ELECTRIC MACHINES WITH COMBINED HETEROPOLAR INDUCTORS

Yu. N. KRONEBERG, A. S. ZHIBINOV, S. N. MARUKHIN

Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering

There exists a class of electric machines with combined excitation (CE), whose inductors consist of heteropolar electromagnetic and magnetoelectric systems [1]. The latter must have an equal number of north and south poles, and it is desirable that the order of their alternation . . . \(N—S—N\) . . . not be disrupted when traversing the circumference of the bore—this leads to an increase in the cross sections of the yoke and the armature back (Fig. 1), and also that the system have no fewer than two axes of symmetry [2], which ensures magnetic balance independently of the current of the excitation winding (EW). Obviously, the armature winding must be a series one.

Fig. 1. Electric machines with combined inductors:
a) with normal alternation of PM; b) with disrupted alternation of PM;
1 — PM, 2 — electromagnetic pole, 3 — EW

When the EW is switched off, the magnetic fluxes of the permanent magnets (PM) will close predominantly through their own poles, inducing the main part of the total emf in the conductors of the armature winding which at that moment intersect the fluxes of the poles of the magnetoelectric part of the system. As the EW current increases, the electromagnetic part of the system comes into action and the armature emf increases. At a certain m.m.f.

the EW fluxes of all poles become identical. According to the full-current law, this means that the m.m.f. of each EW coil must be exactly the same as in the equivalent machine with electromagnetic excitation (EE). But since in a CE machine the EW coils are located only on some of the poles, the total excitation power in this case must be smaller.

For a more detailed assessment of CE machines, it is expedient to compare them with EE machines that differ only in that the magnetoelectric poles are replaced by electromagnetic ones. And, so that the comparison results will be more general, let us assume that the EE machine has a so-called normalized no-load characteristic (Fig. 2), which can be approximated by a hyperbolic tangent [3]:

\[ E = 1.43\,\operatorname{th} 0.87 I , \tag{1} \]

where \(E\) is the armature e.m.f., expressed in fractions of the rated voltage; \(I\) is the excitation current, expressed in fractions of the EW current at \(E=1\).

Making the assumption that the electromagnetic and magnetoelectric systems of the CE machine are independent, we obtain the equation of the no-load characteristic in the form

\[ e = k e_m + 1.43(1-k)\operatorname{th} 0.87 i , \tag{2} \]

where \(e\) is the armature e.m.f.; \(i\) is the EW current; \(k\) is the ratio of the number of magnetoelectric poles to the total number of poles; \(e_m\) is the conditional e.m.f. of a machine in which the flux of each pole is equal to the flux of a magnetoelectric pole of the CE machine. In equation (2), the e.m.f. \(e\) and \(e_m\), and also the current \(i\), are expressed in the same units as the e.m.f. \(E\) and the current \(I\) in equation (1).

Since the EWs of EE and CE machines have different resistance, dependences (1) and (2) are still inconvenient for comparison, and they should be reduced to the form

\[ E = 1.43\,\operatorname{th} 0.87 \sqrt{P_v}, \tag{3} \]

\[ e = k e_m + 1.43(1-k)\operatorname{th} 0.87 \sqrt{\frac{p_v}{1-k}}, \tag{4} \]

where \(P_v\) and \(p_v\) are the EW powers of EE and CE machines, expressed in fractions of the EW power of the EE machine at \(E=1\).

Equations (3) and (4) make it possible to carry out a sufficiently detailed investigation of the no-load mode. Thus, taking \(e=1\) in (4), we find an expression for the excitation power \(p_n\) at an e.m.f. equal to the rated voltage; solving (3) and (4) simultaneously for \(E=e\) and \(P_v=p_v\), we find the e.m.f. \(e_r\) and the power \(p_r\) corresponding to the mode in which the machines being compared are equivalent in excitation power; the regulation depth \(\gamma\) is obtained as the difference between the rated e.m.f. \(e=1\) and the initial e.m.f. found from equation (4) at \(p_v=0\).

Figure 3 presents the parameters calculated by the indicated method and obtained experimentally for a six-pole machine with two magnetoelectric poles (\(k=1/3\)).

The experiments were carried out on a specially designed direct-current generator (generator armature diameter 10 cm, armature length 7.8 cm, rotational speed 3000 rpm), which made it possible to replace the poles and to magnetize the PMs without disassembling the machine. First the no-load characteristic of the EE machine was taken (Fig. 2); its good agreement with the normalized characteristic and the approximating curve ensures sufficient generality of the research results.

Then two diametrically opposed poles were replaced by magnetoelectric ones, and, at different PM magnetizations, a family of no-load curves was taken, which were plotted on one graph with

Fig. 2. No-load characteristic: — experimental; × — normalized; ○ — according to equation (1)

Fig. 3. Relative parameters of a six-pole KV machine with two magnetoelectric poles: — calculation; - - - experiment

characteristic of the EV machine. Equality of the emf at equality of the magnetomotive forces of the electromagnetic and magnetoelectric poles (the points of intersection of the curves of the EV and KV machines) simultaneously corresponds to equality of the fluxes of all poles of both machines. In other words, the emf of each point of intersection of the curves is the conditional emf \(e_m\).

Consequently, each curve of the family can be assigned a known value of \(e_m\), the curves can be replotted as functions of the excitation power, and all the quantities shown in Fig. 3 can be found. The discrepancies between the calculated and experimental curves, especially in the regulation depth \(\gamma\), can be explained by the mutual influence of the excitation systems, as well as by approximation errors.

Nevertheless, the investigations carried out of the no-load mode convincingly show that KV machines, even with PMs of average quality \((0.8 \leq e_m \leq 1.0)\), have a noticeable gain in excitation power and a quite satisfactory regulation depth. Since the armature reaction demagnetizes the magnetoelectric poles relatively weakly, the advantages of the KV machine under load become still more pronounced. For example, at \(e_m = 1\) the maximum output power of the KV machine was \(1.03\ \text{kW}\), whereas the EV machine had only \(0.72\ \text{kW}\).

REFERENCES

1. Yu. N. Kroneberg. Basic principles of constructing combined-excitation systems. Izvestiya TPI, vol. 242, Tomsk, TSU Press, 1972.

2. Yu. N. Kroneberg. A direct-current machine with combined excitation. Decision to issue an inventor’s certificate of July 31, 1964, for application No. 873212/24—7.

3. A. I. Bertinov. Aircraft Electric Generators. Moscow, Oborongiz, 1959.