INFLUENCE OF THE PARAMETERS OF THE OUTPUT WINDING ON THE STIFFNESS OF THE EXTERNAL CHARACTERISTICS OF A BRUSHLESS ELECTRIC MACHINE AMPLIFIER (BEMA)

A. I. Skorospelkin, E. N. Podborskii, E. F. Obergan

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

In connection with the broad development of alternating-current electric drives, transverse-field commutator electric-machine amplifiers operating on alternating current have found application. However, in general the commutator-and-brush assembly is unreliable in operation and requires careful maintenance and adjustment of commutation.

Under conditions of rarefied space, operation of brush equipment is associated with additional difficulties caused by the reduced air density. These conditions are most fully met by the use of brushless electric-machine amplifiers.

Figure 1 shows the schematic diagram of a BEMA, which is a two-stage single-armature amplifier, in the second stage of which excitation from the armature current of the first stage is used. There is no inductive coupling between the windings of the different stages. The first stage is a three-phase synchronous generator feeding, through a rectifier, the excitation winding of the second stage. The second stage is a three-phase synchronous generator. The absence of inductive coupling is achieved by using different pole numbers for the windings of both stages.

Fig. 1. Schematic diagram of a BEMA.

When the amplifier operates under load, the dependence of the output voltage on the load is of definite interest.

With an unsaturated magnetic system and in the absence of inductive coupling of the control winding with the other circuits, the voltage at the amplifier output, for a constant control signal, is equal to

\[ \dot U_S=\dot E_S-\dot I_S Z_S=\dot E_S-I_S r_S-j I_S X_{dS}, \tag{1} \]

where \(\dot E_S\) is the phase emf at no load of the amplifier,

\[ \begin{aligned} U_S&\text{ is the output phase voltage,}\\ I_S&\text{ is the load current,}\\ Z_S&\text{ is the total impedance of a phase of the output winding,}\\ r_S&\text{ is the active resistance of the phase,}\\ X_{dS}&\text{ is the inductive reactance of the output winding.} \end{aligned} \]

Expression (1) corresponds to the vector diagram shown in Fig. 2. From the diagram we find

\[ \dot U_S=\sqrt{E_S^2-I_S^2\left(X_{dS}\cos\varphi-r_S\sin\varphi\right)^2} -I_S r_S\cos\varphi+I_S X_{dS}\sin\varphi . \tag{2} \]

It is evident from this expression that the steepness of the external characteristics of the BEMA is determined both by the parameters of the output stage and by the nature of the load. The change in output voltage as a function of the magnitude and nature of the load is due to the influence of armature reaction and to the voltage drop across the active and reactive resistances of the stator output winding. The armature reaction of the output stage of a brushless electric machine amplifier is analogous to the armature reaction of a synchronous generator.

With an active load (\(\cos\varphi=1\)), the steepness of the external characteristics will be determined only by the parameters of the output winding, and equation (2) takes the form

\[ U_S=\sqrt{E_S^2-I_S^2\cdot X_{dS}^2}-I_S r_S \tag{3} \]

or

\[ U_S=\sqrt{E_S^2-I_S^2\left(X_{adS}+X_{\sigma S}\right)^2}-I_S r_S, \tag{4} \]

where \(X_{adS}\) is the inductive reactance of the armature reaction of the stator output winding,

\[ X_{\sigma S}\text{ is the leakage reactance.} \]

The greatest influence on the change in output voltage is exerted by the armature reaction, which is taken into account by means of the reactance

\[ X_{adS}=2m_S f_S\, \frac{\mu_0 D l_i W_S^2 K_{\mathrm{ob}.S}^2} {K_{\mu}\,\delta' p_S^2}, \tag{5} \]

where \(m_S\) is the number of phases of the stator output winding,

\[ \begin{aligned} f_S&\text{ is the frequency of the emf at the output,}\\ W_S&\text{ is the number of turns per phase,}\\ K_{\mathrm{ob}.S}&\text{ is the winding factor,}\\ p_S&\text{ is the number of pole pairs,}\\ D&\text{ is the diameter of the stator bore,}\\ l_i&\text{ is the calculated length,}\\ \delta'&\text{ is the calculated air gap,}\\ K_{\mu}&\text{ is the saturation coefficient of the second stage.} \end{aligned} \]

Synchronous generators of the same overall dimensions as a BEMA have a much larger air gap; therefore the value of \(X_{adS}\) for a BEMA is considerably higher, and the external characteristics of the brushless amplifier have a much greater steepness than those of synchronous generators.

Expression (5) shows that the most effective means of reducing \(X_{adS}\), and thereby increasing the stiffness of the external characteristics, is to reduce the number of turns of the output wind-

of the winding. It should be noted, however, that a directly proportional reduction in the number of winding turns, with the same flux in the machine, reduces the output voltage, whereas it must be no less than a specified value.

Considering expressions (5), it may be noted that by changing the winding data and the geometrical dimensions of the brushless electric-machine amplifier it is impossible to completely eliminate the undesirable influence of the armature-reaction m.m.f., since in this case \(X_{adS}\) can never be made equal to zero.

We built and investigated a brushless electric-machine amplifier with the following data:

\[ P_n = 4\ \text{kW},\quad f_S = 100\ \text{Hz},\quad n = 3000\ \text{rpm},\quad U_S = 220\ \text{V}. \]

During operation of the amplifier, the external characteristics shown in Fig. 2 were taken. The characteristics obtained are drooping, and their stiffness is unsatisfactory. This is explained by the fact that the armature reaction from the load current strongly weakens the flux of the second stage because of the large value of \(X_{adS}\).

Fig. 2. Vector diagram of the amplifier output stage.

Fig. 3. External characteristics of a BEMA with one parallel branch in the output winding.

An increase in the stiffness of the external characteristics of the BEMA was achieved by switching winding \(W_S\) into two parallel branches. In this case, according to expression (5), the resistance \(X_{adS}\) decreased by a factor of four. For this case, Fig. 4 shows the external characteristics obtained experimentally and by calculation with an active load.

For comparison of the stiffness of the external characteristics of the amplifier with one and with two parallel branches, Fig. 5 gives, in relative units, the external characteristics of a BEMA with one parallel branch in the stator winding (1) and with two parallel branches (2). It is not difficult to see that the stiffness of the external characteristic of the BEMA with two parallel branches is considerably higher. It should be noted that although connecting the output winding into two parallel branches considerably increases the stiffness of the external charac-

characteristics of the BEMA; however, at the same values of the control current the output voltage is reduced by half, while the power taken off remains approximately constant.

Thus, the stiffness of the external characteristics of a BEMA is strongly affected by the parameters of its output winding; however, by varying them within possible limits it is impossible to obtain a high stiffness of the external characteristics. To substantially increase the stiffness of the external characteristics, special measures must be taken.

Fig. 4. External characteristics of a BEMA with two parallel branches in the output winding.

Fig. 5. External characteristics of a BEMA in relative units.
1 — with one parallel branch in the output winding;
2 — with two parallel branches.