Abstract:
The present invention relates to armature windings for DC electrical machines, and in particular to those that use electronic commutation and have relatively few slots per pole-pair. The armature windings are particularly well suited for use with rotating DC electrical machines that have a large diameter and a large number of poles such as those that might be directly coupled to the turbine blade assembly of a wind turbine. The armature winding is arranged in relation to the magnetic field generated by a field winding or by permanent magnets such that a number of commutation events during the time taken for the relative movement between the armature and the field system of one pole-pair is much larger than the number of coils per pole-pair.

Description:
FIELD OF THE INVENTION 
     The present invention relates to armature windings for DC electrical machines, and in particular to those that use electronic commutation and have relatively few coils per pole-pair. The armature windings are particularly well suited for use with rotating electrical machines that have a large diameter and a large number of poles such as those that might be directly coupled to the turbine blade assembly of a wind turbine. 
     BACKGROUND OF THE INVENTION 
     A DC rotating electrical machine typically includes an armature winding mounted on the rotor surrounded by a field system mounted on the stator. A rotor-connected commutator with copper or copper alloy segments and stationary brushgear are used to control the commutation of current in the rotor winding based on the angular position of the rotor. In a further development of the DC rotating electrical machine, the armature winding is mounted on the stator and the field system is mounted on the rotor. An electronic switching circuit is used to control the commutation of current in the armature winding in relation to the angular position of the rotor. The following description is based on a DC rotating electrical machine having this construction. 
     The armature winding will include a plurality of coils that are located in winding slots formed in a surface of the armature assembly. The rotor provides a rotating magnetic field and this can be generated by permanent magnets, superconducting windings with a suitable excitation power supply or conventional windings with slip rings or brushless excitation power supply. Electrical machines using electronic commutation may operate at much higher voltages (voltages of several kV are possible) and proportionally lower currents than conventional electrical machines that use brushes. 
     DC rotating electrical machines employing electronic commutation may be used as generators for wind turbine applications. A turbine blade assembly may be used to drive the rotor of the generator, either directly or by means of a gearbox. If the rotor is connected directly to the turbine blade assembly then the generator will run at very low speeds and, in order to minimise the amount of ineffective copper in the endwindings of the coils, to minimise the amount of magnetic steel that is required and to simplify construction, the generator will normally have a very large number of poles (typically 50 or more for the largest generators) and a very small number of slots per pole-pair. 
     An armature winding with n coils per pole-pair would require only n commutating events during the time taken for the relative movement between the armature and the field system of one pole-pair. For simplicity this is referred to as the number of commutating events per pole-pair. The number of commutating events per pole-pair in a conventional DC rotating electrical machine is equal to the number of coils per pole-pair and n is not necessarily an integer. 
     The purpose of the present invention is to provide an improved armature winding that allows a much larger number of commutation events per pole-pair than the number of coils per pole-pair. 
     SUMMARY OF THE INVENTION 
     The present invention provides a DC electrical machine comprising: field means for providing a magnetic field having at least one pole-pair; an armature having a non-integer number of winding slots per pole-pair, each winding slot having a phase angle being the position of the winding slot in relation to a fundamental waveform of the magnetic field; and a DC armature winding that in use interacts with the magnetic field, the armature winding comprising one or more circuits with each circuit including a plurality of coils; wherein each coil of the armature winding is received in a pair of winding slots; wherein each coil of the armature winding has a phase angle that is the average of the phase angles of the pair of winding slots in which the respective coil is received and the coils in each circuit that have different phase angles at any instant form different phases for the armature winding, the number of different phases for the armature winding being at least twice the number of coils per pole-pair; and wherein the coils in each circuit are connected together in series in the sequence of their phase angles and are separated from adjacent coils in the same circuit by a number of winding slots that is at least twice the number of winding slots per pole-pair. 
     ‘Phase’ is not a term that is generally used for DC windings and is used herein in the manner that is commonly used for AC windings. The phase angle of a winding slot is the position of the winding slot in relation to the fundamental waveform of the magnetic field and is generally expressed in electrical degrees or electrical radians. Each coil of the armature winding will be placed in a respective pair of winding slots and the phase angle of each coil is therefore the average of the phase angles of the two winding slots. As used herein, coils that have different phase angles at any instant are said to form individual phases. As the magnetic field on the rotor moves past a coil its electrical phase will change and the electronic commutation will cause reversal of the current in that coil at a defined instant and this is referred to herein as a ‘commutating event’. 
     The number of phases for the armature winding is at least twice the number of coils per pole-pair but in practice the number of phases may be significantly more. It is believed that the maximum number of phases achievable for any given armature winding is half the total number of coils. An armature winding having 144 coils could therefore have a maximum of 72 phases. If the same armature winding had 3 coils per pole-pair then it will be readily appreciated that there are 24 times more phases than coils per pole-pair. 
     Such an armature winding can be referred to as a ‘distributed connection’ armature winding because of the manner in which semiconductor power switching devices are connected to the winding. The armature winding provides a number of commutating events per pole-pair that is significantly more than the number of coils per pole-pair. 
     Each circuit of the armature winding includes a plurality of coils connected together in series. It will be readily appreciated that in the case where the armature winding is formed with more than one circuit then the total number of coils in the armature winding will be the sum of the number of coils in all of the individual circuits. In some arrangements then the coils in different circuits can be connected together in parallel, e.g. by the use of cross connectors. 
     Each circuit of the armature winding preferably defines a plurality of phase angles. The phase angles of successive coils in each circuit of the armature winding may be equally spaced throughout k×360 electrical degrees or unequally spaced throughout k×360 electrical degrees as required, where k is an integer greater than zero. This means that the coils in each circuit can be spaced (either equally or unequally) through 360 electrical degrees, 720 electrical degrees, 1080 electrical degrees etc. 
     In the case where the phase angles of successive coils are equally spaced then the phase angle θ in electrical degrees between successive coils of a particular circuit can be determined using the following equation:
 
