustable frequency, possessing the advantages of the known electric-machine and electronic converters and free of most of the disadvantages inherent in each of them separately.

At the Department of “Electrical Machines and Apparatus” of TPI, a series of theoretical and experimental studies has been carried out on a contactless electronic-machine alternating-current amplifier of adjustable frequency, and results have been obtained which testify to the promising nature of work in this direction.

One of the main units determining the characteristics and operational reliability of an electronic-machine amplifier and an adjustable-frequency converter is the semiconductor commutator connected with the winding of the electric machine.

Figure 1 shows the schematic diagram of the connection of two cells of a semiconductor commutator.

Figure 2 presents the schematic diagram of a converter with a semiconductor commutator.

Frequency regulation of the electronic-machine converter in Fig. 2 is effected by successive switching of the cells of the semiconductor commutator; in this case the primary winding of the first stage is made of the armature type.

The distinctive features of the converter are determined by the principle of operation of the first stage.

First of all, it is necessary to determine the nature of the change of current in the primary winding when the switching speed of the cells of the semiconductor commutator is varied and when the secondary winding is open, i.e., with the rotor windings open.

Fig. 1. Schematic electrical circuit of two cells of a semiconductor collector connected by a winding.
B — controlled valves. D — diodes. C — commutating capacitor.

Fig. 2. Schematic electrical circuit of a converter with a semiconductor collector.

Neglecting the influence of losses in the steel of the magnetic core, the value of the current in the winding is determined from the equation

\[ I_1 = I_{10}\left\{1+\frac{1}{n-1}\left[\left(1+\frac{t_3\cdot n}{2\cdot \tau_0(n-1)}\right)\cdot t_3\cdot f-\frac{t_3\cdot n}{2\cdot \tau(n-1)}\right]\right\}, \tag{1} \]

where

\[ I_{10}=\frac{U_1}{R_1} \]

is the value of the direct current in the winding in the absence of switching of the collector cells, i.e., when \(f=0\) and \(t_3=0\),

\(f\) — the switching frequency of the cells of the semiconductor collector,

\(t_3\) — the time of the “closed” state of the part of the winding enclosed between adjacent terminals,

\[ \tau_0=\frac{L_1}{R_1} \]

— the time constant of the winding,

\(n\) — the number of pairs of winding terminals connected to the cells of the semiconductor collector.

The value of \(t_3\) is determined by the rating parameters of the semiconductor-controlled valves.

Equation (1) is valid for frequency values \(f\) lying within the limits

\[ \frac{1}{2\cdot \tau_0 \dfrac{n-1}{n}+t_3}< f < \frac{1}{t_3}. \]

The upper limit of the frequency \(f\) is determined by the operating principle of the semiconductor collector, and the lower limit is determined by the simplification admitted in deriving equation (1). However, taking into account the linear character of the change in current with switching frequency, the current value at frequencies below the lower limit is determined graphically and does not exceed \(1\% \div 2\%\) of \(I_{10}\).

Thus, as equation (1) shows, the magnitude of the current in the winding, when the switching frequency changes from \(f=0\) to \(f=f_{\max}\), changes from the value \(I_{10}\) to the value \(I_{10}+\Delta I_1\), while the maximum value \(\Delta I_{1\max}\) at \(f=f_{\max}\) is equal to the ratio of the ohmic resistance of the commutated part of the winding to the ohmic resistance of the parallel branch.

With a sufficiently large number of winding taps, in practical calculations it is possible to assume that the current in the winding is independent of the switching frequency of the semiconductor collector. The amplitude of the current pulsations in the winding is determined by the formula

\[ A_n = I_{10}\cdot \frac{t_3}{\tau_0}\cdot \frac{n}{(n-1)^2}\cdot (1-t_3 f) \tag{2} \]

and decreases as the frequency \(f\) increases.

The nature of the commutation of the current in the part of the winding between adjacent taps is determined by the current equations:

a) during the period of the “closed” state of the winding part

\[ i_3(t)=I_{10}\cdot e^{-n^2 \frac{t_3}{\tau_0}} . \tag{3} \]

b) during the period of the “open” state of the winding part

\[ i_p(t)=I_{10}\, \frac{\dfrac{n}{n-1}} { 1+\left[ \dfrac{1}{n-1} \left( 1-e^{-\frac{n}{\,n-1\,}\cdot \frac{t_p}{\tau_0}} \right) + \dfrac{1}{(n-1)^2}\cdot e^{-\frac{n}{\,n-1\,}\cdot \frac{t_p}{\tau_0}} \right] } \cdot \frac{1} { \left[ 1-e^{-\frac{n}{2}\cdot \frac{t_p}{\tau_0}}\cdot \cos \omega t \right] }, \tag{4} \]

which, by selecting the parameters of the semiconductor collector and the winding, make it possible to prescribe the desired law of current variation during the commutation period.

When the semiconductor collector operates on the commutated parts of the winding, overvoltages arise, the magnitudes of which depend on the parameters of the semiconductor collector and the winding

\[ \left(\frac{U_{ws}}{U_1}\right)_{\max} = \frac{1}{R_1(n-1)} \cdot \sqrt{\frac{4}{C}} \tag{5} \]

where \(U_{ws}\) is the voltage on the part of the winding between adjacent taps. With the aid of equation (5), calculation of the winding parameters is carried out—

taking into account the overvoltages on the switched parts of the winding that are maximally permissible for a semiconductor commutator of the given circuit.

The operation of the first stage of the converter with an open secondary winding is analogous to the operation of a synchronous generator at no load; therefore, the current in the primary winding \(I_1\) will be called the excitation current, and the primary winding the excitation winding.

