US3786387A

US3786387A - Short-circuit testing model for stationary induction apparatuses

Info

Publication number: US3786387A
Application number: US00162601A
Authority: US
Inventors: Y Hori; Y Kashima; K Hiraishi; T Kiuchi
Original assignee: Hitachi Ltd
Current assignee: Hitachi Ltd
Priority date: 1968-01-31
Filing date: 1971-07-14
Publication date: 1974-01-15
Anticipated expiration: 1991-01-15

Abstract

A stationary induction apparatus in which the number of natural vibrations of a winding formed by winding an insulated conductor by a plurality of turns about a leg portion of an iron core is shifted from the power source frequency and the frequency which is double the power source frequency so as to prevent the winding from resonating with the latter freqeuncies and to reduce the electromagnetic force generated in the axial direction of the winding due to a short-circuit current which may flow into the apparatus winding and due to the leakage flux occurring in the apparatus, thereby to obtain a mechanically strong winding structure.

Description

United States Patent [191 Hori et al.

[ Jan. 15, 1974 1 SHORT-CIRCUIT TESTING MODEL FOR STATIONARY INDUCTION APPARATUSES [75] Inventors: Yasuro Hori; Kiyoto Hiraishi;

Tadashi Kiuchi; Yoshitake Kashima, all of Hitachi, Japan [73] Assignee: Hitachi, Ltd., Tokyo, Japan [22] Filed: July 14, 1971 [21] Appl. No.: 162,601

Related U.S. Application Data [62] Division of Ser. No. 794,862, Jan. 29, 1969,

abandoned.

[30] Foreign Application Priority Data .Ian. 31, 1968 Japan 43/5419 [52] US. Cl 336/181, 336/60, 336/197, 336/212 [51] Int. Cl. H011 27/30 [58] Field of Search 336/170, 171, 183, 336/212, 214, 215, 197, 180, 181, 182, 60

[56] References Cited UNITED STATES PATENTS 1,641,659 9/1927 Brand 336/183 X 0 SECT/O/V) Primary Examiner-Thomas J. Kozma Attorney-Craig & Antonelli [57] ABSTRACT A stationary induction apparatus in which the number of natural vibrations of a winding formed by winding an insulated conductor by a plurality of turns about a leg portion of an iron core is shifted from the power source frequency and the frequency which is double the power source frequency so as to prevent the winding from resonating with the latter freqeuncies and to reduce the electromagnetic force generated in the axial direction of the winding due to a short-circuit current which may flow into the apparatus winding and due to the leakage flux occurring in the apparatus, thereby to obtain a mechanically strong winding structure.

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SHEET 7 BF 9 F/G /70 F/G /7b INVENTOR5 ATTORNEYS SHORT-CIRCUIT TESTING MODEL FOR STATIONARY INDUCTION APPARATUSES This is a divisional of Application Ser. No. 794,832, filed Jan. 29, 1969, now abandoned.

BACKGROUND OF THE INVENTION 1. Field OfThe Invention This invention relates to stationary induction apparatus.

2. Description Of The Prior Art Stationary induction apparatus such as transformers and reactors of large capacity employed in power circuits comprise essentially an iron core, windings disposed to surround the iron core, and electrical insulators for electrically insulating the windings from the iron core as well as one winding from the other.

Commonly, the electrical insulator described above is formed from paper comprised essentially of fibrous materials. For example, Kraft paper, Manila paper or pressboard is generally used to form such members as insulating coverings for conductors of individual coils constituting the wiring, insulating cylinders disposed between the windings, insulating rings disposed above and beneath the windings and interposed between the core fastening members and the yokes of the iron core, and inter-coil duct pieces disposed radially between the coils in suitably spaced relation from each other.

When short-circuit trouble occurs in the power transmission system for the stationary induction apparatus formed from materials as described above, an excessively large short-circuit current flows through the related winding of the apparatus, and this short-circuit current cooperates with the radial component of leakage flux in the apparatus to impart an excessively large electromagnetic force to the winding in its axial direction. the axial electromagnetic force acts to create alternate compression and vibration between the coils in the winding and the inter-coil duct pieces as well as between the winding and the insulating rings. Due to the vibration created in this manner, gaps are produced between the coils and the inter-coil duct pieces as well as between the upper and lower ends of the winding and the insulating rings, and because of the presence of the gaps, an excessively large impact is imparted between the coils and the inter-coil duct pieces as well as between the upper and lower ends of the winding and the insulating rings in the succeeding period of vibration.