θ= k× 360 /s  electrical degrees
 
where s is the number of coils in the particular circuit and is preferably larger than the number of winding slots per pole-pair. For example, if k=1 and the particular circuit has 36 equally spaced coils then each coil can have a phase angle θ=10 (or −10) electrical degrees or its equivalent.
 
     Electronic commutation enables the use of alternative forms of armature winding in which the phase angles of successive coils in each circuit are not equally spaced. Moreover, the commutation process is not fixed by the spatial relationship between a commutator and the armature winding of the electrical machine and the switching of the coils forms a quite different sequence from the physical sequence of the coils around the armature. 
     The number of circuits and the number of coils within each circuit may be selected depending on the circumstances. The number of circuits may depend on the construction of the electrical machine such as the number of magnet poles and winding slots, for example. Physically large electrical machines may have six or more circuits. 
     Each circuit will normally contain the same number of coils but it is possible for the circuits to have a different number of coils in come circumstances. 
     The separation between adjacent coils can be selected to achieve a required phase angle and is preferably such that the net voltage around each circuit is zero at all times and there are no circulating currents. The coils in each circuit do not have to be separated from adjacent coils in the circuit by the same number of winding slots whether or not the successive coils have equally spaced phase angles. 
     Although the separation between adjacent coils is expressed herein as a number of winding slots, it will be readily appreciated that the separation of adjacent coils is simply the distance between the circumferential centre-line of a coil and the circumferential centre-line of the next and/or previous coil in the circuit. This can be expressed in other ways, such as a proportion of the pole pitch at the bore of the armature expressed in any convenient form such as a rational fraction or a decimal multiple, for example. Any reference to successive coils in a particular circuit means that the coils should be considered in sequential order running from the first coil to the last coil in the circuit. 
     Although the last coil will normally be connected to the first coil to form a closed loop, the separation of the last and first coils may be different from that between the first coil and the second coil, the second coil and the third coil and so on. In general, it is possible that there are irregular separations between all adjacent pairs of coils in each circuit. However, it will be readily appreciated that uniform separations will make it easier to construct the armature winding. 
     The armature winding may be used with any suitable electronic commutator circuit having any suitable number of switching stages that are connected between the armature winding and first and second DC terminals, for example. Each switching stage will typically include a first semiconductor power switching device having its anode connected to the first DC terminal and a second semiconductor power switching device having its cathode connected to the second DC terminal. The first and second semiconductor switching power devices may be thyristors or reverse blocking devices that are capable of being turned on and off by gate control (e.g. gate turn off thyristors or GTOs) as described in EP 1798847. 
     If a particular circuit includes s coils connected together in series then the electronic commutator circuit for that circuit may include s switching stages, each switching stage being connected between an adjacent pair of coils (i.e. a point of coil interconnection) and the first and second DC terminals. In this case the number of commutating events per pole-pair will be equal to the number of coils in each circuit. Fewer switching stages can be provided to reduce the total number of semiconductor power switching devices. For example, switching stages can be connected between every second or third coil. If a switching stage is only connected at every second coil interconnection then the number of commutating events per pole-pair will be reduced to s/2. If a switching stage is only connected at every third coil interconnection then the number of commutating events per pole-pair will be reduced to s/3 and so on. 
     The number of coils that are commutating at any instant during operation of the electrical machine is two times the number of circuits (before internal connection between circuits, if any) but this is increased if the number of switching stages is reduced by only connecting a switching stage between every second or third coil, for example. If a switching stage is only connected at every second coil interconnection then the number of coils that are commutating at any instant is four times the number of circuits (before internal connection between circuits, if any). If a switching stage is only connected at every third coil interconnection then the number of coils that are commutating at any instant is six times the number of circuits (before internal connection between circuits, if any) and so on. 
     The individual circuits will normally be connected together to form the complete armature winding but may also be arranged to operate independently to provide redundancy and hence operational advantages. Each circuit may include its own network-side inverter to interface the circuit and its associated electronic commutator circuit to an AC supply network or bus. 
     The individual circuits can be connected externally (e.g. at the DC side of the electronic commutator circuit or at the AC side of the associated inverter) or internally. Any suitable method of external or internal connection can be used. For example, when the external connection is made at the DC side of the electronic commutator circuit then the circuits can be connected in series, parallel or an appropriate combination of both. When necessary, the electronic commutation circuits would include components to limit any circulating currents to an acceptable level. When the connection is made internally then a parallel connection between two or more circuits can be achieved by adding interconnections or cross connections between all of the respective points of coil interconnection or only between those respective points of coil interconnection to which a switching stage is connected, for example. 
     The individual coils of the armature winding can be of any suitable type or construction. 
     The armature winding can be used with a DC rotating or linear electrical machine that employs electronic commutation. The electrical machine can be excited by any suitable means (i.e. have any suitable field means) and the type of excitation has no effect on the operation and benefits of the armature winding. The electronic commutator circuit can therefore be used with electrical machines with slip rings or brushless field systems, with conventional or high temperature superconducting or low temperature superconducting field windings, with permanent magnet rotors, in radial, axial and transverse flux orientation and in conventional, inside-out and double sided configurations. 
     In the case of a DC rotating electrical machine that employs electronic commutation then the armature will normally be the stator (i.e. the coils of the armature winding will be received in suitably shaped winding slots formed in the radially inner or radially outer surface of the stator). However it is also possible for the armature winding to be the rotor in some circumstances. 
     When single-layer coils are used the armature winding will preferably include p coils received in 2p winding slots provided in the stator of the electrical machine. When two-layer coils are used then the armature winding will preferably include 2p coils received in 2p winding slots provided in the stator of the electrical machine. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows part of an armature winding for a rotating electrical machine according to one or more embodiments. 
         FIG. 2  shows a table illustrating a distributed connection armature winding according to one or more embodiments. 
         FIG. 3  shows a table illustrating an alternative distributed connection armature winding according to one or more embodiments. 
     
