Patent Publication Number: US-9424978-B2

Title: Magnetically shielded three phase rotary transformer having three magnetic cores

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to the general field of transformers. In particular, the invention relates to a rotary three-phase transformer. 
     A rotary three-phase transformer serves to transfer energy and/or signals without contact between two axes rotating one relative to the other. 
       FIGS. 1 and 2  show respective rotary three-phase transformers  1  of the prior art. 
     The transformer  1  has three rotary single-phase transformers  2  corresponding to phases U, V, and W. Each rotary single-phase transformer  2  has a portion  3  and a portion  4  rotating one relative to the other about an axis A. By way of example, the portion  3  is a stator and the portion  4  is a rotor, or vice versa. In a variant, the portion  3  and the portion  4  are both movable in rotation relative to a stationary frame of reference (not shown). A toroidal coil  5  is received in a slot  6  defined by a body made of ferromagnetic material of the portion  3 . A toroidal coil  7  is received in a slot  8  defined by a body made of ferromagnetic material of the portion  4 . For each rotary single-phase transformer  2 , the coils  5  and  7  form primary and secondary coils (or vice versa). 
       FIG. 1  shows a variant referred to as “U-shaped” in which the portion  3  surrounds the portion  4  about the axis A, while  FIG. 2  shows a variant referred to as “E-shaped” or “pot-shaped”, in which the portion  3  and the portion  4  are one beside the other in the axial direction. 
     The three-phase transformer  1  of  FIG. 1 or 2  presents weight and volume that are large since it is not possible to make best use of the magnetic fluxes of each of the phases, unlike a static three-phase transformer with forced fluxes in which it is possible to couple the fluxes. Furthermore, in the example of  FIG. 2 , it is necessary to use electrical conductors of sections that differ as a function of the distance between the axis of rotation and the phase, in order to conserve balanced resistances. 
     Document US 2011/0050377 describes a four-column rotary three-phase transformer. That transformer presents considerable weight and volume. That document also describes a five-column rotary three-phase transformer. That transformer presents considerable weight and volume. Furthermore, it makes use of radial winding passing via slots in the central columns of the magnetic circuit, where such winding is more complex to perform than the toroidal winding used in the transformers of  FIGS. 1 and 2 . 
     There thus exists a need to improve the topology of a three-phase transformer. 
     OBJECT AND SUMMARY OF THE INVENTION 
     The invention provides a three-phase transformer having a primary portion and a secondary portion;
         the primary portion comprising a first body made of ferromagnetic material and primary coils, the secondary portion comprising a second body made of ferromagnetic material and secondary coils;   the first body defining a first annular slot of axis A and a second annular slot of axis A, the first slot being defined by a first side leg, a central leg, and a ring, the second slot being defined by the central leg, a second side leg, and the ring; and   the primary coils comprise a first toroidal coil of axis A in the first slot, a second toroidal coil of axis A in the second slot, and one or more third coils connected in series, said third coils being wound around one of said legs and passing in the slots in said leg.       

     In this transformer, if three-phase currents are caused to flow in the primary coils in directions that are appropriate, given the directions of the primary coils, then the magnetic potentials of the first, second, and third primary coils are directed towards or away from a common point, thereby leading to the fluxes being coupled. This enables the transformer to be of reduced dimensions in terms of volume and weight. Furthermore, the primary of the transformer makes use in part of simple toroidal coils of axis A, thus enabling its structure to be particularly simple. 
     In an embodiment, said third coils are wound around said central leg. 
     In an embodiment, the primary portion and the secondary portion are movable in rotation relative to each other about the axis A. 
     Under such circumstances, the invention provides a rotary three-phase transformer that, by virtue of its fluxes being coupled, presents weight and volume that are reduced, in particular relative to using three single-phase rotary transformers. 
     In an embodiment, the second body defines a first annular secondary slot of axis A and a second annular secondary slot of axis A, the first secondary slot being defined by a first secondary side leg, a secondary central leg, and a secondary ring, the second secondary slot being defined by the secondary central leg, a second secondary side leg, and the secondary ring;
         the secondary coils comprise a first toroidal secondary coil of axis A in the first secondary slot, a second toroidal secondary coil of axis A in the second secondary slot, and one or more third secondary coils connected in series, said third secondary coils being wound around one of said secondary legs and passing via slots in said secondary leg.       

