VARIABLE-FREQUENCY ELECTROMECHANICAL AMPLIFIER

A. I. SKOROSPELKIN, M. L. KOSTYREV, E. F. OBERGAN

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

The widespread use of frequency control in industry is associated with the development of reliable and economical converters with regulation of frequency and voltage at the output. Static ionic and semiconductor converters, despite their obvious advantages over rotating machine converters, have a number of substantial shortcomings [1], the elimination of which leads to a considerable complication both of the power inverter and of the control circuit. The inclusion in the direct regulating circuit of equalizing reactors and smoothing chokes, necessary for stable operation of the inverter, makes the converter an inertial element. A good voltage waveform at the output over a wide frequency range can be obtained only by substantially complicating the inverter control circuit and by including at the output a filter retuned when the frequency and the load power factor change.

In a number of cases, a more successful solution can be obtained by using a machine–valve system. In systems with an asynchronous converter or a high-frequency synchronous generator and a static converter without a dc link at the output [1], the inverter must be designed for the maximum output power. In addition, in such systems the voltage and current waveforms at the output are strongly distorted. In a brushless asynchronous synchronous machine with an inverter at the output [2], the power supplied to the output from the inverter is equal to the slip power. Therefore, over a large frequency range, the required inverter power will approach the output power.

The proposed brushless asynchronous synchronous machine with a controlled semiconductor commutator (CSC) at the input (Fig. 1), under certain conditions, may be free of this shortcoming. Since two machine stages can amplify the signal from the CSC by tens of times, the proposed circuit can perform the functions of a variable-frequency electromechanical amplifier (EMА-VF).

The main power at the output of the EMA-VF is transmitted from the shaft. This is especially important for solving such problems as, for example, the development of a stable-frequency generator at a variable shaft speed for supplying aircraft electrical systems.

The present work sets forth questions of the theory and the results of experimental investigations of the proposed circuit.

![Diagram labels: \(W_y\); To UPC cells; \(W_{c2}\); Output; Drive motor; \(W_{p1}\); \(W_{p2}\); I stage; II stage]

Fig. 1. Diagram of a variable-frequency electromechanical amplifier.

With continuous sequential switching of the UPC cells, the magnetic control field will rotate at a speed \(n_y\) rev/sec.

When the rotor rotates at a speed \(n\) rev/sec, the EMU-RF gives a frequency at the output

\[ f_{\text{out}} = (p_2 \pm p_1)n \pm p_1 n_y, \tag{1} \]

where \(p_1\) and \(p_2\) are the numbers of pole pairs of stages 1 and 2.

In the most economical mode [3]—with codirectional rotation of the rotor and the field of the second stage, and counter-rotation of the rotor and the field of the first stage—the output frequency is

\[ f_{\text{out}} = (p_2 + p_1)n + p_1 \cdot n_y. \tag{2} \]

The UPC cells permit a high switching frequency. Therefore a high speed of the control field can be obtained (500 rev/sec and more), and consequently a wide range of output frequencies at a constant rotor speed. Since frequency regulation is not associated with a change in rotor speed, the response speed of the EMU-RF is determined only by the electromagnetic time constants of the windings and, as experimental studies show, is at the level of commutator-type EMUs of corresponding power. In more advanced designs one should expect greater, in comparison with commutator-type EMUs, quality factor, since the principal amplification falls on the practically inertia-free UPC.

The control winding of the EMU-RF differs from the armature winding of a direct-current machine only in that its taps are connected not to commutator plates, but to UPC cells. Therefore, in the absence of a significant influence of eddy and commutation currents, the magnetic control flux—analogously to the armature-reaction flux of a direct-current machine—is directed along the axis passing through the open cells. No emf is induced in the control circuit, and when the speed of the control flux changes, an unchanged current flows through the control winding. Small changes in the mean value of the current with frequency \(f_y\) are due only to a change in the ripple level.

The equilibrium equations of the m.m.f. and e.m.f. of the first stage of an ideal EMU-RF correspond to the vector diagram in Fig. 2. In the ideal machine there are no leakage fluxes, the active resistances of the windings and the core losses are equal to zero, and the reaction of the commutation currents is negligible. The diagram is constructed in axes rotating synchronously with the magnetic field of the first stage.

Fig. 2. Vector diagram of the first stage of an ideal EMU-RCh.

When an active load is connected to the rotor or to the amplifier output, the resultant magnetic flux \(\Phi_1\) is deflected by an angle \(\Theta\) from the control axis. An emf appears in the control circuit:

\[ E_y = E_{y\max}\cdot \sin \Theta \tag{3} \]

Using the known expression for the emf in a sinusoidal magnetic field, we obtain

\[ E_y = 2\pi W_y' \Phi_1 \cdot p_1 \cdot n_y \cdot \sin \Theta \tag{4} \]

\(W_y'\) is the number of series turns of the control winding, taking the winding factor into account.

The equation of the control circuit in the steady-state mode is written in the form

\[ U_y \pm E_y = I_y \cdot r_y \tag{5} \]

\(I_y\) is the current in the control circuit,

\(r_y\) is the active resistance of the control winding and of the UPK cells.

The polarity of \(E_y\) depends on the direction of rotation of the control field relative to the rotor. In the most favorable energy mode, the emf \(E_y\) is directed opposite to the source voltage (the “\(-\)” sign in formula 5).

