Symmetrical auto transformer delta topologies

This application is related to U.S. patent application, entitled “SYMMETRICAL AUTO TRANSFORMER WYE TOPOLOGIES”, Ser. No. 12/336,467, filed on even date herewith, the disclosure of which is incorporated herein by reference in its entirety.

1. Field of the Disclosure

This disclosure is directed to transformer topologies.

2. Related Art

In many applications, especially shipboard and aircraft applications, a high voltage direct current (DC) power is used to power motor controllers. Typically, a three phase alternating current (AC) voltage of 230 Volts RMS (root mean square) is generated in a ship or an aircraft. The generated AC voltage is applied to an auto transformer rectifier unit (ATRU) and rectified to generate a DC voltage of +/− 270 Volts. The rectified DC voltage from the ATRU is then used to power motor controllers. The output voltage of the motor controllers is limited by the rectified DC voltage of the ATRU. It is desirable to increase the voltage output of the motor controllers.

In order to increase the output voltage of the motor controllers, various approaches have been tried. One approach is to provide a higher input AC voltage. This approach has shortcoming because if the input AC voltage is increased, due to increased power, one has to increase the overall insulation level of the whole ship or aircraft. Increased input AC voltage may also lead to additional challenges like corona, high voltage spikes and component breakdown.

Another approach has been to cod a step-up autotransformer before the motor controller to get higher rectified output DC voltage or after the motor controller to get higher output AC voltage. Adding an additional step-up transformer before or after the motor controller adds additional heavy magnetic components the power generation system. Especially in a shipboard or aircraft applications, additional autotransformers may significantly add to the weight of the electrical subsystem and hence may not be desirable.

It is with these needs in mind the current disclosure arises.

In one embodiment, a multi-phase transformer is disclosed. The multi-phase transformer includes a first group of windings, a second group of windings and a third group of windings. The first group of windings includes a plurality of primary windings. Each of the primary windings includes one or more sub primary windings coupled in series. A junction of two sub primary windings defines an interior junction.

Each end of the primary windings is coupled to an end of another primary winding to form a delta configuration. The junction of two primary windings defines an exterior junction. Each of the primary windings is configured to receive a phase of a multi-phase input voltage at the exterior junction.

The second group of windings includes a plurality of secondary windings. Each secondary winding has a first end and a second end. Each secondary winding is magnetically coupled to a primary winding. The first end of each secondary winding is coupled to a primary winding.

The third group of windings includes a plurality of third windings. Each third winding has a first end and a second end. Each third winding is magnetically coupled to a primary winding. The first end of each of the third winding is coupled to a secondary winding or to a primary winding.

The third group of windings is configured such that an output voltage at the second end of the third windings is higher than an output voltage at the second end of the secondary windings and the exterior junction of the primary windings.

In another embodiment, another multi-phase transformer is disclosed. The multi-phase transformer includes a first group of windings, second group of windings and third group of windings.

The first group of windings includes a plurality of primary windings. Each primary winding includes one or more sub primary windings that are coupled in series. A junction of two sub primary windings defines an interior junction. Each end of the primary windings is coupled to an end of another primary winding to form a delta configuration. The junction of two primary windings defines an exterior junction. Each of the primary windings is configured to receive a phase of a multi-phase input voltage at the exterior junction.

The second group of windings includes a plurality of secondary windings. Each secondary winding has a first end and a second end. Each secondary winding is magnetically coupled to a primary winding. The first end of each secondary winding is coupled to an interior junction of one of the primary windings.

The third group of windings includes a plurality of third windings. Each third winding has a first end and a second end. Each third winding is magnetically coupled to a primary winding. The first end of each of the third winding is coupled to a second end of a secondary winding or an exterior junction of the primary winding.

The third group of windings is configured such that an output voltage at the second end of the third windings is higher than an output voltage at the second end of the secondary windings and the exterior junction of the primary windings.

In yet another embodiment, a multi-phase transformer is disclosed. The multi-phase transformer includes a first group of windings, a second group of windings and a third group of windings. The first group of windings includes a plurality of primary windings. Each primary winding includes one or more sub primary windings coupled in series.

A junction of two sub primary windings defines an interior junction. Each end of the primary windings is coupled to an end of another primary winding to form a delta configuration. A junction of two primary windings defines an exterior junction. Each of the primary winnings is configured to receive a phase of a multi-phase input voltage at the exterior junction.

The second ground of windings includes a plurality of secondary windings. Each secondary winding has a first end and a second end. Each secondary winding is magnetically coupled to a primary winding. The first end of each secondary winding is coupled to an interior junction of one of the primary windings.

The third group of windings includes a plurality of third windings. Each third winding has a first end and a second end. Each third winding is magnetically coupled to a primary winding. The first end of each of the third winding coupled either to an interior junction of one of the primary windings other than an interior junction to which a secondary winding is coupled or to an exterior junction of the primary winding.

The third group of windings is configured such that an output voltage at the second end of the third windings is higher than an output voltage at the second end of the secondary windings and the exterior junction of the primary windings.

In yet another embodiment, a multi-phase transformer is disclosed. The multi-phase transformer includes a first group of windings, a second group of windings and a third group of windings. The first group of windings includes a plurality of primary windings. Each primary winding includes one or more sub primary windings coupled in series.

A junction of two sub primary winding defines an interior junction. Each end of the primary windings is coupled to an end of another primary winding to form a delta configuration. A junction of two primary windings defines an exterior junction. Each of the primary windings is configured to receive a phase of a multi-phase input voltage at the exterior junction.

The second group of windings includes a plurality of secondary windings. Each secondary winding has a first end and a second end. Each secondary winding is magnetically coupled to a primary winding. The first end of each secondary winding is coupled to an interior junction of one of the primary windings.

The third group of windings includes a plurality of third windings. Each third winding has a first end and a second end. Each third winding is magnetically coupled to a primary winding. The first end of each of the third winding is coupled to a second end of a secondary winding, an interior junction of the primary winding or an exterior junction of the primary winding.

The third group of windings is configured such that an output voltage at the second end of the third windings is higher than an output voltage at the second end of the secondary windings and the exterior junction of the primary windings.

In yet another embodiment, a multi-phase transformer with a first group of windings, a second group of windings and a third group of windings is disclosed. The first group of windings includes a plurality or primary windings. Each primary winding includes ore or more sub primary windings coupled in series.

A junction of two sub primary winding defines an interior junction. Each end of the primary windings is coupled to an end of another primary winding to form a delta configuration. The junction of two primary windings defines an exterior junction. Each of the primary windings is configured to receive a phase of a multi-phase input voltage at the exterior junction.

The second group of windings includes a plurality of secondary windings. Each secondary winding has a first end and a second end. Some of the secondary windings include a plurality of sub-winding connected in series. Junctions of two sub-windings define a sub-junction. Each secondary winding is magnetically coupled to a primary winding. First end of each secondary winding is coupled to an interior junction of one of the primary windings.

The third group of windings includes a plurality of third windings. Each third winding has a first end and a second end. Each third winding is magnetically coupled to a primary winding. The first end of each of the third winding is coupled to a second end of a secondary winding, a sub-junction of a secondary winding or an exterior junction of the primary winding.

The third group of windings is configured such that an output voltage at the second end of the third windings is higher than an output voltage at the second end of the secondary windings and the exterior junction of the primary windings.

In yet another embodiment, a multi-phase transformer with a first group of windings, a second group of windings and a third group of windings is disclosed. The first group of windings includes a plurality of primary windings. Each primary winding includes one or more sub primary windings coupled in series. A junction of two sub primary winding defines an interior junction. Each end of the primary windings is coupled to an end of another primary winding to form a delta configuration. The junction of two primary windings defines an exterior junction. Each of the primary windings is configured to receive a phase of a multi-phase input voltage at the exterior junction. The second group of windings includes a plurality of secondary windings. Each secondary winding has a first end and a second end. Some of the secondary windings include a plurality of sub-windings connected in series. A junction of two sub-windings defines a sub-junction. Each secondary winding is magnetically coupled to a primary winding. The first end of each secondary winding is coupled to an interior junction of one of the primary windings or the exterior junction of the primary windings. The third group of windings includes a plurality of third windings. Each third winding has a first end and a second end. Some of the third windings include a first sub-winding and a second sub-winding. The first sub-winding and the second sub-winding of the third winding are connected in series a one end. A junction of two sub-windings defines a sub-junction. Each of the third winding is magnetically coupled to a primary winding. The first end of each of the third winding is coupled to a sub-junction of a secondary winding or an exterior junction of the primary winding. The third group of windings is configured such that an output voltage at the second end of the third windings is higher than an output voltage at the second end of the secondary windings and the exterior junction of the primary windings.

This brief summary has been provided so that the nature of the disclosure may be understood quickly. A more complete understanding or the disclosure may be obtained by reference to the following detailed description of embodiments, thereof in connection with the attached drawings.

The foregoing features and other features of the present disclosure will now be described with reference to the drawings. In the drawings, the same components have the same reference numerals. The illustrated embodiment is intended to illustrate, but not to limit the disclosure. The drawings include the following figures:

FIG. 1A is a winding diagram for an exemplary multi-phase auto-transformer.

FIG. 1B is a phasor diagram for the multi-phase auto-transformer of FIG. 1A .

FIG. 2 is an exemplary auto-transformer rectifier unit for use with multi-phase auto transformers.

FIG. 3A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 3B is a phasor diagram for the multi-phase auto-transformer of FIG. 3A .

FIG. 4A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 4B is a phasor diagram for the multi-phase auto-transformer of FIG. 4A .

FIG. 5A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 5B is a phasor diagram for the multi-phase auto-transformer of FIG. 5A .

FIG. 6A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 6B is a phasor diagram for the multi-phase auto-transformer of FIG. 6A .

FIG. 7A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 7B is a phasor diagram for the multi-phase auto-transformer of FIG. 7A .

FIG. 8A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 8B is a phasor diagram for the multi-phase auto-transformer of FIG. 8A .

FIG. 9A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 9B is a phasor diagram for the multi-phase auto-transformer of FIG. 9A .

FIG. 10A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 10B is a phasor diagram for the multi-phase auto-transformer of FIG. 10A .

FIG. 11A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 11B is a phasor diagram for the multi-phase auto-transformer of FIG. 11A .

FIG. 12A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 12B is a phasor diagram for the multi-phase auto-transformer of FIG. 12A .

FIG. 13A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 13B is a phasor diagram for the multi-phase auto-transformer or FIG. 13A .

FIG. 14A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 14B is a phasor diagram for the multi-phase auto-transformer of FIG. 14A .

FIG. 15A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 15B is a phasor diagram for the multi-phase auto-transformer of FIG. 15A .

FIG. 16A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 16B is a phasor diagram for the multi-phase auto-transformer of FIG. 16A .

FIG. 17A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 17B is a phasor diagram for the multi-phase auto-transformer of FIG. 17A .

FIG. 18A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 18B is a phasor diagram for the multi-phase auto-transformer of FIG. 18A .

FIG. 19A is a winding diagram for an alternate multi-phase auto-transformer.

FIG. 19B is a phasor diagram for the multi-phase auto-transformer of FIG. 19A .

The following definitions are provided for convenience, as they are used in describing various embodiments of this disclosure.

“Exterior junction” means a junction of two primary windings coupled together at their ends. Three primary windings may be coupled at their ends to form a delta winding configuration.

“First group of winding” means a collection of plurality of primary windings.

“Interior junction” means a junction of two sub primary windings of a primary winding.

“Primary winding” is a winding may have one or more sub primary windings coupled in series. Primary windings may have two ends.

“Second group of windings” means a collection of a plurality of secondary windings.

“Secondary winding” is a winding that may have a winding or a plurality of sub-windings. Secondary windings have at least a first end and a second end. In some embodiments, the sub-windings may be coupled together to form a sub-junction. Secondary windings may be magnetically coupled to a primary winding. Sub-windings of secondary winding may be magnetically coupled to the same primary winding or a different primary winding.

“Sub-junction” means a junction of sub-windings. In some embodiments, two sub-windings may be coupled in series. In some embodiments, three sub-windings may be coupled at one end to form a WYE configuration.

“Third group of windings” means a collection of a plurality of third windings.

“Third winding” means a winding that may have a winding or a plurality of sub-windings. Third windings have at least a first end and a second end. Third windings may be magnetically coupled to a primary winding. Sub-windings of third winding may be magnetically coupled to the same primary winding or a different primary winding.

To facilitate an understanding of the various embodiments, the general architecture of an auto-transformer rectifier system with an exemplary auto-transformer will be described. The specific architecture of various alternate embodiments of auto-transformers will then be described with reference to the general architecture.

A multi-phase transformer 100 is described with reference to FIG. 1A and 1B . FIG. 1A is a winding diagram of a multi-phase transformer 100 . FIG. 1B is a phasor diagram for the multi-phase transformer 100 . Transformer 100 may be six phase or twelve pulse multi-phase transformer.

Referring to FIG. 1A , transformer 100 may include a first group of windings 102 , a second group of windings 104 and a third group of windings 106 .

The first group of windings 102 may include a plurality of primary windings 108 A- 108 C. Each primary winding may include one or more sub primary windings coupled in series, with a junction of two sub primary windings defining an interior junction. For example, primary winding 108 A may include sub primary windings 108 A 1 - 108 A 2 coupled in series to define interior junction 112 A 1 . Similarly, primary winding 108 B may include sub primary windings 108 B 1 - 108 B 2 coupled in series to define interior junction 112 B 1 and primary winding 108 C may include sub primary windings 108 C 1 - 108 C 2 coupled in series to define interior junction 112 C 1 .

Each end of the primary windings is coupled to the ends of the other primary winding to form a delta configuration with the junction of two primary windings defining an exterior junction. For example, an end of primary winding 108 A and 108 C is coupled together to define exterior junction 114 A. Similarly, an end of primary winding 108 A and 108 B is coupled together to define exterior junction 114 B. Furthermore, an end of primary winding 108 B and 108 C is coupled together to define exterior junction 114 C.

Each of the primary winding may be configured to receive a phase of a multi-phase input voltage at the exterior junctions. For example primary winding 108 A may a phase at exterior junctions 114 A and 114 B. Similarly, primary winding 108 B may receive another phase at exterior junctions 114 B and 114 C. Furthermore, primary winding 108 C may receive yet another phase at exterior junctions 114 C and 114 A.

The second group of windings 104 includes a plurality of secondary windings, for example, secondary windings 116 A 1 - 116 C 1 . Each secondary winding 116 A 1 - 116 C 1 includes a first end 118 and a second end 120 . Each secondary winding 116 A 1 - 116 C 1 may be magnetically coupled to one of the primary windings 108 A- 108 C. The first end 118 of each secondary winding 116 A 1 - 116 C 1 may be coupled to one of the primary windings 108 A- 108 C.

The third group of windings 106 may include a plurality of third windings. For example, third windings 122 A 1 , 122 A 2 , 122 B 1 , 122 B 2 , 122 C 1 and 122 C 2 . Each third winding 122 A 1 - 122 C 2 includes a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 2 may be magnetically coupled to one of the primary windings 108 A- 108 C.

The first end 124 of each of the third winding 122 A 1 - 122 C 2 may be coupled to a secondary winding 116 A 1 - 116 C 1 or to a primary winding 108 A- 108 C. The third group of windings 106 may be configured with respect to the first group of windings 102 and the second group of windings 104 such that the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 C 2 is higher than the output voltage Vout 1 at the second end 120 of the secondary windings 116 A 1 - 116 C 1 and the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C.

In one embodiment, the first end of secondary winding may be coupled to the interior junction of a primary winding. For example, the first end 118 of the secondary winding 116 A 1 may be coupled to the interior junction 112 A 1 of primary winding 108 A. The first end 118 of the secondary winding 116 B 1 may be coupled to the interior junction 112 B 1 of the primary winding 108 B. The first end 118 of the secondary winding 116 C 1 may be coupled to the interior junction 122 C 1 of primary winding 108 C.

In one embodiment, the second end of a secondary winding may be coupled to the first end of a third winding. For example, the second end 120 of secondary winding 116 A 1 may be coupled to the first end 124 of the third winding 122 A 2 , the second end 120 of secondary winding 116 B 1 may be coupled to the first end 124 of the third winding 122 B 2 and the second end 120 of the second winding 116 C 1 may be coupled to the first end 124 of the third winding 122 C 2 .