     In this embodiment, the secondary is made on the same principle as the primary. The secondary thus also contributes to limiting the weight and the volume of the transformer, and enables the transformer to be constructed while using only toroidal coils of axis A. 
     In an embodiment, the secondary is made on a principle that differs from that of the primary. For example, it makes use, for each phase, of one or more coils surrounding the corresponding leg. 
     In an embodiment, the first side leg and the first secondary side leg are in line with each other and separated by an airgap, the first central leg and the first secondary central leg are in line with each other and separated by an airgap, and the second side leg and the second secondary side leg are in line with each other and separated by an airgap. 
     The primary portion may surround the secondary portion relative to the axis A, or vice versa. That corresponds to making a transformer that is referred to as being “U-shaped”. 
     The primary portion and the secondary portion may be situated one beside the other in the direction of the axis A. That corresponds to making a transformer that is referred to as being “E-shaped” or “pot-shaped”. 
     In an embodiment, the primary portion and the secondary portion are stationary relative to each other. A static transformer in accordance with the invention presents the same advantages as a rotary transformer in accordance with the invention. 
     In an embodiment, the first and second bodies made of ferromagnetic material completely surround the primary and the secondary coils. 
     Under such circumstances, the transformer is magnetically shielded. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other characteristics and advantages of the present invention appear from the following description made with reference to the accompanying drawings, which show implementations having no limiting character. In the figures: 
         FIGS. 1 and 2  are section views of respective prior art rotary three-phase transformers; 
         FIGS. 3 and 4  are section views of a magnetically shielded three-phase rotary transformer with forced linked fluxes in a first embodiment of the invention; 
         FIG. 5  is an exploded perspective view of the magnetic circuit of the transformer of  FIGS. 3 and 4 ; 
         FIG. 6  is an electrical circuit diagram showing the connections of the coils in the transformer of  FIGS. 3 and 4 ; and 
         FIG. 7  is an exploded perspective view of a magnetically shielded three-phase rotary transformer with forced linked fluxes in a second embodiment of the invention; 
         FIG. 8  is a section view of a magnetically shielded three-phase static transformer with forced linked fluxes in a third embodiment of the invention; 
         FIG. 9  is a section view of a magnetically shielded three-phase rotary transformer with forced linked fluxes in a fourth embodiment of the invention; 
         FIG. 10  is a section view of a three-phase rotary transformer with forced linked fluxes in a first embodiment useful for understanding the invention; 
         FIG. 11  is an exploded perspective view of the magnetic circuit of the  FIG. 10  transformer; 
         FIG. 12  is an electrical circuit diagram showing the operation of the  FIG. 10  transformer; 
         FIG. 13  is an exploded view in perspective of the magnetic circuit of a transformer in a second embodiment useful for understanding the invention, that may be considered as being a variant of the  FIG. 10  transformer; and 
         FIG. 14  is a section view of a rotary transformer with forced linked fluxes in a fifth embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       FIGS. 3 and 4  are section views of a transformer  10  in a first embodiment of the invention. The transformer  10  is a magnetically shielded three-phase rotary transformer with forced linked fluxes. 
     The transformer  10  comprises a portion  11  and a portion  12  that are suitable for rotating relative to each other about an axis A. By way of example, the portion  11  is a stator and the portion  12  is a rotor, or vice versa. In a variant, the portion  11  and the portion  12  are both movable in rotation relative to a stationary frame of reference (not shown). 
     The portion  12  comprises a ring  13  of axis A and three legs  14 ,  15 , and  16  made of ferromagnetic material. Each of the legs  14 ,  15 , and  16  extends radially away from the axis A, starting from the ring  13 . The leg  14  is at one end of the ring  13 , the leg  16  is at another end of the ring  13 , and the leg  15  lies between the legs  14  and  16 . The ring  13  and the legs  14  and  15  define an annular slot  34  that is open in a radially outward direction. The ring  13  and the legs  15  and  16  define an annular slot  35  that is open in a radially outward direction. In general manner, the ring  13  and the legs  14 ,  15 , and  16  form a body of ferromagnetic material defining two annular slots  34  and  35  that are open in a radially outward direction. 