We carried out experiments with direct measurement of the angle \(\Theta\). The axis of the rotating brushes of the mechanical commutator (instead of the UPK) was fixed by means of an optical system with a sensitive photodiode connected into a circuit producing a narrow pulse. The flux axis was fixed by a measuring section in the stator slots. Before the measurements began, the pulse was precisely oriented relative to the axis of the measuring section. The angle \(\Theta\) was read from the oscillograms of Fig. 3. The values of the angle \(\Theta\) calculated from formulas (4), (5) and measured experimentally coincided within the accuracy of the measurements (\(\pm 3^\circ\)).

The experiments confirmed the fact that, with a purely reactive load, the angle \(\Theta\) does not change, as also follows from the vector diagram of Fig. 2. The experiments showed that, with sharply retarded commutation, the angle \(\Theta\) can reach a significant value (up to \(30^\circ\)), which leads to an inadmissibly large emf in the control circuit. Consequently, the UPK must ensure commutation that excludes the presence of a transverse flux.

Fig. 3. Oscillogram for measuring the angle \(\Theta\).

Eddy currents in the EMU-RCh not only cause losses in the steel, but also create a transverse flux, which likewise induces an emf in the control circuit.

Let us determine the active-power gain of an ideal EMU-RCh.

The active power in the rotor circuit is

\[ P_p = m_p \cdot E_p \cdot I_p \cdot \cos \varphi_p \tag{6} \]

The rms value of the emf of the rotor phase is

\[ E_p = \pi \sqrt{2}\,\Phi_1 \cdot W'_p \cdot f_p . \tag{7} \]

Here \(W'_p\) is the number of series turns of the rotor phase, taking into account the winding factor.

The power in the control circuit is

\[ P_y = I_y \cdot E_{y\,\max} \cdot \sin \theta \tag{8} \]

From the vector diagram in Fig. 2,

\[ \sin \theta = \frac{F_p \cdot \cos \psi_p}{F_y}. \tag{9} \]

The amplitudes of the mmf of the rotor and control windings are

\[ F_p = \frac{0.9\,m_p \cdot W'_p \cdot I_p}{p_1}. \tag{10} \]

\[ F_y = \frac{4}{\pi}\cdot \frac{I_y \cdot W'_y}{p_1}. \tag{11} \]

From expressions (4), (6–11), the gain of the first stage is determined as

\[ K_{y1}=\frac{P_p}{P_y}=\frac{f_p}{f_y}=\frac{n_y \pm n}{n_y}. \tag{12} \]

It is not difficult to see that the active-power gain of the second stage in an ideal machine is

\[ K_{y2}=\frac{P_{\text{out}}}{P_p}=\frac{f_{\text{out}}}{f_p}. \tag{13} \]

Then the active-power gain of the machine part of the EMU-RCh is

\[ K_y = K_{y1}\cdot K_{y2} < \frac{f_{\text{out}}}{f_y}. \tag{14} \]

At a low switching speed, a large gain can be obtained. As the switching speed increases, the gain decreases sharply, tending toward unity. In an AC EMU it is customary to deter-

divide the gain factor by the total power. With an active-inductive load, the gain of the EMU-VF is less than the limiting value (14); with an active-capacitive load, the gain increases sharply. Increasing the capacitance at the output or in the rotor beyond the critical value makes it possible to obtain a self-excitation mode.

The gain of the EMU-VF can be increased by means of transverse compensation, which consists in creating such a flux along the transverse axis that, combining with the reaction flux of the rotor, would direct the resultant flux along the control axis. In this case, no emf is induced in the control circuit, and the control power is determined only by the copper losses in the control winding and by the losses in the steel of the magnetic circuit.

Fig. 4. Oscillogram of the voltage at the stationary taps of the control winding.

The advantage of the EMU-VF consists not only in the possibility of substantially reducing the required power of the FPC. Even with a highly distorted form of the control field (Fig. 4), it is possible to obtain a satisfactory voltage waveform at the output (Fig. 5). This is due to the property of the distributed winding of an electrical machine to suppress higher harmonics. To obtain a good voltage waveform at the output, all effective means used in the design of windings of electrical machines may be employed. Connecting a capacitance at the output or in the rotor also improves the shape of the curve.

Fig. 5. Oscillogram of the voltage at the output of the EMU-VF.

The dimensions and weight of the VFEMA–FC are reduced by savings in structural materials when two stages of the VFEMA–FC are combined in a single magnetic core [3].

Conclusions

1. The proposed contactless asynchronized synchronous machine with a semiconductor commutator at the input makes it possible to regulate the voltage and frequency at the output over a wide range.

2. When the switching frequency of the commutator is increased, the gain factor of the VFEMA–FC in active power tends to unity. The use of transverse compensation will make it possible to sharply reduce the required power of the semiconductor commutator.

3. Owing to the inclusion of a semiconductor commutator at the input of the VFEMA–FC, it is easy to obtain a good voltage waveform at the output.

References

1. P. A. Rovinskii, V. A. Tikan. Valve frequency converters without a dc link. Academy of Sciences of the USSR, Nauka Publishing House, 1965.

2. P. A. Kalyan. Energy relations in a contactless alternating-current machine operating with variable rotational speed. Energetika, No. 11, 1965.

3. V. S. Novokshenov. Investigation of an asynchronous brushless frequency converter. Dissertation, Tomsk Polytechnic Institute, 1960.