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends or third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 , 122 A 2 - 122 B 1 , 122 B 1 - 122 B 2 , 122 B 2 - 122 C 1 , 122 C 1 - 122 C 2 and 122 C 2 - 122 A 1 are substantially same.

In one embodiment, the output voltage Vout 2 an the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 C 2 are substantially same.

In one embodiment, output voltage Vout 1 at the second end of secondary windings 116 and at the exterior junction of the primary windings 108 are substantially equal. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 C 1 and at the exterior junction 114 A- 114 C of primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 1A also shows exemplary number of turns for various windings and sub windings, with some of the windings or sub windings having substantially same number of turns. For example, the sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 have substantially same number of turns N 2 . The sub-primary windings 108 A 2 , 108 B 2 and 108 C 2 have substantially same number of turns N 1 . Similarly, the secondary windings 116 A 1 , 116 B 1 and 116 C 1 have substantially same number of turns N 3 . Further, the third windings 122 A 1 - 122 C 2 have substantially same number of turns N 4 .

Now referring to FIG. 1B , an exemplary phasor diagram 130 for the multi-phase transformer 100 of FIG. 1A is disclosed. As one skilled in the art appreciates, the phasor diagram graphically depicts various aspects the multi-phase transformer. For example, the phasor diagram depicts the relationship between the first group of windings, second group of windings and the third group of windings. More specifically, various windings are represented by lines in a phasor diagram and the length of a line represents the number of turns of the winding. The lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. Two vector lines that are parallel to each other represent magnetic coupling between corresponding two windings. The radial length of each segment between two junctions along the circumference represents the phase angle difference between the output signals at those junctions, with the full circle representing 360 degrees. The common center of the circle represents the effective electrical neutral position.

The phasor diagram 130 includes a first circle 132 and a second circle 134 , both having a common center S. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 , B 1 and C 1 on lines AB, BC and CA correspond to the interior junctions 112 A 1 , 112 B 1 and 112 C 1 respectively of the primary windings 108 A- 108 C. Lines A-A 1 , A 1 -B, B-B 1 , B 1 -C, C-C 1 and C 1 -A represent sub primary windings 108 A 1 , 108 A 2 , 108 B 1 , 108 B 2 , 108 B 1 and 108 C 2 respectively.

Points A 1 V 1 , B 1 V 1 and C 1 V 1 represent the second end 120 the secondary windings 116 A 1 , 116 B 1 and 116 C 1 respectively. Similarly, points A 1 V 2 , B 2 V 2 and C 1 V 2 represent second end 126 of third windings 122 A 1 , 122 B 1 and 122 C 1 respectively.

For example, lines A 1 -A 1 V 1 , B 1 -B 1 V 1 and C 1 C 1 V 1 represent the secondary windings 116 A 1 , 116 B 1 and 116 C 1 respectively. Lines A-AV 2 , A 1 V 1 -A 1 V 2 , B-BV 2 , B 1 V 1 -B 1 V 2 , C-CV 2 and C 1 V 1 -C 1 V 2 represent the third windings 122 A 1 , 122 A 2 , 122 B 1 , 122 B 2 , 122 C 1 and 122 C 2 respectively.

For example, the length of the lines A-A 1 , B-B 1 and C-C 1 present the number of turns N 2 for the sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 . The length of the lines A 1 -B, B 1 -C and C 1 -A represent the number of turns N 1 for the sub-primary windings 108 A 2 , 108 B 2 and 108 C 2 .

Length of the lines A 1 -A 1 V 1 , B 1 -B 1 V 1 and C 1 -C 1 V 1 represent the number of turns N 3 for the secondary windings 116 A 1 , 116 B 1 and 116 C 1 respectively. Length of the lines A-AV 2 , A 1 V 1 -A 1 V 2 , B-BV 2 , B 1 V 1 -B 1 V 2 , C-CV 2 and C 1 V 1 -C 1 V 2 represent the number of turns N 4 for the third windings 122 A 1 - 122 C 2 respectively.

In summary, on the phasor diagram, the points A, B and C represent the exterior junction 114 A- 114 C of the primary windings, points A 1 V 1 , S 1 V 1 and C 1 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 C 1 and points AV 2 , A 1 V 2 , BV 2 , B 1 V 2 , CV 2 and C 1 V 2 represent the second end 126 of the third windings 122 A 1 - 122 C 2 respectively.

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 136 , 138 and 140 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 142 and 144 represent the vector of induced voltage in secondary winding 116 A 1 and 116 B 1 respectively. The arrows 146 and 148 represent the vector of induced voltage in the third windings 122 A 1 and 122 A 2 respectively.

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 degrees cut of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 130 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings.

For example, in one embodiment, the vector of induced voltage in each of the secondary windings is in phase with the vector of induced voltage in a primary winding other than the primary winding to which the secondary winding is coupled. For example, the vector of induced voltage in the secondary winding depicted by line A 1 -A 1 V 1 may be in phase with the vector of induced voltage in the primary winding depicted by line CA. Similarly, the vector of induced voltage in the secondary winding depicted by line B 1 -B 1 V 1 and secondary winding depicted by line C 1 -C 1 V 1 are in phase with vector of induced voltage in the primary windings depicted by lines AB and BC respectively.

For example, in one embodiment, the vector of induced voltage in a third winding coupled to a secondary winding may be in-phase with the vector of the corresponding secondary winding. Further, the vector of induced voltage in a third winding coupled to a primary winding may be about 180 degrees out of phase with the vector of induced voltage in one of the primary windings coupled to the third winding, such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

FIG. 2 shows an exemplary auto-transformer rectifier system 200 for use with this disclosure. The auto-transformer rectifier system includes an auto-transformer 202 , a first multi-pulse rectifier 204 and a second multi-pulse rectifier 206 . The auto-transformer 202 may be similar to the auto-transformer described with reference to FIGS. 1A and 1B .

The first multi-phase rectifier 204 includes a first input block 208 and a first output block 210 . The first input block 208 may be configured to couple to the second end of secondary windings to receive the first output voltage VoutF 1 from the auto-transformer 202 . The first multi-phase rectifier 204 rectifies the first output voltage VoutF 1 and provides a rectified first output voltage VRoutF 1 . The first output voltage VoutF 1 may be same as the output voltage Vout 1 of the auto-transformer described with reference to FIGS. 1A and 1B .

The second multi-phase rectifier 206 includes a second input block 212 and a second output block 212 . The second input block 212 may be configured to couple to the second end of third windings to receive second output voltage VoutF 2 from the auto-transformer. The second multi-phase rectifier 206 rectifies the second output voltage VoutF 2 and provides a rectified second output voltage VRoutF 2 . The second output voltage VoutF 2 may be same as the output voltage Vout 2 of the auto-transformer described with reference to FIGS. 1A and 1B .

The first output voltage VoutF 1 may be same as the output voltage Vout 1 of the auto-transformer described with reference to FIGS. 1A and 1B . The second output voltage VoutF 2 may be same as the output voltage Vout 2 of the auto-transformer described with reference to FIGS. 1A and 1B . As previously described, the auto-transformer 100 of FIG. 1A and 1B in one embodiment, provides a six phase output Vout 1 at the second end of the secondary windings and a six phase output voltage Vout 2 at the second end of third windings.

In an exemplary system, an input voltage of 230 Volts rms AC voltage may be applied to the auto-transformer. This will generate a 230 Volts rms AC voltage at the output of the second end of secondary windings, with six phases, with each phase having a positive pulse and a negative pulse. The input voltage of 230 Volts rms AC voltage also generates a 307 Volts rms AC voltage at the output of the second end of third windings.

The six 230 Volts rms positive pulses are applied to the first input block and rectified by the first multi-phase rectifier 204 to provide +270 Volts DC at the first output block 210 . The six negative 230 Volts rms pulses are also applied to the first input block 208 and rectified by the first multi-phase rectifier 204 to provide −270 Volts CC at the first output block 210 .

The six 307 Volts rms positive pulses are applied to the second input block 212 and rectified by the second multi-phase rectifier 206 to provide +360 Volts DC at the second output block 214 . The six negative 307 Volts rms pulses are applied to the second input block 212 and rectified by the second multi-phase rectifier 206 to provide −360 Volts DC at the second output block 214 .

Although the exemplary embodiment has been described with reference to a six phase (12 pulse) auto-transformer and a 12 pulse rectifier, the disclosure is not limited to this specific example and can be modified suitably to construct auto-transformer rectifier systems to support auto-transformers with different number of output phases. For example, the auto-transformer rectifier system may be adapted for use with various embodiments of multi-phase transformers described in this disclosure.

Another embodiment of a multi-phase transformer 300 is described with reference to FIGS. 3A and 3B . Transformer 300 is another exemplary six phase or twelve pulse multi-phase transformer. The multi-phase transformer 300 described with reference to FIGS. 3A and 3B is substantially similar to the multi-phase transformer 100 described with reference to FIGS. 1A and 1B except that the third group of windings 106 include a plurality of third windings 122 A 1 - 122 C 2 , with each third winding 122 A 1 - 122 C 2 including at least two sub-windings connected in series. Similarities and differences between auto-transformer 100 and auto-transformer 300 will be described in more detail below.

FIG. 3A is a winding diagram for an exemplary multi-phase transformer 300 . The transformer 300 includes a first group of windings 102 , a second group of windings 104 and a third group of windings 106 . The first group of windings 102 and the second group of windings 104 of auto-transformer 200 are constructed and coupled similar to the auto-transformer 100 described with reference to FIGS. 1A and 1B , with same reference numerals describing the same elements.

The third group of windings 106 includes a plurality of third windings 122 A 1 - 122 C 2 , with ends of the third windings 122 A 1 - 122 C 2 defining a first end 124 and a second end 126 . Each of the third winding 122 A 1 - 122 C 2 includes at least two sub-windings connected in series. For example, third winding 122 A 1 includes a first sub-winding 122 A 11 and second sub-winding 122 A 12 connected in series at one end. The other end of first sub-winding 122 A 11 corresponds to the first end 124 of the third winding 122 A 1 and the other end of second sub-winding 122 A 12 corresponds to the second end 126 of the third winding 122 A 1 .

Each of the third winding 122 A 1 - 122 C 2 may be magnetically coupled to a primary winding 108 A- 108 C. For example, the first sub-winding 122 A 11 may be magnetically coupled to a primary winding 108 A- 108 C and the second sub-winding 122 A 12 may be magnetically coupled to a primary winding 108 A- 108 C. The second sub-winding 122 A 12 may be magnetically coupled to a primary winding 108 A- 108 C different than the primary winding that the first sub-winding 122 A 11 may be magnetically coupled to.

The first end 124 of each of the third winding 122 A 1 - 122 C 2 may be coupled to a secondary winding 116 A- 116 C or to a primary winding 108 A- 108 C with the third group of windings 106 configured with respect to the first group of windings 102 and the second group of windings 104 such that the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 C 2 may be higher than the output voltage Vout 1 at the second end 120 of the secondary windings 116 A 1 - 116 C 1 and the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C respectively.

In one embodiment, the first end 118 of the secondary winding 116 A 1 - 116 C 1 may be coupled to the interior junction of the primary winding 108 A- 108 C. For example, the first end 118 of the secondary winding 116 A 1 may be coupled to interior junction 112 A 1 of primary winding 108 A.

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 2 may be coupled to the second end 120 of the secondary windings 116 A 1 - 116 C 1 . For example, the first end 124 of the third winding 122 A 2 may be coupled to the second end 120 of secondary winding 116 A 1 .

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends 126 of third windings 122 A 1 - 122 C 2 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 C 2 are substantially equal and the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 C 1 and at the exterior junction 114 A- 114 C the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 3A also shows exemplary number of turns for various windings and sub windings, with some of the windings or sub windings having substantially same number of turns. For example, the sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 have substantially same number of turns N 2 . The sub-primary windings 108 A 2 , 108 B 2 and 108 C 2 have substantially same number of turns N 1 . Similarly, the secondary windings 116 A 1 , 116 B 1 and 116 C 1 have substantially same number of turns N 3 . For example, the first sub-windings 122 A 21 and 122 B 21 of third windings 122 A 2 and 122 B 2 have substantially same number of turns N 4 .

Now referring to FIG. 3B , an exemplary phasor diagram 330 tar the multiphase transformer 300 of FIG. 3A is disclosed.

The phasor diagram 330 includes a first circle 332 and a second circle 334 , both having a common center S. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. The phasor diagram details within the first circle 332 is similar to the phasor diagram 130 described with reference to FIG. 1B . Only differences between phasor diagram 330 and phasor diagram 130 as it relates to the third windings will be discussed now.

For example, the line A-A′ represents the first sub-winding 122 A 11 of third winding 122 A 1 . Similarly the line A′-AV 2 represents the second sub-winding 122 A 12 of third winding 122 A 1 . The arrow 148 ′ represents the vector of induced voltage in the first sub-winding 122 A 11 and the arrow 148 ″ represents the vector of induced voltage in the second sub-winding 122 A 12 . Other third windings 122 A 2 - 122 C 2 are similarly represented in the phasor diagram 330 .

The lines SA, SB and SC represent the input AC voltage Vin may be applied to the exterior junctions A, B and C of the primary windings. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and C are depicted by the arrows 136 , 138 and 140 .

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings and sub-windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the third windings and sub-windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 330 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings.

In one embodiment, the vector of induced voltage in a sub-winding of a third winding is different than the vector of induced voltage in another sub-winding of the third winding. For example, the vector of induced voltage in sub-winding 122 A 11 is different than the vector of induced voltage in sub-winding 122 A 12 of third winding 122 A 1 .

In one embodiment, for the third winding coupled to a second winding, (for example, third winding 112 A 2 coupled to second winding 116 A 1 ) the vector of induced voltage in the first sub-winding (example, 122 A 21 ) may be in-phase with the vector of induced voltage in the second winding and the vector of induced voltage in the second sub-winding (example, 122 A 22 ) may be 180 degrees out phase with the vector of induced voltage in a primary winding other than the primary winding to which the corresponding secondary winding may be coupled and that may be different than the primary winding that may be in-phase with the second winding (example, primary winding 108 B).

In one embodiment, for the third winding coupled to an external junction of a primary winding (example, third winding 122 A 1 ), the vector of induced voltage in the first sub-winding (example, 122 A 11 ) may be 180 degrees out of phase with the vector of induced voltage in a primary winding coupled to the external junction (example, 108 A) and the vector of induced voltage in the second sub-winding (example, 122 A 12 ) may be in phase with the vector of induced voltage in a primary winding coupled to the external junction that may be different than the primary winding that may be 180 degrees out of phase with the first sub-winding (example, primary winding 108 C).

Another embodiment of a multi-phase transformer 400 is described with reference to FIGS. 4A and 4B . Transformer 400 is another exemplary six phase or twelve pulse multi-phase transformer. The multi-phase transformer 400 described with reference to FIGS. 4A and 4B is similar to the multi-phase transformer 100 described with reference to FIGS. 1A and 1B and multi-phase transformer 300 described with reference to FIGS. 3A and 3B in that all have a primary group of windings 102 , secondary group of windings 104 and third group of windings 106 . One of the differences is that some of the third windings of the third group of windings are coupled to an interior junction of the primary windings of primary group of windings 102 .

Referring to FIG. 4A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 3 , 108 B 1 - 108 B 3 , 108 C 1 - 108 C 3 that are coupled in series, with junction of two sub primary windings defining an interior junction. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 and 108 A 2 define an interior junction 112 A 1 and the junction of sub primary windings 108 A 2 and 108 A 3 define an interior junction 112 A 2 . Similarly, primary winding 108 B includes interior junction 112 B 1 and 112 B 2 . And, primary winding 108 C includes interior junction 112 C 1 and 112 C 2 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with the junction of two primary windings defining an exterior junction 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A- 116 C. Each secondary winding 116 A- 116 C has a first end 118 and a second end 120 . Each secondary winding 116 A- 116 C may be magnetically coupled to one of the primary windings 108 A- 108 C. The first end 118 of each secondary winding 116 A- 116 C may be coupled to one of the primary windings 108 A- 108 C.

