ON THE SELECTION OF THE ROTOR WINDING IN BRUSHLESS ELECTRIC MACHINE AMPLIFIERS (BEMA) AND FREQUENCY CONVERTERS

A. I. SKOROSPELKIN, K. A. KHOR'KOV, E. K. DERGOBUZOVA

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

The BEMAs and frequency converters that we are developing are two-stage and combined. The first stage is, in essence, a synchronous machine. But the magnitude of the air gap in them is taken as in asynchronous machines. Therefore one may expect that, without the use of stabilizing means, the external characteristic of the synchronous stage will have a steeply drooping character. Experiment confirms this.

Existing methods of voltage stabilization by means of feedback are more suitable for converters and amplifiers of direct current and fixed frequency. In converters and amplifiers with regulated frequency, the use of feedback leads to an additional load on the controlled semiconductor commutator (CSC), which, for wide limits of frequency regulation, may exceed the rated power (at the base frequency) several times. In other words, the presence of feedback through the CSC leads to a reduction in the rated load of the machine.

The above makes it necessary to seek new methods of voltage stabilization.

We have proposed a method for improving the stiffness of the external characteristic of the synchronous stage of the machine by reducing the influence of the demagnetizing action of armature reaction with the aid of a special structural design of the rotor winding, called a “zigzag.”

The essence of this winding design is that each phase of the winding is divided into parts shifted in space relative to one another by a certain angle \(\alpha\) (Fig. 1).

Thanks to such a connection, a shift is created between the main flux and the flux of armature reaction, as a result of which the demagnetizing action of the armature reaction is reduced. The resultant emf of the machine also decreases, but only slightly, in any case to a lesser degree than the demagnetizing action of the armature reaction decreases.

Logic suggests that the best arrangement will be the division of the phase into two equal parts,

Fig. 1.

shifted in space by 90 electrical degrees. For the synchronous inductive reactance of a three-phase synchronous generator we have the following calculation formula:

\[ X_p = 2mf\,\frac{\mu_0 D l K_w W_p}{K_\delta K_\mu p^2 \delta}, \tag{1} \]

where \(m\) is the number of winding phases,
\(f\) is the emf frequency,
\(\mu_0\) is the magnetic permeability of air,
\(K_w\) is the winding factor,
\(W_p\) is the number of turns of the winding,
\(K_\delta\) is the air-gap coefficient,
\(K_\mu\) is the saturation coefficient,
\(p\) is the number of pole pairs,
\(\delta\) is the size of the air gap.

An analogous expression derived for the inductive reactance of the winding when it is connected according to the “zigzag” scheme has the form:

\[ X_{pz} = 2mf\,\frac{\mu_0 D l K_{wz}}{K_\delta K_\mu p^2 \delta} \left[(W_1 + W_2 \cos \alpha)^2 + (W_2 \sin \alpha)^2\right]. \tag{2} \]

Fig. 2. External characteristics of the cascade at \(f_y = 0\)

Under the condition that the number of turns of the “zigzag” winding \(W_z = W_1 + W_2\) is equal to the number of turns of the ordinary winding \(W_p\), we obtain

\[ \frac{X_{pz}}{X_p} = \frac{ K_{wz}\left[(W_1 + W_2 \cos \alpha)^2 + (W_2 \sin \alpha)^2\right] }{ K_w (W_1 + W_2)^2 } = \frac{K_{wz}}{K_w} \left[ 1 + \frac{2W_1W_2}{(W_1 + W_2)^2} (\cos \alpha - 1) \right]. \tag{3} \]

The optimum ratio of the numbers of turns \(W_1\) and \(W_2\), and the optimum value of the angle \(\alpha\), are obtained after setting the partial derivatives of expression (3) equal to zero; they are:

\[ W_1 = W_2 \quad \text{and} \quad \alpha = \frac{\pi}{2}. \tag{4} \]

The experiments carried out fully confirm this conclusion. For the investigations, a model was built with the overall dimensions of the AOK 42-4. The armature winding was placed on the rotor. The following types of windings were investigated:

1) an ordinary lap winding with number of turns \(W_p\),

2) a “zigzag” winding with \(W_1 + W_2 = W_p\) for \(W_2 = \dfrac{1}{2} W_1\).

The effect of the angle \(\alpha\) on the stiffness of the external characteristics was investigated at a control-field frequency \(f_y = 0\).

The test results are presented in Fig. 2 in the form of the dependence \(U = f(I)\). It is seen from the figure that at \(\alpha = 90^\circ\) (curve 1) the external characteristic is stiffer than at \(\alpha = 60^\circ\) (curve 2) and \(\alpha = 0\) (curve 3).

Fig. 3. Developed diagram of the “zigzag” winding at \(\alpha = 90^\circ\) electrical.

The developed diagram of the “zigzag” windings at \(\alpha = 90^\circ\) is shown in Fig. 3.

Thus, connecting the winding in a “zigzag” significantly increases the stiffness of the machine’s external characteristic. However, the most indicative are the regulating characteristics (Fig. 4), obtained with a stationary control field \(f_y = 0\) and a rotor emf frequency \(f_p = 100\) Hz.

It is seen from the curves that, at small load currents, to obtain the same output voltage when the winding is connected according to the “zigzag” scheme, greater excitation power of the machine is required (curve 1) than with a normal winding. However, at currents close to the rated current, the picture changes sharply. This indicates that the cascade gain coefficient at normal load will be considerably greater for the “zigzag” winding, since the control powers for both windings are related as the squares of the currents.

Fig. 4. Control characteristics of the cascade at \(f_y = 0\).

For example, at a power \(P = 4\ \text{kW}\), the following amplification factors were obtained:
\[ K_y = 37 \]
for the conventional winding,
\[ K_y = 54 \]
for the “zigzag” circuit.

It is especially important that these dependences, obtained with a stationary control field, remain valid also for operation of the cascade with a rotating field of the control winding.

Figure 5 presents the external and control characteristics of the cascade, taken at a control-field frequency \(f_y = 30\ \text{Hz}\), which gives an emf frequency in the rotor winding \(f_p = 130\ \text{Hz}\). It is evident from the curves that, when the frequency is controlled, the stiffness of the external characteristics for the “zigzag” circuit (curve 1) is considerably greater.

It should also be noted that, when operating with a capacitive load (for example, when a compensating capacitance is connected to the cascade output), the winding connected according to the “zigzag” circuit behaves in the same way as a conventional winding. The external characteristics of the cascade with a capacitive load are shown in Fig. 6.

Thus, the use in converters and amplifiers of the combined type of a winding connected according to the “zigzag” circuit instead of the usual winding makes it possible to increase the stiffness of the external characteristic of the cascade and to reduce the control power at nominal load, which is especially important for machines with adjustable frequency.

REFERENCES

1. M. P. Kostenko, L. M. Piotrovskii. Electrical Machines, GEI, Part II, 1958.

Fig. 5. External and regulating characteristics of the cascade at
\(f_y = 30\) Hz,
\(f_p = 130\) Hz.

Fig. 6. External characteristics of a cascade with a “zigzag” winding under capacitive load and \(F_y = 30\) c.u.
1 — at \(C = 0\).
2 — at \(C = 15\ \mu\mathrm{F}\).