ON THE CHOICE OF STATOR TOOTH-ZONE GEOMETRY FOR A MULTIPOLE SHOCK GENERATOR

G. L. Sipailov, K. A. Khorkov, V. Z. Khorkova,
V. S. Baklin, V. I. Andreev

(Recommended by the scientific seminar of the Department of Electrical Machines and by the Electrical Machines Division of the Scientific Research Institute of Automation and Electromechanics)

Numerous theoretical studies of two-pole shock-power generators, carried out within the limiting dimensions of turbogenerators [1, 2], show that when a generator operates into an inductive load, for a single current pulse of duration 0.02 sec, energy on the order of 25–30 million J can be delivered to the load.

A further increase in the power of an individual shock-power generator is possible by transition to multipole design variants. It is precisely multipole machines that include the largest modern breaking-capacity generators:

a) a four-pole shock generator of the Mitsubishi firm with a symmetrical short-circuit power of 4550 MVA [3];

b) an eight-pole shock generator of the Siemens-Schuckertwerke firm with a symmetrical short-circuit power of 4300 MVA [4];

c) an eight-pole shock generator of the AEG firm with a symmetrical short-circuit power of 3000 MVA [5].

The principal advantage of multipole shock generators is the more complete utilization of the model power at the lowest mechanical stresses in the machine, especially in the end portions of the stator winding.

The available literature on multipole shock generators is, as a rule, devoted to descriptions of designs and technical-economic characteristics of breaking-capacity generators. Engineering recommendations for design are of a very approximate nature. For example, in [5], concerning the design of the tooth zone, it is stated: “the open slots are made very wide so that the pressure of the bar on the slot bottom under shock current does not damage the sleeves,” and further, “slot leakage is low because of the low and wide slots.”

For two-pole generators we have studied in detail the influence of the geometry of the stator tooth zone on the magnitude of the energy delivered by the generator to the load [2]. Optimal ratios have been established between the width and height of the slots, and between the tooth width and the magnitude of the stator tooth pitch. Calculations show that deviations from the optimal values of the indicated quantities can lead to a reduction in generator power by a factor of 1.5–2 or more. It is of interest to consider the influence of these basic parameters of the tooth zone on the magnitude

energy and for multipole shock-power generators, which have a number of distinctive features.

Theoretical studies on optimizing the geometry of the tooth zone of multipole generators were carried out on an electronic digital computer.

In the calculations it was assumed that the shock-power generators are made within the limiting dimensions of multipole machines and that the salient-pole rotors have a powerful damper system.

Thus, the following principal dimensions of the generators are known to us:

\(\tau\) — stator pole pitch,
\(l\) — calculated length of the active part,
\(\delta\) — size of the machine air gap.

For a 4-pole shock generator, \(\tau = 1.65\ \text{m}\) was adopted; for 6- and 8-pole generators, \(\tau = 1.57\ \text{m}\). The possibility of constructing multipole shock generators with the indicated pole pitches is shown in [6], and is also confirmed by the practice of manufacturing high-speed hydrogenerators [7].

For convenience in comparing the calculated design variants of shock generators, for all machines \(l = 6\ \text{m}\), \(\delta = 0.03\ \text{m}\), and the maximum permissible induction in the stator tooth \(B_{zm} = 2.65\ \text{T}\) were adopted. In order to maintain identical electromagnetic loadings when calculating different generator design variants, the induction in the machine air gap \(B_{\delta}\) was rigidly related to the permissible induction in the narrowest section of the stator tooth through the coefficient \(\xi\):

\[ B_{\delta} = \xi \cdot k_c \cdot B_{zm}, \]

where \(K_c\) is the stacking factor of the steel package.

As for 2-pole shock generators, the following are taken as the principal variable quantities:

\(k_1\) — ratio of slot height to its width,
\(\xi\) — ratio of tooth width to tooth pitch.

The main criterion for comparing the calculated variants is considered to be the permissible current density in the stator winding. As for 2-pole shock generators, we take the maximum possible value of current density equal to \(400\ \text{A/mm}^2\).

The calculations show complete identity of the dependences of the energy delivered by the shock generators to the load on the geometry of the stator tooth zone for all the variants considered. Characteristic curves for 4-, 6-, and 8-pole machines are presented in Figs. 1 and 2.

In multipole shock generators, an increase is observed in the energy transferred to the load in one current pulse with an increase in the ratio of tooth width to tooth pitch, i.e., with an increase in the induction in the air gap, Fig. 1. In the figures, the sign * indicates the energy values at current densities in the winding of \(400\ \text{A/mm}^2\), within the range of variation of the number of slots per pole and phase from \(q = 18\) to \(q = 6\) (with a corresponding increase in induction from \(B_{\delta} = 0.98\ \text{T}\) to \(B_{\delta} = 1.72\ \text{T}\)). For each number of slots per pole and phase there is a certain limiting value of \(\xi\), determined by the permissible current density in the stator winding. At the same time, for a smaller value of slots per pole and phase, larger values of \(\xi\) are permissible. For example, for a 4-pole generator, at \(q = 8\) the largest \(\xi = 0.70\); at \(q = 12\), \(\xi = 0.62\); for a 6-pole generator at \(q = 8\), \(\xi = 70\); at \(q = 12\), \(\xi = 0.61\); for an 8-pole generator at \(q = 8\), \(\xi = 0.70\); at \(q = 12\), \(\xi = 0.60\).