     The portion  11  comprises a ring  17  of axis A and three legs  18 ,  19 , and  20  made of the ferromagnetic material. The ring  17  surrounds the ring  13 . Each of the legs  18 ,  19 , and  20  extends radially towards the axis A, starting from the ring  17 . The leg  18  is at one end of the ring  17 , the leg  20  is at another end of the ring  17 , and the leg  19  lies between the legs  18  and  20 . The ring  17  and the legs  18  and  19  define an annular slot  22  that is open in a radially inward direction. The ring  17  and the legs  19  and  20  define an annular slot  23  that is open in a radially inward direction. In general manner, the ring  17  and the legs  18 ,  19 , and  20  form a body of ferromagnetic material defining two annular slots  22  and  23  that are open in a radially inward direction. 
     The legs  14  &amp;  18 ,  15  &amp;  19 , and also  16  &amp;  20  face each other as to define an airgap  21 , thereby forming the columns of the transformer  10 . 
     The rings  13  and  17  together with the legs  14  to  16  and  18  to  20  form a magnetic circuit of the transformer  10 . The transformer  10  is thus a three-column transformer. More precisely, the magnetic circuit of the transformer  10  has a first column (corresponding to the legs  14  and  18 ), a second column (corresponding to the legs  15  and  19 ), and a third column (corresponding to the legs  16  and  20 ). 
     The transformer  10  comprises coils  24 ,  25   a ,  25   b ,  25   c ,  25   d , and  26  fastened to the portion  11 , and coils  28 ,  29   a ,  29   b ,  29   c ,  29   d , and  30  fastened to the portion  12 . Below, the notation p and s is used with reference to a configuration in which the coils  24  to  26  are the primary coils of the transformer  10  and the coils  28  to  30  are the secondary coils of the transformer  10 . Nevertheless, primary and secondary may naturally be inverted relative to the example described. 
     The coil  24  is a toroidal coil of axis A corresponding to a phase Up of the transformer  10 . It is in the slot  22  and it presents n 1  turns. 
     The coils  25   a ,  25   b ,  25   c , and  25   d  are connected in series and correspond to a phase Vp of the transformer  10 . Each of the coils of  25   a ,  25   b ,  25   c , and  25   d  surrounds a portion of the leg  19 , passing via slots  36  formed in the leg  19 , as shown in  FIG. 4 . Together, the coils  25   a ,  25   b ,  25   c , and  25   d  present n 1  turns. 
     Finally, the coil  26  is a toroidal coil of axis A corresponding to a phase Wp of the transformer  10 . It is in the slot  23  and presents n 1  turns. 
     In other words, the winding of the phases Up and Wp is annular, around the axis A, while the winding of the phase Vp takes place at a radially around the central column (corresponding to the legs  15  and  19 ). 
     The term “toroidal coil of axis A” is used to mean a coil having its turns wound around the axis A. The term “toroidal” is not used in the limited meaning referring to a solid as generated by rotating a circle about an axis. On the contrary, as in the examples shown, the section of a toroidal coil may be rectangular, in particular. 
     The coil  28  is a toroidal coil of axis A corresponding to a phase Up of the transformer  10 . It is in the slot  34  and presents n 2  turns. 
     The coils  29   a ,  29   b ,  29   c , and  29   d  are connected in series and correspond to a phase Vs of the transformer  10 . Each of the coils  29   a ,  29   b ,  29   c , and  29   d  surrounds a portion of the leg  15 , passing via slots  37  formed in the leg  15 , as shown in  FIG. 4 . Together, the coils  29   a ,  29   b ,  29   c , and  29   d  present n 2  turns 
     Finally, the coil  30  is a toroidal coil of axis A corresponding to a phase Ws of the transformer  10 . It is in the slot  35  and presents n 2  turns 
     In other words, as in the primary, the winding of the phases Us and Ws is annular, around the axis A, whereas the winding of the phase Vs takes place radially around the central column (corresponding to the legs  15  and  19 ). 
     The coils  24  and  28  surround a magnetic core  32  situated in the ring  13 . The term “magnetic core” is used to mean a portion of the magnetic circuit in which the same-direction flux created by the coil is in the majority. Electric currents flowing in the coils  24  and  28  thus correspond to magnetic potentials in the magnetic core  32 . In corresponding manner, the coils  26  and  30  surround a magnetic core  33  situated in the ring  13 . Electric currents flowing in the coils  26  and  30  thus correspond to magnetic potentials in the magnetic core  33 . Furthermore, the coils  25   a ,  25   b ,  25   c ,  25   d ,  29   a ,  29   b ,  29   c , and  29   d  surround a magnetic core  38  situated in the central column formed by the legs  15  and  19 . 
