PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
OF THE ORDER OF THE OCTOBER REVOLUTION
AND THE ORDER OF THE RED BANNER OF LABOR
named after S. M. Kirov

Volume 284　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1974

DESIGN FEATURES OF A SHOCK GENERATOR FOR REDUCED FREQUENCY

G. A. Sipailov, K. A. Khorkov, L. O. Oganyan

(Presented by the scientific seminar of the departments of electrical machines and apparatus
and general electrical engineering)

When a shock generator operates into an inductive load, the expression for the electromagnetic energy of the load can be represented in the form

\[ W_{\mathrm{n}}=\frac{c_{\mathrm{ud}}}{\dfrac{\Sigma \lambda}{pq}}\cdot l(\tau B_{\delta})^2; \tag{1} \]

where

\[ c_{\mathrm{ud}}=\frac{k_{\mathrm{z}}^{2}k_{\omega}^{2}}{6\tau^{2}\mu_{0}}. \]

Analysis of this expression shows that an increase in the energy delivered by the generator to the load is possible by:

1) reducing the leakage inductive reactance of the stator winding;
2) increasing the dimensions of the machine;
3) increasing the induction in the air gap.

Earlier studies [1, 2] of two-pole and multipole shock generators made it possible to determine the amount of energy delivered to the load for the optimum geometry of the tooth zone of the generators, the maximum permissible dimensions, and the maximum permissible induction in the air gap.

A further increase in the energy in the current pulse requires new solutions. One possible way to increase the electromagnetic energy transmitted to the load in a single current pulse is to design the shock generator for a reduced frequency, with a corresponding increase in the pole division of the machine.

Thus, for example, within the dimensions of an eight-pole generator it is possible to make a four-pole shock generator, thereby increasing the pole division twofold by lowering the voltage frequency to 25 Hz while maintaining the magnitude of the rotor rotational speed. Designing a two-pole shock generator within the same dimensions makes it possible, with a reduction of the generator voltage frequency to 12.5 Hz, to increase the generator pole division fourfold. According to relation (1), a significant increase in energy should be expected. In this connection

of interest is determining the optimal geometry of the toothed zone of the stator of a shock generator at reduced frequency.

An analysis of the influence of the geometry of the toothed zone of the stator on the magnitude of the electromagnetic energy delivered to the load was carried out with the aid of a digital computer. In the calculations it was assumed that the following basic generator parameters are known: \(l=6\ \text{m}\); \(D_p=3.9\ \text{m}\); number of poles \(2p=4\) or 2; maximum permissible induction in the stator tooth \(B_z=2.7\ \text{T}\); maximum permissible current density in the stator winding \(400\ \text{A}/\text{mm}^2\).

The magnitude of the induction in the air gap is determined through the coefficient \(\xi\), equal to the ratio of the tooth width to the stator tooth pitch:

\[ B_\delta = k_c \xi B_{z\max}, \tag{2} \]

where

\(k_c\) is the steel stacking factor.

In the calculations the coefficient \(\xi\) was varied from \(\xi=0.5\) to \(\xi=0.9\). Another variable quantity was taken to be the ratio of the height of the stator slot to its width, \(k_1\), the value of which was varied from \(k_1=1\) to \(k_1=5\). The calculations

Fig. 1. Dependences of energy and current density on \(\xi\) for various \(q\) and \(k_1\) for a generator at a frequency of 25 Hz

were performed for numbers of slots per pole and phase from \(q=4\) to \(q=10\). The method for calculating the parameters of the shock generator, the current when the stator winding is connected to the load, and the energy delivered to the load is set forth in [1]. The calculation results are presented in the form of dependences \(W_n=f(q,k_1,\xi)\) and \(j_{ud}=f(q,k_1,\xi)\) in Figs. 1–4.

The dependences presented reveal the interrelation between the energy, the current density, and the basic parameters defining the geometry of the toothed zone of the stator: \(q\), \(\xi\), and \(k_1\).

From an analysis of the curves in Figs. 1 and 2 it is seen that, for any number of slots per pole and phase and for any value of the slot height relative to its width, as \(\xi\) increases and, consequently, as \(B_\delta\) increases according to relation (2), an increase is observed in the energy delivered by the generator to the load. However, at the same time the current density in the wind—

of the stator winding. On the curves, the asterisk sign (*) marks the points corresponding to the maximum permissible current density. Limiting the permissible value of the current density leads, for the adopted \(q\), to a limitation of the value of \(\xi\). Calculations show that for each \(q\) there is its own permissible \(\xi_{(*)}\).

For example, for a generator with \(2p=4\), at \(k_1=2\) and \(q=4\), the permissible \(\xi_{(*)}=0.8\); for \(q=6\), \(\xi_{(*)}=0.75\); \(q=8\), \(\xi_{(*)}=0.7\); \(q=10\), \(\xi_{(*)}=0.65\). For a generator with \(2p=2\), at \(k_1=2\), for \(q=4\) we have the optimum \(\xi_{(*)}=0.9\); for \(q=6\), \(\xi_{(*)}=0.85\); \(q=8\), \(\xi_{(*)}=0.8\), and \(q=10\), \(\xi_{(*)}=0.77\).

