Brushless Synchronous Machine with Hybrid Excitation

Yu. N. Kroneberg

(Presented by the scientific and technical seminar of the Department of Electrical Equipment, AEMF)

To satisfy the constantly growing requirements for the quality of the output parameters, machines with permanent magnets must have effective methods of regulation. The main prospects here are associated with improving known machines [1, 2, 3] and developing new machines in which the advantages of electromagnetic and magnetoelectric excitation would be successfully combined.

Fig. 1. Brushless synchronous machine.
1 — armature, 2 — yoke, 3 — side magnetic circuit, 4 — excitation winding, 5 — claw-shaped pole, 6 — magnet

In our opinion, these also include a synchronous machine (Fig. 1), some of whose poles are excited by a star-shaped magnet, while the remaining ones are excited by a winding located on the external magnetic circuit [4]. In this case the order of alternation of north and south poles is preserved not only as a whole, but also for each system—electromagnetic and magnetoelectric—separately. When the excitation winding is switched off, the emf is induced practically only in the conductors of the series armature winding located opposite the magnets (Fig. 2). As the excitation current increases, the flux of the claw-shaped poles increa—

decreases, and accordingly the e.m.f. increases. As can be seen from the oscillograms, the field contains lower harmonics (in this case of order \(1/3\)); however, they do not induce an e.m.f. owing to the series connection of the coil groups.

As a first approximation it may be assumed that the fluxes of the magnet and of the excitation winding are independent (in fact, as the excitation current increases, the flux of the magnet increases only slightly). This is explained by the fact that the mutual coupling appears only owing to the voltage drop in the armature back, which is very small, and to the leakage fluxes of the poles, which are also relatively small. The machine under consideration is conveniently compared with the electromagnetically excited machine structurally related to it, with an externally closed magnetic flux (in essence, this is the same machine, in which all poles are claw-shaped).

Fig. 2. Experimental no-load characteristics: solid line—combined excitation; dashed line—inductor—electromagnetic.

Let us assume that the magnetization curve of the electromagnetic machine is typical for synchronous machines and close to the normalized one. Then, at excitation currents not exceeding the rated current by \(2.5 \div 3\) times, it is approximated by the hyperbolic tangent

\[ E = 1{,}43\,\operatorname{th} 0{,}87 \sqrt{N}, \tag{1} \]

where

\[ E \text{ and } N \]

are, respectively, the e.m.f. and the excitation power (the rated voltage is taken as the unit of e.m.f., and its value at this e.m.f. as the unit of power).

Similarly, the equation of the no-load characteristic of a combined-excitation machine, under the assumption that the fluxes are independent,

\[ e = \frac{m}{p} e_m + 1{,}43\left(1 - \frac{m}{p}\right)\operatorname{th} 0{,}87 \sqrt{n}, \tag{2} \]

where

$e$ and $n$ are the EMF and excitation power;

$p$ and $m$ are the number of pole pairs and permanent magnets;

$e_m$ is the conditional EMF, equal in relative units to the ratio of the magnet flux to the arithmetic mean flux of the poles at the nominal EMF.

The regulation depth (the difference between the relative values of the nominal and initial EMF) in this case is

\[ \gamma = 1 - \frac{m}{p} e_m , \tag{3} \]

Fig. 3. Excitation power and regulation depth

Assuming in equation (2) that $e=e_{\text{n}}=1$, we find the nominal excitation power:

\[ n_{\text{n}} = 1.32 \left( \operatorname{Arth} 0.7 \frac{p-me_m}{p-m} \right)^2 . \tag{4} \]

From equations (2)—(4) it is obvious that, for the selected structure of the pole system (with $p$ and $m$ specified), the magnitude of the conditional EMF has a decisive influence on the performance indicators of the machine. In Fig. (3), as an example, the indicated dependences are presented for a machine with $2p=12$ and $2m=4$, from which it follows that, as $e_m$ increases, the excitation power decreases sharply and, when $e_m>1$, becomes already smaller than in an electromagnetic machine. In other words, a gain in excitation power at no load is achieved when the flux of the magnet poles exceeds—

is the mean pole flux. There are real grounds for this, since the magnet has a relatively large volume (the length of the line of force is greater than in a similar magnetoelectric machine by a factor of 2.5–3).

The difference in weight is due to two circumstances: the introduction of the magnet and the absence of some of the claw-shaped poles, with a corresponding reduction in the cross section of the yoke.