    
    
     Exemplary embodiments of the invention will now be described, with reference to the accompanying drawings, in which: 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     With reference to  FIG. 1 , the stator  2  of a low-speed large-diameter electrical generator contains 288 equally spaced winding slots  4   a - 4   d  formed in its inner surface. Each winding slot contains a portion of a distributed connection armature winding that includes 144 coils (i.e. p=144). The winding slots  4   a - 4   d  are separated by teeth  6 . 
     The coil  8  shown in  FIG. 1  is a single-layer coil (also known as a ‘concentric’ coil) that is formed from one or more insulated conductors as a complete loop and has several turns. The coil  8  includes axially-extending runs  10  that are located in a corresponding pair of winding slots  4   a ,  4   d  and endwindings  12  that protrude out of the ends of the stator  2 . The distributed connection armature winding may be a two-tier or three-tier winding where the endwindings of the coils forming the inner tier or tiers (i.e. the tier or tiers closest to the end of the stator) are bent away from the axis of the stator by up to 90 degrees so that they may pass over the coils forming the outer tier or tiers. The endwindings of the coils forming the outermost tier do not need to pass over other coils and can be substantially parallel to the axis of the stator or bent away from the axis of the stator by up to 90 degrees. In practice, it will be readily appreciated that the distributed connection armature winding can use any suitable type of coil. In addition to the single-layer, multiple-turn coils mentioned above, these include single-layer, single-turn coils; two-layer coils with a single turn or multiple turns per coil; single- and two-layer round wire coils (also known as ‘mush’ coils); bar windings; and lap and wave windings, for example. The armature winding shown in  FIG. 1  has one coil in each group but other configurations are possible. 
     A rotor (not shown) is rotatably mounted within the stator  2  and has 88 magnet poles mounted around its outer rim. The electrical machine therefore has 44 pole-pairs. The magnet poles provide a magnet field that interacts with the armature winding in use. Other field means for providing a magnetic field can be provided on the rotor. 
     The number of coils per pole-pair for the electrical machine is 144/44 (i.e. n=p/44=144/44). 
     The number of winding slots per pole-pair for the electrical machine is 288/44. In practice, designs with a few as 5 slots per pole-pair are feasible and there is no upper limit. The angle between adjacent winding slots in the presence of the 44 pole-pair field (i.e. the winding slot pitch) is 55 electrical degrees. 
     As shown in  FIG. 2 , the distributed connection armature winding has four independent circuits, each circuit having 36 coils with identical sets of phase angles. The coils for each circuit are connected together in series and are distributed through the winding slots as shown in Table 1 therein where the coils in the first circuit are labelled A 1 , A 2  . . . A 26 , the coils in the second circuit are labelled B 1 , B 2  . . . B 36  and so on. The distributed connection armature phase winding has 36 plates, which is significantly more than the number of coils per pole-pair (i.e., 144/44). 
     The winding slots  4   a ,  4   d  that receive the axially-extending runs of the coil shown in  FIG. 1  are separated by two intermediate winding slots  4   b ,  4   c  (i.e. the coils have a ‘pitch’ of three winding slots). With reference to the first circuit, it can be seen that coil A 1  is received in winding slots  1  and  4 . This gives a pitch for coil A 1  of 165 electrical degrees (i.e. 3×55=165 electrical degrees). Coil A 2  is received in winding slots  27  and  30  and is therefore displaced by 26 slots from the coil A 1 . The electrical angle between the coils A 1  and A 2  is 1430 electrical degrees (i.e. 26×55=1430 electrical degrees) and this is equivalent to −10 electrical degrees. Coil A 3  is received in winding slots  53  and  56  and is therefore displaced by 26 slots from the coil A 2 . The electrical angle between the coils A 2  and A 3  is 1430 electrical degrees and this is equivalent to −10 electrical degrees. 
     Successive coils A 1  . . . A 36  in the first circuit are therefore displaced by 26 slots to give a retrogressive circuit with successive coils being separated by −10 electrical degrees. 
     Coil A 36  is received in winding slots  47  and  50  and is connected to coil A 1  to form a closed-loop. Coils A 36  and A 1  are separated by 46 slots in the reverse direction and the electrical angle between them is −2530 degrees (46×−55=−2530) electrical degrees and this is equivalent to −10 electrical degrees. The coils A 1  . . . A 36  in the first circuit are therefore separated from adjacent coils by a number of slots that is significantly more than the number of winding slots per pole-pair (i.e. 288/44). 