Fig. 2. Dependences of energy and current density on \(\xi\) for various \(q\) and \(k_1\), for a generator at a frequency of 12.5 Hz

The calculation results presented show that, for the adopted \(k_1=\mathrm{const}\), with an increase in the number of slots per pole and phase, the value of the permissible \(\xi_{(*)}\) decreases. Comparison with the permissible values of \(\xi_{(*)}\) for an eight-pole shock generator at a frequency of 50 Hz [2], which has, at \(k_1=2\), for \(q=4\), \(\xi_{(*)}=0.7\); \(q=6\), \(\xi_{(*)}=0.62\); \(q=8\), \(\xi_{(*)}=0.54\), and \(q=10\), \(\xi_{(*)}=0.45\), shows that with a reduction in the generator frequency (that is

Fig. 3. Dependences of energy and current density on \(k_1\) for various \(q\) and \(\xi\), for a generator at a frequency of 25 Hz

with a decrease in the number of machine poles) for the same values of \(q\), the value of the permissible \(\xi_{(*)}\) increases.

It is clear from Figs. 1 and 2 that the value of the permissible \(\xi_{(*)}\) depends on the slot geometry: as the slot depth increases, the permissible \(\xi_{(*)}\) increases. The dependences of the energy delivered by the shock generator to an inductive load on the geometrical factor \(k_1\), characterizing the ratio of the height of the stator slot to its width, for various values of \(q\) and \(\xi\), are presented in Figs. 3 and 4. It is evident that, for any value of the number of slots per pole and phase, a reduction in the slot height leads to an increase in electromagnetic energy only up to a certain limit. At the same time, for each \(q\) there is its own critical value of \(k_1\),

Fig. 4. Dependences of energy and current density on \(k_1\) for different \(q\) and \(\xi\) for a generator at a frequency of \(12.5\ \mathrm{Hz}\)

at which the energy curve has a maximum. On the curves, the asterisk (*) indicates the minimum permissible values \(k_{1(*)}\), at which the current density in the stator winding reaches \(400\ \mathrm{A/mm^2}\).

Unlike two-pole and multipole shock generators at a frequency of \(50\ \mathrm{Hz}\), for which the permissible \(k_{1(*)}\) lies, as a rule, above the critical value—that is, the increase in current density limits the reduction of slot height before the energy reaches a maximum—in shock generators for reduced frequency the permissible value \(k_{1(*)}\) coincides with the critical value or is even somewhat smaller than the latter. It should be noted that, as the voltage frequency decreases, the character of the curves becomes more rigid.

For example, for generators with \(q=4\), when \(k_1\) is increased from 1.5 to 4 at \(f=50\ \mathrm{Hz}\) and \(\xi=0.7\), the energy value decreases by a factor of 1.35; at \(f=25\ \mathrm{Hz}\) and \(\xi=0.75\), by a factor of 1.25; and at \(f=12.5\ \mathrm{Hz}\) and \(\xi=0.8\), by a factor of 1.12. For larger values of \(q\), equal to 6, 8, and 10, the change in energy as \(k_1\) increases from its critical value is still less significant. Consequently, for shock generators at reduced frequency, deeper slots can be recommended than for shock generators at \(50\ \mathrm{Hz}\).

The latter makes it possible to significantly reduce the current density in the stator winding. Thus, for example, at \(f=12.5\ \mathrm{Hz}\), \(q=8\), and \(\xi=0.8\) (Fig. 4), the perm—

an energy on the order of 260 MJ is achieved at \(k_1=2.2\) and a current density \(j=350\ \mathrm{A/mm^2}\), and also at \(k_1=4.5\) and \(j=60\ \mathrm{A/mm^2}\).

Thus, making shock generators for reduced frequency makes it possible not only to increase the amount of energy transmitted to the load in one current pulse, but also to substantially reduce the thermal loading of the stator winding by increasing the copper cross section of this winding.

Figure 5 presents the values of the energy delivered by a shock generator to a matched inductive load, found from the results of the investigations given above for generators having the dimensions of an eight-pole turbogenerator with \(D_p=3.9\ \mathrm{m}\), \(l=6\ \mathrm{m}\), when the number of poles and the frequency of the voltage of the generator stator winding are varied from

Fig. 5. Limiting values of the energy delivered by a shock generator to a matched inductive load, when the generator is made for different frequencies in one set of dimensions

\(2p=8\) and \(f=50\ \mathrm{Hz}\) to \(2p=2\) and \(f=12.5\ \mathrm{Hz}\). Calculations show that making the shock generator two-pole in the dimensions of an eight-pole machine makes it possible to transmit energy to the load of up to 260 MJ in one current pulse, which is three times higher than when the shock generator is made eight-pole. Making the shock generator with a limiting length of the active part of the machine equal to \(12\ \mathrm{m}\) will make it possible to obtain in the load an energy on the order of 500 MJ. Thus, calculations show that in those cases where there are no restrictions on the duration of the current pulse, it is expedient to use shock generators for reduced frequency.

REFERENCES

1. 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 toothed zone of the stator of a shock generator. Izv. TPI, vol. 211, 1970.

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 toothed zone of the stator of a multipole shock generator. Izv. TPI, vol. 229, 1972.