With some approximation it may be assumed that a gain in weight is obtained when the inequality

\[ \frac{l_j g_j k_{\sigma j}}{l_{\mathrm{m}} g_{\mathrm{m}} k_{\sigma \mathrm{m}}} > \frac{B_j}{B_{\mathrm{m}}}, \tag{5} \]

is satisfied, where

\(l_j\) — total length of the line of force in the yoke, side magnetic circuits, and claw-shaped poles;

\(l_{\mathrm{m}}\) — length of the line of force of the pair of magnet poles;

\(g_j\) and \(g_{\mathrm{m}}\) — specific weights of the materials of the yoke (steel) and of the magnet;

\(B_j\) and \(B_{\mathrm{m}}\) — rated inductions in the yoke (for the machines being compared they are considered identical) and in the magnet;

\(k_{\sigma j}\) and \(k_{\sigma \mathrm{m}}\) — reduced leakage coefficients of the claw-shaped poles and of the magnet.

In this inequality, which as a rule is satisfied, usually

\[ l_j > l_{\mathrm{m}}, \quad g_j > g_{\mathrm{m}}, \quad k_{\sigma j} > k_{\sigma \mathrm{m}} \quad \text{and} \quad B_j > B_{\mathrm{m}}. \]

Table

When operating under load, another important advantage of the machine with combined excitation appears—an increased stiffness of the external characteristic, which is associated with a reduction in inductive reactances. Indeed, \(2m\) pole sections of the series armature winding will have the longitudinal and transverse inductive reactances \(x_{ad\mathrm{m}}\) and \(x_{aq\mathrm{m}}\), corresponding to a magnetoelectric machine, and only the remaining \(2(p - m)\) sections will have the reactances \(x_{ad\mathrm{e}}\) and \(x_{aq\mathrm{e}}\), corresponding to an electromagnetic machine. Then the reactances of the combined-excitation machine:

\[ x_{adk}=\frac{1}{p}\left[(p-m)x_{adэ}+mx_{adм}\right], \tag{6} \]

\[ x_{aqk}=\frac{1}{p}\left[(p-m)x_{aqэ}+mx_{aqм}\right]. \tag{7} \]

If the difference in the quadrature-axis inductive reactances is relatively small and does not introduce substantial differences, then the difference between \(x_{adэ}\) and \(x_{adм}\) is always significant. For example, if one assumes [1] that \(x_{adм}/x_{adэ}=0.5 \div 0.05\), then according to equation (6), for \(2p=12\) and \(2m=4\), the direct-axis inductance is \(x_{adk}=(0.68 \div 0.83)x_{adэ}\) and \(x_{adk}=(1.67 \div 13.7)x_{adм}\).

Fig. 4. Load characteristics: solid line — combined excitation, line — combined excitation, dashed line — electromagnetic

Experimental studies were carried out on two laboratory samples, the basic data of which are given in the table. For a number of extraneous reasons connected with manufacturing conditions, the poles of the electromagnetic machine turned out to be 1.18 times wider than those of the machine with combined excitation, which adversely affects the characteristics of the latter. However, even in this case, at the rated no-load voltage (Fig. 2), the excitation current decreased by a factor of 2.11, and the excitation power by a factor of 4.47. Such a large gain is due to the fact that in the tested sample the magnets produced a very substantial flux. Judging from the field oscillograms (Fig. 2), it exceeds the average by approximately a factor of 1.9, which, according to equation (3), should lead to a reduction in power by approximately a factor of 5. The discrepancy of about 12% is probably explained primarily by differences in pole width.

Under load (Fig. 4), the gain in excitation current is 1.29 times, and in power, 1.67 times. At rated excitation currents of \(0.88\) and \(0.68\) A, the no-load emf values of the machines with electromagnetic and combined excitation are \(52.3\) V and \(55.2\) V, and the currents of co-

Fig. 5. External characteristics: solid line—combined excitation, dashed line—electromagnetic.

short-circuit current (Fig. 5) is 24.8 A and 31 A, i.e., the external characteristic of the combined-excitation machine is indeed noticeably stiffer.

Thus, the combined-excitation machine investigated possesses a number of important advantages and, in certain cases, may be considered one of the principal options in the design, for example, of low-power power supplies with a voltage regulation depth on the order of 0.4–0.7. At the same time, the question arises of a more detailed study of the machine and the development of methods for its calculation.

REFERENCES

1. A. I. Vertinov. Aircraft Electrical Generators. Oborongiz, 1959.

2. L. M. Palastin. Regulated Electrical Machines with Excitation from Permanent Magnets. TsINTI of the Electrical Engineering Industry and Instrument Engineering, 1962.

3. V. A. Balagurov, F. F. Galteev, A. N. Larionov. Electrical Machines with Permanent Magnets. “Energiya,” 1964.

4. Yu. N. Kroneberg. Brushless synchronous machine. USSR Author’s Certificate, class 21 d², 3 No. 188563, 18/VII, 1962.