Abstract:
A brushless, synchronous machine is provided. A brushless, synchronous motor includes a rotor, a stator extending around at least a portion of the rotor and separated from the rotor by an air gap, a first stator winding, a second stator winding, a third stator winding, a drive circuit, a first rotor winding, a second rotor winding, and a diode bridge. The first stator winding, the second stator winding, and the third stator winding are mounted to the stator to generate square waves. The drive circuit is configured to provide a current to the first stator winding, the second stator winding, and the third stator winding, wherein the current includes an alternating current (AC) component and a direct current (DC) component. The first rotor winding is mounted to the rotor to form a plurality of third harmonic coils. The second rotor winding is mounted to the rotor. The generated square waves induce a voltage in the first rotor winding that is applied to the second rotor winding to create a brushless, synchronous motor. The diode bridge is mounted to the rotor to rectify the voltage induced in the first rotor winding and to apply the resulting DC voltage to the second rotor winding.

Description:
BACKGROUND 
     Existing electrical machines provide the ability to capture power from a mechanically rotating source, such as a wind turbine or deliver power to load such as a pump or compressor. A synchronous machine may therefore comprise a synchronous motor or a synchronous generator. As an example, a synchronous motor includes a stator, which carries an armature winding, and a rotor, which carries a field winding and which rotates at a supply frequency or a submultiple of the supply frequency. The armature winding is spatially distributed for poly-phase alternating current (AC), which creates a rotating magnetic field inside the synchronous motor. The magnetic field on the rotor is either generated by current delivered through slip rings and brushes to the field winding of the rotor or by a rotor comprised of a permanent magnet. On excitation through carbon brushes connected to slip rings on the rotor shaft, the field winding behaves as the equivalent of a permanent magnet. A drawback to synchronous machines utilizing brushes and slip rings is that the slip rings and brushes present reliability and maintenance issues because they are often a source of mechanical failure. Conversely, embodiments utilizing a permanent magnet are becoming increasingly expensive due to the scarcity of the raw materials used to form the permanent magnet. 
     SUMMARY 
     A brushless, synchronous motor is provided that includes a rotor, a stator extending around at least a portion of the rotor and separated from the rotor by an air gap, a first stator winding, a second stator winding, a third stator winding, a drive circuit, a first rotor winding, a second rotor winding, and a diode bridge. The first stator winding, the second stator winding, and the third stator winding are mounted to the stator to generate square waves. The drive circuit is configured to provide a current to the first stator winding, the second stator winding, and the third stator winding, wherein the current includes an alternating current (AC) component and a direct current (DC) component. The first rotor winding is mounted to the rotor to form a plurality of third harmonic coils. The second rotor winding is mounted to the rotor. The generated square waves induce a voltage in the first rotor winding that is applied to the second rotor winding to create a brushless, synchronous motor. The diode bridge is mounted to the rotor to rectify the voltage induced in the first rotor winding and to apply the resulting DC voltage to the second rotor winding. 
     A method of operating a brushless, synchronous motor is provided. A current is provided to a first stator winding, a second stator winding, and a third stator winding. The current includes an alternating current (AC) component and a direct current (DC) component. The first stator winding, the second stator winding, and the third stator winding are mounted to a stator. A first rotating magnetomotive force (MMF) is generated in an air gap between the stator and a rotor in response to the AC component. A second rotating MMF is generated in the air gap between the stator and the rotor in response to the DC component. A voltage is induced in a first rotor winding mounted to the rotor to form a plurality of third harmonic coils. The induced voltage is rectified using a rectifier. The rectified voltage is applied to a second rotor winding mounted to the rotor to cause rotation of the rotor. 
     Other principal features and advantages of the invention will become apparent to those skilled in the art upon review of the following drawings, the detailed description, and the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Illustrative embodiments of the invention will hereafter be described with reference to the accompanying drawings, wherein like numerals denote like elements. 
         FIG. 1  depicts a cross-sectional view of a synchronous machine in accordance with an illustrative embodiment. 