The third group of windings 106 includes a plurality of third windings 122 A 1 , 122 A 2 , 122 B 1 , 122 B 2 , 122 C 1 and 122 C 2 . Each third winding 122 A 1 - 122 C 2 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 2 may be magnetically coupled to one of the primary windings 108 A- 108 C.

The first end 124 of each of the third winding 122 A 1 - 122 C 2 may be coupled to a primary winding 108 A- 108 C, with the third group of windings 106 configured with respect to the first group of windings 102 and the second group of windings 104 such that the output voltage Vout 2 at the second end 126 of the third windings 122 A- 122 F may be higher than the cutout voltage Vout 1 at the second end 120 A- 120 F of the secondary windings 116 A- 116 C and the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C.

In one embodiment, the first end of a secondary winding may be coupled to the interior junction of primary winding. For example, the first end 118 of the secondary winding 116 A may be coupled to the interior junction 112 A 2 of primary winding 108 A. The first end 118 of the secondary winding 116 B may be coupled to the interior junction 112 B 2 of the primary winding 108 B. The first end 118 of the secondary winding 116 C may be coupled to the interior junction 112 C 2 of primary winding 108 C.

In one embodiment, the first end of a third winding may be coupled to an interior junction of a primary winding or to the exterior junction of primary windings. For example, the first end 124 of third winding 122 A 2 may be coupled to the interior junction 112 A 1 of the primary winding 108 A, the first end 124 of the third winding 122 B 2 may be coupled to the interior junction 112 B 1 of the primary winding 108 B, the first end 124 of the third winding 122 C 2 may be coupled to the interior junction 112 C 1 of the primary winding 108 C. Also, the first end 124 of the third winding 122 A 1 may be coupled to the exterior junction 114 A of primary windings 108 A and 108 C; the first end 124 of the third winding 122 B 1 may be coupled to the exterior junction 114 B of primary windings 108 A and 108 B; the first end 124 of the third winding 122 C 1 may be coupled to the exterior junction 114 C of primary windings 108 B and 108 C.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 , 122 A 2 - 122 B 1 , 122 B 1 - 122 B 2 , 122 B 2 - 122 C 1 , 122 C 1 - 122 C 2 and 122 C 2 - 122 A 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 C 2 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings 116 A- 116 C and at the exterior junction of the primary windings 108 A- 108 C are substantially equal. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A- 116 C and at the exterior junction 114 A- 114 C of primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 4A also shows exemplary number of turns for various windings and sub windings, with some of the windings or sub windings having substantially same number of turns. For example, the sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 have substantially same number of turns N 3 . The sub-primary windings 108 A 2 , 108 B 2 and 108 C 2 have substantially same number of turns N 2 . Similarly, the secondary windings 116 A, 116 B and 116 C have substantially same number of turns N 5 . For example, the third windings 122 A 2 and 122 B 2 have substantially same number of turns N 6 .

Now referring to FIG. 4B , an exemplary phasor diagram 430 for the multi-phase transformer 400 of FIG. 4A is disclosed.

The phasor diagram 430 includes a first circle 432 and a second circle 434 , both having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 -A 2 , B 1 -B 2 and C 1 -C 2 correspond to the interior junctions 112 A 1 - 112 A 2 , 112 B 1 - 112 B 2 and 112 C 1 - 112 C 2 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 and A 2 -B represent sub-primary windings 108 A 1 - 108 A 3 respectively. Similarly, Lines B-B 1 , B 1 -B 2 and B 2 -C represent sub-primary windings 108 B 1 - 108 B 3 respectively. Similarly, lines C-C 1 , C 1 -C 2 and C 2 -A represent sub-primary windings 108 C 1 - 108 C 3 respectively.

Points A 2 V 1 , B 2 V 1 and C 2 V 1 represent the second end 120 of the secondary windings 116 A, 116 B and 116 C respectively. Similarly, points AV 2 , A 1 V 2 , BV 2 , B 1 V 2 , CV 2 and C 1 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 2 , 122 B 1 - 122 B 2 and 122 C 1 - 122 C 2 respectively.

For example, lines A 2 -A 2 V 1 , B 2 -B 2 V 1 and C 2 -C 2 V 1 represent the secondary windings 116 A- 116 C respectively.

For example, lines A-AV 2 , A 1 -A 1 V 2 represent third windings 122 A 1 - 122 A 2 respectively.

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 3 for sub-primary winding 108 A 1 . Similarly, the length of line A 2 -A 2 V 1 represent number of turns N 5 for secondary winding 116 A. And the length of line A 1 -A 1 V 2 represent the number of turns N 6 for third winding 122 A 2 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage in the secondary winding 116 A and 116 B respectively. The rows 546 and 548 represent the vector of inducted voltage in the third winding 122 A 2 and 122 B 1 .

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 430 shows an exemplary vector if induced voltage in the primary windings, secondary windings and the third windings.

In one embodiment, the vector of induced voltage in each of the plurality of secondary windings is in-phase with the vector of induced voltage in a primary winding other than the primary winding to which the secondary winding is coupled. For example, the vector of induced voltage for secondary winding 116 A coupled to primary winding 108 A is in-phase with the vector of induced voltage in the primary winding 108 C.

In one embodiment, the vector of induced voltage in a third winding coupled to an interior junction of the primary winding and an exterior junction of the primary winding is in-phase with the induced voltage in the secondary winding that is coupled to the same primary winding as the third winding that is coupled to the interior junction of the primary winding.

For example, the vector of induced voltage in third winding 122 A 2 is the same as the vector of induced voltage in secondary winding 116 A and the vector of induced voltage in third winding 122 B 1 .

Another embodiment of a multi-phase transformer is described with reference to FIGS. 5A and 5B . Transformer 500 is an exemplary twelve phase or twenty four pulse multi-phase transformer. The multi-phase transformer 500 described with reference to FIGS. 5A and 5B is similar to the multi-phase transformer 400 described with reference to FIGS. 4A and 4B in that multi-phase transformer 500 has a primary group of windings 102 , secondary group of windings 104 and third group of windings 106 . One of the differences is that some of the third windings of the third group of windings are coupled to an interior junction of the primary windings of primary group of windings 102 and some of the third group of windings are coupled to the second end of the second windings.

Referring to FIG. 5A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 5 , 108 B 1 - 108 B 5 , 108 C 1 - 108 C 5 that are coupled in series. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 and 108 A 2 coupled in series define an interior junction 112 A 1 and the junction or sub primary windings 108 A 2 and 108 A 3 coupled in series define an interior junction 112 A 2 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 3 , 116 B 1 - 116 B 3 and 116 C 1 - 116 C 3 . Each secondary winding 116 A 1 - 116 C 3 has a first end 118 and a second end 120 . Each secondary winding 116 A 1 - 116 C 3 may be magnetically coupled to one of the primary windings 108 A- 108 C. The first end 118 of each secondary winding 116 A 1 - 116 C 3 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary winding 116 A 1 may be coupled to interior junction 112 A 2 of primary winding 108 A.

In one embodiment, two of the secondary windings are coupled to the same interior junction of the primary winding. For example, the first end 118 of secondary winding 116 A 2 and the first end 118 of secondary winding 116 A 3 are coupled to interior junction 112 A 4 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 4 , 122 B 1 - 122 B 4 and 122 C 1 - 122 C 4 . Each third winding 122 A 1 - 122 C 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 4 may be magnetically coupled to one of the primary windings 108 A- 108 C.

The first end 124 of some of the third windings 122 A 1 - 122 C 4 are coupled to a primary winding 108 A- 108 C and the first end 124 of some of the third windings 122 A 1 - 122 C 4 are coupled to some of the secondary windings 116 A 1 - 116 C 3 with the third group of windings 106 configured with respect to the first group of windings 102 and the second group of windings 104 such that the output voltage Vout 2 at the second end 126 of the third winding 122 A 1 - 122 C 4 may be higher than the output voltage Vout 1 at the second end 120 of the secondary windings 116 A 1 - 116 C 3 and the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C.

In one embodiment, some of the first end of a third winding may be coupled to an interior junction of primary winding. For example, the first end 124 of third winding 122 A 2 may be coupled to the interior junction 112 A 1 of the primary winding 108 A. Similarly the first end 124 of the third winding 122 A 4 may be coupled to the interior junction 112 A 3 of the primary winding 108 A.

In one embodiment, some of the first end of third winding may be coupled to the second end 120 of secondary winding. For example, the first end 124 of third winding 122 A 3 may be coupled to the second end 120 of secondary winding 116 A 2 .

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example, 122 A 4 - 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 4 , 122 B 1 - 122 B 4 and 122 C 1 - 122 C 4 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 as the second end 120 of secondary windings 116 A 1 - 116 A 3 , 116 B 1 - 116 B 3 and 116 C 1 - 116 C 3 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 5A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 11 are shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 5 . Similarly, secondary windings 116 A 1 and 116 A 3 each have substantially same number of turns, for example, N 7 . Similarly, third windings 122 A 1 and 122 A 1 each have substantially same number of turns, for example, N 6 .

Now referring to FIG. 5B , an exemplary phasor diagram 530 for the multi-phase transformer 500 of FIG. 5A is disclosed.

The phasor diagram 530 includes a first circle 532 and a second circle 534 , both having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 -A 4 , B 1 -B 4 and C 1 -C 4 correspond to the interior junctions 112 A 1 - 112 A 4 , 112 B 1 - 112 B 4 and 112 C 1 - 112 C 4 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 , A 2 -A 3 , A 3 -A 4 and A 4 -B represent sub-primary windings 108 A 1 - 108 A 5 respectively. Similarly, Lines B-B 1 , B 1 -B 2 , B 2 -B 3 , B 3 -B 4 and B 4 -C represent sub-primary windings 108 B 1 - 108 B 5 respectively. Similarly, lines C-C 1 , C 1 -C 2 , C 2 -C 3 , C 3 -C 4 and C 4 -A represent sub-primary windings 108 A 1 - 108 A 5 respectively.

Points A 1 V 1 -A 3 V 1 , B 1 V 1 -B 3 V 1 and C 1 V 1 -C 3 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 3 , 116 B 1 - 166 B 3 and 116 C 1 - 116 C 3 respectively. Similarly points AV 2 -A 3 V 2 , BV 2 -B 3 V 2 and CV 2 -C 3 V 2 represent the second end 126 or the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 respectively.

For example, lines A 2 -A 1 V 1 , A 4 -A 2 V 1 , A 4 -A 3 V 1 ; B 2 -B 1 V 1 , B 4 -B 2 V 1 , B 4 -B 3 V 1 and C 2 -C 1 V 1 , C 4 -C 2 V 1 , C 4 -C 3 V 1 represent the secondary windings 116 A 1 - 116 A 3 , 115 B 1 - 116 B 3 and 116 C 1 - 116 C 3 respectively.

Lines A-AV 2 , A 1 -A 1 V 2 , A 2 V 1 -A 2 V 2 , A 3 - 3 V 2 represent third windings 122 A 1 - 122 A 4 respectively. Similarly, B-BV 2 , B 1 -B 1 V 2 , B 2 V 1 -B 2 V 2 , B 3 -B 3 V 2 represent third windings 122 B 1 - 122 B 4 respectively. And, lines C-CV 2 , C 1 -C 1 V 2 , C 2 V 1 -C 2 V 2 , C 3 -C 3 V 2 represent third windings 122 C 1 - 122 C 4 respectively.

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 5 for sub-primary winding 108 A 1 . Similarly, the length of line A 2 -A 1 V 1 represent number of turns N 7 for secondary winding 116 A 1 . And, the length of line A 1 -A 1 V 2 represent the number of turns N 11 for third winding 122 A 2 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 522 and 524 represent the vector of induced voltage in the secondary winding 116 A 1 and 116 A 2 respectively. The arrows 526 and 528 represent the vector or inducted voltage in the third winding 122 A 2 and 122 A 3 .

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 530 shows an exemplary vector induced voltage in the secondary windings and the third windings.

Another embodiment of a multi-phase transformer is described with reference to FIGS. 6A and 6B . Transformer 600 is an exemplary nine phase or eighteen pulse multi-phase transformer. The multi-phase transformer 600 described with reference to FIGS. 6A and 6B is similar to the multi-phase transformer 500 described with reference to FIGS. 5A and 5B in that multi-phase transformer 600 has a primary group of windings 102 , secondary group of windings 104 and third group of windings 106 . One of the differences is that some of the third windings of the third group of windings include at least two sub-windings connected in series. One other difference is that all the third windings are coupled only to an exterior junction.

Referring to FIG. 6A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 3 , 108 B 1 - 108 B 3 , 108 C 1 - 108 C 3 that are coupled in series. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 ant 108 A 2 coupled in series define an interior junction 112 A 1 and the junction of sub primary windings 108 A 2 and 108 A 3 coupled in series define an interior junction 112 A 2 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 . Each secondary winding 116 A 1 - 116 C 2 has a first end 118 and a second end 120 . Each secondary winding 116 A 1 - 116 C 2 may be magnetically coupled to one the primary windings 108 A- 108 C. The first end 118 of each secondary winding 116 A 1 - 116 C 2 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary winding 116 A 1 may be coupled interior junction 112 A 1 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 . Each third winding 122 A 1 - 122 C 3 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 3 may be magnetically coupled to one of the primary windings 108 A- 108 C.

Some of the third windings include at least two sub-windings connected in series. For example, third windings 122 A 1 , 122 B 1 and 122 C 1 have at least two sub-windings. For example, third winding 122 A 1 has a first sub-winding 122 A 11 and a second sub-winding 122 A 12 connected in series at one end. The other end of first sub-winding 122 A 11 corresponds to the first end 124 of third winding 122 A 1 . The other end of second sub-winding 122 A 12 corresponds to the second end 126 of third winding 122 A 1 .

The first end 124 of all of the third windings 122 A 1 - 122 C 3 are coupled to a primary winding 108 A- 108 C. In some embodiments, the first end 124 of the third windings 122 A 1 - 122 C 3 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third windings 122 A 1 , 122 A 2 and 122 C 3 are coupled to exterior junction 114 A.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example, 122 A 3 - 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 6A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-winding having substantially same number of turns. For example, the number of turns N 1 -N 5 are shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 5 . Similarly, secondary windings 116 A 1 and 116 A 2 each have substantially same number of turns, for example, N 3 . Similarly, third windings 122 A 2 and 122 A 3 each have substantially same number of turns, for example, N 4 . Similarly, first sub-winding 122 A 11 and the second sub-winding 122 A 12 each have substantially same number of turns, for example, N 5 .

Now referring to FIG. 6B , an exemplary phasor diagram 630 for the multi-phase transformer 600 at FIG. 6A is disclosed.

The phasor diagram 630 includes a first circle 632 and a second circle 634 , both having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA or triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 -A 2 , B 1 -B 2 and C 1 -C 2 correspond to the interior junctions 112 A 1 - 112 A 2 , 112 B 1 - 112 B 2 and 112 C 1 - 112 C 2 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 , and A 2 -B represent sub-primary windings 108 A 1 - 108 A 3 respectively. Similarly, Lines B-B 1 , B 1 -B 2 , B 2 -C represent sub-primary windings 108 B 1 - 108 B 3 respectively. Similarly, lines C-C 1 , C 1 -C 2 and C 2 -A represent sub-primary windings 108 C 1 - 108 C 3 respectively.

Points A 1 V 1 -A 2 V 1 , B 1 V 1 -B 2 V 1 ant C 1 V 1 -C 2 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 166 B 2 and 116 C 1 - 116 C 2 respectively. Similarly points AV 2 , A 1 V 2 and A 2 V 2 ; BV 2 , B 1 V 2 and B 2 V 2 ; and CV 2 , C 1 V 2 and C 2 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 respectively.

For example, lines A 1 -A 1 V 1 , A 2 -A 2 V 1 ; B 1 -B 1 V 1 , B 2 -B 2 V 1 and C 1 -C 1 V 1 , C 2 -C 2 V 1 represent the secondary windings 116 A 1 - 116 A 2 , 115 B 1 - 116 B 2 and 116 C 1 - 116 C 2 respectively.