It is known that the winding in the electrical apparatus of this kind has the natural vibrations or the natural frequencies of the first order, second order and third order which lie in the vicinity of 30 cycles per second, 70 cycles per second and 120 cycles per second, respectively. Thus, these natural frequencies of the winding are very close to the power source frequency, 50 hertz or 60 hertz, and its double frequency, 100 hertz or 120 hertz. Since the natural frequencies of the winding are thus very close to the power source frequencies which impart vibration to the winding, the displacement due to the vibration is quite large, and in some cases, resonance takes place to further enlarge the above displacement. As a result, the winding is subject to permanent plastic deformation due to the abovedescribed impact or displacement until finally it is broken.

The inter-coil duct pieces and the insulating rings described above must have the function of insulating the individual coils from each other and insulating the windings from the earth, and at the same time, the function of mechanically holding the individual coils and the entire windings. However, these inter-coil duct pieces and insulating rings have a certain limit in their mechanical strength because of the fact that they consist essentially of paper material. As a result, these inter-coil duct pieces and insulating rings are quite weak against the electromagnetic force and impact described above and are liable to move out of their predetermined position to be easily broken down. The collapse of the duct pieces and insulating rings would further promote the deformation of the winding.

SUMMARY OF THE INVENTION It is therefore an object of the present invention to provide a stationary induction apparatus having a winding structure which does not easily deform even if a short-circuit current occurring in an associated system may flow into the winding.

Another object of the present invention is to provide a model for a stationary induction apparatus which verifies economically the fact that the windings thereof have a sufficient strength against an electromagnetic force applied thereto.

The present invention contemplates the provision of a stationary induction apparatus having a mechanically stable and strong winding in which, on the basis of the result of analysis of the electromagnetic force applied to the winding in the case of short-circuiting, the number of natural vibrations of the winding is so set that it is higher than the frequency of a power source and is suitably shifted from the value which is double the power source frequency in order to thereby suppress the axial vibrational compression and displacement of the winding due to impartation thereto of the electromagnetic force.

In accordance with the present invention, the winding itself has a rigidity greater than that of the insulating ring so that the winding is sufficiently mechanically stable and strong. The total pressure receiving area of the inter-coil duct pieces disposed between the adjacent coils is made larger than the pressure receiving area of the insulating ring in the axial direction of the winding so that the winding can be made quite strong mechanically. Further, the ampereturn distribution in the axial direction of the winding may be varied so that the electromagnetic force developed in the axial direction of the winding has a distribution with a mode of the fourth or higher order in order thereby to attain the effect similar to that which is attained by increasing the number of natural vibrations of the winding itself.

Moreover, in accordance with the present invention, it is possible to obtain a test model by which the practical investigation of the manner of occurrence of the above-described electromagnetic force can easily be carried out. By virtue of the fact that the test model may be so constructed as to eliminate a part of the iron core and windings without in any way losing the equivalency to a proper stationary induction apparatus, the test of this kind which has heretofore been considered difficult to execute from an economical point of view can inexpensively be carried out.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I is a vertical sectional side elevational view showing part of the winding structure wound around an iron core in the stationary induction apparatus of the present invention.

FIG. 2 is a sectional view taken on the line II-II in FIG. 1.

FIG. 3 is a diagrammatic illustration of leakage flux distribution in a two-winding transformer.

FIGS. 4a, 4b and 4c are diagrammatic illustrations of the distribution of electromagnetic forces developed in the axial direction of the winding when short-circuit takes place in an associated system.

FIG. 5 is a diagrammatic illustration of an equivalent vibration circuit in which the apparatus winding is represented by a concentrated constant system.

FIG. 6 is a diagrammatic illustration of an equivalent vibration circuit in which the apparatus winding is represented by a distributed constant system.

FIG. 7 is a diagrammatic illustration of the coordinates of vibration in the distributed constant systern.

FIGS. 8 through 12 are vertical sectional views showing various forms of the winding structure according to the present invention.

FIGS. 13a and 1312 are diagrammatic illustrations of the mode of electromagnetic force distribution and the form of normal vibrations of various orders, respectively.

FIGS. 14a 14b are diagrammatic illustrations of the distribution of the participation factor Ki corresponding to the mode of various orders.

FIGS. 15a, 15b through 17a, 17b are diagrammatic illustrations of various arrangements of the low-voltage winding according to the present invention and corresponding distributions of the electromagnetic force developed in the axial direction of the winding, respectively.

FIG. 18a is a diagrammatic view showing the structure of a transformer model according to the present invention for testing for the electromagnetic force developed in the axial direction of the winding. FIGS. 18b and 180 are sections taken on the lines b-o and c.-o in FIG. 18a, respectively.

FIGS. 19 is a diagrammatic illustration of one example of the distribution of the electromagnetic force in the axial direction of the winding in the transformer model.

FIGS. 20a and 2012 are diagrammatic illustrations of another form of the transformer model and the distribution of the electromagnetic force in the axial direction of the winding, respectively.