     The transformer  410  thus has three magnetic cores: The axial cores  32  and  33 , and a radial core  38  along the central column. 
       FIG. 5  is an exploded perspective view of the magnetic circuit of the transformer  10 . 
     With reference to  FIG. 6 , there follows an explanation of how the transformer  10  operates. In  FIG. 6 , the following notation is used:
         A p , B p , and C p , are the inlet points of the primary coils of the transformer  10 . The phases U, V, and W of  FIG. 3  correspond respectively to the phases A, B, and C of  FIG. 6 , but all other types of correspondence are possible providing the same correspondence is used for the secondary.   I ap , I bp , and I cp  are the respective incoming currents at the points A p , B p , and C p .   O ap , O bp , and O cp  are the connection points making possible electrical couplings identical to all kinds of static three-phase transformer (star-star, star-delta, delta-delta, delta-star, zigzag, . . . ).   Black dots show the relationship between the current flowing in a coil and the direction of the corresponding magnetic potential.   Pa, Pb, and Pc are the magnetic potentials in the cores  32 ,  38 , and  33  corresponding respectively to the currents I ap , I bp , and I cp ;   A s , B s , C s , O as , O bs , and O cs , are the outlet points and the points for connection to the secondary.       

     As shown in  FIG. 6 , for the current I ap , the coil  24  corresponds to an axial magnetic potential Pa directed to the right in the magnetic core  32 . The coils  25   a ,  25   b ,  25   c , and  25   d  correspond, for a current I bp , to a radial magnetic potential Pb directed downwards in the magnetic core  38 . Finally, for the current I cp , the coil  26  corresponds to an axial magnetic potential Pc directed to the left in the magnetic core  33 . The magnetic potentials Pa, Pb, and Pc are equal in modulus and opposite in direction on each magnetic core and they are symmetrical relative to the point of symmetry  39  situated at the intersection of the three cores. 
     In a variant that is not shown, the winding directions of the coils and/or their connection points are different, such that the magnetic potentials Pa, Pb, and Pc are in the opposite directions compared with the example shown. 
     This configuration enables fluxes to be properly coupled. More precisely, the topology of the transformer  10  makes it possible to obtain a coupling coefficient of 3/2. 
     In the embodiment shown, the transformer  10  has four primary coils  25   a  to  25   d  in series, and four secondary coils  29   a  to  29   d  in series. In a variant, the number of coils on the central column could be greater or smaller. There may be different numbers of coils on the central column for the primary and for the secondary. 
     In the example shown, the slots  36  &amp;  37  are arranged in the central column (legs  15  &amp;  19 ). The coils of  25   a  to  25   d  and  29   a  to  29   d  thus surround of the central column and the magnetic core  38  is situated in the central column. In a variant that is not shown, the slots  36  and  37  are arranged in one of the side columns (legs  14  &amp;  18  or  16  &amp;  20 ). The coils  25   a  to  25   d  and  29   a  to  29   d  thus surround one of the side columns and the magnetic core  38  is situated in this side column. Nevertheless, such a variant is not magnetically shielded. 
     The transformer  10  presents several advantages. 
     In particular, it can be seen that the magnetic circuit completely surrounds the coils  24  to  30 . The transformer  10  is thus magnetically shielded. Furthermore, some of the coils  24  to  30  are toroidal coils of axis A. The transformer  10  thus makes it possible to use coils of simple shape. 
     Furthermore, the phases of the transformer  10  may be balanced in inductance and in resistance. 
     In order to obtain the theoretical coupling coefficient and three-phase balance, it suffices for the reluctances between the midpoint of the ring  17  and the midpoint of the ring  13  and passing via each of the columns to be identical. 
     If the airgap creates reluctances that are large compared with the reluctances of the rings  13  and  17 , then the reluctances of the rings can be ignored, and it is therefore possible to obtain partial balancing for columns having the same reluctance. The magnetic circuit can then be particularly simple to design. 