Lines A-A 1 V 2 , B-A 2 V 2 , B-B 1 V 2 , C-B 2 V 2 , C-C 1 V 2 and A-C 2 V 2 represent third windings 122 A 2 , 122 A 3 , 122 B 2 , 122 B 3 , 122 C 2 and 122 C 3 respectively. As previously discussed, some of the third windings include at least two sub-windings connected in series, for example, third winding 122 A 1 . The line A-A′, B-B′ and C-C′ represent the first sub-windings 122 A 11 , 122 B 11 and 122 C 11 of third windings 122 A 1 , 122 B 1 and 122 C 1 respectively. Similarly, the line A′-AV 2 , B′-BV 2 and C′-CV 2 represent the second sub-windings 122 A 12 , 122 B 12 and 122 C 12 of third windings 122 A 1 , 122 B 1 and 122 C 1 .

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 2 for sub-primary winding 108 A 1 . Similarly, the length of line A 1 -A 11 represent number of turns N 3 for secondary winding 116 A 1 . And, the length of line A-A 1 V 2 represent the number of turns N 4 for third winding 122 A 2 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage in the secondary winding 116 A 1 and 116 A 2 respectively. The arrows 546 and 548 represent the vector of inducted voltage in the third winding 122 A 2 and 122 A 3 .

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 degrees out at phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings of the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-winding of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 630 shows an exemplary vector of induced voltage in the secondary windings and the third windings.

Another embodiment of a multi-phase transformer is described with reference to FIGS. 7A and 7B . Transformer 700 is an exemplary nine phase or eighteen pulse multi-phase transformer. The multi-phase transformer 700 described with reference to FIGS. 7A and 7B is similar to the multi-phase transformer 600 described with reference to FIGS. 6A and 6B in that multi-phase transformer 700 has a primary group of windings 102 , secondary group of windings 104 and third group of windings 106 . In addition, some of the third windings of the third group of windings include at least two sub-windings connected in series. One difference is that some of the third windings are coupled to interior junctions of the primary windings.

Referring to FIG. 7A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 4 , 108 B 1 - 108 B 4 , 108 C 1 - 108 C 4 that are coupled in series. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 and 108 A 2 coupled in series define an interior junction 112 A 1 and the junction of sub primary windings 108 A 2 and 108 A 3 coupled in series define an interior junction 112 A 2 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 . Each secondary winding 116 A 1 - 116 C 2 has a first end 118 and a second end 120 . Each secondary winding 116 A 1 - 116 C 2 may be magnetically coupled to one of the primary windings 108 A- 108 C. The first end 118 of each secondary winding 116 A 1 - 116 C 2 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary winding 116 A 1 may be coupled to interior junction 112 A 2 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 . Each third winding 122 A 1 - 122 C 3 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 3 may be magnetically coupled to one of the primary windings 108 A- 108 C.

Some of the third windings include at least two sub-windings connected in series. For example, third windings 122 A 3 , 122 B 3 and 122 C 3 have at least two sub-windings. For example, third winding 122 A 3 has a first sub-winding 122 A 31 and a second sub-winding 122 A 32 connected in series at one end. The other end of first sub-winding 122 A 31 corresponds to the first end 124 of third winding 122 A 3 . The other end of second sub-winding 122 A 32 corresponds to the second end 126 of third winding 122 A 3 .

The first end 124 of all of the third windings 122 A 1 - 122 C 3 are coupled to a primary winding 108 A- 108 C. In some embodiments, the first end 124 of the third windings without sub-windings and with sub-windings are coupled to one of the exterior junctions 114 A- 114 C. For example, third windings 122 A 1 and 122 B 3 are coupled to one of the exterior junctions, for example, exterior junction 114 A. In some embodiments, the first end 124 of the third windings are coupled to one of the interior junctions of the primary windings. For example, the first end 124 of the third windings 122 A 2 , 122 B 2 and 122 C 2 are coupled to interior junctions 112 A 1 , 112 B 1 and 112 C 1 respectively.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example, 122 A- 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 7A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 9 are shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 6 . Similarly, secondary windings 116 A 1 and 116 A 2 each have substantially same number of turns, for example, N 3 . Similarly, third windings 122 A 2 , 122 B 2 and 122 C 2 each have substantially same number of turns, for example, N 4 . Similarly, first sub-winding 122 A 31 and first sub-winding 122 B 31 each have substantially same number of turns, for example, N 7 .

Now referring to FIG. 7B , an exemplary phasor diagram 730 for the multi-phase transformer 700 of FIG. 7A is disclosed.

The phasor diagram 730 includes a first circle 736 and a second circle 734 , both having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 -A 3 , B 1 -B 3 and C 1 -C 3 correspond to the interior junctions 112 A 1 - 112 A 3 , 112 B 1 - 112 B 3 and 112 C 1 - 112 C 3 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 , A 2 -A 3 and A 3 -B represent sub-primary windings 108 A 1 - 108 A 4 respectively. Similarly, Lines B-B 1 , B 1 -B 2 , B 2 -B 3 and B 3 -C represent sub-primary windings 108 B 1 - 108 B 4 respectively. Similarly, lines C-C 1 , C 1 -C 2 , C 2 -C 3 and C 3 -A represent sub-primary windings 108 C 1 - 108 C 4 respectively.

Points A 1 V 1 -A 2 V 1 , B 1 V 1 -B 2 V 1 and C 1 V 1 -C 2 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 166 B 2 and 116 C 1 - 116 C 2 respectively. Similarly points AV 2 , A 1 V 2 and A 2 V 2 ; BV 2 , B 1 V 2 and B 1 V 2 ; and CV 1 , C 1 V 2 and C 2 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 respectively.

For example, lines A 2 -A 1 V 1 , A 3 -A 2 V 1 ; B 2 -B 1 V 1 , B 3 -B 2 V 1 and C 2 -C 1 V 1 , C 3 -C 2 V 1 represent the secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 respectively.

Lines A-AV 2 , A 1 -A 1 V 2 , B-BV 2 , B 1 -B 1 V 2 , C-CV 2 , C 1 -C 1 V 2 represent third windings 122 A 1 , 122 A 2 , 122 B 1 , 122 B 2 , 122 C 1 and 122 C 2 respectively. As previously discussed, some of the third windings include at least two sub-windings connected in series, for example, third winding 122 A 3 . The line A-A′, B-B′ and C-C′ represent the first sub-windings 122 C 31 , 122 A 31 and 122 B 31 of third windings 122 C 1 , 122 A 1 and 122 B 1 respectively. Similarly, the line A′-C 2 V 2 , B′-A 2 V 2 and C′-B 2 V 2 represent the second sub-windings 122 C 32 , 122 A 32 and 122 B 32 of third windings 122 C 1 , 122 A 1 and 122 B 1 .

As previously discussed, the length or lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 6 for sub-primary winding 108 A 1 . Similarly, the length of line A 2 -A 1 V 1 represent number of turns N 3 for secondary winding 116 A 1 . And, the length of line A 1 -A 1 V 2 represent the number of turns N 4 for third winding 122 A 2 .

The lines SA, SB and SC represent the input AC voltage Vin applied tm the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage in the secondary winding 116 A 1 and 116 A 2 respectively. The arrows 546 and 548 represent the vector of inducted voltage in the third winding 122 A 2 and the first sub-winding 122 A 31 of third winding 122 A 3 .

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings of the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-winding of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 730 shows an exemplary vector of induced voltage in the secondary windings and the third windings of auto transformer 700 .

Another embodiment of a multi-phase transformer is described with reference to FIGS. 8A and 8B . Transformer 800 is another exemplary twelve phase or twenty four pulse multi-phase transformer. The multi-phase transformer 800 described with reference to FIGS. 8A and 8B is similar to the multi-phase transformer 600 described with reference to FIGS. 6A and 6B in that multi-phase transformer 800 has a primary group of windings 102 , secondary group of windings 104 and third group of windings 106 . One of the similarities is that some of the third windings of the third group of windings include at least two sub-windings connected in series. One other difference is that some of the third windings are also coupled to second end of secondary windings.

Referring to FIG. 8A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 3 , 108 B 1 - 108 B 3 , 108 C 1 - 108 C 3 that are coupled in series. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 and 108 A 2 coupled in series define an interior junction 112 A 1 and the junction of sub primary windings 108 A 2 and 108 A 3 coupled in series define an interior junction 112 A 2 . Each ends of the primary windings 108 A- 108 C are coupled to one ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 3 , 116 B 1 - 116 B 3 and 116 C 1 - 116 C 3 . Each secondary winding 116 A- 116 C 3 has a first end 118 and a second end 120 . Each secondary winding 116 A 1 - 116 C 3 may be magnetically coupled to one of the primary windings 108 A- 108 C. The first end 118 of each secondary winding 116 A 1 - 116 C 3 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary winding 116 A 1 may be coupled to interior junction 112 A 1 of primary winding 108 A.

In one embodiment, two first ends 118 of secondary windings are coupled to the same interior junction of primary winding. For example, first ends 118 of secondary windings 116 A 2 and 116 A 3 are coupled to the same interior junction 112 A 2 .

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 4 , 122 B 1 - 122 B 4 and 122 C 1 - 112 C 4 .

Each third winding 122 A 1 - 122 C 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 4 may be magnetically coupled to one of the primary windings 108 A- 108 C.

Some of the third windings include at least two sub-windings connected in series. For example, third windings 122 A 1 , 122 A 3 , 122 B 1 , 122 B 3 , 122 C 1 and 122 C 3 have at least two sub-windings. For example, third winding 122 A 1 has a first sub-winding 122 A 11 and a second sub-winding 122 A 12 connected in series at one end. The other end of first sub-winding 122 A 11 corresponds to the first end 124 of third winding 122 A 1 . The other end of second sub-winding 122 A 12 corresponds to the second end 126 of third winding 122 A 1 .

The first end 124 of some of the third windings 122 A 1 - 122 C 4 are coupled to a primary winding 108 A- 108 C. In some embodiments, the first end 124 of some of the third windings 122 A 1 - 122 C 4 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third windings 122 A 1 , 122 B 1 and 122 C 1 are coupled to exterior junction 114 A, 114 B and 114 C respectively.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example, 122 A 4 - 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 4 , 122 B 1 - 122 B 4 and 122 C 1 - 122 C 4 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 3 , 116 B 1 - 116 B 3 and 116 C 1 - 116 C 3 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 8A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 8 are shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 3 . Similarly, secondary windings 116 A 1 and 116 A 3 each have substantially same number of turns, for example, N 4 . Similarly, third windings 122 A 2 and 122 A 4 each have substantially same number of turns, for example, N 5 . Similarly, first sub-winding 122 A 11 and the first sub-winding 122 B 11 each have substantially same number of turns, for example, N 6 .

Now referring to FIG. 8B , an exemplary phasor diagram 830 for the multi-phase transformer 800 of FIG. 8A is disclosed.

The phasor diagram 830 includes a first circle 832 and a second circle 834 , both having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 -A 2 , B 1 -B 2 and C 1 -C 2 correspond to the interior junctions 112 A 1 - 112 A 2 , 112 B 1 - 112 B 2 and 112 C 1 - 112 C 2 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 , and A 2 -B represent sub-primary windings 108 A 1 - 108 A 3 respectively. Similarly, Lines B-B 1 , B 1 -B 2 , B 2 -C represent sub-primary windings 108 B 1 - 108 B 3 respectively. Similarly, lines C-C 1 , C 1 -C 2 , and C 2 -A represent sub-primary windings 108 C 1 - 108 C 3 respectively.

Points A 1 V 1 -A 3 V 1 , B 1 V 1 -B 3 V 1 and C 1 V 1 -C 3 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 3 , 116 B 1 - 166 B 3 and 116 C 1 - 116 C 3 respectively. Similarly points AV 2 , A 1 V 2 , A 2 V 2 and A 3 V 2 ; BV 2 , B 1 V 2 , B 2 V 2 and B 3 V 2 ; and CV 2 , C 1 V 2 , C 2 V 2 and C 3 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 4 , 122 B 1 - 122 B 4 and 122 C 1 - 122 C 4 respectively.

For example, lines A 1 -A 1 V 1 , A 2 -A 2 V 1 , A 2 -A 3 V 1 ; B 1 -B 1 V 1 , B 2 -B 2 V 1 , B 2 -B 3 V 1 and C 1 -C 1 V 1 , C 2 -C 2 V 1 , C 2 -C 3 V 1 represent the secondary windings 116 A 1 - 116 A 3 , 115 B 1 - 116 B 3 and 116 C 1 - 116 C 3 respectively.

Lines A 1 V 1 -A 1 V 2 , A 3 V 1 -A 3 V 2 , B 1 V 1 -B 1 V 2 , B 3 V 1 -B 3 V 2 , C 1 V 1 -C 1 V 2 and C 3 V 1 -C 3 V 2 represent third windings 122 A 2 , 122 A 4 , 122 B 2 , 122 B 4 , 122 C 2 and 122 C 4 respectively. As previously discussed, some of the third windings include at least two sub-windings connected in series, for example, third winding 122 A 1 . For example, line A-A′, B-B′ and C-C′ represent the first sub-windings 122 A 11 , 122 B 11 and 122 C 11 of third windings 122 A 1 , 122 B 1 and 122 C 1 respectively. Similarly, the line A′-AV 2 , B′-BV 2 and C′-CV 2 represent the second sub-windings 122 A 12 , 122 A 12 and 122 C 12 of third windings 122 A 1 , 122 B 1 and 122 C 1 .

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 3 for sub-primary winding 108 A 1 . Similarly, the length of line A 1 -A 1 V 1 represent number of turns N 4 for secondary winding 116 A 1 . And, the length of line A 1 V 1 -A 1 V 2 represent the number of turns N 5 for third winding 122 A 2 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phase_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage in the secondary winding 116 A 1 and 116 A 2 respectively. The arrows 546 and 548 represent the vector of inducted voltage in the third winding 122 A 2 and 122 A 4 .

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 decrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings of the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-winding of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 830 shows an exemplary vector of induced voltage in the secondary windings and the third windings.

Another embodiment of a multi-phase transformer is described with reference to FIGS. 9A and 9B . The multi-phase transformer 900 described with reference to FIGS. 9A and 9B is similar to the multi-phase transformer 300 described with reference to FIGS. 3A and 3B in that multi-phase transformer 900 has a primary group of windings 102 , secondary group of windings 104 and third group of windings 106 . In addition, all of the third windings of the third group of windings include at least two sub-windings connected in series.

Referring to FIG. 9A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 3 , 108 B 1 - 108 B 3 , 108 C 1 - 108 C 3 that are coupled in series. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 and 108 A 2 coupled in series define an interior junction 112 A 1 and the junction of sub primary windings 108 A 2 and 108 A 3 coupled in series define an interior junction 112 A 2 . Each ends of the primary windings 108 A- 103 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 . Each secondary winding 116 A 1 - 116 C 2 has a first end 118 and a second end 120 . Each secondary winding 116 A 1 - 116 C 2 may be magnetically coupled to one of the primary windings 108 A- 108 C. The first end 118 of each secondary winding 116 A 1 - 116 C 2 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary winding 116 A 1 may be coupled to interior junction 112 A 1 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 . Each third winding 122 A 1 - 122 C 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 4 may be magnetically coupled to one of the primary windings 108 A- 108 C.

In one embodiment, all of the third windings include at least two sub-windings connected in series. For example, third windings 122 A 1 , 122 B 1 and 122 C 1 have at least two sub-windings. For example, third winding 122 A 1 has a first sub-winding 122 A 11 and a second sub-winding 122 A 12 connected in series at one end. The other end of first sub-winding 122 A 11 corresponds to the first end 124 of third winding 122 A 1 . The other end of second sub-winding 122 A 12 corresponds to the second end 126 of third winding 122 A 1 .

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 3 are coupled to a primary winding 108 A- 108 C. For example, some of the first end 124 of the third windings 122 A 1 - 122 C 3 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third windings 122 A 1 , 122 B 1 and 122 C 1 are coupled to exterior junction 114 A- 114 C respectively.

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 3 are coupled to the second end 120 of the secondary windings 116 A 1 - 116 C 2 . For example, the first end 124 of the third windings 122 A 2 , 122 A 3 , 122 B 2 , 122 B 3 , 122 C 2 and 122 C 3 are coupled to second end 120 of secondary winding 116 A 1 , 116 A 2 , 116 B 1 , 116 B 2 , 116 C 1 and 11612 respectively.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example, 122 A 3 - 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 9A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 6 are shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 2 . Similarly, secondary windings 116 A 1 and 116 A 2 each have substantially same number of turns, for example, N 3 . Similarly, first sub-winding 122 A 11 and the second sub-winding 122 A 12 each have substantially same number of turns, for example, N 5 .