         FIG. 2  depicts a diagram of a first stator circuit configured to generate a third harmonic component in accordance with a first illustrative embodiment. 
         FIG. 3  depicts a diagram of a second stator circuit configured to generate a third harmonic component in accordance with a second illustrative embodiment. 
         FIG. 4   a  depicts a first layout diagram of stator and rotor windings in accordance with a first illustrative embodiment of the synchronous machine of  FIG. 1 . 
         FIG. 4   b  depicts a block diagram of a circuit represented by the first layout diagram of  FIG. 4   a.    
         FIG. 5   a  depicts a second layout diagram of stator and rotor windings in accordance with a second embodiment of the synchronous machine of  FIG. 1 . 
         FIG. 5   b  depicts a field magnetomotive force (MMF) generated using the stator and rotor windings represented by the second layout diagram of  FIG. 5   a.    
         FIG. 6   a  depicts a third layout diagram of stator and rotor windings in accordance with a third embodiment of the synchronous machine of  FIG. 1 . 
         FIG. 6   b  depicts a field MMF generated using the stator and rotor windings represented by the third layout diagram of  FIG. 6   a.    
         FIG. 7  depicts a fourth layout diagram of stator and rotor windings in accordance with a fourth embodiment of the synchronous machine of  FIG. 1 . 
         FIG. 8  depicts a pole geometry based on the fourth layout diagram of stator and rotor windings of  FIG. 7  in accordance with an illustrative embodiment. 
         FIG. 9  depicts an implementation of the synchronous machine of  FIG. 4   a  for operation as an isolated power source in accordance with an illustrative embodiment. 
         FIG. 10  depicts a control algorithm for starting the synchronous machine of  FIG. 1  when operated as a motor fed from a sinusoidal power supply in accordance with an illustrative embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     With reference to  FIG. 1 , a cross-sectional view of a machine  100  is shown in an illustrative embodiment. In general, machine  100  may be used as a motor or a generator dependent on the driving mechanism. Machine  100  may include a stator  102  and a rotor  104  mounted to a shaft  106  for rotation. Rotor  104  may be mounted to a shaft  106  through a variety of means as known to those skilled in the art. If machine  100  is utilized as a motor, stator  102  causes rotor  104  to rotate utilizing electrical energy thereby rotating shaft  106  to provide mechanical energy; whereas, if machine  100  is utilized as a generator, shaft  106  is rotated by an external mechanical force/torque that causes rotor  104  to rotate thereby causing stator  102  to generate electrical energy. 
     As shown with reference to the illustrative embodiment of  FIG. 1 , stator  102  includes six electromagnet, salient or projecting poles with each pair of poles having a concentrated, full pitch winding. For example, a first pair of poles  108 ,  110  have a first full pitch winding  112  and may be associated with a phase denoted as A; a second pair of poles  114 ,  116  have a second full pitch winding  118  and may be associated with a phase denoted as B; and a third pair of poles  120 ,  122  have a third full pitch winding  124  and may be associated with a phase denoted as C. Each stator pole may be positioned at 60° angular intervals and have a common arc length dimension. Stator  102  may have a greater or a fewer number of pairs of poles depending on the embodiment. 
     As shown with reference to the illustrative embodiment of  FIG. 1 , rotor  104  includes two salient or projecting poles  126 ,  128 , which act as salient magnetic poles though rotor  104  may have a greater or a fewer number of poles and include poles having different dimensions depending on the embodiment. Each rotor pole may be positioned at equal angular intervals and have a common arc length dimension. Stator  102  and rotor  104  are separated by an air gap  134 . 
     In a synchronous motor, application of three-phase AC power to stator  102  causes a rotating magnetic field to be setup around rotor  104 . In a conventional machine, rotor  104  may be energized with a direct current (DC) through slip rings and brushes. The rotating magnetic field attracts the rotor field activated by the DC resulting in a turning force on shaft  106 . 
     The magnetomotive force (MMF) produced in air gap  134  for motor  100  can be expressed by the winding function
 
 F (Ø, i )=Σ i=1   m   N   i (Ø) i   i ( t )  (1)
 
where Ø  130  denotes the angular measure around air gap  134  of machine  100 , N i (Ø) is the winding function describing the position and polarity of all of the coil sides of the winding of interest  112 ,  118 ,  124 , and i i (t) is the current in the respective winding. The MMF for a three phase winding can therefore be expressed as
 
 F   ABC (Ø, i )= N   A (Ø) i   A ( t )+ N   B (Ø) i   B ( t )+ N   C (Ø) i   C ( t ).  (2)
 
