Operating Characteristics of a Three-Phase Magnetic Amplifier Feeding the Armature of a DC Motor at Low Speeds

M. A. Borovikov

(Presented by the scientific seminar of the Electromechanical Faculty)

The operation of a three-phase magnetic amplifier with self-saturation (Fig. 1), for saturation angles of the cores \(\alpha_s > 60^\circ\) and a small value of the opposing emf, differs substantially from that described in [1] for modes with \(\alpha_s < 60^\circ\). Figure 2 gives the equivalent circuit of the amplifier for intervals during which, owing to the delay in the current decay process up to the extinction angles \(\alpha_i > 120^\circ\), the potential of terminal P may become negative relative to N, and negative voltages appear at the motor armature. At the moments when negative voltages appear, two cores which previously had been in the process of demagnetization (in Fig. 2, cores B and C′) are again magnetized by positive voltages. Of the six amplifier cores, three are magnetized because positive voltages are present on their working windings; two remain saturated owing to the flow of load current through the working windings; and only one is demagnetized, with a negative emf induced in its working winding.

The magnitude of this emf can be determined approximately if it is assumed that the ohmic resistance of the control circuits is zero. In this case, in steady operation the magnetic amplifier can operate at a control voltage \(U_y = 0\), that is,

\[ 0 = U_{yA} + U_{yA'} + U_{yB} + U_{yB'} + U_{yC} + U_{yC'} \tag{1} \]

In the interval \(0 < \Theta < \alpha_s - 60^\circ\) (see Fig. 3), the voltage on winding A is equal to \(U_{1-3}\); on windings B and C′, \(U_{\rho B} = U_{\rho C'} = U_{2-3}\) (Fig. 2); and on windings B′ and C the voltages are zero. Since cores A, B, and C′ are not saturated, the voltages \(U_{\rho A}\), \(U_{\rho B}\), and \(U_{\rho C'}\) are transformed into the control circuit:

Fig. 1.

\[ \left. \begin{aligned} U_{\mathrm{у}A} &= U_{\mathrm{p}A}\frac{w_{\mathrm{у}}}{w_{\mathrm{p}}} = U_{1-3}\frac{w_{\mathrm{у}}}{w_{\mathrm{p}}},\\[6pt] U_{\mathrm{у}B} &= U_{\mathrm{p}B}\frac{w_{\mathrm{у}}}{w_{\mathrm{p}}} = U_{2-3}\frac{w_{\mathrm{у}}}{w_{\mathrm{p}}},\\[6pt] U_{\mathrm{у}C'} &= U_{\mathrm{p}C'}\frac{w_{\mathrm{у}}}{w_{\mathrm{p}}} = U_{2-3}\frac{w_{\mathrm{у}}}{w_{\mathrm{p}}},\\[6pt] U_{\mathrm{у}B'} &= U_{\mathrm{у}C}=0 \end{aligned} \right\} \tag{2} \]

Comparing (1) and (2), we find the voltage on the control winding \(U_{\mathrm{у}A'}\):

Fig. 2.

Fig. 3.

\[ \mathrm{U}_{yA'}=-\frac{w_y}{w_p}\left(2\mathrm{U}_{2-3}+\mathrm{U}_{1-3}\right). \tag{3} \]

This negative voltage causes demagnetization of core \(A'\), and in this case an emf is induced in the working winding,

\[ \mathrm{U}_{pA'}=\mathrm{U}_{yA'}\frac{w_p}{w_y} =-\left(2\mathrm{U}_{2-3}+\mathrm{U}_{1-3}\right). \tag{4} \]

In Fig. 3a the operating voltage is shown only for winding \(A\), in which an emf is also induced in accordance with (4), but only \(180^\circ\) after the interval under consideration.

This emf, even allowing for transformation losses, proves to be greater than the line voltage (\(\mathrm{U}_{1-2}\) for the instant according to Fig. 2). Owing to the voltage difference \(\mathrm{U}_{pA'}\) and \(\mathrm{U}_{1-2}\) in the circuit: terminal 2—winding

\(B'\)—valves V4, V2—winding A—terminal 1—there can flow a current \(i_{pA'}\), whose magnitude is limited by the ohmic resistance of the circuit and by the leakage inductance of the working winding, but which cannot be greater than the direct current through valve V4. Since core \(A'\) is not saturated, the current \(i_{pA'}\) will cause the corresponding current to flow in the control winding by transformation,

\[ i_y = i_p \frac{w_p}{w_y}. \tag{5} \]

The current transformed into the control circuit, flowing from the end of the winding to its beginning, can bring the cores \(B'\) and \(C\) out of saturation, so that the load current \(i_a\) will then flow through the windings of the unsaturated cores, which causes a further increase in the transformation current in the control circuit. Diagrams of the current of the working winding and of the voltage on the armature are given in Fig. 3a.