     One possible improved embodiment enabling a better balance to be obtained is to increase the reluctance of the central column a little so as to compensate for the unbalance in the reluctances due to the secondary reluctances (reluctance of the ring, reluctance of the legs, . . . ). To do this, it is possible among other things to reduce the width of the central column a little or to increase the airgap in the central column a little compared with the other columns. 
     Account must also be taken of the reluctance of the slots  36  and  37 . 
     Finally, the transformer  10  presents reduced weight and volume. 
     Specifically, if the transformer  10  is compared with the transformer  1  of  FIG. 1  or  FIG. 2 , and assuming it is designed to provide the same performance, the following assumptions can be made:
         Conductive material: Let Q be the quantity of conductive material in a coil of one of the three single-phase transformers of the transformer  1 . The quantity of conductive material in the coils of the transformer  1  is thus 3Q.   Magnetic material: If the same reluctance Re is concerned for each column, each single-phase transformer of the transformer  1  has an overall reluctance of the magnetic circuit close to 2Re. For the transformer  10 , the overall reluctance of the magnetic circuit is close to (3/2)Re.       

     For the transformer  10 , with the same magnetizing current and the same number of turns n 1  as for the transformer  1 , the induction field and the flux is thus doubled. Specifically, for the transformer  1 , the multiplying coefficient is 0.5 (i.e. the coupling coefficient=1 divided by the reluctance ratio=2) and for the transformer  10  with linked fluxes the modifying coefficient is 1 (i.e. the coupling coefficient=3/2 divided by the reluctance ratio=3/2). The ratio is thus indeed equal to 2 (1/0.5). This property makes it possible to evaluate approximately the possibilities for optimizing the transformer  10  relative to the transformer  1 , for the same performance. 
     It is decided to reduce the number of turns by √2, thereby giving rise to an increase in the induction field of √2, while making it possible to have the same voltage for the same magnetizing current. 
     For a design having the same losses in joules and the same phase resistance, this gives:
         For the coil  24 , there need to be √2 fewer turns, and thus the quantity of conductive material is Q/√2. For constant losses in joules, the resistance (ρl/S) is also divided by √2 (length divided by √2), so in order to conserve losses in joules it is possible to divide the section by √2 for the same load current, magnetizing current, and voltage (in practice the saving might not be so great, since it is necessary to avoid local overheating, which depends on thermal conduction). The quantity of conductive material for the coil  24  is thus Q/2. The same reasoning applies to the coil  26 .   For the coils  25   a ,  25   b ,  25   c  and  25   d , there need to be √2 fewer turns, and thus the quantity of conductive material is 2*Q/√2=√2*Q. At constant losses in joules, since the length is multiplied by √2 relative to a U-shaped single-phase transformer, the section is multiplied by √2. Consequently, these coils require a quantity of conductive material equal to 2Q.       

     For constant phase resistance for the transformer  10 , the overall quantity of conductive material is thus: Q/2+2Q+Q/2=3*Q. For the transformer  1 , the quantity of conductive material was 3*Q, i.e. the same quantity. By way of comparison, for a static three-phase transformer, the quantity of conductive material is 3Q/2. 
     Concerning iron losses, in spite of the increase in the induction field B, it is assumed that its increase by √2 makes it possible to remain within non-saturated conditions (the high reluctance of the airgap favors designing the transformer  10  with a weak induction field in the magnetic material, it being necessary to increase the area of the airgap in order to decrease its reluctance, and that requires the area of magnetic material to be increased). 
     Losses by hysteresis are given by K H B 2 f*V and current losses are given by K F B 2 f 2 *V, with:
         V: volume;   f: utilization frequency;   B: maximum induction field;   K H : a constant associated with the magnetic materials and with the structure of the magnetic circuit; and       

     K F : a constant associated with the magnetic materials and with the structure of the magnetic circuit. 
     Losses are thus twice as great per unit volume when transposing the standard rotary transformer  1  to the three-phase transformer  10  with forced flux ((√2B) 2 =2B 2 ). 
     If the saving in volume of the magnetic circuit is evaluated, it can be estimated that the volume is decreased by about 42%, which means that there is an overall increase of about 16% for iron losses (0.58*2=1.16). This naturally depends on the initial dimensioning. With a rotary transformer, iron losses are much less than joule losses and it can thus be considered that the increase in overall losses (less than 8%) is negligible. 