     In conventionally wound three phase armatures, the three currents are considered to be a balanced three phase set and the three winding functions are configured to approximate sinusoidal functions of the angle which are also balanced (mutually displaced by 120° with respect to Ø). The result can be shown to produce a constant amplitude uniformly rotating MMF along the air gap as known to a person of skill in the art. 
     If windings are instead configured to have a full pitch and concentrated layout as shown with reference to machine  100  of  FIG. 1 , the three winding functions of the three phases become rectangular waves. The three rectangular wave winding functions can be expressed as a Fourier series of odd harmonics. Assuming that only the first harmonic and the next most significant harmonic are retained in the series, the winding function for phases A, B, C can be represented as a function of the spatial angle φ as 
     
       
         
           
             
               
                 
                   
                     
                       N 
                       A 
                     
                     ⁡ 
                     
                       ( 
                       ∅ 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         4 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         N 
                       
                       π 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ∅ 
                         
                         + 
                         
                           
                             1 
                             3 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           ∅ 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       N 
                       B 
                     
                     ⁡ 
                     
                       ( 
                       ∅ 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         4 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         N 
                       
                       π 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               ∅ 
                               - 
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                 
                                 3 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             1 
                             3 
                           
                           ⁢ 
                           
                             sin 
                             ⁡ 
                             
                               [ 
                               
                                 3 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     ∅ 
                                     - 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                               ] 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     = 
                     
                       
                         
                           4 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           N 
                         
                         π 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 ∅ 
                                 - 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               1 
                               3 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                             ⁢ 
                             ∅ 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       N 
                       C 
                     
                     ⁡ 
                     
                       ( 
                       ∅ 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         4 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         N 
                       
                       π 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               ∅ 
                               + 
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                 
                                 3 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             1 
                             3 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           ∅ 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     A drive circuit generates three armature currents, i A (t), i B (t), i C (t), that are applied to first full pitch winding  112 , second full pitch winding  118 , and third full pitch winding  124 , respectively, and have the form 
     
       
         
           
             
               
                 
                   
                     
                       i 
                       A 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         I 
                         1 
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       t 
                     
                     + 
                     
                       I 
                       n 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       i 
                       B 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         I 
                         1 
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                             - 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                               3 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       I 
                       n 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       i 
                       C 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         I 
                         1 
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                               3 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       I 
                       n 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Utilizing equation (2), the MMF becomes 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       ABC 
                     
                     ⁡ 
                     
                       ( 
                       
                         ∅ 
                         , 
                         i 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           4 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           N 
                         
                         π 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ∅ 
                                 
                                 + 
                                 
                                   
                                     1 
                                     3 
                                   
                                   ⁢ 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   3 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ∅ 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     I 
                                     1 
                                   
                                   ⁢ 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ω 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   I 
                                   n 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 ∅ 
                                 - 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               1 
                               3 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ∅ 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               I 
                               1 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     ω 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   - 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                     
                                     3 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             I 
                             n 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 ∅ 
                                 + 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               1 
                               3 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                             ⁢ 
                             ∅ 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               
                                 I 
                                 1 
                               
                               ⁢ 
                               
                                 sin 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       t 
                                     
                                     + 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               I 
                               n 
                             
                           
                           } 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Rearranging equation (10), the MMF becomes 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       ABC 
                     
                     ⁡ 
                     
                       ( 
                       
                         ∅ 
                         , 
                         i 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         4 
                         π 
                       
                       ⁢ 
                       
                         NI 
                         1 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ∅sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   ∅ 
                                   - 
                                   
                                     
                                       2 
                                       ⁢ 
                                       π 
                                     
                                     3 
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     ω 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   - 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                     
                                     3 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   ∅ 
                                   + 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                     
                                     3 
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     ω 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                     
                                     3 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         4 
                         π 
                       
                       ⁢ 
                       
                         NI 
                         1 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             3 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ∅ 
                             ⁡ 
                             
                               [ 
                               
                                 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ω 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         t 
                                       
                                       - 
                                       
                                         
                                           2 
                                           ⁢ 
                                           π 
                                         
                                         3 
                                       
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         t 
                                       
                                       + 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           π 
                                         
                                         3 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               ] 
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         4 
                         π 
                       
                       ⁢ 
                       
                         
                           
                             NI 
                             n 
                           
                           3 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ∅ 
                             
                             + 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   ∅ 
                                   - 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                     
                                     3 
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   ∅ 
                                   + 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                     
                                     3 
                                   
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                     
                     + 
                     
                       
                         4 
                         π 
                       
                       ⁢ 
                       
                         NI 
                         n 
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                       ⁢ 
                       
                         ∅ 
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The first of the four terms produces a rotating constant amplitude uniformly rotating vector corresponding to the fundamental component of the current I 1 . The second and third terms are zero because the sum of three balanced sine waves is zero. The fourth term is an additional term which is defined here as 
     