Now referring to FIG. 9B , an exemplary phasor diagram 930 for the multi-phase transformer 900 of FIG. 9A is disclosed.

The phasor diagram 930 includes a first circle 632 and a second circle 634 , both having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 -A 2 , B 1 -B 2 C 1 -C 2 correspond to the interior junctions 112 A 1 - 112 A 2 , 112 B 1 - 112 B 2 and 112 C 1 - 112 C 2 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 , and A 2 -B represent sub-primary windings 108 A 1 - 108 A 3 respectively. Similarly, Lines B-B 1 , B 1 -B 2 , B 2 -C represent sub-primary windings 108 B 1 - 108 B 3 respectively. Similarly, lines C-C 1 , C 1 -C 2 , and C 2 -A represent sub-primary windings 108 C 1 - 108 C 3 respectively.

Points A 1 V 1 -A 2 V 1 , B 1 V 1 -B 2 V 1 and C 1 V 1 -C 2 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 166 B 2 and 116 C 1 - 116 C 2 respectively. Similarly points AV 2 , A 1 V 2 and A 2 V 2 ; BV 2 , B 1 V 2 and B 2 V 2 ; and CV 2 , C 1 V 2 and C 2 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 respectively.

For example, lines A 1 -A 1 V 1 , A 2 -A 2 V 1 ; B 1 -B 1 V 1 , B 2 -B 2 V 1 and C 1 -C 1 V 1 , C 2 -C 2 V 1 represent the secondary windings 116 A 1 - 116 A 2 , 115 B 1 - 116 B 2 and 116 C 1 - 116 C 2 respectively.

As previously discussed, all of the third windings include at least two sub-windings connected in series, for example, third winding 122 A 1 . For example, the lines A-A′, B-B′ and C-C′ represent the first sub-windings 122 A 11 , 122 B 11 and 122 C 11 of third windings 112 A 1 , 122 B 1 and 122 C 1 respectively. Similarly, the line A′-AV 2 , B′-BV 2 and C′-CV 2 represent the second sub-windings 121 A 12 , 122 B 12 and 122 C 12 of third windings 122 A 1 , 122 B 1 and 122 C 1 .

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 2 for sub-primary winding 108 A 1 . Similarly, the length of line A 1 -A 1 V 1 represent number of turns N 3 for secondary winding 116 A 1 . And, the length of line A-A′ represent the number of turns N 5 for third sub-winding 122 A 11 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 280 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage in the secondary winding 116 A 1 and 116 A 2 respectively. The arrows 546 and 548 represent the vector of inducted voltage in the third sub-winding 122 A 11 and 122 A 12 .

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings of the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-winding of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage to adjacent second ends of the third windings are substantially same.

The phasor diagram 930 shows an exemplary vector of induced voltage in the secondary windings and the third windings.

In one embodiment, for a third winding coupled to a second winding (for example, third winding 122 A 3 coupled to second winding 116 A 2 ), the vector of induced voltage in the first sub-winding ( 122 A 31 ) may be 180 degrees out of phase with the vector of induced voltage in a primary winding other than the primary winding to which the corresponding secondary winding is coupled and that is different than the primary winding that is in-phase with the corresponding second winding (primary winding 108 B) and the vector of induced voltage in the second sub-winding ( 122 A 32 ) is in phase with the vector of induced voltage in a primary winding other than the primary winding to which the corresponding secondary winding may be coupled and that may be different than the primary winding that may be in-phase with the second winding (primary winding 108 C).

In one embodiment, for the third winding coupled to an external junction of a primary winding (example, third winding 122 A 1 ), the vector of induced voltage in the first sub-winding ( 122 A 11 ) may be in phase with the vector of induced voltage in a primary winding coupled to the external junction (primary winding 108 A) and the vector of induced voltage in the second sub-winding ( 122 A 12 ) may be 180 degrees out of phase with the vector of induced voltage in a primary winding coupled to the external junction that is different than the primary winding that may be in phase with the first sub-winding (primary winding 108 A).

Another embodiment of a multi-phase transformer is described with reference to FIGS. 10A and 10B . Transformer 1000 is an exemplary fifteen phase or thirty pulse multi-phase transformer. The multi-phase transformer 1000 described with reference to FIGS. 10A and 10B is similar to the multi-phase transformer 900 described with reference to FIGS. 9A an 9 B in that multi-phase transformer 1000 has a primary group of windings 102 , secondary group of windings 104 and third group of windings 105 . In addition, all of the third windings of the third group of windings include at least two sub-windings connected in series.

Referring to FIG. 10A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 5 , 108 B 1 - 108 B 5 , 108 C 1 - 108 C 5 that are coupled in series. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 and 108 A 2 coupled in series define an interior junction 112 A 1 and the junction of sub primary windings 108 A 2 and 108 A 3 coupled in series define an interior junction 112 A 2 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 4 , 116 B 1 - 116 B 4 and 116 C 1 - 116 C 4 . Each secondary winding 116 A 1 - 116 C 4 has a first end 118 and a second end 120 . Each secondary winding 116 A 1 - 116 C 4 may be magnetically coupled to one of the primary windings 108 A- 108 C. The first end 118 of each secondary winding 116 A 1 - 116 C 4 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary wincing 116 A 1 may be coupled to interior junction 112 A 1 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 5 , 122 B 1 - 122 B 5 and 122 C 1 - 122 C 5 . Each third winding 122 A 1 - 122 C 5 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 5 may be magnetically coupled to one of the primary windings 108 A- 108 C.

In one embodiment, all of the third windings include at least two sub-windings connected in series. For example, third windings 122 A 1 , 122 B 1 and 122 C 1 have at least two sub-windings. For example, third winding 122 A 1 has a first sub-winding 122 A 11 and a second sub-winding 122 A 12 connected in series at one end. The other end of first sub-winding 122 A 11 corresponds to the first end 124 of third winding 122 A 1 . The other end of second sub-winding 122 A 12 corresponds to the second end 126 of third winding 122 A 1 .

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 5 are coupled to a primary winding 108 A- 108 C. For example, some of the first end 124 of the third windings 122 A 1 - 122 C 5 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third windings 122 A 1 , 122 B 1 and 122 C 1 are coupled to exterior junction 114 A- 114 C respectively.

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 5 are coupled to the second end 120 of the secondary windings 116 A 1 - 116 C 4 . For example, the first end 124 of the third windings 122 A 2 , 122 A 3 , 122 A 4 and 122 A 5 are coupled to second end 120 of secondary winding 116 A 1 , 116 A 2 , 116 A 3 and 116 A 4 respectively.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, The phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third winding 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example, 122 A 3 - 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 5 , 122 B 1 - 122 B 5 and 122 C 1 - 122 C 5 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 4 , 116 B 1 - 116 B 4 and 116 C 1 - 116 C 4 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 10A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 13 a shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 2 . Similarly, secondary windings 116 A 1 and 116 A 4 each have substantially same number of turns, for example, N 4 . Similarly, first sub-winding 122 A 11 and the first sub-winding 122 B 11 each have substantially same number of turns, for example, N 6 .

Now referring to FIG. 10B , an exemplary phasor diagram 1030 for the multi-phase transformer 1000 of FIG. 10A is disclosed.

The phasor diagram 1030 includes a first circle 1032 and a second circle 1034 , both having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 -A 4 , B 1 -B 4 and C 1 -C 4 correspond to the interior junctions 112 A 1 - 112 A 4 , 112 B 1 - 112 B 4 and 112 C 1 - 112 C 4 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 , A 2 -A 3 , A 3 -A 4 and A 4 -B represent sub-primary windings 108 A 1 - 108 A 5 respectively. Similarly, Lines B-B 1 , B 1 -B 2 , B 2 -B 3 , B 3 -B 4 and B 4 -C represent sub-primary windings 108 B 1 - 108 B 5 respectively. Similarly, lines C-C 1 , C 1 -C 2 , C 2 -C 3 , C 3 -C 4 and C 4 -A represent sub-primary windings 108 C 1 - 108 C 5 respectively.

Points A 1 V 1 -A 4 V 1 , B 1 V 1 -B 4 V 1 and C 1 V 1 -C 4 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 4 , 116 B 1 - 166 B 4 and 116 C 1 - 116 C 4 respectively. Similarly points AV 2 , A 1 V 2 -A 4 V 2 ; BV 2 , B 1 V 2 -B 4 V 2 ; and CV 2 , C 1 V 2 -C 4 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 4 , 122 B 1 - 122 B 4 and 122 C 1 - 122 C 4 respectively.

For example, lines Al-A 1 V 1 , A 2 -A 3 V 1 , A 3 -A A 4 -A 4 V 1 ; B 1 -B 1 V 1 , B 2 -B 3 V 1 , B 3 -B 2 V 1 , B 4 -B 4 V 1 and C 1 -C 1 V 1 , C 2 -C 3 V 1 , C 3 -C 2 V 1 , C 4 -C 4 V 1 represent the secondary windings 116 A 1 - 116 A 4 , 115 B 1 - 116 B 4 and 116 C 1 - 116 C 4 respectively.

As previously discussed, all of the third windings include at least two sub-windings corrected in series, for example, third winding 122 A 1 . For example, the lines A-A′, B-B′ and C-C′ represent the first sub-windings 122 A 11 , 122 B 11 and 122 C 11 of third windings 122 A 1 , 122 B 1 and 122 C 1 respectively. Similarly, the line A′-AV 2 , B′-BV 2 and C′-CV 2 represent the second sub-windings 122 A 12 , 122 B 12 and 122 C 12 of third windings 122 A 1 , 122 B 1 and 122 C 1 .

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 2 for sub-primary winding 108 A 1 . Similarly, the length of line A 1 -A 1 V 1 represent number of turns N 4 for secondary winding 116 A 1 . And, the length of line A-A′ represent the number of turns N for third sub-winding 122 A 11 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage in the secondary winding 116 A 1 and 116 A 2 respectively. The arrows 546 and 548 represent the vector of inducted voltage in the third sub-winding 122 A 11 and 122 A 12 .

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings of the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-winding of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 1030 shows an exemplary vector of induced voltage in the secondary windings and the third windings.

Another embodiment of a multi-phase transformer is described with reference to FIGS. 11A and 11B . Transformer 1100 is another exemplary nine phase or eighteen can pulse multi-phase transformer. The multi-phase transformer 1100 described with reference to FIGS. 11A and 11B is similar to the multi-phase transformer 900 described with reference to FIGS. 9A and 9B in that multi-phase transformer 900 has a primary group of windings 101 , secondary group of windings 104 and third group of windings 106 . In addition, all of the third windings of the third group of windings include at least two sub-windings connected in series. One of the differences is that the secondary windings include a plurality of sub-windings connected in series. The junction of two sub-windings of the secondary windings defines a sub-junction of the secondary winding. Also, some of the third windings are coupled to a sub-junction of the secondary windings.

Referring to FIG. 11A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 3 , 108 B 1 - 108 B 3 , 108 C 1 - 108 C 3 that are coupled in series. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 and 108 A 2 coupled in series define an interior junction 112 A 1 and the junction of sub primary windings 108 A 2 and 108 A 3 coupled in series define an interior junction 112 A 2 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 . Each secondary winding 116 A 1 - 116 C 2 has a first end 118 and a second end 120 . Each secondary winding includes at least a first sub-winding and a second sub-winding connected in series at a sub-junction.

For example, the secondary winding 116 A 1 includes a first sub-winding 116 A 11 and a second sub-winding 116 A 12 and coupled an series at one end to define a sub-junction 120 ′. The other end of first sub-winding 116 A 11 corresponds to the first end 118 of secondary winding 116 A 1 . The other end of second sub-winding 116 A 12 corresponds to the second end 120 of secondary winding 116 A 1 .

Each secondary winding 116 A 1 - 116 C 2 may be magnetically coupled to one of the primary windings 108 A- 108 C. In one embodiment, each of the sub-winding for example, first sub-winding and second sub-winding may be magnetically coupled to different primary windings. The first end 118 of each secondary winding 116 A 1 - 116 C 2 may be coupled to one of the primary windings 108 A- 108 B. For example, the first end 118 of secondary winding 116 A 1 may be coupled to interior junction 112 A 1 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 . Each third winding 122 A 1 - 122 C 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 4 may be magnetically coupled to one of the primary windings 108 A- 108 C.

In one embodiment, all of the third windings include at least two sub-windings connected an series. For example, third windings 122 A 1 , 122 B 1 and 122 C 1 have at least two sub-windings. For example, third winding 122 A 1 has a first sub-winding 122 A 11 and a second sub-winding 122 A 12 connected in series at one end. The other end of first sub-winding corresponds to the first end 124 of third winding 122 A 1 . The other end of second sub-winding 122 A 12 corresponds to the second end 126 of third winding 122 A 1 .

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 3 are coupled to a primary winding 108 A- 108 C. For example, some of the first end 124 of the third windings 122 A 1 - 122 C 3 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third windings 122 A 1 , 122 B 1 and 122 C 1 are coupled to exterior junction 114 A- 114 C respectively.

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 3 are coupled to the sub-junction 120 ′ of the secondary windings 116 A 1 - 116 C 2 . For example, the first end 124 of the third windings 122 A 2 , 122 A 3 , 122 B 2 , 122 B 3 , 122 C 2 and 122 C 3 are coupled to sub-junction 120 ′ of secondary winding 116 A 1 , 116 A 2 , 116 B 1 , 116 B 2 , 116 C 1 and 116 C 2 respectively.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example, 122 A 3 - 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 1 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 11A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 7 are shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 2 . Similarly, sub-winding 116 A 11 of secondary winding 116 A 1 and sub-winding 116 A 21 of secondary winding 116 A 2 each have substantially same number of turns, or example, N 4 . Similarly, first sub-winding 122 A 11 and the second sub-winding 122 A 12 each have substantially same number of turns, for example, N 3 .

Now referring to FIG. 11B , an exemplary phasor diagram 1130 for the multi-phase transformer 1100 of FIG. 11A is disclosed.

The phasor diagram 1130 includes a first circle 1132 and a second circle 1134 , both having a common center S. The paints A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 -A 2 , B 1 -B 2 and C 1 -C 2 correspond to the interior junctions 112 A 1 - 112 A 2 , 122 B 1 - 112 B 2 and 112 C 1 - 112 C 2 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 , and A 1 -B represent sub-primary windings 108 A 1 - 108 A 3 respectively. Similarly, Lines B-B 1 , B 1 -B 2 , B 2 -C represent sub-primary windings 108 B 1 - 108 B 3 respectively. Similarly, lines C-C 1 , C 1 -C 2 , and C 2 -A represent sub-primary windings 108 C 1 - 108 C 3 respectively.

Points A 1 V 1 -A 2 V 1 , B 1 V 1 -B 2 V 1 and C 1 V 1 -C 2 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 166 B 2 and 116 C 1 - 116 C 2 respectively. Similarly points AV 2 , A 1 V 2 and A 2 V 2 ; BV 2 , B 1 V 2 and B 2 V 2 ; and CV 2 , C 1 V 2 and C 2 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 respectively.

As previously discussed, all of the secondary windings include at least two sub-windings connected in series, for example, secondary winding 116 A 1 . For example, the lines A 1 -A 1 ′, B 1 -B 1 ′ and C 1 -C 1 ′ represent the first sub-windings 116 A 11 , 116 B 11 and 116 C 11 of secondary windings 116 A 1 , 116 B 1 and 116 C 1 respectively. Similarly, the line A 1 ′-A 1 V 1 , B 1 ′-B 1 V 1 and C 1 ′-C 1 V 1 represent the second sub-windings 116 A 12 , 116 B 12 and 116 C 12 of secondary windings 116 A 1 , 116 B 1 and 116 C 1 .

As previously discussed, all of the third windings include at least two sub-windings connected in series, for example, third winding 122 A 1 . For example, the lines A-A′, B-B′ and C-C′ represent the first sub-windings 122 A 11 , 122 B 11 and 122 C 11 of third windings 122 A 1 , 122 B 1 and 122 C 1 respectively. Similarly, the line A′-AV 2 , B′-BV 2 and C′-CV 2 represent the second sub-windings 122 A 12 , 122 B 12 and 122 C 12 of third windings 122 A 1 , 122 B 1 and 122 C 1 .