FIG. 21 is a diagrammatic illustration of a further form of the transformer model for verifying the distribution of the electromagnetic force in the axial direction of the winding.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to FIGS. 1 and 2 showing the internal structure of a two-winding transformer, a pair of

concentric windings

4 and 7 are disposed to surround an iron core I. As is commonly known, the transformer iron core I comprises a leg portion la which is assembled by laminating a multiplicity of steel sheets and yoke portions lb which are assembled by laminating a multiplicity of concentric iron sheets and are magnetically coupled to the top and bottom of the leg portion la. The leg portion la and yoke portions 1b are fastened together by suitable means. An insulating cylinder 2 of pressboard tits on the leg portion la of the iron core 1. A plurality of rod-like insulating spacers 3, commonly made of pressboard, are bonded to the outer peripheral surface of the insulating cylinder 2 in suitably parallelly spaced relation from each other.

The low-voltage winding 4 of the transformer is disposed to surround the leg portion 1a of the iron core l with the spacers 3 interposed therebetween and comprises a multiplicity of coils 4 4 4 4,, 4 t -2, 4,, and 4,, wound in its axial direction. These coils are successively electrically connected with each other to form a discal winding, or insulated conductors 4a constituting the individual coils are bundled and continuously wound to form a helical winding. A plurality of

inter-coil duct pieces

5,, 5 5 5,, 5 5 and 5 are radially disposed between the adjacent coils in suitably spaced relation from each other. The inner end of each duct piece situated on the side of the inner periphery of the coil makes a dovetail joint with the corresponding insulating spacer 3. Insulating layers 6 comprising a plurality of concentric insulating cylinders are disposed to surround the outer peripheral surface of the low-voltage winding 4 so that oil gaps formed between the adjacent cylinders and the insulating cylinders constitute the main insulation.

The high-voltage winding 7 is disposed to surround the main insulation and is commonly in the form of a discal winding or a cylindrical winding. In the illustrated embodiment, the high-voltage winding 7 is in the form of a discal winding. The high-voltage winding 7 comprises an alternate arrangement of coils 7 7 7,, and 7,, formed by winding insulated conductors 7a from the outer periphery toward the inner periphery of the winding and coils 7 7 7 and 7 formed by winding the insulated conductors 7a from the inner periphery toward the outer periphery of the winding. A plurality of inter-coil duct pieces 8 8 8 8,, 8, and 8 are radially disposed between the adjacent coils in suitably spaced relation from each other. The inner end of each duct piece situated on the side of the inner periphery of the coil makes a dovetail joint with a corresponding one of insulating spacers 9 parallelly disposed on the outermost layer of the main insulation.

Shielding rings 10 are disposed on the upper and lower ends of the low-voltage winding 4. Shielding rings 11 are disposed on the upper and lower ends of the high-voltage winding 7. These shielding rings 10 and 11 are made by covering a conductor with an insulating tape. Insulating rings 12 are interposed between the yoke portions lb of the iron core 1 and the shielding rings 10. Insulating rings 13 are interposed between the yoke portions lb of the iron core 1 and the shielding rings 11. These insulating rings 12 and 13 support insulatingly the low-voltage winding 4 and the high-voltage winding 7 in their vertical direction.

FIG. 3 shows the manner of distribution of leakage flux in a two-winding transformer as described above. With the leakage flux distribution as such, when a short-circuit current flows into one of the windings, a large electromagnetic force is developed in the internally disposed low-voltage winding 4 and the externally disposed high-voltage winding 7. Such an electromagnetic force is commonly of the order of several hundred tons.

FIG. 4 shows the distribution of the electromagnetic force developed in the axial direction of the lowvoltage winding 4. In FIG. 4a, it will be seen that electromagnetic forces f ,f ,f ,f,, .f fl f .f,, and f are developed in the

respective coils

4,, 4 4 4 4,, 4 4,], 4,, and 4,, when the shortcircuit current flows into the winding. The electromagnetic forces developed in the coils have a distribution as shown in FIG. 4b from which it will be seen that the electromagnetic forces are substantially opposite to each other on opposite sides of the central portion of the winding 4 and are maximum at the upper and lower ends of the winding 4 where the radial component of the leakage flux is large. However, the electromagnetic force developed in the individual coil is transmitted intact to the adjacent coils since the

inter-coil duct pieces

5,, 5,, are generally merely interposed between the adjacent coils. As a result, the electromagentic forces described above are combined together and the resultant force produces a maximum compression at the central portion of the winding 4. the resultant force is distributed in the form of if as shown by the solid line in FIG. 4c in which the vertical axis represents the axial length L of the winding 4 and the horizontal axis represents the developed mechanical force F.