This phenomenon leads to unstable operation of the amplifier with a passive load, similar to the relay effect in single-phase amplifiers with a midpoint when operating into an active-inductive dc load [2]. The control characteristic of the three-phase MA when operating into a passive load is shown in Fig. 4a.

When the magnetic amplifier is operated according to the circuit of Fig. 1 on a motor having a sufficiently large \(t_{\mathrm{e}}\varphi\), the phenomenon described leads to unstable operation of the drive at low speeds. In this case, when negative voltages appear on the armature, a process arises in which the saturation angle decreases and the armature voltage and current increase; and with a load of the form \(M_c=\mathrm{const}\), the motor begins to operate in a self-oscillatory mode: as the armature current increases, the motor accelerates, the emf increases and blocks the amplifier—the motor brakes, the emf decreases, and now the current increases again, etc. The mechanical characteristics of the motor when operating at low speeds according to the circuit of Fig. 1 are shown in Fig. 4b.

Fig. 4.

The portions of the characteristics on which self-oscillations occur are drawn with dashed lines.

The phenomenon described always arises in drives if the amplifier provides a “free magnetization” mode, in which one or several control windings are supplied from a source with low internal resistance and when relation (1) turns out to be close to the actual one. From the point of view of ensuring normal operation of the drive, the effect described is harmful and must be eliminated.

The instability of the drive according to the circuit of Fig. 1 can be eliminated by providing a “forced magnetization” mode of the amplifier cores. This is achieved either by introducing a large active resistance or by introducing an inductance into the circuit of the control windings. Both of these methods are practically unacceptable: in the first case the gain of the magnetic amplifier is reduced, and in the second case its dynamic characteristics deteriorate.

It proves more rational to use a shunting valve (Fig. 5a). In this case the negative voltages at the armature are cut off and the magnetization of the amplifier cores occurs practically in the same way as with an active resistance in the load circuit (see Fig. 3b); the discharge current of the armature inductance now closes through the shunting valve \(V_{\text{sh}}\), and therefore excessive voltages cannot appear on the working windings and transformation of the working currents into the control circuit is impossible. The mechanical characteristics of the drive according to the circuit of Fig. 5a have no unstable portions (see Fig. 5b).

Fig. 5.

The circuit of a magnetic amplifier with so-called contour internal feedback has the same property (Fig. 6). In this circuit the bridge of rectifiers \(2V\) performs the role of the shunting valve, and a relay effect is impossible.

The circuit of Fig. 6 may prove more advantageous than the circuit of Fig. 5a when selenium rectifiers are used: the number of rectifiers in

in both cases turns out to be approximately the same, but the reverse voltage on valves 1V in Fig. 6 in qualitative amplifiers is lower (per washer) than on valves 1V--6V of the circuit in Fig. 5a; therefore the demagnetization of the amplifier by reverse currents is less, and the circuit of Fig. 6 provides a larger amplification factor. When germanium or silicon rectifiers are used, the circuit of Fig. 5a is not inferior in quality to the circuit of Fig. 6, and in terms of valve consumption may prove more advantageous.

Fig. 6.

Analysis of the circuit of Fig. 5a for \(a_s > 60^\circ\), according to the method described in [1], makes it possible to obtain the necessary relations for the currents:

\[ I_{ya}=\frac{3U_m}{\pi R}\left[1+\cos\left(a_s-\frac{\pi}{3}\right)-\frac{E}{U_m}-\frac{\pi}{3}\right], \tag{6} \]

\[ I_{vsh}=I_{ya}\left(\frac{3a_s}{\pi}-1\right); \tag{7} \]

where

\[ R=r_{ya}+2r_v+2r_r, \]

\[ \gamma = 2 - \frac{3a_s}{\pi} - \frac{r'_a}{R}\left(\frac{3a_s}{\pi} - 1\right), \]

where \(r'_a\) is the resistance of the armature and \(V_{\mathrm{sh}}\).

For \(a_s < 60^\circ\), the shunting valve has no effect on the operation of the circuit, and the corresponding expression [1] is valid.

Conclusions

To eliminate the influence of inductance in the load circuit of a three-phase magnetic amplifier—which, when the impedance of the control circuits is small, causes a relay effect of the amplifier when it operates into a passive load, or self-oscillations of the motor when the drive operates at low speeds—it is advisable to install a valve shunting the load in opposition to the output voltage of the MA. The shunting valve, moreover, broadens the limits of the continuous-load-current mode and, consequently, the limits of linearity of the motor characteristics, which in turn simplifies calculations.

The same result is obtained by using an MA circuit with a separate rectifier bridge.

References

1. M. A. Borovikov. Operation of a three-phase magnetic amplifier on the armature of an independently excited DC motor. Proceedings of the Fourth All-Union Conference on Automated Electric Drive. Energiya Publishing House, 1965.

2. G. F. Storm. Magnetic Amplifiers. Foreign Literature Publishing House, 1957.