     With reference to the second circuit, it can be seen that coil B 1  is received in winding slots  73  and  76 . This gives a pitch for coil B 1  of 165 electrical degrees (i.e. 3×55=165 electrical degrees). Coil B 2  is received in winding slots  99  and  102  and is therefore displaced by 26 slots from the coil B 1 . The electrical angle between the coils B 1  and B 2  is 1430 electrical degrees (i.e. 26×55=1430 electrical degrees) and this is equivalent to −10 electrical degrees. Coil B 3  is received in winding slots  125  and  128  and is therefore displaced by 26 slots from the coil B 2 . The electrical angle between the coils B 2  and B 3  is 1430 electrical degrees and this is equivalent to −10 electrical degrees. 
     Successive coils B 1  . . . B 36  in the second circuit are therefore displaced by 26 slots to give a retrogressive circuit with successive coils being separated by −10 electrical degrees. 
     Coil B 36  is received in winding slots  119  and  122  and is connected to coil B 1  to form a closed-loop. Coils B 36  and B 1  are separated by 46 slots in the reverse direction and the electrical angle between them is −2530 degrees (46×−55=−2530) electrical degrees and this is equivalent to −10 electrical degrees. The coils B 1  . . . B 36  in the second circuit are therefore separated from adjacent coils by a number of slots that is significantly more than the number of winding slots per pole-pair (i.e. 288/44). 
     The third and fourth circuits are formed in a similar manner. 
     Each circuit contains 36 coils (i.e. s=36) defining  36  phase angles with equally spaced electrical angles between 0 and 360 electrical degrees and as a result the net voltage around each circuit is zero at all times and there are no circulating currents. Each circuit extends slightly more than three times around the circumference of the stator. 
     The number of independent circuits and the number of coils in each circuit will depend on the number of poles and the number of winding slots of the electrical machine. 
     The coils of each circuit are connected in series and each circuit has 36 points of coil interconnection (i.e. the interconnections between adjacent pairs of coils). Although not shown, an electronic commutator circuit may include 36 switching stages, each switching stage being connected between a respective one of the points of coil interconnection and first and second DC terminals. Each switching stage will typically include a first semiconductor power switching device having its anode connected to the first DC terminal and a second semiconductor power switching device having its cathode connected to the second DC terminal. The first and second semiconductor power switching devices may be thyristors or reverse blocking devices that are capable of being turned on and off by gate control (e.g. gate turn off thyristors or GTOs) as described in EP 1798847. In practice, it will be readily appreciated that any suitable electronic commutator circuit can be used. Alternative arrangements would have a switching stage between every second or third coil to reduce the total number of semiconductor power switching devices. 
     The four independent circuits may be connected together to form the complete distributed connection armature winding. The circuits can be connected externally at the DC side of the electronic commutator circuits or at the AC side of any associated inverters (not shown). The circuits can also be connected internally. Any suitable method of external or internal connection can be used. For example, when the external connection is made at the DC side of the electronic commutator circuit then the circuits can be connected in series, parallel or an appropriate combination of both. When necessary, the electronic commutation circuits would include components to limit any circulating current to an acceptable level. When the connection is made internally then a parallel connection between two or more circuits can be achieved by adding interconnections between all of the respective points of coil interconnection or only between those respective points of coil interconnection to which a switching stage is connected. It is also possible for coils in two or more circuits to be connected together in series. For example, coils A 1  and B 1  can be connected in series, coils A 2  and B 2  can be connected in series, coils A 3  and B 3  can be connected in series and so on, followed by connecting coils A 2  and B 1  in series, coils A 3  and B 2  in series, coils A 4  and B 3  in series and so on. This would result in a single circuit with twice the voltage. 
     It can be seen from Table 1 of  FIG. 2  that the circuits are interleaved and that each circuit extends slightly more than three times around the circumference of the stator. An alternative (or ‘concentrated’) distributed connection armature winding is shown in Table 2 of  FIG. 3  where each circuit is concentrated on a portion of the stator circumference. For an armature winding having four circuits, each circuit may be concentrated on approximately a quarter of the stator circumference, there will be a slight overlap of circuits at the ends and the extent of this depends on the pitch of the coils. 