In an attempt to analyze the electromagnetic force developed in the axial direction of the winding, the inventors investigated the vibration system of the winding. In the analysis, a concentrated constant system as shown in FIG. 5 is replaced. by a distributed constant system as shown in FIG. 6.

Suppose now that each coil in the winding has weight a, each inter-coil duct piece has a spring constant k, and each insulating ring has a spring constant K. Then, an equivalent vibration circuit according to the concentrated constant system will be as shown in FIG. 5. However, the winding of a stationary induction apparatus such as a transformer or reactor includes many particles due to the fact that the number of coils ranges from several tens to several hundreds. Thus, it is very troublesome to analyze the concentrated constant system in such a complicated form. Therefore, the inventors replaced the vibration system of the winding by a distributed constant system by noting the fact that there are very many coils. The error due to regarding a concentrated constant system as a distributed constant system is substantially negligible as a matter of practice. This is because the natural vibrations of the first order in the winding of the electrical apparatus of this kind lie generally in the vicinity of 20 to 50 cycles per second and the natural vibrations of the hundredth order are the winding consisting of, for example, one hundred coils is far higher than the power source frequency of 50 Hz or 60 Hz, and thus the error attributable to the distributed constant system is negligible even if the number of natural vibrations of the hundredth or higher order may be introduced in the systern.

In FIG. 6 there is shown an equivalent vibration circuit of the distributed constant system based on the above way of thinking. For the conversion of the concentrated constant system into the distributed constant system, the following equations may only be satisfied;

a a' l/ d L1 d'g' where E,,: modulus of longitudinal elasticity of the distributed constant system in kg/cm k,,: spring constant of the inter-coil duct piece in kg/cm X mean pitch of the coil in cm 8, pressure receiving area of the coil in cm Q density of the distributed constant system in w mean weight of the coil in kg g acceleration of gravity in cm/S FIG. 7 shows the co-ordinates of the distributed constant system under consideration, in which the X-axis lies in the direction of height of the winding 4. Now, the response of the vibration system in FIG. 7 when an external force F is imparted to an arbitrarily selected point x al will be obtained. The solution in the steady state will be obtained supposing that the external force F F e Since the wave equation holds in the winding shown in FIG. 7, the following equation is obtained when the displacement in the axial direction is y(x, t):

where C is the velocity of sound V E /p in cm/sec. As is commonly known, the solution in the steady state when 0 x al is given by and the solution in the steady state when al 5 x g 1 is giveny by )2 (Ce D -J w lcr d d 1 (x, l yl (L By inserting y (x,t) in the equation (4) into the equation (6), we obtain the following equation:

jm/c EdSd (A B) K (A B) At x al, the displacement is continuous and we obtain the following equation:

yl (M) )2 (M) Similarly, at x =al, the pressure is continuous and we obtain the following equation:

By inserting y (x,t) in the equation (4) and y (x,t) in the equation (5) into the respective equations (8) and (9), the following equations can be obtained:

5,5,, (Ae We Be'j /c al) F,

...j E s 01c al D j rule 111) Atx=l,

By inserting y (oc,t) in the equation (5) into the equation (12), we obtain the following equation:

The factors A, B, C and D can be sought from the equations (7), (10), (ll) and (13). Suppose that (wE S /cK) 'y' and by inserting 'y' and 8' into the equations (7), (10), (11) and (13), we obtain the following equations, respectively:

considered to be equivalent to each other when 7' and 6' are the same for both.

Suppose that y is the quotient obtained by dividing the equation (l4) by the equation (15) and 8 is the product obtained by multiplying the equation (14) by the equation (15), then we obtain the following equations:

Y d d/ 5 (w IE S /C K) (w MlKg) where M is the total weight of the winding in kilograms. It will be seen that the quantity 7 is independent of the frequency.

Consider the physical meaning of the equation (20). It is apparent that y is the ratio of the spring constant E S /l when the entire winding is regarded as a spring to the spring constant K of the insulating ring. In other words, 7 may be considered as representing the ratio of the total height of the insulators disposed between the coils to the height of the insulators including the insulating rings which are disposed outside of the coils.

Next, consider the physical meaning of the equation (21). By multiplying the denominator and numerator of the equation (21) by a certain displacement u, we obtain the following equation:

(2 The numerator of the equation (22) represents the inertia force when it is supposed that the winding moves as an integral body, while the denominator of the equation (22) represents the spring force of the insulating ring. In other words, 5 in the equation (22) may be considered as representing the ratio of the weight of the winding to the spring constant of the insulating ring.

Although the exciting force is distributed in the axial direction of the practical winding, the equivalency can be maintained in the present analysis since the relation obtained in the above discussion holds at any axial position and the value may be integrated over the entire force.

