Brushless Electric Machine Amplifier (BEMA)
Abstract Generated abstract
This paper describes the design and investigation of a brushless alternating-current electric-machine amplifier intended for automatic-control systems where commutator machines are unreliable or unsuitable. It explains the operating principle of a two-stage single-armature amplifier with semiconductor rectification, load-current feedback through current transformers, and a shared magnetic core. The main theoretical contribution is the derivation of compatibility conditions that prevent inductive coupling between the control winding and the second-stage excitation winding for concentrated, distributed, and concentric control windings. A constructed 4.2 kW, 220 V, 3000 rpm, 100 Hz prototype is used to illustrate the feasibility of the proposed winding arrangements, while the authors note that further development and investigation are continuing.
Full Text
BRUSHLESS ELECTRIC MACHINE AMPLIFIER (BEMA)
A. I. Skorospeleshkin, E. N. Podborskii, E. F. Obergan
(Recommended by the seminar of the Departments of Electrical Machines and General Electrical Engineering.)
In solving the problem of automation, the most important role belongs to electrified automatic-control systems, used both in industry and in power installations. One of the principal elements of an automatic-control system is the amplifier, which makes it possible, by means of small powers, to control large electric machines. With the broad development of various automatic-control systems, commutator electric-machine amplifiers have become widely used. Having a high amplification factor, good speed of response, and good technical and economic characteristics, commutator EMAs are widely employed in power electric drives.
However, because of the presence of sliding contacts, commutator amplifiers are not sufficiently reliable in operation and require careful maintenance and adjustment of commutation. Under conditions of rarefied space and in dusty rooms, operation of the brush gear is especially greatly impeded, and operation of the machine may become impossible.
The presence of brush contact is extremely undesirable, and in some cases inadmissible, in amplifiers operating in fire- and explosion-hazardous rooms, in coal mines, and in installations where stringent requirements are imposed on the level of radio interference.
The use of brushless amplifiers, which have no sliding contacts, most fully corresponds to the indicated operating conditions. Therefore they do not require careful maintenance and are more reliable in operation.
It should be noted that neither the domestic nor the foreign literature covers questions of the general theory of brushless amplifiers or gives a method for designing them. In [1, 2] only possible circuits of these amplifiers are given, but there are no recommendations for their design. Therefore, at the Department of Electrical Machines of the Tomsk Polytechnic Institute, a brushless electric-machine amplifier (BEMA) of alternating current of fixed frequency was designed, manufactured, and investigated:
\[ P = 4.2\ \text{kW}, \quad U = 220\ \text{V}, \quad n = 3000\ \text{rpm}, \quad f = 100\ \text{Hz}. \]
Principle of operation. The brushless amplifier is a two-stage single-armature amplifier, in the second stage of which excitation by the armature current of the first stage is used. Both stages are made in accordance with the conditions of compatibility of two
cascades (stages) in a single magnetic core, which will be described below. The schematic diagram of the amplifier is shown in Fig. 1.
The designations in the figure are:
\(W_y\) — control winding,
\(W_{p1}\) — three-phase rotor winding with number of poles \(2p_1\),
\(W_{p2}\) — excitation winding of the second cascade,
\(W_s\) — output stator winding,
\(W_k\) — compensating winding,
\(R_n\) — load rheostat,
\(TT\) — current transformers.
Its operation may be explained as follows. When the control winding is connected to a dc voltage \(U_y\), a control current flows through it equal to
\[ I_y=\frac{U_y}{r_y}, \tag{1} \]
where \(r_y\) is the ohmic resistance of the control winding. The control current creates an m.m.f. \(F_y\), equal to
\[ F_y=I_y W_y, \tag{2} \]
where \(W_y\) is the number of series-connected turns of the control winding.
The m.m.f. \(F_y\) creates in space a stationary magnetic flux \(\Phi_y\) with number of poles \(2P_1=2\). Since the rotor of the amplifier is rotated by the drive motor at speed \(n\), an e.m.f. \(E_{p1}\) with frequency
\[ f_{p1}=\frac{P_1\cdot n}{60}. \tag{3} \]
will be induced in the three-phase rotor winding of the first cascade \(W_{p1}\), with number of poles \(2P_1=2\).