       
         
           
             
               
                 
                   
                     F 
                     n 
                   
                   = 
                   
                     
                       4 
                       π 
                     
                     ⁢ 
                     
                       NI 
                       n 
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                     ⁢ 
                     
                       ∅ 
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     As a result, neglecting harmonics higher than the third, first full pitch winding  112 , second full pitch winding  118 , and third full pitch winding  124 , or the armature windings, produce two components of MMF that are decoupled from each other, a first MMF being the normal, constant amplitude, uniformly rotating MMF and a second MMF defined by equation (12), which is stationary in space. Of note, the “zero sequence” component or second MMF term, which normally is considered to involve only the third harmonic component with respect to time, can be a pulsating component the frequency of which is arbitrary and includes zero (DC). 
     If the second MMF term involves only a DC component I 0 , the additional stator component of stator MMF appears in the reference frame of rotor  104  as 
                     F   o     =       4   π     ⁢     NI   o     ⁢   sin   ⁢           ⁢   3   ⁢     θ   r               (   13   )               
where θ r    132  is the angle of rotor rotation with respect to a defined stator reference point as shown in  FIG. 1 .
 
     Assuming synchronous speed, i.e. θ r =ωt, as a result, at any spatial position around the air gap φ, the rotor  104  experiences a sinusoidal constant amplitude MMF waveform. 
     With reference to  FIG. 2 , a first stator circuit  200  including an open winding connection  202  is shown in accordance with an illustrative embodiment. Using an open winding connection  202 , a first added pulsating or single phase component of current, I n , can be created by controlling operation of switches  204  across each phase A, B, C as known to a person of skill in the art. In an illustrative embodiment, each switch of the switches  204  may include a switch circuit  206  as shown with reference to  FIG. 2 . 
     With reference to  FIG. 3 , a second stator circuit  300  including a fourth inverter leg  302  is shown in accordance with an illustrative embodiment. Using the fourth inverter leg  302 , a DC component of current, I 0 , can be created by controlling operation of switches  304  across each phase A, B, C as known to a person of skill in the art. In an illustrative embodiment, each switch of the switches  304  may include a switch circuit  206  as shown with reference to  FIG. 3 . 
     With reference to  FIGS. 4   a  and  4   b , a layout of stator and rotor windings for machine  100  and a diagram of a circuit representation for the stator and rotor windings for machine  100 , respectively, are shown to illustrate a principle of operation of machine  100  in accordance with an illustrative embodiment. A pulsating MMF as viewed from rotor  104  can be utilized by installing a first rotor winding  400  having a third harmonic spatial component in a first slot  402  and in a second plurality of slots  404 . The voltage induced in first rotor winding  400  can be rectified using a rectifier  406 , and the resulting voltage applied to a second rotor winding  408  having a full pitch in first slot  402  creating the equivalent of a DC field winding without the use of brushes or slip rings. In an illustrative embodiment, rectifier  406  is a diode bridge. 
     Because the zero sequence stator current creating the DC field current is DC, no inductive drop in stator  102  occurs to limit the field current that can be induced. Also, the current on the DC side of rectifier  406  is limited only by a very small resistance drop. Therefore, the maximum field current is set essentially by the reactive drop across first rotor winding  400 . The current on the DC side of rectifier  406  (i.e. the field current) is proportional to the current on the AC side (i.e. the spatial third harmonic current). However, since the MMF created by the field winding is the product of the field turns times the DC current, multiple field turns can be utilized to produce whatever field MMF is desired. The limit is determined by both the reactive drop of the AC side and the resistance of the DC field winding. 
     With reference to  FIG. 5   a , a layout of stator and rotor windings for machine  100  is shown in accordance with an illustrative embodiment utilizing a cylindrical rotor configuration. It is preferred that the field winding not create any third harmonic spatial components which could interfere with utilization of the third harmonic spatial component creating the excitation of rotor  104 . As shown with reference to  FIG. 5   a , sides of a field winding coil are placed in adjacent slots  500 ,  502  displaced by 60 electrical degrees producing an MMF distribution, which does not contain a third spatial harmonic, as shown with reference to  FIG. 5   b.    
     With reference to  FIG. 6   a , a layout of stator and rotor windings for machine  100  is shown in accordance with an illustrative embodiment utilizing a cylindrical rotor configuration. In the illustrative embodiment of  FIG. 6   a , stator  102  includes a first plurality of saliencies  600  and a second plurality of saliencies  602  creating variations in air gap  134  which create a third harmonic saliency. Using this illustrative embodiment, a conventional three leg inverter can be used instead of the circuits shown with reference to  FIGS. 2 and 3 . However, if desired, the circuits shown with reference to  FIGS. 2 and 3  can be used together with machine  100  shown with reference to  FIG. 6   a . The DC current component added to the stator MMF can be used to add or subtract from the MMF provided by the saliencies to achieve the function of an adjustable field winding. With reference to  FIG. 6   b , the resulting field MMF is shown. 
     With reference to  FIG. 7 , a layout of stator and rotor windings for machine  100  is shown in accordance with an illustrative embodiment utilizing rotor  104  having a salient pole configuration including a first saliency  700  and a second saliency  702  First saliency  700  includes a first third harmonic coil  704  and a second third harmonic coil  706 . Second saliency  702  includes a first third harmonic coil  708  and a second third harmonic coil  710 . Therefore, only two third harmonic coils are utilized per pole rather than three. Again, no third harmonics are created in air gap  134  as a result of the field winding. 
     With reference to  FIG. 8 , a pole geometry for machine  100  of  FIG. 7  is shown in accordance with a more illustrative actual embodiment where first saliency  700  includes a first projection  800  and a second projection  802  such that first third harmonic coil  704  of first saliency  700  is wound around first projection  800  and second third harmonic coil  706  of first salience  700  is wound around second projection  802 . 
     The brushless concept can be expanded to include operation as a generator  900  providing power to an AC grid  902  or other load. Generator  900  may provide a constant 60 Hz power to AC grid  902 . The added DC current component in the stator can be implemented using three silicon controlled rectifiers (SCRs)  904 ,  906 ,  908  as shown with reference to  FIG. 9 . SCRs  904 ,  906 ,  908  are controlled to produce the desired component of DC current in first full pitch winding  112 , second full pitch winding  118 , and third full pitch winding  124 , respectively. However, additional harmonics are produced when using simple phase control. Nonetheless, generator  900  can be used where the quality of the voltage waveform is not critical such as in isolated power supplies. 
     A disadvantage of a synchronous motor using this concept is that it cannot be started from a standstill by applying a component of DC power to stator  102 . However, this problem can be overcome by first utilizing an AC component for the zero sequence current rather than a DC one. For example, if a third time harmonic component is chosen, the MMF impressed on rotor  104  is 
               F   n     =       4   π     ⁢     NI   3             
sin 3ωt sin 3(Ø−θr, where θr≅0. The MMF at zero speed is then simply a third time harmonic. When the rotor speed begins to increase, frequencies 3(ωt−θ r ) and 3(ωt+θ r ) appear causing the amplitude to slowly pulsate. Because the third time harmonic now induces a voltage in the first rotor winding the motor can be started. A pulsating component however, produces noise and torque pulsations. Before the pulsating effect becomes pronounced, the pulsating or single phase component of current, I n , can be switched to a DC value through control of the power converter.
 