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 2 for sub-primary winding 108 A 1 . Similarly, the length of line A 1 -A 1 ′ represent number of turns N 4 for sub-winding 116 A 11 of secondary winding 116 A 1 . And, the length of line A-A′ represent the number of turns N 5 for third sub-winding 122 A 11 of third winding 122 A 1 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phased_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage on the sub-winding 116 A 11 and 122 A 12 of secondary winding 116 A 1 and 116 A 2 respectively. The arrows 546 and 548 represent the vector of inducted voltage in the sub-winding 122 A 11 and 122 A 12 of third windings 122 A 1 .

In one embodiment, the vector of induced voltage in the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings of the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding or which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-winding of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 1130 shows an exemplary vector of induced voltage in the secondary windings and the third windings.

Another embodiment of a multi-phase transformer is described with reference to FIGS. 12A and 12B . Transformer 1200 is another exemplary nine phase or eighteen pulse multi-phase transformer. The multi-phase transformer 1200 described with reference to FIGS. 12A and 12B is similar to the multi-phase transformer 1100 described with reference to FIGS. 11A and 11B in that multi-phase transformer 1100 has a primary group of windings 102 , secondary group of windings 104 and third group of windings 106 . In addition, all of the secondary windings of the second group of windings include at least two sub-windings connected in series. Also, some of the third windings are coupled to a sub-junction of the secondary windings. One of the differences is that the third windings do not include a plurality of sub-windings connected in series.

Referring to FIG. 12A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 3 , 108 B 1 - 108 B 3 , 108 C 1 - 108 C 3 that are coupled in series. For example, for the primary wording 108 A, the junction of sub primary windings 108 A 1 and 10812 coupled in series define an interior junction 112 A 1 and the junction of sub primary windings 108 A 2 and 108 A 3 coupled in series define an interior junction 112 A 2 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 . Each secondary winding 116 A 1 - 116 C 2 has a first end 118 and a second end 120 . Each secondary winding includes at least a first sub-winding and a second sub-winding connected in series at a sub-junction.

For example, the secondary winding 116 A 1 includes a first sub-winding 116 A 11 and a second sub-winding 116 A 12 and coupled in series at one end to define a sub-junction 120 ′. The other end of first sub-winding 116 A 11 corresponds to the first end 118 of secondary winding 116 A 1 . The other end of second sub-winding 116 A 12 corresponds to the second end 120 of secondary winding 116 A 1 .

Each secondary winding 116 A 1 - 116 C 2 may be magnetically coupled to one of the primary windings 108 A- 108 C. In one embodiment, each of the sub-winding for example, first sub-winding and second sub-winding may be magnetically coupled to different primary windings. The first end 118 of each secondary winding 116 A 1 - 116 C 2 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary winding 116 A 1 may be coupled to interior junction 112 A 1 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 . Each third winding 122 A 2 - 122 C 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 4 may be magnetically coupled to one of the primary windings 108 A- 108 C.

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 3 are coupled to a primary winding 108 A- 108 C. For example, some of the first end 124 of the third windings 122 A 1 - 122 C 3 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third windings 122 A 1 , 122 B 1 and 122 C 1 are coupled to exterior junction 114 A- 114 C respectively.

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 3 are coupled to the sub-junction 120 ′ of the secondary windings 116 A 1 - 116 C 2 . For example, the first end 124 of the third windings 122 A 2 , 122 A 3 , 122 B 2 , 122 B 3 , 122 C 2 and 122 C 3 are coupled to sub-junction 120 ′ of secondary winding 116 A 1 , 116 A 2 , 116 B 1 , 116 B 2 , 116 C 1 and 116 C 2 respectively.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example, 122 A 3 - 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 12A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 10 are shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 3 . Similarly, sub-winding 116 A 11 of secondary winding 116 A 1 and sub-winding 116 B 11 of secondary winding 11631 each have substantially same number of turns, for example, N 4 . Similarly, third winding 122 A 1 and third winding 122 B 1 each have substantially same number of turns, for example, N 5 .

Now referring to FIG. 12B , an exemplary phasor diagram 1230 for the multi-phase transformer 1200 of FIG. 12A is disclosed.

The phasor diagram 1230 includes a first circle 1232 and a second circle 1234 , both haying a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 -A 2 , B 1 -B 2 and C 1 -C 2 correspond to the interior junctions 112 A 1 - 112 A 2 , 112 B 2 - 112 B 2 and 112 C 1 - 112 C 2 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 , and A 2 -B represent sub-primary windings 108 A 1 - 108 A 3 respectively. Similarly, Lines B-B 1 B 1 -B 2 , B 2 -C represent sub-primary windings 108 B 1 - 108 B 3 respectively. Similarly, lines C-C 1 , C 1 -C 2 , and C 2 -A represent sub-primary windings 108 C 1 - 108 C 3 respectively.

Points A 1 V 1 -A 2 V 1 , B 1 V 1 -B 2 V 1 and C 1 V 1 -C 2 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 166 B 2 and 116 C 1 - 116 C 2 respectively. Similarly points AV 2 , A 1 V 2 and A 2 V 2 ; BV 2 , B 1 V 2 and B 2 V 2 ; and CV 2 , C 1 V 2 and C 2 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 respectively.

As previously discussed, all of the secondary windings include at least two sub-windings connected in series, for example, secondary winding 116 A 1 . For example, the lines A 1 -A 1 ′, B 1 -B 1 ′ and C 1 -C 1 ′ represent the first sub-windings 116 A 11 , 116 B 11 and 116 C 11 of secondary windings 116 A 1 , 116 B 1 and 116 C 1 respectively. Similarly, the line A 1 ′-A 1 V 1 , B 1 ′-B 1 V 1 and C 1 ′-C 1 V 1 represent the second sub-windings 116 A 12 , 116 B 12 and 116 C 12 of secondary windings 116 A 1 , 116 B 1 and 116 C 1 .

The third windings are also represented in the phasor diagram. For example, the lines A-AV 2 , B-BV 2 and C-CV 2 represent the third windings 122 A 1 , 122 B 1 and 122 C 1 respectively. Similarly, the line A 1 ′-A 1 V 2 , B 1 ′-B 1 V 2 and C 1 ′-CV 2 represent the third windings 122 A 2 , 122 B 2 and 122 C 2 respectively.

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 3 for sub-primary winding 108 A 1 . Similarly, the length of line A 1 -A 1 ′ represent number of turns N 4 for sub-winding 116 A 11 of secondary winding 116 A 1 . And, the length of line A-AV 2 represent the number of turns N 5 for third winding 122 A 1 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage in the sub-winding 116 A 11 and 116 A 21 of secondary wind 116 A 1 and 116 A 2 respectively. The arrow 546 represents the vector of inducted voltage in the third winding 122 A 1 .

In one embodiment, the vector of induced voltage in the secondary windings and the sub-windings of the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same. In one embodiment, the first sub-winding and second sub-winding of a secondary winding may be magnetically coupled to two different primary windings.

In one embodiment, the vector of induced voltage in the third windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 1230 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings.

Another embodiment of a multi-phase transformer is described with reference to FIGS. 13A and 13B . Transformer 1300 is another exemplary nine phase or eighteen pulse multi-phase transformer. The multi-phase transformer 1300 described with reference to FIGS. 13A and 13 B is similar to the multi-phase transformer 1200 described with reference to FIGS. 12A and 12B in that multi-phase transformer 1300 has a primary group of windings 102 , secondary group of windings 104 and third group of windings 106 . In addition, all of the secondary windings of the second group of windings include at least two sub-windings connected in series. Also, some of the third windings are coupled to a sub-junction of the secondary windings. One of the differences is that some of the third windings include a plurality of sub-windings connected in series.

Referring to FIG. 13A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 2 , 108 B 1 - 108 B 2 , 108 C 1 - 108 C 2 that are coupled in series. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 and 108 A 2 coupled in series define an interior junction 112 A 1 and the junction of sub primary windings 108 B 1 and 108 B 2 coupled in series define an interior junction 112 B 1 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 . Each secondary winding 116 A 1 - 116 C 2 has a first end 118 and a second end 120 . Each secondary winding includes at least a first sub-winding and a second sub-winding connected in series at a sub-junction.

For example, the secondary winding 116 A 1 includes a first sub-winding 116 A 11 and a second sub-winding 116 A 12 and coupled in series at one end to define a sub-junction 120 ′. The other end of first sub-winding 116 A 11 corresponds to the first end 118 of secondary winding 116 A 1 . The other end of second sub-winding 116 A 12 corresponds to the second end 120 of secondary winding 116 A 1 .

Each secondary winding 116 A 1 - 116 C 2 may be magnetically coupled to one of the primary windings 108 A- 108 C. In one embodiment, each of the sub-winding for example, first sub-winding and second sub-winding may be magnetically coupled to different primary windings. The first end 118 of each secondary winding 116 A 1 - 116 C 2 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary winding 116 A 1 may be coupled to interior junction 112 A 1 of primary winding 108 A. The first end 118 of secondary winding 116 A 2 may be coupled to exterior junction 114 B.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 . Each third winding 122 A 1 - 122 C 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 4 may be magnetically coupled to one of the primary windings 108 A- 108 C.

In one embodiment, some of the third windings include at least two sub-windings connected in series. For example, third windings 122 A 3 , 122 B 3 and 122 C 3 have at least two sub-windings. For example, third winding 122 A 3 has a first sub-winding 122 A 31 and a second sub-winding 122 A 32 connected in series at one end. The other end of first sub-winding 122 A 31 corresponds to the first end 124 of third winding 122 A 3 . The other end of second sub-winding 122 A 32 corresponds to the second end 126 of third winding 122 A 3 .

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 3 are coupled to a primary winding 108 A- 108 C. For example, some of the first end 124 of the third windings 122 A 1 - 122 C 3 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third windings 122 A 1 , 122 B 1 and 122 C 1 are coupled to exterior junction 114 A- 114 C respectively.

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 3 are coupled to the sub-junction 120 ′ of the secondary windings 116 A 1 - 116 C 2 . For example, the first end 124 of the third windings 122 A 3 , 122 B 3 and 122 C 3 are coupled to sub-junction 120 ′ of secondary winding 116 A 2 , 116 B 2 and 116 C 2 respectively.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example, 122 A 3 - 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 3 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 are substantially same,

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 13A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-winding having substantially same number of turns. For example, the number of turns N 1 -N 10 are shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 6 . Similarly, sub-winding 116 A 11 of secondary winding 116 A 1 and sub-winding 116 B 11 of secondary winding 116 B 1 each have substantially same number of turns, for example, N 4 . Similarly, third winding 122 A 1 and third winding 122 B 1 each have substantially same number of turns, for example, N 5 .

Now referring to FIG. 13B , an exemplary phasor diagram 1330 for the multi-phase transformer 1300 of FIG. 13A is disclosed.

The phasor diagram 1330 includes a first circle 1332 and a second circle 1334 , both having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 , B 1 and C 1 correspond to the interior junctions 112 A 1 , 112 B 1 and 112 C 1 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 and A 1 -B represent sub-primary windings 108 A 1 - 108 A 2 respectively. Similarly, Lines B-B 1 , B 1 -C represent sub-primary windings 108 B 1 - 108 B 2 respectively. Similarly, lines C-C 1 and C 1 -A represent sub-primary windings 108 C 1 - 108 C 2 respectively.

Points A 1 V 1 -A 2 V 1 , B 1 V 1 -B 2 V 1 and C 1 V 1 -C 2 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 166 B 2 and 116 C 1 - 116 C 2 respectively. Similarly points AV 2 , A 1 V 2 and A 2 V 2 ; BV 2 , B 1 V 2 and B 2 V 2 ; and CV 2 , C 1 V 2 and C 2 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 3 , 122 B 1 - 122 B 3 and 122 C 1 - 122 C 3 respectively.

As previously discussed, all of the secondary windings include at least two sub-windings connected in series, for example, secondary winding 116 A 1 . For example, the lines A 1 -A 1 ′, B 1 -B 1 ′ and C 1 -C 1 ′ represent the first sub-windings 116 A 11 , 116 B 11 and 116 C 11 of secondary windings 116 A 1 , 116 B 1 and 116 C 1 respectively. Similarly, the line A 1 ′-A 1 V 1 , B 1 ′-B 1 V 1 and C 1 ′-C 1 V 1 represent the second sub-windings 116 A 12 , 116 B 12 and 116 C 12 of secondary windings 116 A 1 , 116 B 1 and 116 C 1 .

The third windings are also represented in the phasor diagram. For example, the lines A-AV 2 , B-BV 2 and C-CV 2 represent the third windings 122 A 1 , 122 B 1 and 122 C 1 respectively. Similarly, the line A 1 ′-A 1 V 2 , B 1 ′-B 1 V 2 and C 1 ′-C 1 V 2 represent the third windings 122 A 2 , 122 B 2 and 122 C 2 respectively.

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 6 for sub-primary winding 108 A 1 . Similarly, the length of line A 1 -A 1 ′ represent number of turns N 4 for sub-winding 116 A 11 of secondary winding 116 A 1 . And, the length of line A-AV 2 represent the number of turns N 5 for third winding 122 A 1 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage in the sub-winding 116 A 11 and 116 A 21 of secondary winding 116 A 1 and 116 A 2 respectively. The arrow 546 represents the vector of inducted voltage in the third winding 122 A 1 .

In one embodiment, the vector of induced voltage in the secondary windings and the sub-windings of the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same. In one embodiment, the first sub-winding and second sub-winding of a secondary winding may be magnetically coupled to two different primary windings.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-winding of a third winding may be magnetically coupled to two different primary windings, In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 1330 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings.

Another embodiment of a multi-phase transformer is described with reference to FIGS. 14A and 14B . Transformer 1400 is another exemplary twelve phase or twenty four pulse multi-phase transformer. The multi-phase transformer 1400 described with reference to FIGS. 14A and 14B is similar to the multi-phase transformer 1300 described with reference to FIGS. 13A and 13B in that multi-phase transformer 1400 has a primary group of windings 102 , secondary group of windings 104 and third group of windings 106 . In this embodiment, some of the secondary windings of the second group of windings include at least two sub-windings connected in series. Also, some of the third windings are coupled a sub-junction of the secondary windings.

Referring to FIG. 14A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings 108 A 1 - 108 A 4 , 108 B 1 - 108 B 4 , 108 C 1 - 108 C 4 that are coupled in series. For example, for the primary winding 108 A, the junction of sub primary windings 108 A 1 and 108 A 2 coupled in series define an interior junction 112 A 1 and the junction of sub primary windings 108 B 1 and 108 B 2 coupled in series define an interior junction 112 B 1 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multiple-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings 116 A 1 - 116 A 2 , 116 B 1 - 116 B 2 and 116 C 1 - 116 C 2 . Each secondary winding 116 A 1 - 116 C 2 has a first end 118 and a second end 120 . Some of the secondary windings includes at least a first sub-winding and a second sub-winding connected in series at a sub-junction.

For example, the secondary winding 116 A 1 includes a first sub-winding 116 A 11 and a second sub-winding 116 A 12 and coupled in series at one end to define a sub-junction 120 ′. The other end of first sub-winding 116 A 11 corresponds to the first end 118 of secondary winding 116 A 1 . The other end of second sub-winding 116 A 12 corresponds to the second end 120 of secondary winding 116 A 1 .

Each secondary winding 116 A 1 - 116 C 2 may be magnetically coupled to one of the primary windings 108 A- 108 C. In one embodiment, each of the sub-winding for example, first sub-winding and second sub-winding may be magnetically coupled to different primary windings. The first end 118 of each secondary winding 116 A 1 - 116 C 2 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary winding 116 A 1 may be coupled to interior junction 112 A 1 of primary winding 108 A. The first end 118 of secondary winding 116 A 2 may be coupled to exterior junction 114 B.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 4 , 122 B 1 - 122 B 4 and 122 C 1 - 122 C 4 . Each third winding 122 A 1 - 122 C 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 C 4 may be magnetically coupled to one of the primary windings 108 A- 108 C.