Comparison with two-pole shock generators [2] shows complete identity of the patterns of the relationship between \(\xi\) and \(q\). The optimum width of the stator slots of multipole shock generators

Fig. 1. Dependence of the energy delivered by a shock generator to the load on \(\xi\), for generators of different pole numbers.

Panels: \(2p=4\), \(2p=6\), \(2p=8\). The vertical axis is \(W\), MJ; the horizontal axis is \(\xi\). Curves are marked \(8\), \(10\), \(12\), \(14\), and \(400\ \mathrm{A/mm^2}\).

Fig. 2. Dependence of the maximum specific energy \(W_{\max}\) and stress on \(K_1\) for generators of different pole numbers.

depends on the number of slots per pole and phase and does not exceed one half of the tooth pitch. Thus, the question of reducing the inductive resistance of the phase part of the stator winding by changing the geometry of the slot is reduced to choosing an expedient reduction in the slot height.

Figure 2 presents the dependences of the energy transferred by the shock generator to the load in one current pulse on the ratio between the height and width of the stator slots. It is evident from the figure that reducing the slot height (reducing \(\kappa_1\)) leads to an increase in energy only up to a certain limit. In addition, reducing the slot height leads to a reduction in the copper cross section of the winding and is accompanied by a significant increase in current density. The energy values corresponding to current densities of \(400\ \mathrm{A/mm^2}\) are marked with an asterisk (*).

It is evident that for each number of slots per pole and phase there is its own optimal value of \(\kappa_1\). For different numbers of slots per pole and phase, such values of \(\kappa_1\) can be selected at which the energy of the shock generators of this series will be the same.

A comparison of calculation variants for multipole shock generators shows that there is a certain tendency toward deepening the slots as the polarity of the machine increases; for example, for a 4-pole generator at \(q = 8\) the optimum is \(\kappa_1 = 1.0\), at \(q = 12\), \(\kappa_1 = 1.9\); for a 6-pole generator at \(q = 8\) the optimum is \(\kappa_1 = 1.20\), at \(q = 12\), \(\kappa_1 = 1.95\); for an 8-pole generator at \(q = 8\) the optimum is \(\kappa_1 = 1.20\), at \(q = 12\), \(\kappa_1 = 2.0\).

In comparison with 2-pole shock generators, the optimal slot depth of multipole generators is greater by 10–20%.

Calculations show that, with optimal geometry of the stator tooth zone and permissible electromagnetic loadings \(B_\delta = 1.5\ \mathrm{T}\); \(B_z = 2.3\ \mathrm{T}\); \(j = 400\ \mathrm{A/mm^2}\), the following energy can be transferred from a shock generator to an inductive load in one pulse: from a 4-pole shock generator, 30 MJ; from a 6-pole shock generator, 45 MJ; from an 8-pole shock generator, 60 MJ.

With further forcing of the excitation, with an increase of the induction in the gap to \(1.7\ \mathrm{T}\), we obtain, respectively: from a 4-pole shock generator, 40 MJ; from a 6-pole shock generator, 55 MJ; from an 8-pole shock generator, 75 MJ.

REFERENCES

1. G. A. Sipailov, K. A. Khor’kov. Specific energy of a shock generator. Izvestiya TPI, vol. 132, 1965.

2. G. A. Sipailov, K. A. Khor’kov, V. Z. Khor’kova, V. S. Baklin, V. I. Andreev. On the choice of the geometry of the tooth zone of the stator of a shock generator. Izvestiya TPI, vol. 211, 1970.

3. Mitsubisi Denki Giho, 1964, V. 38, No. 9; 1963, V. 37, No. 8. High-power shock generator of a high-power breaking laboratory.

4. J. Tittle. Der neue 4300 mva Stoßleistungsgenerator für das Schaltwerk der Siemens — Schuckertwerke Siemens — Zeitschrift, 1962, 36, 48.

5. G. Hagedorn. Der neue Stoßkurzschlußgenerator der AEG elektrotechnisch betrachtet; AEG — Mitt, 1962, 52 No. 7—8.

6. G. A. Sipailov, V. F. Kulakov. On the possibilities of multipole shock generators. Proceedings of the VII Interuniversity Conference on Electron Accelerators. Atomizdat, 1969.

7. M. P. Kostenko, V. Kh. Safiulina, L. A. Sukhanov. Design features and parameters of powerful high-speed generators. In: Investigation of electromagnetic fields, parameters, and losses in electrical machines. Nauka, 1966.