When the rotor windings are connected to one another, the interrelation of the excitation, rotor, and load currents and voltages is expressed by equations on the basis of which the vector diagram shown in Fig. 3 can be constructed.

The use of a semiconductor commutator connected with the excitation winding introduces a specific feature into the interrelation of currents and voltages, the power balance, and the law governing regulation of the excitation voltage when regulating the frequency of the output voltage.

Fig. 3. Vector diagram of the two stages of the converter under load.

First of all, the excitation flux rotating in space is produced by a direct current which, as indicated above, is practically independent of the commutator switching frequency. The axis of the excitation flux at any given moment coincides with the axis connecting the connection points to the excitation-voltage winding or, by analogy with a mechanical commutator, with the “brush axis” (in the vector diagram, the axis \(0—0_1\)).

When both stages of the converter are operating, the axis of the resultant flux of the first stage will in general not coincide with the axis of the excitation current, and its transverse component, perpendicular to the “brush axis,” will induce an e.m.f. in the excitation winding directed opposite to or in the same direction as the excitation voltage, depending on the direction of commutation of the commutator and on the nature of the load.

Introducing the notation of the slip \(S_1\) of the field of the first cascade,

\[ S_1=\frac{\mp[\omega_{\mathrm{p}}-(\pm\omega_{\mathrm{v}})]}{\omega_{\mathrm{p}}} \tag{6} \]

and the slip \(S_2\) of the field of the second cascade,

\[ S_2=\frac{\omega_{\mathrm{n}}-\omega_{\mathrm{p}}}{\omega_{\mathrm{n}}}, \tag{7} \]

where \(\omega_{\mathrm{p}}, \omega_{\mathrm{v}}, \omega_{\mathrm{n}}\) are the angular velocities of rotation of the rotor, of the excitation field relative to the stator, and of the field of the second cascade relative to the rotor, it is possible to determine from the vector diagram of Fig. 3 the value of the voltage \(E_{\mathrm{v}}\) induced in the excitation winding:

\[ E_{\mathrm{v}}=\pm I_0'\cdot \sin\Theta\cdot x_0'\cdot(1-S_1). \tag{8} \]

The sign \((+)\) is taken for a positive value of \(S_1\), and the sign \((-)\) for a negative value of \(S_1\).

For a constant value of the excitation voltage \(U_1\), the current \(I_1'\) in the excitation winding, referred to the rotor, is equal to:

\[ \dot{i}_1'=\dot{i}_{30}'\pm i_0\sin\Theta\cdot x_0\cdot(1-S_1). \tag{9} \]

Taking into account that

\[ \dot{i}_0=\dot{i}_1'+\dot{i}_{\mathrm{p}}=\dot{i}_1'+\dot{i}_{\mathrm{m}}-\dot{i}_{\mathrm{n}}', \qquad \dot{i}_{\mathrm{m}}=\frac{-\dot{E}_{\mathrm{p}}\cdot S_1}{Z_{\mathrm{m}}}, \]

one can express the value of the excitation current of the primary winding of the first cascade as a function of the converter parameters, the magnitude and nature of the load, and the operating modes determined by the magnitudes and signs of the slips of the first and second cascades:

\[ \dot{i}_1= \frac{ \dot{i}_{10}\pm\dot{i}_{\mathrm{m}}' \left( 1+\frac{x_{\mathrm{m}}'}{z_{\mathrm{n}}''}\cdot S_1\cdot S_2 \right) \cdot x_0'\cdot(1-S_1)\cdot\sin\Theta }{ 1\mp x_0'\cdot(1-S_1)\cdot\sin\Theta } \tag{10} \]

Here

\[ z_{\mathrm{n}}''=\sqrt{R_{\mathrm{n}}''+j x_{\mathrm{n}}''\cdot S_2} \]

In the numerator, before the second term, the sign \((+)\) is taken for positive values of \(S_1\) and \(S_2\), and the sign \((-)\) for negative \(S_1\) and \(S_2\). In the denominator, before the second term, the signs are taken in the reverse order.

Analysis of equation (10) shows that combining a semiconductor commutator with an electric-machine converter makes it possible to regulate the frequency \(f_{\mathrm{n}}\) of the output voltage over several wide ranges, including from \(f_{\mathrm{n}}=0\). With an appropriate choice of the converter parameters, the number of pole pairs of the first and second cascades, and the slips \(S_1\) and \(S_2\), the excitation power may amount to a smaller percentage of the output power than in a synchronous generator; moreover, the law of regulation of the excitation voltage with variation of the output-voltage frequency and the load power may be analogous to the law of regulation of the excitation of a synchronous generator when the load changes.

The use of a semiconductor commutator in an electric-machine converter intended for generating an alternating voltage adjustable over a wide frequency range introduces a number of fundamentally new features both into the operating character-

characteristics of the electric drive and in the calculation of the electrical machine. In particular, in certain operating modes the converter gain reaches values that make it possible to regard the converter as an amplifier, which is very important, since it substantially reduces the size and cost of the semiconductor commutator. In addition, calculating the influence of commutation processes on the operation of an electrical machine when a semiconductor commutator is used differs in many ways from the analogous calculation for a mechanical commutator and makes it possible to predict the nature of these processes more accurately.

REFERENCES

1. M. P. Kostenko. Electrical Machines. Special Part, GEI, 1949.

2. Sh. I. Lutigdze. Equations and circuits of electrical machines with a controlled semiconductor commutator. Izvestiya AN SSSR, No. 6, 1964.

3. S. M. Damyanov. On one variety of electrical machine. Izvestiya AN SSSR, No. 6, 1964.