     Coil A 1  is received in winding slots  1  and  4 . This gives a pitch for coil A 1  of 165 electrical degrees (i.e. 3×55=165 electrical degrees). Coil A 2  is received in winding slots  27  and  30  and is therefore displaced by 26 slots from the coil A 1 . The electrical angle between the coils A 1  and A 2  is 1430 electrical degrees (i.e. 26×55=1430 electrical degrees) and this is equivalent to −10 electrical degrees. Coil A 3  is received in winding slots  53  and  56  and is therefore displaced by 26 slots from the coil A 2 . The electrical angle between the coils A 2  and A 3  is 1430 electrical degrees and this is equivalent to −10 electrical degrees. If each circuit is allocated a quarter of the slots then it will be readily appreciated that the first circuit is to be concentrated in slots  1  to  72 . Coil A 4  is received in winding slots  7  and  10  and is therefore displaced by 26 slots from the coil A 3  (i.e. slots  53  to  72  and  1  to  7 ). The electrical angle between coils A 3  and A 4  is 1430 electrical degrees and this is equivalent to −10 electrical degrees. 
     Successive coils A 1  . . . A 36  in the first circuit are therefore displaced by 26 slots to give a retrogressive circuit with successive coils being separated by −10 electrical degrees and concentrated in approximately a quarter of the stator circumference. The only overlap is with coil A 12  where one of the axially-extending runs is received in winding slot  74 . 
     Coil A 36  is received in winding slots  47  and  50  and is connected to coil A 1  to form a closed-loop. Coils A 36  and A 1  separated by 46 slots in the reverse direction and the electrical angle between them is −2530 degrees (46×−55=−2530) electrical degrees and this is equivalent to −10 electrical degrees. The coils A 1  . . . A 36  in the first circuit are therefore separated from adjacent coils by a number of slots that is significantly more than the number of winding slots per pole-pair (i.e. 288/44). 
     With reference to the second circuit, coil B 1  is received in winding slots  73  and  76 . This gives a pitch for coil B 1  of 165 electrical degrees (i.e. 3×55=165 electrical degrees). Coil B 2  is received in winding slots  99  and  102  and is therefore displaced by 26 slots from the coil B 1 . The electrical angle between the coils B 1  and B 2  is 1430 electrical degrees (i.e. 26×55=1430 electrical degrees) and this is equivalent to −10 electrical degrees. Coil B 3  is received in winding slots  125  and  128  and is therefore displaced by 26 slots from the coil B 2 . The electrical angle between the coils B 2  and B 3  is 1430 electrical degrees and this is equivalent to −10 electrical degrees. If each circuit is allocated a quarter of the slots then it will be readily appreciated that the second circuit is to be concentrated in slots  73  to  144 . Coil B 4  is received in winding slots  79  and  82  and is therefore displaced by 26 slots from the coil B 3  (i.e. slots  125  to  144  and  73  to  79 ). The electrical angle between coils B 3  and B 4  is 1430 electrical degrees and this is equivalent to −10 electrical degrees. 
     Successive coils B 1  . . . B 36  in the second circuit are therefore displaced by 26 slots to give a retrogressive circuit with successive coils being separated by −10 electrical degrees and concentrated in approximately a quarter of the stator circumference. The only overlap is with coil B 12  where one of the axially-extending runs is received in winding slot  146 . 
     Coil B 36  is received in winding slots  119  and  122  and is connected to coil B 1  to form a closed-loop. Coils B 36  and B 1  are separated by 46 slots in the reverse direction and the electrical angle between them is −2530 degrees (46×−55=−2530) electrical degrees and this is equivalent to −10 electrical degrees. The coils B 1  . . . B 36  in the second circuit are therefore separated from adjacent coils by a number of slots that is significantly more than the number of winding slots per pole-pair (i.e. 288/44). 
     The third and fourth circuits are formed in a similar manner and are concentrated in slots  145  to  216  and  217  to  288 , respectively. 
     Each circuit contains 36 coils defining  36  phase angles with equally spaced electrical angles between 0 and 360 electrical degrees and as a result the net voltage around each circuit is zero at all times and there are no circulating currents. 
     In examples described above, the number of winding slots per pole-pair is 288/44 and the number of coils per pole-pair is 144/44. The distributed connection armature windings shown in Tables 1 and 2 have 36 phases and this is significantly more than the number of coils per pole-pair. If the electronic commutator circuit has 36 switching stages then the distributed connection armature winding will provide 36 commutating events per pole-pair. This is also significantly more than the number of coils per pole-pair. 
     A DC electrical machine that incorporates a distributed connection armature winding will have significantly less torque ripple than a similar size machine with fewer phases and fewer commutating events per pole-pair. 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Distributed connection armature winding 
               