     An important application area for the use of machine  100  is as a motor fed from a sinusoidal power source. However, this case requires a more sophisticated control algorithm in order to start machine  100 . In this case, the best choice for the neutral current, I n , is the use of a single phase current. Since induced rotor current must flow to produce induction motor type starting torque, the rotor circuits may be short circuited by switches  1000  as shown with reference to  FIG. 10 . Switches  1000  are activated upon starting and are opened when rotor  104  approaches synchronous speed. A centrifugal switch  1002  may be used if centrifugal switch  1002  can be reliably opened at the correct instant. The alternative is to use a controlled switch, opened by sensing a frequency of the stator slots or the frequency induced in the third harmonic rotor windings as rotor  104  reaches synchronous speed. In an illustrative embodiment, the stator and rotor winding configuration is the same as shown with reference to  FIG. 4   a.    
     The word “illustrative” is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “illustrative” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Further, for the purposes of this disclosure and unless otherwise specified, “a” or “an” means “one or more”. Still further, the use of “and” or “or” is intended to include “and/or” unless specifically indicated otherwise. 
     The foregoing description of illustrative embodiments of the invention have been presented for purposes of illustration and of description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the invention. The embodiments were chosen and described in order to explain the principles of the invention and as practical applications of the invention to enable one skilled in the art to utilize the invention in various embodiments and with various modifications as suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto and their equivalents.