Fig. 1. Schematic diagram of a brushless electromagnetic amplifier with fixed frequency (BEMA).
The winding \(W_{p1}\) is connected to a three-phase rectifier \(B\), assembled on semiconductor diodes.
The load of the rectifier is the rotor winding of the second stage \(W_{p2}\), with number of poles \(2P_2=4\).
The rectified direct current \(I_{p2}\), flowing through the single-phase rotor winding \(W_{p2}\), creates an m.m.f.
\[ F_{p2}=I_{p2}W_{p2}. \tag{4} \]
Under the action of \(F_{p2}\), a magnetic flux \(\Phi_{p2}\) arises with number of poles \(2P_2=4\), stationary relative to the rotor. Rotating together with the ro-
relative to the stator at speed \(n\), this flux induces in the turns of the stator output winding an emf with frequency
\[ f_s=\frac{P_2\cdot n}{60}. \tag{5} \]
When the stator output winding \(W_s\) is connected to a symmetrical load, the load current will flow through the stator winding. The armature reaction due to the load current will affect the flux \(\Phi_{p2}\), but will not affect the flux of the control winding, provided the condition of compatibility of the two cascades in one magnetic core is satisfied.
As the load current increases, the voltage at the amplifier output changes as a function of the magnitude and nature of the load, under the influence of the armature reaction of the output winding and of the voltage drop in its active and reactive resistances.
To increase the stiffness of the external characteristics of the BEMA, positive feedback with respect to the load current is used.
The primary windings of the current transformers are connected in series with the load. The ends of their secondary windings are connected in star, and the beginnings are connected to a three-phase rectifier assembled according to the Larionov circuit. A feedback winding, hereinafter called the compensating winding, is connected to the rectifier output. It is placed in the stator slots according to the same arrangement as the control winding.
A direct current flows through the compensating winding; its magnitude is proportional to the magnitude of the load current, since the current transformers have an unsaturated magnetic system. The direction of current in the compensating winding must be such that its mmf is directed in accordance with the control mmf. Directly proportional to the increase in load current are the mmf of the compensating winding and the flux of the first cascade.
Compatibility conditions for two BEMA cascades in one magnetic core
The principle of combining two electric machines in one magnetic core has long been known. Thus, for example, P. Richter [3] proposed several cascade induction motors, each of which represents one or another combination of two induction motors combined in one magnetic core. Later, works [4, 5, 6] were devoted to the question of combining two electric machines—an induction motor and an induction converter—in one magnetic core. They note that the choice of the numbers of pole pairs and the design of the windings of the combined electric machines is not arbitrary. To combine the windings of two electric machines in one magnetic core, it is necessary:
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That there be no inductive coupling between the two windings.
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That the sum of the two electromagnetic fields not create an asymmetrical field causing unilateral magnetic attractions and vibrations.
Let us consider, as applied to the BEMA, the conditions under which there is no inductive coupling between two windings placed in one magnetic core.
In the BEMA it is necessary and sufficient that there be no inductive coupling between the control winding and the excitation winding of the sec—
of the second cascade. The single-phase control winding of a BEMA may be concentrated, distributed, or concentric.
First let us consider the compatibility condition for two cascades in one magnetic circuit with a concentrated control winding.
During operation of the BEMA, the excitation flux of the second stage, \(\Phi_{p2}\), will rotate together with the rotor relative to the stator; therefore, emf’s will be induced in both sides of the control coil. For the BEMA it is necessary that the flux \(\Phi_{p2}\) not induce an emf in the control winding. Consequently, the sum of the emf’s in both sides of the control coil must be equal to zero.