In one embodiment, the first end 24 of some of the third windings 122 A 1 - 122 C 3 are coupled to a primary winding 108 A- 108 C. For example, some of the first end 124 of the third windings 122 A 1 - 122 C 3 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third windings 122 A 1 , 122 B 1 and 122 C 1 are coupled to exterior junction 114 A- 114 C respectively.

In one embodiment, the first end 124 of some of the third windings 122 A 1 - 122 C 4 are coupled to the sub-junction 120 ′ of the secondary windings 116 A 1 - 116 C 3 . For example, the first end 124 of the third windings 122 A 2 , 122 B 2 and 122 C 2 are coupled to sub-junction 120 ′ of secondary winding 116 A 1 , 116 B 1 and 116 C 1 respectively.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same. Similarly the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings, for example 122 A 4 - 122 B 1 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 4 , 122 B 1 - 122 B 4 and 122 C 1 - 122 C 4 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage out at the second end 120 of secondary windings 116 A 1 - 116 A 3 , 116 B 1 - 116 B 3 and 116 C 1 - 116 C 3 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 14A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 13 are shown. For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 4 . Similarly, sub-winding 116 A 11 of secondary winding 116 A 1 and sub-winding 116 B 11 of secondary winding 116 B 1 each have substantially same number of turns, for example, N 6 . Similarly, third winding 122 A 1 and third winding 122 B 1 each have substantially same number of turns, for example, N 5 .

Now referring to FIG. 14B , an exemplary phasor diagram 1430 for the multi-phase transformer 1400 of FIG. 14A is disclosed.

The phasor diagram 1430 includes a first circle 1432 and a second circle 1434 , both having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 , B 1 and C 1 correspond to the interior junctions 112 A 1 , 112 B 1 and 112 C 1 respectively of the primary windings 108 A- 108 C.

Lines A-A 1 , A 1 -A 2 , A 2 -A 3 and A 3 -B represent sub-primary windings 108 A 1 - 108 A 4 respectively. Similarly, Lines B-B 1 , B 1 -B 2 , B 2 -B 3 and B 3 -C represent sub-primary windings 108 B 1 - 108 B 4 respectively. Similarly, lines C-C 1 , C 1 -C 2 , C 2 -C 3 and C 3 -A represent sub-primary windings 108 C 1 - 108 C 4 respectively.

Points A 1 V 1 -A 3 V 1 , B 1 V 1 -B 3 V 1 and C 1 V 1 -C 3 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 3 , 116 B 1 - 116 B 3 and 116 C 1 - 116 C 3 respectively. Similarly points AV 2 , A 1 V 2 , A 2 V 2 and A 3 V 2 ; BV 2 , B 1 V 2 , B 2 V 2 and B 3 V 2 ; and CV 2 , C 1 V 2 , C 2 V 2 and C 3 V 2 represent the second end 126 of the third windings 122 A 1 - 122 A 4 , 122 B 1 - 122 B 4 and 122 C 1 - 122 C 4 respectively.

As previously discussed, some of the secondary windings include at least two sub-windings connected in series, for example, secondary winding 116 A 1 . For example, the lines A 1 -A 1 ′, B 1 -B 1 ′ and C 1 -C 1 ′ represent the first sub-windings 116 A 11 , 116 B 11 and 116 C 11 of secondary windings 116 A 1 , 116 B 1 and 116 C 1 respectively. Similarly, the line A 1 ′-A 1 V 1 , B 1 ′-B 1 V 1 and C 1 ′-C 1 V 1 represent the second sub-windings 116 A 12 , 116 B 12 and 116 C 12 of secondary windings 116 A 1 , 116 B 1 and 116 C 1 .

The third windings are also represented in the phasor diagram. For example, the lines A-AV 2 , B-BV 2 and C-CV 2 represent the third windings 122 A 1 , 122 B 1 and 122 C 1 respectively. Similarly, the line A 1 ′-A 1 V 2 , B 1 ′-B 1 V 2 and C 1 ′-C 1 V 2 represent the third windings 122 A 2 , 122 B 2 and 122 C 2 respectively.

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 4 for sub-primary winding 108 A 1 . Similarly, the length of line A 1 -A 1 ′ represent number of turns N 6 for sub-winding 116 A 11 of secondary winding 116 A 1 . And, the length of line A-AV 2 represent the number of turns N 5 for third winding 122 A 1 .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrows 542 and 544 represent the vector of induced voltage in the secondary winding 116 A 2 and 116 B 2 respectively. The arrow 546 represents the vector of inducted voltage in the third winding 122 A 1 .

In one embodiment, the vector of induced voltage in the secondary windings and the sub-windings of the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same. In one embodiment, the first sub-winding and second sub-winding of a secondary winding may be magnetically coupled to two different primary windings.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-winding of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 1430 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings.

Various additional embodiments will now be described with reference to FIGS. 15A , 15 B, 16 A, 16 B 17 A, 17 B, 18 A, 18 B, 19 A and 19 B. FIGS. 15A , 16 A, 17 A, 18 A and 19 A show exemplary winding diagrams of multi-phase transformers similar to the winding diagrams described previously. FIGS. 15B , 16 B, 17 B, 18 B and 19 B show exemplary phasor diagrams for multi-phase transformers described with reference to FIGS. 15A , 16 A, 17 A, 18 A and 19 A respectively.

In all of the embodiments of multi-phase transformer described with reference to FIGS. 15A-19B , at least one of the secondary windings includes a plurality of sub-windings and further, ends of more than one sub-winding define a second end. For example, secondary winding 116 A 2 includes more than one second end 120 .

Multi-phase transformers with reference to FIGS. 15A-19B will now be described. The description will be focused on secondary winding 116 A 2 with reference to primary winding 108 A and associated third windings. In one embodiment, secondary windings 116 B 2 and 116 C 2 are similar to secondary winding 116 A 2 . Other details of the multi-phase transformer will be apparent one skilled in the art by referring to FIGS. 15A-19B , based upon various other embodiments of multi-phase transformers described in detail in this disclosure.

Referring to FIGS. 15A , 16 A and 15 B and 16 B, multi-phase transformer 1500 and 1600 will now be described. Transformers 1500 and 1600 are another exemplary fifteen phase or thirty pulse multi-phase transformers. The multi-phase transformers 1500 and 1600 are substantially similar in the structure and differ in the magnetic coupling of some secondary windings, which will be highlighted while describing the phasor diagrams with reference to FIGS. 15B and 16B .

Referrings to FIG. 15A and 16A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings. For example, primary winding 108 A includes sub primary windings 108 A 1 - 108 A 4 that are coupled in series. The sub primary windings are coupled at interior junctions 112 A 1 - 112 A 3 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings. For example, secondary windings 116 A 1 - 116 A 3 . Each secondary winding 116 A 1 - 116 C 2 has a first end 118 and at least a second end 120 . Some of the secondary windings include a plurality of sub-windings connected in series at a sub-junction. For example, secondary winding 116 A 2 .

For example, the secondary winding 116 A 2 includes a first sub-winding 116 A 21 and a plurality of second sub-windings 116 A 22 and 116 A 23 . One end of the first sub-winding 116 A 21 , second sub-winding 116 A 22 and second sub-winding 116 A 23 are coupled together to define a sub-junction 118 ′. The other end of first sub-winding 116 A 21 correspond to the first end 118 of secondary winding 116 A 2 . The other end of second sub-windings 116 A 22 and 166 A 23 corresponds to two second end 120 of secondary winding 116 A 2 .

Each secondary winding 116 A 1 - 116 C 2 may be magnetically coupled to on of the primary windings 108 A- 108 C. In one embodiment, each of the sub-windings for example, first sub-windings and second sub-windings may be magnetically coupled to different primary windings. The first end 118 of each secondary winding 116 A 1 - 116 C 2 may be coupled to one of the primary windings 108 A- 108 C. For example, the first end 118 of secondary winding 116 A 2 may be coupled to interior junction 112 A 2 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 5 . Each third winding, for example 122 A 1 - 122 A 5 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 A 5 may be magnetically coupled to one of the primary windings 108 A- 108 C.

In one embodiment, the first end 124 of some of the third windings, for example, 122 A 1 - 122 A 4 may be coupled to a primary winding, for example, primary winding 108 A. For example, some of the first end 124 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third winding 122 A 1 may be coupled to exterior junction 114 A.

In one embodiment, the first end 124 of some of the third windings, for example, third windings 122 A 2 - 122 A 5 are coupled to the second ends of the secondary windings, for example, secondary windings 116 A 1 - 116 A 3 .

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 4 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 3 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 15A and 15B also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 14 are shown in FIG. 15A and the number of turns N 1 -N 14 are shown in FIG. 16A . For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 2 and N 2 respectively.

Now referring to FIGS. 15B and 16B , exemplary phasor diagram 1530 and 1630 for the multi-phase transformer 1500 of FIG. 15A and exemplary phasor diagram 1630 for the multi-phase transformer 1600 of FIG. 16A is disclosed.

The phasor diagrams 1530 and 1630 include a first circle 1532 and 1632 , and second circle 1534 and 1634 , both circles having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. Points A 1 , A 2 and A 3 correspond to the interior junction 112 A 1 - 112 A 3 respectively of the primary winding 108 A.

Lines A-A 1 , A 1 -A 2 , A 2 -A 3 and A 3 -B represent sub-primary windings 108 A 1 - 108 A 4 respectively.

Points A 1 V 1 , A 21 V 1 , A 22 V 1 and A 3 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 3 respectively. As previously discussed, secondary winding 116 A 2 has two second ends, represented by A 21 V 1 and A 22 V 1 .

As previously discussed, some of the secondary windings include at least two sub-windings, for example, secondary winding 116 A 2 . For example, the line A 2 -A 2 ′ represents the first sub-winding 116 A 21 . The line A 2 ′-A 21 V 1 represents the second sub-winding 116 A 22 and the line A 2 ′-A 22 V 1 represents the second sub-winding 116 A 22 .

The third windings are also represented in the phasor diagram. For example, the lines A-A′-AV 2 represent the third winding 122 A 1 .

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 2 for sub-primary winding 108 A 1 of multi-transformer 1500 of FIG. 15A . Similarly, the length of line A-A 1 represent number of turns N 2 for sub-primary winding 108 A 1 of multi-transformer 1600 of FIG. 16A

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrow 542 represent the vector of induced voltage in the secondary winding 116 A 3 . The arrow 546 represents the vector of inducted voltage on the sub-winding 122 A 11 of third winding 122 A 1 .

In one embodiment, the vector of induced voltage in the secondary windings and the sub-windings of the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same. In one embodiment, first sub-windings and second sub-windings of a secondary winding may be magnetically coupled to two different primary windings.

Note that the vector of induced voltage in the secondary winding 116 A 3 of multi-phase transformer 1500 is different than the vector of induced voltage in the secondary winding 116 A 3 of multi-phase transformer 1600 . For example, the secondary winding 116 A 3 of multi-phase transformer 1500 may be magnetically coupled to and in-phase with primary winding 108 C, as depicted by arrows 540 and 542 in FIG. 15B . On the other hand, the secondary winding 116 A 3 of multi-phase transformer 1600 may be magnetically coupled to and 180 degrees cut of phase with primary winding 108 B, as depicted by arrows 538 and 542 in FIG. 16B .

In one embodiment, the vector of induced voltage in the third windings and the sub-windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-winding of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 1530 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings of multi-phase transformer 1500 . The phasor diagram 1630 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings of multi-phase transformer 1600 .

Multi-phase transformer 1700 will be described with reference to FIGS. 17A and 17B . Transformer 1700 is another exemplary fifteen phase or thirty pulse multi-phase transformer. One of the similarities between the multi-phase transformer 1700 and multi-phase transformers 1500 and 1600 described with reference to FIGS. 15A-16B is that the structure of some of the secondary windings, for example, secondary winding 116 A 2 is similar. One of the differences is that at least one of the thirds windings includes a plurality of sub-windings. Additionally, some of the third windings include more than one second end.

Referring to FIG. 17A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings. For example, primary winding 108 A includes sub primary windings 108 A 1 - 108 A 7 that are coupled in series. The sub primary windings are coupled at interior junctions 112 A 1 - 112 A 6 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings. For example, secondary windings 116 A 1 - 116 A 3 . Each secondary winding 116 A 1 - 116 C 2 has a first end 118 and at least a second end 120 . Some of the secondary windings include a plurality of sub-windings connected in series at a sub-junction. For example, secondary winding 116 A 2 .

For example, the secondary winding 116 A 2 includes a first sub-winding 116 A 21 and a plurality of second sub-windings 116 A 22 and 116 A 23 . One end of the first sub-winding 116 A 21 , second sub-winding 116 A 22 and second sub-winding 116 A 23 are coupled together to define a sub-junction 118 ′. The other end of first sub-winding 116 A 21 corresponds to the first end 118 of secondary winding 116 A 2 . The other end of second sub-windings 116 A 22 and 166 A 23 corresponds to two second end 120 of secondary winding 116 A 2 .

Each secondary winding 116 A 1 - 116 A 3 may be magnetically coupled to one of the primary windings 108 A- 108 C. In one embodiment, each of the sub-windings for example, first sub-windings and second sub-windings may be magnetically coupled to different primary windings. The first end 118 of each secondary winding, for example, secondary winding 116 A 1 - 116 A 3 may be coupled to one of the primary windings, for example, primary winding 108 A. For example, the first end 118 of secondary winding 116 A 2 may be coupled to interior junction 112 A 4 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 4 . Each third winding, for example 122 A 1 - 122 A 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 A 4 may be magnetically coupled to one of the primary windings, for example, primary winding 108 A.

In one embodiment, some of the third windings include a plurality of sub-windings connected at a sub-junction. For example, third winding 122 A 3 .

The third winding 122 A 3 includes a first sub-winding 122 A 31 and a plurality of second sub-windings 122 A 32 and 122 A 33 . One end of the first sub-winding 122 A 31 , second sub-winding 122 A 32 and second sub-winding 122 A 33 are coupled together to define a sub-junction 124 ′. The other end of first sub-winding 122 A 31 corresponds to the first end 124 of third winding 122 A 3 . The other end of second sub-windings 122 A 32 and 122 A 33 corresponds to two second end 126 of third winding 122 A 3 .

In one embodiment, the first end 124 of some of the third windings, for example, third windings 122 A 1 - 122 A 4 may be coupled to a primary winding, for example, primary winding 108 A. For example, some of the first end 124 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third winding 122 A 1 may be coupled to exterior junction 114 A. Similarly, the first end 124 of third windings 122 A 2 - 122 A 4 are coupled to interior junction 112 A 2 , 112 A 3 and 112 A 5 respectively.

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 4 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 3 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 17A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 16 are shown in FIG. 17A . For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 6 .

Now referring to FIG. 17B , exemplary phasor diagram 1730 for the multi-phase transformer 1700 of FIG. 17A is disclosed.

The phasor diagram 1730 includes a first circle 1732 and second circle 1734 , both circles having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. For example, points A 1 -A 6 correspond to the interior junction 112 A 1 - 112 A 6 respectively of the primary winding 108 A. Lines A-A 1 , A 1 -A 2 , A 2 -A 3 , A 3 -A 4 , A 4 -A 5 , A 5 -A 6 and A 6 -B represent sub-primary windings 108 A 1 - 108 A 7 respectively.

Points A 1 V 1 , A 41 V 1 , A 42 V 1 and A 6 V 1 represent the second end 120 of the secondary windings 116 A 1 - 116 A 3 respectively. As previously discussed, secondary winding 116 A 2 has two second ends, represented by A 41 V 1 and A 42 V 1 .

As previously discussed, some of the secondary windings include at least two sub-windings, for example, secondary winding 116 A 2 . For example, the line A 4 -A 4 ′ represents the first sub-winding 116 A 21 . The line A 4 ′-A 41 V 1 represents the second sub-winding 116 A 22 and the line A 4 ′-A 42 V 1 represents the second sub-winding 116 A 22 .

The third windings are also represented in the phasor diagram. For example, the lines A-A′-AV 2 represent the third winding 122 A 1 . As previously discussed, some of the third windings include at least two sub-windings, for example, third winding 122 A 3 . For example, the line A 3 -A 3 ′ represents the first sub-winding 122 A 31 . The line A 3 ′-A 31 V 2 represents the second sub-winding 122 A 32 and the line A 3 ′-A 32 V 2 represents the second sub-winding 122 A 32 .

