FEATURES OF COMPENSATION ADJUSTMENT IN A TRANSVERSE-FIELD ELECTRIC MACHINE AMPLIFIER DURING ALTERNATING-CURRENT OPERATION

B. I. KOSTYLEV, A. I. SKOROSPEШKIN, E. F. OBERTAN

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

Transverse-field electric machine amplifiers are widely used in automatic-control systems and regulated electric drives. Most often, in these systems EMAs operate in a dynamic mode. In addition, transverse-field EMAs are used in alternating-current systems and in installations with parametric generators [1, 2]. In these installations EMAs operate with a continuously varying control signal.

When a transverse-field EMA operates on alternating current, and in a dynamic mode on direct current, certain specific features arise in comparison with the static mode of operation on direct current; these are due to the alternating control signal. These features primarily concern the adjustment of compensation of the armature reaction along the longitudinal axis of the amplifier.

On direct current, the required degree of compensation of the armature reaction in an EMA is adjusted by means of a variable resistance \(R_{\text{sh}}\), which shunts the compensating winding \(K\), designed for a certain overcompensation (5–8%). This method of adjusting compensation has proved satisfactory in direct-current operation, providing stable compensation over the entire load range.

When an EMA operates with an alternating control signal, the indicated method of compensation adjustment impairs such basic characteristics as the gain, response speed, and stability of the degree of compensation.

The compensating winding with a shunting resistance may be regarded as the secondary circuit of a transformer with respect to the control winding. Therefore the current of the control winding, as the primary winding of the transformer, is written by the following expression:

\[ \dot I_y = \dot I_{y0} + (-\dot I_{\text{sh}}), \tag{1} \]

where \(I_{y0}\) is the magnetizing component of the current of the control winding,

\(I_{\text{sh}}\) is the component of the current of the control winding required to compensate the magnetomotive force of the compensating winding arising when the secondary transformer current flows through it.

Expression (1) shows that, by shunting the compensation winding with a resistor, the control current during alternating-current operation must increase in comparison with direct current at the same control flux. Moreover, as the frequency of the control signal increases, the control current must increase owing to the growth of the second component.

Fig. 1. Schematic diagram of a transverse-field EMA.

Since the e.m.f. of the transverse circuit is proportional to the control flux, the change in the control current can be determined from the no-load characteristics of the first stage at various frequencies of the control signal. Figure 2 presents such characteristics, obtained experimentally for an EMU-12A having the following data:
\(P_{\mathrm{n}} = 1.2\ \text{kW};\ U_{\mathrm{n}} = 115\ \text{V};\ I_{\mathrm{dn}} = 10.4\ \text{A};\ n = 2900\ \text{rpm};\ W_{\mathrm{y}} = 675\) turns; compensation on direct current is unity.

From the curves given it is evident that, as the frequency of the control signal increases, the control current increases for the same flux. Thus, at a frequency \(f = 25\ \text{Hz}\) the control current doubles, and at \(f = 50\ \text{Hz}\) it triples.

compared with the current under a constant control signal. This means that the gain of the EMA, equal to

\[ K_y=\frac{U_d I_d}{U_y I_y}, \tag{2} \]

where \(U_y\) and \(I_y\) are the voltage and current of the control winding;
\(U_d\) and \(I_d\) are the voltage and current at the amplifier output,

Fig. 2. No-load characteristics of the first stage of the amplifier at various frequencies of the control signal.

decreases by a factor of 2 at \(f=25\) cps, and by a factor of 3 at \(f=50\) cps, solely due to the transformer coupling between the control winding and the compensation-winding circuit.

The stability of the principal characteristics of the EMA depends to a considerable degree on the stability of compensation of the armature reaction. In direct-current operation, the magnetomotive forces of the compensation winding and of the armature winding along the longitudinal axis are directed oppositely; moreover, the magnetomotive force of the compensation winding is adjusted in magnitude by distributing the current between the compensation winding and the shunting resistance.

When the EMA operates on alternating current, the distribution of current and the condition of antiphase magnetomotive forces are disturbed, since a phase shift appears between the armature current and the current of the compensation winding.

winding. Indeed, for a compensating winding with a shunting resistance one can construct the vector diagram shown in Fig. 3. The following notation is used in the diagram:

\(I_{\text{sh}}\)—shunt current;
\(I_k\)—current of the compensating winding;
\(U_k\)—total voltage drop in the compensating circuit;

\[ \Psi = \operatorname{arctg}\frac{x_k}{R_k} \]

—the phase-shift angle of the compensating-winding current relative to the voltage-drop vector;

\(R_k\) and \(x_k\)—active and reactive resistances of the compensating winding;
\(I_d\)—total circuit current, or armature current;
\(\varphi\)—phase-shift angle of the total current relative to the voltage-drop vector.

Fig. 3. Vector diagram of the circuit: compensating winding—shunting resistance.