Finally, we will investigate as to how the parameters 7 and 8 should be designed in order to reduce the vibration of the actual transformer winding and to reduce the force imparted to the coils and the upper and lower supports for the coils.

It will be known from the equations (4) and 5) that the displacement of the coils is related with the factors A, B, C and D. The equation 18) among the equations (16) through (19) determines the factors A, B, C and D, and it is known that the displacement of the coils is proportional to F /yK. In other words, the relation can be expressed as by the spring constant K of the insulating ring as follows:

upper and lower insulating rings is a matter of special consideration. Now, we will investigate the equation (24). From the equations (20) and (21 the following equation is obtained:

W V tEdsmm d d/ H wee/ K (2 Therefore, the equation (24) can be expressed as 5 CKFO fll (26) wE S 1 (E (1S1! (0S4 [IE 1 On the basis of the above analysis, it was found that the desired reduction in the displacement of the winding when a short-circuit current flows therethrough and .the desired reduction in the force imparted to the W twEdsm m 8. eal/K) Therefore, an effective practical arrangement for the winding so that it is sufficiently resistive to the electromagnetic force is such that the winding and the upper and lower supports therefor have a unitary structure in which the upper and lower supports are soft and the winding is rigid. The number of natural vibrations of the winding can be increased by making the winding rigid in this manner. The increase in the number of natural vibrations of the winding is quite preferable in that there is utterly no chance for the winding to resonate with the power source frequency or with the frequency which is double the power source frequency. The resonance is objectionable since it results in an increase in the amplitude of vibration, hence in an increase in the displacement of the winding.

The present invention will more practically be described on the basis of the above elucidation.

The spring constant K of the insulating rings disposed above and beneath the winding is given by K I/ l) 1 where S, is the pressure receiving area of the insulating ring, I, is the height of the insulating ring and E is the modulus of longitudinal elasticity of the insulating ring.

The modulus of longitudinal elasticity E, of the winding and the pressure receiving area S of the winding can be calculated from the shape, number, modulus of longitudinal elasticity and other factors of the inter-coil duct pieces included within the winding. The modulus of longitudinal elasticity E of the winding is given by the following equation:

E =1 ,nli E where l height of the winding including the inter-coil duct pieces h height (thickness) of each inter-coil duct piece n number of stages of the inter-coil duct pieces in the axial direction of the winding E modulus of longitudinal elasticity of the inter-coil duct piece On the other hand, the pressure receiving area 8,, of the coil is given by the following equation:

S1] mS where m; number of the inter-coil duct pieces interposed between a pair of coils S; pressure receiving area of each inter-coil duct piece In order to increase the values of'y and 6 described pre viously, the value of K in the equation (27) may be decreased or the value of E in the equation (28) may be increased.

The above relations may be summarized as follows:

i. The modulus of longitudinal elasticity E of the inter-coil duct piece should be increased.

2. The modulus of longitudinal elasticity E of the insulating ring should be decreased.

3. The number m of inter-coil duct pieces interposed between a pair of coils should be increased.

4. The pressure receiving area S of each inter-coil duct piece should be increased.

5. The pressure receiving area S, of the insulating ring should be decreased.

6. The height l of the insulating ring should be increased.

7. The height 1 of the winding should be increased.

8. The height (thickness) h of each inter-coil duct piece should be decreased.

The item (3) among the above-described items is undesirable because it is difficult to secure an enough space for the passage of the cooling medium for the winding as the number of the inter-coil duct pieces increases. The item (6) is also undesirable in that an increase in the height of the insulating ring beyond the required insulation distance of the winding to the! ground results in a large size of the iron core, hence bulkiness of the apparatus as a whole. The item (7) is also undesirable in that the apparatus as a whole becomes bulky in size. The item (8) is subject to a limitation because there must be a sufficient insulation distance between the adjacent coils.

It is therefore preferable to put the items l (2), (4)

cording to an experiment, good results were obtained when the modulus of longitudinal elasticity of the intercoil duct pieces was substantially five times or more than that of the insulating rings.

For example, the insulating ring may be made from conventional pressboard which is manufactured according to Grade PB-1 or PB-2 of Japanese Industrial Standards C2305, and the inter-coil duct piece may be made from high-density highly-compressed pressboard prepared by strongly heating pulp, forming the fibres into paper, applying a pressure which is several times the prior pressure to the paper at a high temperature to compress the same and drying the compressed product.