       FIG. 7  shows the magnetic circuit of a transformer (not shown) in a second embodiment. The transformer may be considered as being an “E-shaped” or a “pot-shaped” variant of the “U-shaped” transformer  10  of  FIG. 3 . The same references are therefore used as in  FIG. 7  and in  FIG. 3 , without risk of confusion, and a detailed description of the transformer in the second embodiment is omitted. It is merely stated that the references  13  and  17  correspond to two axially spaced-apart rings, the legs  14  to  16  and  18  to  20  extending axially between the two rings  13  and  17 , and that the magnetic cores in this example are situated in the columns. 
       FIG. 8  shows a transformer  110  in a third embodiment of the invention. The transformer  110  may be considered as a static transformer corresponding to the rotary transformer  10  of  FIG. 3 . In  FIG. 8 , the same references are therefore used as in  FIG. 3 , plus 100, in order to designate elements that are identical or similar to those of  FIG. 3 . 
     The transformer  110  has a ring  113  about the axis A, three legs  114 ,  115 , and  116 , and a ring  117  of ferromagnetic material about the axis A. Each of the legs  114 ,  115 , and  116  extends radially away from the axis A, starting from the ring  113 . The leg  114  is at one end of the ring  113 , the leg  116  is at another end of the ring  113 , and the leg  115  lies between the legs  114  and  116 . The ring  117  surrounds the ring  113  and the legs  114  to  116 , defining an airgap  121 . 
     The rings  113  and  117  together with the legs  114  to  116  form a three-column magnetic circuit of the transformer  110 . More precisely, the magnetic circuit of the transformer  110  has a first column (corresponding to the leg  114 ), a second column (corresponding to the leg  115 ), and a third column (corresponding to the leg  116 ). 
     The magnetic circuit of the transformer  110  defines a slot  122  between the two rings, the first column, and the second column, and a slot  123  between the two rings, the second column, and the third column. 
     As shown in  FIG. 8 , the transformer  110  has coils  124 ,  125   a ,  125   d  (together with two coils not shown),  126 ,  128 ,  129   a ,  139   c  (together with two coils not shown), and  130  corresponding to the coils  24  to  30  of the transformer  10 . 
     The transformer  110  is a magnetically shielded three-phase static transformer with forced linked fluxes, and with a three-column magnetic circuit. It presents operation and advantages similar to the transformer  10  of  FIG. 3 . 
       FIG. 9  shows a transformer  210  in a fourth embodiment of the invention. The transformer  210  may be considered as being a magnetically non-shielded variant of the magnetically shielded transformer  110  of  FIG. 8 . The same references are therefore used as in  FIG. 9  and in  FIG. 8 , without risk of confusion, and a detailed description of the transformer  210  is omitted. It is merely stated that the magnetic circuit of the transformer  210  does not completely surround of the coils  124 ,  128 ,  126 , and  130 , and that the transformer  210  is therefore not magnetically shielded, unlike the transformer  110 . 
       FIG. 10  is a section view of a transformer  310  in a first embodiment useful for understanding the invention. The transformer  310  may be considered as a three-phase rotary transformer with forced linked fluxes, and it may be considered as a variant of the transformer  10  of  FIG. 3 . Thus, in  FIG. 10 , (and in  FIGS. 11 to 13 ), elements that are identical or similar to elements of the transformer  10  of  FIG. 3  are designated by the same references, without risk of confusion. Below, the specific features of the transformer  310  are described in detail. 
     Instead of the toroidal coil  24 , the transformer  310  has four coils, of which a coil  324   a  and a coil  324   d  are shown in  FIG. 10 , these coils are connected in series and are received in slots  436  formed in the leg  18  (the slots  36  can be seen in  FIG. 11 ). In corresponding manner, instead of the toroidal coil  28 , the transformer  310  has four coils, of which a coil  328   a  and a coil  328   d  are shown in  FIG. 10 , these coils are connected in series and are received in slots  37  formed in the leg  15 . 
     Likewise, instead of the toroidal coil  26 , the transformer  310  has four coils, of which a coil  326   a  and a coil  326   d  are shown in  FIG. 10 , these coils are connected in series and are received in slots  36  formed in the leg  20 . In corresponding manner, instead of the toroidal coil  30 , the transformer  310  has four coils, of which a coil  330   a  and a coil  330   d  are shown in  FIG. 10 , these coils are connected in series and are received in slots  37  formed in the leg  16 . 