If the control coil is made with full pitch with respect to the flux \(\Phi_{p2}\), then the latter will induce in it an emf \(E_y\); but if the pitch of the control coil differs from the pole pitch \(\tau_2\), then an emf will be induced in the control winding \(W_y\)
\[ E'_y = K'_y E_y, \tag{6} \]
where
\[ K'_y = \sin \frac{\pi}{2}\frac{\tau_1}{\tau_2} \]
is the pitch-shortening coefficient of the control winding, taking into account the reduction of the emf due to the flux \(\Phi_{p2}\) when the winding pitch is shortened;
\(\tau_1\) — pole pitch of the first cascade;
\(Z_s\) — number of stator slots;
\(2P_1\) — number of poles of the first cascade;
\[ \tau_2 = \frac{Z_s}{2P_2} \]
— pole pitch of the second cascade;
\(2P_2\) — number of poles of the second stage.
From (6) it is seen that the control winding will not be inductively coupled with the winding \(W_{p2}\) in the case when \(K'_y = 0\), that is,
\[ \sin \frac{\pi}{2}\frac{\tau_1}{\tau_2} = 0. \tag{7} \]
This is possible in the case when
\[ \frac{\tau_1}{\tau_2} = \text{an even number} \ (8). \tag{8} \]
If in expression (8) we substitute the values of the pole pitches through the number of slots and pole pairs, we obtain
\[ \frac{P_2}{P_1} = \text{an even number}. \tag{9} \]
Thus, (9) is the mathematical expression of the compatibility condition for two cascades of a BEMA with a concentrated control winding.
With a distributed control winding, the emf of the latter due to the flux \(\Phi_{p2}\) is equal to
\[ E_y = E \cdot K_w, \tag{10} \]
where \(E\) is the emf of a concentrated winding with the same pitch and the same number of turns as the distributed one;
\[ K_w = K_p K'_y \]
is the winding factor,
\(K_p\) — distribution coefficient of the winding \(W'_y\) for the field \(\Phi_{p2}\).
From (10) it is seen that \(E_y = 0\) when \(K_w = 0\), or
\[ K_w = K_p \cdot K'_y = \frac{\sin \dfrac{q\alpha}{2}}{q \sin \dfrac{\alpha}{2}} \sin \frac{\pi}{2}\frac{\tau_1}{\tau_2}, \tag{11} \]
where \(q\) is the number of slots per pole and phase of winding \(W_y\),
\(\alpha\) is the angle of displacement between two adjacent slots in electrical degrees \(\Phi_{p2}\).
Expression (11) will be equal to zero when
\[ \frac{\tau_1}{\tau_2}=\text{an even number}, \]
\[ \frac{P_2}{P_1}=\text{an even number}. \tag{12} \]
Thus, (12) is the mathematical expression of the compatibility condition for two BEMA stages with a distributed control winding.
In a concentric control winding, the flux \(\Phi_{p2}\) will induce an emf in each control coil. Since the axes of all coils of the concentric winding coincide, the emfs of all coils will add algebraically.
Suppose that in the \(n\)-th coil with a pitch equal to \(\tau_2\), the flux \(\Phi_{p2}\) induces an emf \(E_{ky}\); then in any other coil an emf will be induced:
\[ E'_{ky}=E_{ky}K'_{yp}. \tag{13} \]
The pitch-shortening coefficient for this coil is equal to
\[ K'_y=\sin \frac{\pi}{2}\frac{Y_n}{\tau_2}, \tag{14} \]
where \(Y_n\) is the pitch of the \(n\)-th coil of the control winding \(W_y\). The coil pitch should be counted from the beginning of the coil to its end in one direction for all coils (for example, in the direction of rotor rotation).
For a BEMA it is necessary that the sum of the emfs of all coils of the control winding be equal to zero, i.e.,
\[ E_y=E_{ky}\left(K'_{y1}+K'_{y2}+\ldots+K'_{yn}\right)=0. \tag{15} \]
From (15) it is evident that this is possible only in the case when
\[ K'_{y1}+K'_{y2}+\ldots+K'_{yn}=0 \tag{16} \]
or
\[ \sum_{1}^{n} K'_y=0, \tag{17} \]
where \(n\) is the number of coils of the control winding.
Taking (15) into account, expression (17) assumes the form
\[ \sum \sin \frac{\pi}{2}\frac{Y_n}{\tau_2}=0. \tag{18} \]
Thus, (18) is the mathematical expression of the condition for the absence of inductive coupling between individual BEMA stages with a concentric control winding.