The properties of the conventional pressboard according to Grade PB-2 are compared with the properties of the high-density, highly-compressed pressboard and the results are given in the following table:

High PB-Z density (prior highlyproduct) compressed pressboard Density O .9-l.l l.l5l.3 Oil absorption rate 20% Deflection by compression (1.00

kg/cm*) 2.5% 0.2% Dry shrinking rate Below 8% Below 6% (thickness) Longitudinal Tensile direction Above 6.0 Above 10.0 strength (kg/mm) (with thickness of Lateral 3.2 mm) direction Above 2.5 Above .0

(kg/mm) Materials having a modulus of longitudinal elasticity larger than that of the pressboard Grade PB-l or PB-2 include electrical insulating sheets of phenol resin or epoxy resin and reinforced wood. Good results can also be obtained when these materials are employed to form the inter-coil duct piece. Since these materials are satisfactory in their corona suppression property in the oil, they can very easily be incorporated in the transformer.

Short-circuit current was made to flow through the transformer winding whose inter-coil duct pieces were made from the high-density, highly-compressed pressboard described above and whose insulating rings were made from the conventional pressboard Grade PB-Z. Test results proved that the electromagnetically produced mechanical force 2] was distributed in a manner as shown by the two-dot chain line in FIG. 40 and the resultant maximum compressive force imparted to the winding could be made far smaller than the force appearing in the prior art system. Thus, the winding itself can be made sufficiently strong against the shortcircuit current by reducing the mechanical force developed in the winding.

In the present invention, the items (4) and (5) described previously may be adopted in order that the inter-coil duct pieces disposed between the coils have a total pressure receiving area which is larger than that of the insulating ring.

FIGS. 8 through 12 illustrate several embodiments of the present invention in which the pressure receiving area of the inter-coil duct piece is increased relative to that of the insulating ring so as to increase the modulus of longitudinal elasticity of the winding without reducing the cooling area of the winding. Referring to FIG. 8, inter-coil duct pieces 17 are interposed between coils I6 16 16 16 I6 forming a transformer winding 16. Each inter-coil duct piece 17 has a U-like sectional shape and comprises portions 17a and 17b disposed opposite to the upper and lower surfaces of the corresponding coil and a portion 17c connecting between the portions 17a and 17b at the inner or outer periphery of the coil. According to this embodiment, the inter-coil duct piece 17 has a quite large pressure receiving area which includes the areas of the portions 17a and 17b plus the cross-sectional area of the connecting portion 17c.

Embodiments shown in FIGS. 9 through 12 comprise an insulating cylinder 18 disposed to surround a winding 16, and inter-coil duct pieces 17 disposed between the insulating

cylinders

2 and 18 in such a manner that each inter-coil duct piece 17 covers the outer peripheral surface as well as the inner peripheral surface of the corresponding coil. In the case of the embodiment shown in FIG. 9, a cut 17d is provided in the outer peripheral portion of the duct piece 17 so that the duct piece 17 is urged to open at this cut when it is fitted on the corresponding coil. In the case of the embodiment shown in FIG. 10, oppositely aligned cuts 17d and l7e are provided in the inner and outer peripheral portions of the duct piece 17 so that the duct piece 17 can be split into upper and lower halves. In the case of the embodiment shown in FIG. 11, diagonally

opposite cuts

17d and 17e are provided in the inner and outer peripheral portions of the duct piece 17 so that the duct piece 17 can be split into upper and lower L-shaped halves.

I In the case of the embodiment shown in FIG. 12, two

L-shaped duct pieces 17f similar to that shown in FIG. 11 are combined with a T-shaped duct piece 17g to surround a pair of coils.

The embodiments shown in FIGS. 9 through 12 are advantageous over the embodiment shown in FIG. 8 in that the duct piece has an increased effective pressure receiving area and thus the modulus of longitudinal elasticity of the winding can be further increased. It will be apparent for those skilled in the art that the duct pieces 17 in any one of the embodiments shown in FIGS. 8 through 12 are radially disposed between the coils in the radial direction of the latter in suitably spaced relation from each other as in the case of the embodiment shown in FIG. 2 so as to define a cooling passage.

According to the embodiments shown in FIGS. 8 through 12, part of the mechanical forces F 1 through f which have heretofore been distributed to the winding as shown in FIG. 4a are carried by the inter-coil duct piece 17, and as a result, the resultant force acting upon the entire winding can be reduced in a manner as shown by the curve if in FIG. 40 like the preceding embodiment.

In the above description, the number of natural vibrations of the winding is increased as a result of the analysis of the vibration system of the winding. In an alternative arrangement, suitable electomagnetic means may be employed to vary the vibration mode of the winding for the same purpose of increasing the number of natural vibrations of the winding so as to similarly reduce the displacement of the winding and to decrease the force imparted to the insulating rings disposed above and beneath the winding.