             
          
           
               
                 Coil 
                 Slots 
                 Coil 
                 Slots 
                 Coil 
                 Slots 
                 Coil 
                 Slots 
               
               
                   
               
             
          
           
               
                 A1  
                 1 
                 4 
                 B1  
                 73 
                 76 
                 C1  
                 145 
                 148 
                 D1  
                 217 
                 220 
               
               
                 A2  
                 27 
                 30 
                 B2  
                 99 
                 102 
                 C2  
                 171 
                 174 
                 D2  
                 243 
                 246 
               
               
                 A3  
                 53 
                 56 
                 B3  
                 125 
                 128 
                 C3  
                 197 
                 200 
                 D3  
                 269 
                 272 
               
               
                 A4  
                 79 
                 82 
                 B4  
                 151 
                 154 
                 C4  
                 223 
                 226 
                 D4  
                 7 
                 10 
               
               
                 A5  
                 105 
                 108 
                 B5  
                 177 
                 180 
                 C5  
                 249 
                 252 
                 D5  
                 33 
                 36 
               
               
                 A6  
                 131 
                 134 
                 B6  
                 203 
                 206 
                 C6  
                 275 
                 278 
                 D6  
                 59 
                 62 
               
               
                 A7  
                 157 
                 160 
                 B7  
                 229 
                 232 
                 C7  
                 13 
                 16 
                 D7  
                 85 
                 88 
               
               
                 A8  
                 183 
                 186 
                 B8  
                 255 
                 258 
                 C8  
                 39 
                 42 
                 D8  
                 111 
                 114 
               
               
                 A9  
                 209 
                 212 
                 B9  
                 281 
                 284 
                 C9  
                 65 
                 68 
                 D9  
                 137 
                 140 
               
               
                 A10 
                 235 
                 238 
                 B10 
                 19 
                 22 
                 C10 
                 91 
                 94 
                 D10 
                 163 
                 166 
               
               
                 A11 
                 261 
                 264 
                 B11 
                 45 
                 48 
                 C11 
                 117 
                 120 
                 D11 
                 189 
                 192 
               
               
                 A12 
                 287 
                 2 
                 B12 
                 71 
                 74 
                 C12 
                 143 
                 146 
                 D12 
                 215 
                 218 
               
               
                 A13 
                 25 
                 28 
                 B13 
                 97 
                 100 
                 C13 
                 169 
                 172 
                 D13 
                 241 
                 244 
               
               
                 A14 
                 51 
                 54 
                 B14 
                 123 
                 126 
                 C14 
                 195 
                 198 
                 D14 
                 267 
                 270 
               
               
                 A15 
                 77 
                 80 
                 B15 
                 149 
                 152 
                 C15 
                 221 
                 224 
                 D15 
                 5 
                 8 
               
               
                 A16 
                 103 
                 106 
                 B16 
                 175 
                 178 
                 C16 
                 247 
                 250 
                 D16 
                 31 
                 34 
               
               
                 A17 
                 129 
                 132 
                 B17 
                 201 
                 204 
                 C17 
                 273 
                 276 
                 D17 
                 57 
                 60 
               
               
                 A18 
                 155 
                 158 
                 B18 
                 227 
                 230 
                 C18 
                 11 
                 14 
                 D18 
                 83 
                 86 
               