It makes it possible to determine very simply whether a given BEMA variant can be realized. For example, to determine whether a BEMA can be made with \(Z_s = 36\), \(2P_2 = 4\), \(2P_1 = 2\).
The control winding is concentric, consisting of fourteen coils with pitches
\[ Y_n = 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, \]
\[ \tau_2 = \frac{Z_s}{2P_2} = \frac{36}{4} = 9. \]
We use expression (18)
\[ \sum \sin \frac{\pi}{2}\frac{Y_n}{\tau_2} = \sin \frac{\pi}{2}\frac{5}{9} + \sin \frac{\pi}{2}\frac{7}{9} + \sin \frac{\pi}{2} + \sin \frac{\pi}{2}\frac{11}{2} + \]
\[ + \sin \frac{\pi}{2}\frac{13}{9} + \sin \frac{\pi}{2}\frac{15}{9} + \sin \frac{\pi}{2}\frac{17}{9} + \sin \frac{\pi}{2}\frac{19}{9} + \sin \frac{\pi}{2}\frac{21}{9} + \]
\[ + \sin \frac{\pi}{2}\frac{23}{9} + \sin \frac{\pi}{2}\frac{25}{9} + \sin \frac{3\pi}{2} + \sin \frac{\pi}{2}\frac{29}{9} + \sin \frac{\pi}{2}\frac{31}{9} = 0. \]
If the left-hand side of this expression is calculated, we obtain
\[ 0 = 0. \]
Consequently, such a BEMA can be made.
This example can be solved graphically; for this purpose a star of phase e.m.f.’s is constructed for the flux \(\Phi_{p2}\), and by geometric addition of the e.m.f.’s of both sides, the e.m.f. of each control coil is determined. If the e.m.f. vectors of all the coils balance one another, this means that the control winding will not be inductively coupled with the winding \(W_{p2}\).
Fig. 2. Diagram of the concentric control winding of the BEMA.
In Fig. 2 a diagram of the concentric control winding is given, and in Fig. 3 a star of phase e.m.f.’s is constructed for the flux \(\Phi_{p2}\), with the number of poles \(2P_2 = 4\); the e.m.f. of each coil of the wind—
the control winding from the flux \(\Phi_{p2}\). It follows from this that the sum of the e.m.f.s of all coils is equal to zero.
The brushless electric-machine amplifier with a concentric control winding that we constructed was made in accordance with this example.
Fig. 3. Star of phase e.m.f.s for the flux \(\Phi_{p2}\)
To satisfy the condition under which the superposition of two rotating magnetic fields in one magnetic circuit does not cause forces of unilateral magnetic attraction and vibrations, it is advisable to follow the recommendation given by R. Richter [3]. The inequality
\[ P_1 \pm P_2 \ne \pm 1. \tag{20} \]
must be satisfied.
In the BEMA that we constructed this condition is not satisfied. Development and investigations of BEMAs are continuing.
Conclusions
- In view of the importance of using amplifiers in various automatic-control circuits, the need to develop brushless EMAs for direct and alternating current, which have definite advantages in comparison with commutator-type ones, is obvious.
- The stated compatibility conditions for two cascades in a single magnetic circuit serve as the basis for designing brushless EMAs with concentrated, distributed, and concentric control windings.
REFERENCES
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RZhE, No. 8, 1960, 3.5505P.
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U.S. Patent, Cl. 318—148, No. 2966623, 27.12.60. Alternating-current machines with multiple excitation. RZhE, 1962, No. 2, and 113P.
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R. Richter. Electrical Machines. Vol. IV, ONTI, 1939.
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A. D. Imas. Development and investigation of high-frequency electrical drills. Report on Topic No. 16, DONUGI, Donetsk, 1948.
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V. S. Novokshchenov. Winding coefficient and compatibility conditions for two heteropolar machines in a single magnetic circuit. Izvestiya TPI, Vol. 117, 1963.
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M. S. Mikhailov-Mikulin. Calculation of the magnetic circuit of electrical machines with two rotating fields. Elektromekhanika, No. 10, 1962.