     In other words, in similar manner to the central phase, the side phases are no longer wound around the axis of rotation A, but radially around each of the columns. The transformer  310  thus has three radial magnetic cores: A core  38  in the central column formed by the legs  15  and  19 , a core  39  in the column formed by the legs  14  and  18 , and a core  40  in the column formed by the legs  16  and  20 . 
       FIG. 12  uses the same notation as  FIG. 6  and illustrates the operation of the transformer  310 . 
     In  FIG. 12 , the coils  324   a ,  324   d , and the coils that are not shown and that are connected thereto correspond, for a current I ap , to a radial magnetic potential Pa directed towards the axis A in the magnetic core  39 . Likewise, the coils  25   a ,  25   b ,  25   c , and  25   d  correspond, for a current I bp , to a radial magnetic potential Pb directed towards the axis A in the magnetic core  38 . Finally, the coils  326   a ,  326   d , and the coils that are not shown and that are connected thereto correspond, for a current I cp , to a radial magnetic potential Pc directed towards the axis A in the magnetic core  40 . 
     The magnetic potentials Pa, Pb, and Pc are equal in modulus, and they are all directed towards the axis A. In a variant that is not shown, the magnetic potentials Pa, Pb, and Pc are in the direction opposite relative to the example shown, i.e. they are all directed away from the axis A. 
     This configuration enables fluxes to be properly coupled. More precisely, the topology of the transformer  310  makes it possible to obtain the same coupling coefficient of 3/2 as in the above-described transformer  10 . In order to obtain the theoretical coupling coefficient and three-phase balance, it suffices for the reluctances between the midpoint of the ring  17  and the midpoint of the ring  13  and passing via each of the columns to be identical. 
     The transformer  310  presents the same advantages as the transformer  10 , other than using only toroidal coils. In particular, the transformer  310  makes it possible to obtain coupling of the phases that enables the multiplicative coefficient of 3/2 to be obtained. 
     In the embodiment shown, the transformer  310  comprises, for each phase, four primary coils in series (coils  25   a  to  25   d  for the central phase) and four secondary coils in series (coils  29   a  to  29   d  for the central phase). In a variant, the number of coils on each column could be greater or smaller. There may be different numbers of coils on each column for the primary and for the secondary. 
     The transformer  310  shown in  FIGS. 10 to 12  is a “U-shaped” transformer. In a variant that is not shown, an “E-shaped” or a “pot” transformer would present similar topology. Under such circumstances, the magnetic cores would be axial.  FIG. 13  shows, in an exploded perspective view, a magnetic circuit suitable for making such an “E-shaped” variant. Elements corresponding to elements of  FIG. 11  are designated by the same references, without risk of confusion. 
     In the transformer  10  of  FIG. 3 , and in the transformer  310  of  FIG. 10 , the coils enable three-phase fluxes to be reproduced in the three columns of the transformer in a manner that is equivalent to a three-phase static transformer with forced linked fluxes. Likewise, in the “E-shaped” variants of the transformer (not shown but based on the magnetic circuit of  FIG. 7  or  FIG. 13  respectively), the coils enable three-phase fluxes to be reproduced in the three columns of the transformer in a manner that is equivalent to a three-phase static transformer with forced linked fluxes. 
     Thus, the primaries and the secondaries of these transformers are compatible. In general manner, the primary of the transformer  10  is compatible with any secondary of topology making it possible to reproduce the three-phase fluxes in the three columns in a manner that is equivalent to a three-phase static transformer with forced linked fluxes. Thus, in the transformer  10 , the primary and the secondary are made on the same principle. Nevertheless, in a variant, the primary or the secondary could be made on a different principle, e.g. on the principle of the transformer  310  of  FIGS. 10 to 12 . 
       FIG. 15  is a section view of a transformer  410  in a fifth embodiment of the invention, using the primary of the transformer  10  and the secondary of the transformer  310 . In  FIG. 15 , the same references are therefore used as in  FIG. 3 , or in  FIG. 10 , and a detailed description is omitted. 
     In known manner, a transformer may have a plurality of secondaries. Thus, in an embodiment not shown, the coils of each secondary may be made simultaneously using the principle of the transformer  10  and the principle of the transformer  310  on a common body, providing it possesses the necessary slots in its legs for passing coils using the principle of the transformer  310 .