In the case of a transformer, for example, its electromagnetic force distribution takes generally the form of the second order corresponding to the distribution of the radial components of the leakage flux. Therefore, the vibration mode of the second order corresponding to this manner of distribution is most liable to appear. Since the number of natural vibrations in the case of the vibration mode of the second order lies in the vicinity of 70 cycles per second as described previously and is thus close to the power source frequency, the displacement due to vibration becomes correspondingly greater.

Now, a participation factor Ki is used to define the relation between the electromagnetic force distribution and the mode of natural vibration of respective orders. The participation factor Ki represents the rate at which the electromagnetic force distribution participates in the vibration mode of the ith order and can be given by the following equation:

above relation. FIG. 13a shows the mode of the electro-- magnetic force distribution F(x) and FIG. 13b shows the normal mode of vibration of the ith order, for example, those of the first order, second order and fourth order. In FIGS. 13a and 13b, x represents the axial length of the winding. In FIG. 13a, the mode shown by the solid line represents the electromagnetic force distribution of the second order in a conventional transformer, while the mode shown by the one-dot chain line represents the electromagnetic force distribution of the fourth order which is improved in accordance with the present invention.

Since the vibration mode tends to be induced in relation to the electromagnetic force distribution, a vibration mode of higher order can be developed when the electromagnetic force distribution is shifted to its higher order. On the basis of he above fact, the vibration mode can be shifted to a number of natural vibrations of higher order by varying the electromagnetic force distribution while keeping the numbers of natural vibrations of various orders unchanged. In such an arrangement, the electromagnetic forces cancel each other at the numbers of natural vibrations of lower orders, and the displacement of the winding can be made corresponding smaller. This is equivalent to the effect as when the number of natural vibrations of the winding is increased.

In FIG. 14a there is shown the state in which the number of natural vibrations of the winding itself is shifted to a higher order without varying the electromagnetic force distribution as well as the participation factor Ki. The solid curve in FIG. 14a represents the distribution of the participation factor Ki in a conventional transformer and it will be apparent that the participation factor has a peak in the vibration mode of the second order. The distribution of the participation factor Ki can parallelly be shifted toward a higher order by shifting the number of natural vibrations of the winding toward its higher order. The dotted curve in FIG. 14a shows the fact that a peak appears in the vibration mode of the third order, while the one-dot chain curve shows the fact that a peak appears in the vibration mode of the fourth order.

It will be understood that, according to the present invention, the vibration mode can be shifted toward a higher order by increasing the number of natural vibrations of the winding. It will be further understood that the same purpose can be attained by varying the electromagnetic force distribution in a manner as described above so as to improve the vibration mode in order that the peak is shifted toward a higher order. The latter state is shown in FIG. 14b. More precisely, the peak of the participation factor Ki is shifted from its previous position in the vibration mode of the second order to a position in the vibration mode of the fourth order so that consequently the participation factor corresponding to the vibration mode of the second order is reduced.

It will be understood from the above description that the displacement or force can be descreased as a whole by arranging in such a manner that the winding has a vibration mode of the fourth or higher order.

FIGS. 15 through 17 illustrate a few forms of a twowinding transformer employing the above arrangement. In addition, although these drawings only schematically show a high-voltage winding, a low-voltage winding and an insulating material therefor by omitting detailed illustration thereof, the construction of each portion in FIGS. 15 through 17 is similar to that shown in FIG. 1. Referring to FIG. 15a, a low-voltage winding 14 disposed closer to an iron core 1 is provided with a substantially centrally disposed gap portion 14a having a large axial gap or a portion at which the number of turns is descreased to reduce the ampere-turn. A highvoltage winding 15 is disposed on the outside of the low-voltage winding 14. According to this arrangement, the electromagnetic forces developed in the axial direction of the winding can be distributed as shown in FIG. 15b so that the vibration mode of the fourth order has a node at a substantially central portion of the winding. This arrangement is advantageous in that any appreciable exciting force is not imparted to the winding even when the winding resonates with the power source frequency or the frequency which is double the power source frequency in the vibration mode of lower order and that, in the vibration mode of the fourth order, its number of natural vibrations is considerably high compared with the number of exciting vibrations, resulting in a decrease in the displacement of the winding due to vibration. Therefore, the electromagnetic forces thus developed are distributed as shown by F F F and F and it is possible to minimize the resultant electromagnetic force.

Referring to FIG. 16a, a low-voltage winding 14 is substantially trisected to have portions 14b and which have a large axial gap, or the winding 14 is provided with portions 14b and 140 at which the number of turns is decreased to reduce the ampere-tum product. According to this arrangement, the electromagnetic forces developed in the winding can be distributed as shown in FIG. 16b so that the vibration mode of the sixth order has two nodes adjacent to the trisecting points. Therefore, the electromagnetic forces thus developed are distributed as shown by F,, F F F F and F and it is possible to minimize the resultant electromagnetic force.

