STUDY OF THE CHARACTERISTICS OF A BRUSHLESS DC ELECTROMECHANICAL AMPLIFIER (BDEMA)

A. I. SKOROSPECHKIN, E. N. PODBORSKII

(Recommended by the seminar of the Departments of Electrical Machines and General Electrical Engineering)

Modern semiconductor technology makes it possible to solve problems connected with the development of brushless electromechanical amplifiers. We have developed and are studying models of a DC BDEMA. Such an amplifier consists of two synchronous generators with different numbers of pole pairs, combined in a single magnetic circuit. The first generator feeds the excitation winding of the second generator.

Figure 1 presents a diagram explaining the operation of the amplifiers. The nominal data of the models are as follows:

Fig. 1.

1. \(P_{\mathrm{н}} = 3\ \text{kW},\)  \(U_{\mathrm{н}} = 230\ \text{V},\)  \(n = 3000\ \text{rpm}\)

2. \(P_{\mathrm{iн}} = 1.2\ \text{kW},\)  \(U_{\mathrm{н}} = 115\ \text{V},\)  \(n = 3000\ \text{rpm}\)

The difference between these models is that in one of the amplifiers the output winding of the first stage on the rotor is made three-phase, while in the other it is eight-phase.

The numbers of rotor phases made it possible to build the first model with numbers of phases \(m = 3, 6, 12\), and the second model with \(m = 2, 4, 8, 16\).

By choosing \(m = 8\) in the second model, we were able to study operation also at \(m = 4\), by disconnecting half of the phases.

The rotor rectifiers are assembled according to a half-wave circuit, since it requires the minimum number of valves, which is important when the rotor dimensions are small.

In the manufactured models, theoretical and experimental study is carried out of the principal characteristics: external characteristics, regulation characteristics, gain factor, and speed of response. Curves of current, emf, and output-voltage pulsations are analyzed.

With linear current feedback, the external characteristics for both amplifiers are presented in Fig. 2a, b. The nonlinearity of the characteristics is explained by the fact that the transverse component of the armature-reaction mmf is not fully compensated, although it amounts to more than 90% of the resultant mmf.

Fig. 2a.

The external characteristics (Fig. 2a) correspond to regulation characteristics (Fig. 3a), which have the same form as the regulation characteristics of synchronous generators.

The conditions under consideration correspond to oscillograms of phase currents and voltages. As can be seen from the oscillograms of the phase voltages of both amplifiers, presented in Fig. 4a, b, the transverse armature reaction demagnetizes the leading edge and magnetizes the trailing edge of the pole, which strongly distorts the phase-voltage curve.

To compensate the transverse mmf of the armature reaction, compensating windings were placed in both models, shifted by 90 electrical degrees relative to the excitation windings of the second stage. The load current, flowing through this winding, compensates the transverse component of the armature-reaction mmf. The degree of transverse compensation is adjusted by a resistance shunting the compensating winding.

Fig. 2b.

Axes and labels: \(U_n\) (V); \(I_n\) (A). Curves: 1, 2, 3.

Fig. 3a.

Axes and labels: \(I_y\); \(I_n\). Curve labels: \(U_n = 220\ \text{V}\), \(U_n = 200\ \text{V}\), \(U_n = 180\ \text{V}\).

Fig. 4a.

Fig. 4b.

If it is assumed that the parameters of the amplifier are constant, and that the current, voltage, and e.m.f. vary with time according to a sinusoidal law, then the voltage at the amplifier output in the general case will be equal to:

\[ U_n = \frac{1}{K_g} \left[ \sqrt{ \left( E_{z0} - R_{yaq}\frac{W_{ocd}}{W_y}K_{ocd} I_n \right)^2 + \left( R_{yaq}K_{ocq}I_n \right)^2 } - K_1^2 I_n^2 \left( X_{Cv}\cos\varphi - r_s\sin\varphi \right)^2 - K_1 X_{Cx} I_n\sin\varphi - K_1 I_n r_s\cos\varphi \right], \tag{1} \]

where

\[ K_u=\frac{U_s}{U_n} \]

is the ratio of the rms value of the phase voltage to the rectified voltage;

\[ K_i=\frac{I_s}{I_n} \]

is the ratio of the rms value of the phase current to the rectified current;

$E_{s0}$ — phase emf at no load;

$R_{\alpha d}=\dfrac{E_{s0}}{I_y}$ — magnetizing resistance along the longitudinal axis;

$I_{\mathrm{oc}d}=K_{\mathrm{oc}d}$ — current in the feedback winding along the longitudinal axis;

$R_{\alpha q}$ — magnetizing resistance along the transverse axis;

$K_{\mathrm{oc}q}\cdot I_{\mathrm{н}}$ — current in the compensation winding along the transverse axis;

$X_{\mathrm{cx}}$ — synchronous inductive reactance of the output winding;

$W_{\mathrm{oc}d}$ — number of turns in the feedback winding along the longitudinal axis;

— number of turns in the control winding;

$r_s$ — active resistance of the output winding;

$\cos\varphi$ — power factor.