               
                 A19 
                 181 
                 184 
                 B19 
                 253 
                 256 
                 C19 
                 37 
                 40 
                 D19 
                 109 
                 112 
               
               
                 A20 
                 207 
                 210 
                 B20 
                 279 
                 282 
                 C20 
                 63 
                 66 
                 D20 
                 135 
                 138 
               
               
                 A21 
                 233 
                 236 
                 B21 
                 17 
                 20 
                 C21 
                 89 
                 92 
                 D21 
                 161 
                 164 
               
               
                 A22 
                 259 
                 262 
                 B22 
                 43 
                 46 
                 C22 
                 115 
                 118 
                 D22 
                 187 
                 190 
               
               
                 A23 
                 285 
                 288 
                 B23 
                 69 
                 72 
                 C23 
                 141 
                 144 
                 D23 
                 213 
                 216 
               
               
                 A24 
                 23 
                 26 
                 B24 
                 95 
                 98 
                 C24 
                 167 
                 170 
                 D24 
                 239 
                 242 
               
               
                 A25 
                 49 
                 52 
                 B25 
                 121 
                 124 
                 C25 
                 193 
                 196 
                 D25 
                 265 
                 268 
               
               
                 A26 
                 75 
                 78 
                 B26 
                 147 
                 150 
                 C26 
                 219 
                 222 
                 D26 
                 3 
                 6 
               
               
                 A27 
                 101 
                 104 
                 B27 
                 173 
                 176 
                 C27 
                 245 
                 248 
                 D27 
                 29 
                 32 
               
               
                 A28 
                 127 
                 130 
                 B28 
                 199 
                 202 
                 C28  
                 271 
                 274 
                 D28 
                 55 
                 58 
               
               
                 A29 
                 153 
                 156 
                 B29 
                 225 
                 228 
                 C29 
                 9 
                 12 
                 D29 
                 81 
                 84 
               
               
                 A30 
                 179 
                 182 
                 B30 
                 251 
                 254 
                 C30 
                 35 
                 38 
                 D30 
                 107 
                 110 
               
               
                 A31 
                 205 
                 208 
                 B31 
                 277 
                 280  
                 C31 
                 61 
                 64 
                 D31 
                 133 
                 136 
               
               
                 A32 
                 231 
                 234 
                 B32 
                 15 
                 18 
                 C32 
                 87 
                 90 
                 D32 
                 159 
                 162 
               
               
                 A33 
                 257 
                 260 
                 B33 
                 41 
                 44 
                 C33 
                 113 
                 116 
                 D33 
                 185 
                 188 
               
               
                 A34 
                 283 
                 286 
                 B34 
                 67 
                 70 
                 C34 
                 139 
                 142 
                 D34 
                 211 
                 214 
               
               
                 A35 
                 21 
                 24 
                 B35 
                 93 
                 96 
                 C35 
                 165 
                 168 
                 D35 
                 237 
                 240 
               
               
                 A36 
                 47 
                 50 
                 B36 
                 119 
                 122 
                 C36 
                 191 
                 194 
                 D36 
                 263  
                 266 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Alternative distributed connection armature winding 
               
             
          
           
               
                 Coil 
                 Slots 
                 Coil 
                 Slots 
                 Coil 
                 Slots 
                 Coil 
                 Slots 
               
               
                   
               
             
          
           
               
                 A1  
                 1 
                 4 
                 B1  
                 73 
                 76 
                 C1  
                 145 
                 148 
                 D1  
                 217 
                 220 
               
               
                 A2  
                 27 
                 30 
                 B2  
                 99 
                 102 
                 C2  
                 171 
                 174 
                 D2  
                 243 
                 246 
               
               
                 A3  
                 53 
                 56 
                 B3  
                 125 
                 128 
                 C3  
                 197 
                 200 
                 D3  
                 269 
                 272 
               
               
                 A4  
                 7 
                 10 
                 B4  
                 79 
                 82 
                 C4  
                 151 
                 154 
                 D4  
                 223 
                 226 
               
               
                 A5  
                 33 
                 36 
                 B5  
                 105 
                 108 
                 C5  
                 177 
                 180 
                 D5  
                 249 
                 252 
               
               
                 A6  
                 59 
                 62 
                 B6  
                 131 
                 134 
                 C6  
                 203 
                 206 
                 D6  
                 275 
                 278 
               
               
                 A7  
                 13 
                 16 
                 B7  
                 85 
                 88 
                 C7  
                 157 
                 160 
                 D7  
                 229 
                 232 
               
               
                 A8  
                 39 
                 42 
                 B8  
                 111 
                 114 
                 C8  
                 183 
                 186 
                 D8  
                 255 
                 258 
               