Referring to FIG. 17a, a low-voltage winding 14 is provided adjacent to its quadrisecting points with portions 14d, 144? and 14f at which the number of turns is decreased to reduce the ampere-turn product. According to this arrangement, the electromagnetic forces developed in various parts of the winding can be distributed in the vibration mode of the eighth order as shown by F through F in FIG. 17b, and it is possible to minimize the resultant electromagnetic force. It will be understood that the electromagnetic force developed in the winding can be reduced by shifting the electromagnetic force distribution in the winding toward a vibration mode of higher order.

In the above embodiments, a tertiary winding may be arranged concentrically with respect to the leg portion of the iron core, the tertiary winding of these windings being such that the ampere-turns thereof are reduced at respective local portions which are substantially equally spaced at predetermined distances from each other in the axial direction of the tertiary winding.

FIGS. 18 through 21 show several preferred models for examining the mechanical force developed in the axial direction of a transformer winding.

FIG. 18 shows a model ofa two-winding transformer having concentrically arranged windings and 21. A block of rigid ferromagnetic material such as a laminated iron core 22 is disposed at the nodal point of vibration of the inner winding 20 and outer winding 21, that is, at the point at which the magnetic flux distribution in the radial direction of the windings is symmetri cal about the axis of the windings. The illustrated example represents a 50 percent model employing solely the upper halves of the windings. The model includes a transformer iron core 23, insulating

rings

24 and 25 supporting the upper part of the inner winding 20 and outer winding 21, respectively, with respect to the transformer iron core 23, and an insulating base 26 supporting the laminated iron core 22 on the lower part of the transformer iron core 23.

The inner winding 20 is connected in series with the outer winding 21, and the direction of turns of the windings is so selected that the ampere-turn of one winding is opposite to the ampere-turn of the other when current is supplied to both these two windings. Therefore, when a short-circuit current is supplied to one of these windings, the lines of main magnetic flux generated within the transformer iron core 23 cancel each other. Thus, the transformer iron core 23 may have a simple structure which is sufficient to simulate only the leakage flux of each winding, and iron plates may be employed to construct a frame structure which suits the shape of the iron core.

FIG. 19 shows the distribution of the radial components of the leakage flux generated in the winding in the model shown in FIG. 18, that is, the distribution of the axial electromagnetic forces acting upon the winding. By use of the above-described model, the state of generation of electromagnetic forces in a practical transformer winding can inexpensively be observed.

FIGS. 20 and 21 show models for examining the electromagnetic forces generated in a sandwich arrangement of windings. The models comprise a simulation iron core 27, and a high-voltage winding 28 sandwiched between an upper low-voltage winding 29a and' a lower low-voltage winding 29b. These windings are connected in series and are wound in such a manner that their ampere-tums are opposite to each other as shown byeBandSin the drawing. A block of rigid ferromagnetic material 30 is disposed at the nodal point of vibration so that the model is equivalent to a practical transformer electro-magnetically as well as mechanically. Portions indicated by dotted lines in FIG. 20a show the images of the windings.

Thus, according to the present invention, a model equivalent to a practical transformer can inexpensively be obtained and the examination of the electromagnetic forces generated in the windings can be carried out as if in the case of a practical transformer.

What is claimed is:

1. A short-circuit testing model for stationary induction apparatuses having a magnetic core comprising a leg portion and upper and lower yoke portions arranged above and below said leg portion, an inner winding having a plurality of turns disposed around the leg portion of the magnetic core, an outer winding having turns equal in number but reverse in direction to said plurality of turns of said inner winding arranged concentrically around said inner winding and connected in series therewith, an insulating ring provided at one end of each of said inner and outer windings, and a ferromagnetic element provided at the other end of each of said inner and outer windings.

2. A short-circuit testing model for stationary induction apparatuses according to claim 1, in which said insulating ring is separated for each of the inner and outer windings, each of said separated insulating rings being disposed to be opposite to one of the yoke portions of said magnetic core, and said ferromagnetic element is disposed to be opposite to the other yoke portion opposite to said one yoke portion of said magnetic core through an insulating ring.

3. A short-circuit testing model for stationary induction apparatuses according to claim 2, in which'said ferromagnetic element is a unitary block which comprises laminated silicon steel plates and faces an end surface of each of said inner and outer windings.

4. A short-circuit testing model for stationary induction apparatuses according to claim 1, in which the leg portion of said magnetic core is a solid ferromagnetic element having a frame construction.

Claims

3. A short-circuit testing model for stationary induction apparatuses according to claim 2, in which said ferromagnetic element is a unitary block which comprises laminated silicon steel plates and faces an end surface of each of said inner and outer windings.