With complete transverse compensation,

\[ R_{\alpha q}K_{\mathrm{oc}q}=K_1\left(X_{\mathrm{cx}}\cos\varphi-r_s\sin\varphi\right). \]

In this case the equation of the external characteristic is considerably simplified and assumes the form:

\[ U_{\mathrm{н}}=\frac{1}{K_U}\left[\left(E_{s0}+R_{\alpha d}\frac{W_{\mathrm{oc}d}}{W_y}K_{\mathrm{oc}d}I_{\mathrm{н}}\right)-K_1X_{\mathrm{cx}}I_{\mathrm{н}}\sin\varphi-K_1r_sI_{\mathrm{н}}\cos\varphi\right]. \tag{2} \]

It should be noted that when the load changes, the inductance of the output winding and the mutual inductance of the output winding and the excitation winding change. But, taking into account that the ratio of these inductances is practically independent of the load current, the equation of the external characteristic of the brushless EMA with complete transverse compensation and an unsaturated first stage will take the form:

\[ U_{\mathrm{н}}=\frac{1}{K_U}\left(E_{s0}+K_{\mathrm{oc}d}R_{\alpha d}I_{\mathrm{н}}\right)\frac{X_{\mathrm{cx}}}{X_{\mathrm{cx}0}} -\frac{K_1}{K_U}X_{\mathrm{cx}}\sin\varphi\, I_{\mathrm{н}} -\frac{K_1}{K_U}r_s I_{\mathrm{н}}\cos\varphi . \]

In this equation the angle

\[ \varphi=\frac{\gamma}{2}+\alpha, \]

where $\gamma$ is the commutation angle,
$\alpha$ is the ignition angle.

The angles $\gamma$ and $\alpha$ can be calculated from the formulas [1].

$X_{\mathrm{cx}0}$ — unsaturated synchronous inductive reactance of the output stage.

In Fig. 5 the solid lines show the external characteristics obtained experimentally for the second model, and, for comparison, the dotted lines show the characteristics calculated from equation (3). Noteworthy are the straight-line nature of the characteristics, due to a sufficient degree of compensation of the transverse component of the armature reaction mmf, and the satisfactory agreement of the experimental data and calculations.

These characteristics correspond to the oscillograms of the phase emfs (Fig. 6). As can be seen from the oscillogram of the phase voltage, the distorting effect of the transverse mmf of the armature reaction is considerably smaller than was the case without transverse compensation. The straight-line nature of the external characteristics and the minimum level of ripple of the output voltage are an important advantage of the operating mode with complete transverse compensation.

Figures 7a, b show oscillograms of the output voltage for identical values of currents and load voltages, obtained

In Fig. 5: vertical axis \(U_n(\mathrm{V})\); horizontal axis \(I_n(\mathrm{A})\). Curve labels: \(K_{ocd} > K_{ocd}\), \(K_{ocd_e}\).

Fig. 5.

Fig. 6.

Fig. 7a.

Fig. 7b.

with full transverse compensation and without transverse compensation for the second model. The level of voltage ripple, as is evident from these oscillograms, is considerably lower with full transverse compensation.

As was established experimentally, the external characteristics are rectilinear only up to a certain value of the load current. With a further increase in the load, saturation of the first and additional stages of the amplifier begins. This leads to a slowing of the increase in the currents in the excitation and transverse-compensation windings; the armature reaction along the longitudinal and transverse axes proves to be undercompensated, and the linearity of the external characteristics is disturbed. The output voltage then begins to decrease more sharply.

The amplification factor is one of the most important indices of the amplifier and is estimated by the ratio of output and input powers

\[ K_y = \frac{ \left( E_{s0} + R_{xd}\frac{W_{ocd}}{W_y}K_{ocd} I_{\mathrm{н}} \right) \frac{X_{cx}}{X_{cx0}} I_{\mathrm{н}} - K_I X_{cx}\sin\varphi\, I_{\mathrm{н}}^{2} - K_I r_s\cos\varphi\, I_{\mathrm{н}}^{2} }{ K_c \cdot U_y \cdot I_y } \tag{4} \]

Figure 8 presents the dependences of the amplification factor on the load current for various coefficients of feedback along the longitudinal axis; these show that with full transverse compensation the amplification factor depends linearly on the load current. For the first model the maximum amplification factor obtained experimentally is 500, and for the second, 80. With optimization of the models, the amplification factors can be increased.

The speed of response of the brushless EMA determines its operability in dynamic modes. In Fig. 9a, b, c are shown, respectively, oscillograms of the rise of the control current, the excitation current of the second stage, and the output voltage for the second model.

The speed of response of the brushless EMA is approximately the same as that of the commutator type \((T = 0.07)\).

A drawback of the amplifiers under investigation is the absence of reversal of the polarity of the output voltage when the polarity of the control signal is changed. Its elimination is included in the further part of the work.

On the whole, the DC brushless EMAs being developed by us correspond in their properties to the requirements imposed on them and can be used in various branches of the national economy.

Fig. 8.

Fig. 9a.

Fig. 9b.

Fig. 9c.