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 6 for sub-primary winding 108 A 1 of multi-transformer 1700 of FIG. 17A .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induce voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrow 542 represent the vector of induced voltage in the secondary winding 116 A 3 . The arrow 546 represents the vector of inducted voltage in the third winding 122 A 1 .

In one embodiment, the vector of induced voltage in the secondary windings and the sub-windings of the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same. In one embodiment, first sub-windings and second sub-windings of a secondary winding may be magnetically coupled to two different primary windings.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-windings of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 1730 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings of multi-phase transformer 1700 .

Multi-phase transformer 1800 will be described with reference to FIGS. 18A and 18B . Transformer 1800 is another exemplary twelve phase or twenty four pulse multi-phase transformer. One of the similarities between the multi-phase transformer 1800 and multi-phase transformers 1700 described with reference to FIGS. 17A-17B is that some of the secondary windings, for example, secondary winding 116 A 2 include a plurality sub-windings. The coupling of some of the sub-windings of the secondary winding is different.

Referring FIG. 18A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings. For example, primary winding 108 A includes sub primary windings 108 A 1 - 108 A 3 that are coupled in series. The sub primary windings are coupled at interior junctions 112 A 1 - 112 A 2 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings. For example, secondary windings 116 A 1 - 116 A 2 . Each secondary winding, for example, secondary winding 116 A 1 - 116 A 2 has a first end 118 and at least a second end 120 . Some of the secondary windings include a plurality of sub-windings connected at a sub-junction. For example, secondary winding 116 A 2 .

For example, the secondary winding 116 A 2 includes a first sub-winding 116 A 21 and a plurality of second sub-windings 116 A 22 , 116 A 23 and 116 A 24 . One end of the first sub-winding 116 A 21 , second sub-winding 116 A 22 and second sub-winding 116 A 23 are coupled together to define a sub-junction 118 ′. The other end of first sub-winding 116 A 21 corresponds to the first end 118 of secondary winding 116 A 2 . The other end of second sub-winding 116 A 22 corresponds to a second end 120 of secondary winding 116 A 2 . The other end of second sub-winding 116 A 23 may be coupled to an end of another second sub-winding 116 A 24 at sub-junction 120 ′. The other end of second sub-winding 116 A 24 corresponds to another second end of sub-winding 116 A 22 .

Each secondary winding 116 A 1 - 116 A 2 may be magnetically coupled to one of the primary windings 108 A- 108 C. In one embodiment, each of the sub-windings for example, first sub-windings and second sub-windings may be magnetically coupled to different primary windings. The first end 118 or each secondary winding, for example, secondary winding 116 A 1 - 116 A 2 may be coupled to one of the primary windings, for example, primary winding 108 A. For example, the first end 118 of secondary winding 116 A 2 may be coupled to interior junction 122 A 2 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 4 . Each third winding, for example 122 A 1 - 122 A 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 A 4 may be magnetically coupled to one of the primary windings, for example, a primary winding 108 A- 108 C.

In one embodiment, the first end 124 of some of the third windings, for example, third windings 122 A 1 - 122 A 4 may be coupled to a primary winding, for example, primary winding 108 A. For example, some of the first end 124 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third winding 122 A 1 may be coupled to exterior junction 114 A.

In one embodiment, the first end 124 of some of the third windings, for example, third windings 122 A 1 - 122 A 4 may be coupled to a secondary winding, for example, secondary winding 116 A 1 and 116 A 2 . For example, some of the first end 124 are coupled to one of the second end of a secondary winding, for example, the first end 124 of third winding 122 A 3 may be coupled to one of the second end 120 of secondary winding 116 A 2 . The first end 124 of third winding 122 A 4 may be coupled to a sub-junction 120 ′ of secondary winding 116 A 2 .

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 4 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 2 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 may be greater than output voltage Vout 1 .

FIG. 18A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 13 are shown in FIG. 18A . For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 3 .

Now referring to FIG. 18B , exemplary phasor diagram 1830 for the multi-phase transformer 1800 of FIG. 18A is disclosed.

The phasor diagram 1830 includes a first circle 1832 and second circle 1834 , both circles having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. For example, points A 1 -A 2 correspond to the interior junction 112 A 1 - 112 A 2 respectively of the primary winding 108 A. Lines A-A 1 , A 1 -A 2 and A 2 -B represent sub-primary windings 108 A 1 - 108 A 3 respectively.

Points A 1 V 1 , A 21 V 1 and A 22 V 1 represent the second ends 120 of the secondary windings 116 A 1 - 116 A 2 respectively. As previously discussed, secondary winding 116 A 2 has two second ends, represented by A 21 V 1 and A 22 V 1 .

As previously discussed, some of the secondary windings include at least two sub-windings, for example, secondary winding 116 A 2 . For example, the line A 2 -A 2 ′ represents the first sub-winding 116 A 21 . The line A 2 ′-A 21 V 1 represents the second sub-winding 116 A 22 the line A 2 ′′-A 22 V 1 represents the second sub-winding 116 A 24 .

The third windings are also represented in the phasor diagram. For example, the lines A-AV 2 represent the third winding 122 A 1 .

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the length of line A-A 1 represent number of turns N 3 for sub-primary winding 108 A 1 of multi-transformer 1800 of FIG. 18A .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by the arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third winding represent the vector of induced voltage. For example, arrow 542 represent the vector of induced voltage in the sub-winding 116 A 22 of secondary winding 116 A 2 . The arrow 546 represents the vector of inducted voltage in the third winding 122 A 1 .

In one embodiment, the vector or induced voltage in the secondary windings and the sub-windings of the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same. In one embodiment, first sub-windings and second sub-windings of a secondary winding may be magnetically coupled to two different primary windings.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-windings of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 1830 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings of multi-phase transformer 1800 .

Multi-phase transformer 900 will be described with reference to FIGS. 19A and 19B . Transformer 1900 is another exemplary fifteen phase or thirty pulse multi-phase transformer. One of the similarities between the multi-phase transformer 1900 and multi-phase transformer 1800 described with reference to FIG. 18A-18B is that some of the secondary windings, for example, secondary winding 116 A 2 include a plurality of sub-windings. The coupling of some of the sub-windings of the secondary winding is different.

Referring to FIG. 19A , in this specific embodiment, each of the primary windings 108 A- 108 C include a plurality of sub primary windings. For example, primary winding 108 A includes sub primary windings 108 A 1 - 108 A 4 that are coupled in series. The sub primary windings are coupled at interior junctions 112 A 1 - 112 A 3 . Each ends of the primary windings 108 A- 108 C are coupled to the ends of the other primary winding 108 A- 108 C to form a delta configuration with exterior junctions 114 A- 114 C. Each of the primary windings 108 A- 108 C are configured to receive one phase of a multi-phase input voltage at the exterior junction 114 A- 114 C.

The second group of windings 104 includes a plurality of secondary windings. For example, secondary windings 116 A 1 - 116 A 3 . Each secondary winding, for example, secondary winding 116 A 1 - 116 A 3 has a first end 118 and at least a second end 120 . Some of the secondary windings include a plurality of sub-windings connected at a sub-junction. For example, secondary winding 116 A 2 .

For example, the secondary winding 116 A 2 includes a first sub-winding 116 A 21 and a plurality of second sub-windings 116 A 22 , 116 A 23 , 116 A 24 and 116 A 25 . One end of the first sub-winding 116 A 21 , second sub-winding 116 A 22 and second sub-winding 116 A 23 are coupled together to define a sub-junction 118 ′. The other end of first sub-winding 116 A 21 corresponds to the first end 118 of secondary winding 116 A 2 . The other end of second sub-winding 116 A 23 corresponds to a second end 120 of secondary winding 116 A 2 . The other end of second sub-winding 116 A 22 may be coupled to an end of another second sub-winding 116 A 24 at sub-junction 118 ″. The other end of second sub-winding 116 A 24 may be coupled to an end of another second sub-winding 116 A 25 at sub-junction 120 ′. The other end of second sub-winding 116 A 25 corresponds to another second end 120 of secondary winding 116 A 2 .

Each secondary winding 116 A 1 - 116 A 3 may be magnetically coupled to one of the primary windings 108 A- 108 C. In one embodiment, each of the sub-windings for example, first sub-windings and second sub-windings may be magnetically coupled to different primary windings. The first end 118 of each secondary winding, for example, secondary winding 116 A 1 - 116 A 3 may be coupled to one of the primary windings, for example, primary winding 108 A. For example, the first end 118 of secondary winding 116 A 2 may be coupled to interior junction 112 A 2 of primary winding 108 A.

The third group of windings 106 includes a plurality of third windings. For example, plurality of third windings 122 A 1 - 122 A 5 . Each third winding, for example 122 A 1 - 122 A 4 has a first end 124 and a second end 126 . Each third winding 122 A 1 - 122 A 5 may be magnetically coupled to one of the primary windings, for example, a primary winding 108 A- 108 C.

In one embodiment, the first end 124 of some of the third windings, for example, third windings 122 A 1 - 122 A 5 may be coupled to a primary winding, for example, primary winding 108 A. For example, some of the first end 124 are coupled to one of the exterior junctions 114 A- 114 C. For example, the first end 124 of the third winding 122 A 1 may be coupled to exterior junction 114 A.

In one embodiment, the first end 124 of some of the third windings, for example, third windings 122 A 1 - 122 A 4 may be coupled to a secondary winding, for example, secondary winding 116 A 1 , 116 A 2 and 116 A 3 . For example, some of the first end 124 are coupled to one of the sub-junctions of a secondary winding. For example, the first end 124 of third winding 122 A 3 may be coupled to sub-junction 120 ′ of secondary winding 116 A 2 . The first end 124 of third winding 122 A 4 may be coupled to sub-junction 118 ″ of secondary winding 116 A 2 .

In one embodiment, the phase angle difference of the output voltage Vout 2 at two adjacent second ends of third windings are substantially same. For example, the phase angle difference of the output voltage Vout 2 at second end 126 of two adjacent third windings 122 A 1 - 122 A 2 are substantially same.

In one embodiment, the output voltage Vout 2 at the second end of the third windings are substantially equal. For example, the output voltage Vout 2 at the second end 126 of the third windings 122 A 1 - 122 A 5 are substantially same.

In one embodiment, the output voltage Vout 1 at the second end of secondary windings and at the exterior junction of the primary windings are the same. For example, the output voltage Vout 1 at the second end 120 of secondary windings 116 A 1 - 116 A 3 and at the exterior junction 114 A- 114 C of the primary windings 108 A- 108 C are substantially equal.

In one embodiment, the output voltage Vout 2 is greater than output voltage Vout 1 .

FIG. 19A also shows exemplary number of turns for various windings and sub-windings, with some of the windings or sub-windings having substantially same number of turns. For example, the number of turns N 1 -N 17 are shown in FIG. 19A . For example, sub-primary windings 108 A 1 , 108 B 1 and 108 C 1 each have substantially same number of turns, for example, N 4 .

Now referring to FIG. 19B , exemplary phasor diagram 1930 for the multi-phase transformer 1900 of FIG. 19A is disclosed.

The phasor diagram 1930 includes a first circle 1932 and second circle 1934 , both circles having a common center S. The points A, B and C represent the exterior junction 114 A- 114 C of the primary windings. The sides AB, BC and CA of triangle ABC represent the primary windings 108 A- 108 C respectively. For example, points A 1 -A 3 correspond to the interior junction 112 A 1 - 112 A 3 respectively of the primary winding 108 A. Lines A-A 1 , A 1 -A 2 , A 2 -A 3 and A 3 -B represent sub-primary windings 108 A 1 - 108 A 4 respectively.

Points A 1 V 1 , A 21 V 1 , A 22 V 1 and A 23 V 1 represent the second ends 120 of the secondary windings 116 A 1 - 116 A 3 respectively. As previously discussed, secondary winding 116 A 2 has two second ends, represented by A 21 V 1 and A 22 V 1 .

As previously discussed, some of the secondary windings include at least two sub-windings, for example, secondary winding 116 A 2 . For example, the line A 2 -A 2 ′ represents the first sub-winding 116 A 21 . The line A 2 ′-A 22 V 1 represents the second sub-winding 116 A 23 and the line A 2 ′-A 2 ″ represents the second sub-winding 116 A 22 .

The third windings are also represented in this phasor diagram. For example, the lines A-AV 2 represent the third winding 122 A 1 .

As previously discussed, the length of lines in a phasor diagram represent the number of turns for the windings. For example, the lines of line A-A 1 represent number of turns N 4 or sub-primary winding 108 A 1 of multi-transformer 1900 of FIG. 19A .

The lines SA, SB and SC represent the input AC voltage Vin applied to the exterior junctions A, B and C of the primary windings 108 A- 108 C. As it is evident from the phasor diagram, a three phase input voltage Vin depicted as phaseA_ 230 , phaseB_ 230 and phaseC_ 230 is applied, with each phase separated by about 120 degrees.

As previously described, the lines in a phasor diagrams are vector lines depicting the vector of the induced voltage. For example, the vector of induced voltage in primary windings AB, BC and CA are depicted by arrows 536 , 538 and 540 . Similarly, the arrows on lines representing the secondary windings and the third windings represent the vector of induced voltage. For example, arrow 542 represent the vector of induced voltage in the sub-winding 116 A 23 of secondary winding 116 A 2 . The arrow 546 represents the vector of inducted voltage in the third winding 122 A 1 .

In one embodiment, the vector of induced voltage in the secondary windings and the sub-windings of the secondary windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the vector of induced voltage in the secondary windings are such that the phase angle difference of the output voltage at two adjacent second ends of the secondary windings are substantially same. In one embodiment, first sub-windings and second sub-windings of a secondary winding may be magnetically coupled to two different primary windings.

In one embodiment, the vector of induced voltage in the third windings and the sub-windings are such that they are either in phase or 180 degrees out of phase with the vector of induced voltage in a primary winding to which they are magnetically coupled. In one embodiment, the first sub-winding and second sub-windings of a third winding may be magnetically coupled to two different primary windings. In one embodiment, the vector of induced voltage in the third windings are such that the phase angle difference of the output voltage at two adjacent second ends of the third windings are substantially same.

The phasor diagram 1930 shows an exemplary vector of induced voltage in the primary windings, secondary windings and the third windings of multi-phase transformer 1900 .

As one skilled in the art appreciates, various embodiments of multi-phase transformers have been described. Using various variations of the first group of windings, second group of windings and third group of windings, multi-phase transformers providing different number of phases or pulses may be configured.

The number of turns for windings shown in each of the winding diagrams are exemplary for the multi-phase transformer described with reference to that winding diagram only. For example, number of turns N 1 described with reference to transformer 100 of FIG. 1A may not be equal to the number of turns N 1 described with reference to transformer 1500 of FIG. 15A .

Although exemplary vector of induced voltage in the primary windings, secondary windings and third windings have been shown with reference to various phasor diagrams, as one skilled in the art appreciates, modifications may be made to magnetic coupling configurations.

In one embodiment, with reference to six phase or twelve pulse transformers, the phase angle difference of the output voltage at two adjacent second ends of third windings are about 60 degrees. In one embodiment, the phase angle difference of the output voltage at two adjacent second ends of secondary windings and the exterior junctions are about 60 degrees.

In one embodiment, with reference to nine phase or eighteen pulse transformers, to phase angle difference of the output voltage at two adjacent second ends of third windings are about 40 degrees. In one embodiment, the phase angle difference of the output voltage at two adjacent second ends of secondary windings and the exterior junctions are about 40 degrees.

In one embodiment, with reference to twelve phase or twenty four pulse transformers, the phase angle difference of the output voltage at two adjacent second ends of third windings are about 30 degrees. In one embodiment, the phase angle difference of the output voltage at two adjacent second ends of secondary windings and the exterior junctions are about 30 degrees.

In one embodiment, with reference to fifteen phase or thirty pulse transformers, the phase angle difference of the output voltage at two adjacent second ends of third windings are about 24 degrees. In one embodiment, the phase angle difference of the output voltage at two adjacent second ends of secondary windings and the exterior junctions are about 24 degrees.

Although the present disclosure has been described with reference to specific embodiments, these embodiments are illustrative only and not limiting. Many other applications and embodiments of the present disclosure will be apparent in light or this disclosure and the following claims.