As can be seen from the diagram, the phase shift between the current of the compensating winding and the armature current is \(\Theta = \Psi - \varphi\), and the phase shift between their magnetomotive forces, owing to the opposing connection of the windings, is \(180^\circ - \Theta\). For \(x_k > 0\) the angle \(\Theta > 0\), and the condition of opposition of the magnetomotive forces will always be violated, which will lead to a change in the degree of compensation. In addition, the distribution of currents between the compensating winding and the shunting resistance, which depends on the magnitude of the leakage inductive reactance of the compensating winding \(x_k\), will vary with frequency. In this case, as the frequency increases, the current of the compensating winding will decrease, while the shunt current will increase. Consequently, in the presence of a shunting resistance the magnetomotive force of the compensating winding will be variable in magnitude and in phase, depending on the frequency of the control signal.

The change in the degree of compensation can be analyzed from the relative change in the transverse-circuit current, which, to a first approximation, is proportional to the flux of the longitudinal axis. Figure 4 gives the curves \(I_q^* = f(I_d^*)\), obtained experimentally for an EMU-12A with unity compensation adjusted on direct current, and at various frequencies of the control signal. The current values are given in relative units; the nominal value of the load current \(I_{dn}\) and the transverse-circuit current at no load \(I_{q0}\) are taken as unity.

The curves obtained show that the degree of compensation depends both on frequency and on load. Owing to the redistribution of current between the compensating winding and the shunting resistance, the magnetomotive force of the compensating winding decreases, which corresponds to operation of the amplifier in the undercompensation mode. It would seem that, in this case, the degree of undercompensation should increase with increasing frequency, as occurs for the curves at \(f = 5\) Hz and \(f = 10\) Hz. However, as can be seen from the curves, at higher frequencies the undercompensation decreases, and at certain values of frequency and

under load there appears a tendency toward overcompensation. This can be explained with the aid of the vector diagram of the amplifier, shown in Fig. 5.

Fig. 4. Dependences of the transverse-circuit current on the load current during operation of the EMA on alternating current of different frequencies according to the conventional circuit.

In the diagram shown, the vector $\kappa_d \dot I_d$ determines the uncompensated armature-reaction flux on the scale of the control current. This flux is proportional to the load current $I_d$ and, in the case of undercompensation, is in phase opposition to it. Under certain conditions

\[ \left(\Psi_d+\Psi_q>\frac{\pi}{2}\right) \]

a longitudinal magnetizing component of the load current will appear, that is, overcompensation will occur. As can be seen from the diagram, the conditions for the occurrence of overcompensation are determined by the parameters of the transverse circuit, the longitudinal circuit, and the load. Since the reactive resistances are proportional to frequency, the nature of the compensation will be different for different frequencies, and the probability of overcompensation increases with increasing frequency. Therefore, the curves in Fig. 4, with increasing frequency, have a greater upward deviation from the abscissa axis.

The analysis carried out shows that shunting of the compensation winding adversely affects the dynamic properties and their principal characteristics during operation on alternating current. Therefore

Fig. 5. Vector diagram of the amplifier under undercompensation.

Fig. 6. Dependences of the transverse-circuit current on the load current during operation of the EMA on alternating current of various frequencies according to the circuit without a shunt resistor.

it is advisable to design the compensation winding for unit compensation, varying the number of turns and the distribution. In this case, compensation will be provided independently of the control-signal frequency, which will increase the stability of the amplifier’s principal characteristics.

To verify this proposition, tests were carried out on two EMU-12A amplifiers having a compensation winding that provides close to unit compensation without a shunting resistance. The dependences obtained in the tests, \(I_q^u = f(I_d^u)\), are presented in Fig. 6. These curves confirm that, under such conditions, the degree of compensation changes little with changes in frequency.

From the results obtained, the following conclusions may be drawn.

Shunting the compensation winding with a resistance during operation of a transverse-field EMU on alternating current and in the dynamic regime on direct current adversely affects the principal characteristics of the amplifier.

As a result of the transformer coupling of the control winding and the compensation winding, the amplification factor is reduced.

As a result of changes in the magnetomotive force of the compensation winding in magnitude and in phase, the degree of compensation of the armature reaction is disturbed, which leads to instability of the amplifier’s principal characteristics.

The use of a compensation winding designed for unit compensation without connecting a shunting resistance improves the dynamic properties and the stability of the amplifier characteristics.

REFERENCES

1. V. V. Rudakov. Electric-Machine Amplifiers in Automation Systems. GEI, 1961.

2. Yu. M. Aleksandrov. Application of a transverse-field electric-machine amplifier in generator drive systems for alternating-frequency current. In: Collection of Papers on Problems of Electromechanics, issue 2, 1958.

3. N. A. Monoszon. The Electric-Machine Amplifier and Principles of Its Application in Circuits. Publishing House of the Naval Academy of Shipbuilding named after Krylov, 1950.