               
                 A9  
                 65 
                 68 
                 B9  
                 137 
                 140 
                 C9  
                 209 
                 212 
                 D9  
                 281 
                 284 
               
               
                 A10 
                 19 
                 22 
                 B10 
                 91 
                 94 
                 C10 
                 163 
                 166 
                 D10 
                 235 
                 238 
               
               
                 A11 
                 45 
                 48 
                 B11 
                 117 
                 120 
                 C11 
                 189 
                 192 
                 D11 
                 261 
                 264 
               
               
                 A12 
                 71 
                 74 
                 B12 
                 143 
                 146 
                 C12 
                 215 
                 218 
                 D12 
                 287 
                 2 
               
               
                 A13 
                 25 
                 28 
                 B13 
                 97 
                 100 
                 C13 
                 169 
                 172 
                 D13 
                 241 
                 244 
               
               
                 A14 
                 51 
                 54 
                 B14 
                 123 
                 126 
                 C14 
                 195 
                 198 
                 D14 
                 267 
                 270 
               
               
                 A15 
                 5 
                 8 
                 B15 
                 77 
                 80 
                 C15 
                 149 
                 152 
                 D15 
                 221 
                 224 
               
               
                 A16 
                 31 
                 34 
                 B16 
                 103 
                 106 
                 C16 
                 175 
                 178 
                 D16 
                 247 
                 250 
               
               
                 A17 
                 57 
                 60 
                 B17 
                 129 
                 132 
                 C17 
                 201 
                 204 
                 D17 
                 273 
                 276 
               
               
                 A18 
                 11 
                 14 
                 B18 
                 83 
                 86 
                 C18 
                 155 
                 158 
                 D18 
                 227 
                 230 
               
               
                 A19 
                 37 
                 40 
                 B19 
                 109 
                 112 
                 C19 
                 181 
                 184 
                 D19 
                 253 
                 256 
               
               
                 A20 
                 63 
                 66 
                 B20 
                 135 
                 138 
                 C20 
                 207 
                 210 
                 D20 
                 279 
                 282 
               
               
                 A21 
                 17 
                 20 
                 B21 
                 89 
                 92 
                 C21 
                 161 
                 164 
                 D21 
                 233 
                 236 
               
               
                 A22 
                 43 
                 46 
                 B22 
                 115 
                 118 
                 C22 
                 187 
                 190 
                 D22 
                 259 
                 262 
               
               
                 A23 
                 69 
                 72 
                 B23 
                 141 
                 144 
                 C23 
                 213 
                 216 
                 D23 
                 285 
                 288 
               
               
                 A24 
                 23 
                 26 
                 B24 
                 95 
                 98 
                 C24 
                 167 
                 170  
                 D24 
                 239 
                 242 
               
               
                 A25 
                 49 
                 52 
                 B25 
                 121 
                 124 
                 C25 
                 193 
                 196 
                 D25 
                 265 
                 268 
               
               
                 A26 
                 3 
                 6 
                 B26 
                 75 
                 78 
                 C26 
                 147 
                 150  
                 D26 
                 219 
                 222 
               
               
                 A27 
                 29 
                 32 
                 B27 
                 101 
                 104 
                 C27 
                 173 
                 176 
                 D27 
                 245 
                 248 
               
               
                 A28 
                 55 
                 58 
                 B28 
                 127 
                 130 
                 C28 
                 199 
                 202 
                 D28 
                 271 
                 274 
               
               
                 A29 
                 9 
                 12 
                 B29 
                 81 
                 84 
                 C29 
                 153 
                 156 
                 D29 
                 225 
                 228 
               
               
                 A30 
                 35 
                 38 
                 B30 
                 107 
                 110 
                 C30 
                 179 
                 182 
                 D30 
                 251 
                 254 
               
               
                 A31 
                 61 
                 64 
                 B31 
                 133 
                 136 
                 C31 
                 205 
                 208 
                 D31 
                 277 
                 280 
               
               
                 A32 
                 15 
                 18 
                 B32 
                 87 
                 90 
                 C32 
                 159 
                 162 
                 D32 
                 231 
                 234 
               
               
                 A33 
                 41 
                 44 
                 B33 
                 113 
                 116 
                 C33 
                 185 
                 188 
                 D33 
                 257 
                 260 
               
               
                 A34 
                 67 
                 70 
                 B34 
                 139 
                 142 
                 C34 
                 211 
                 214 
                 D34 
                 283 
                 286 
               
               
                 A35 
                 21 
                 24 
                 B35 
                 93 
                 96 
                 C35 
                 165 
                 168 
                 D35 
                 237 
                 240 
               
               
                 A36 
                 47 
                 50 
                 B36 
                 119 
                 122 
                 C36 
                 191 
                 194 
                 D36 
                 263 
                 266