Abstract:
A dual stator winding induction machine has two windings with input terminals which are supplied separately with drive power. The two stator windings have a different number of poles to essentially eliminate the magnetic coupling between the two windings and to decouple the torques produced by each set of windings. Power is supplied to the two windings by two separate variable frequency inverter drives to provide two independently controllably torque components. At low speed, the power supplied to one of the windings can produce torque which opposes the torque from the power applied to the other winding, so that very low speed and standstill operation can be achieved while the frequency of the power supplied by the inverters is always greater than the minimum frequency. At higher operating speeds, power is supplied to the two windings so that the torque from the windings adds. The dual stator machine can be built with minimal modifications to standard winding configurations.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of provisional patent application No. 60/079,140, filed Mar. 24, 1998. 
    
    
     This invention was made with United States Government support awarded by the following agencies: NSF Grant No.: 9510115. The United States Government has certain rights in this invention. 
    
    
     FIELD OF THE INVENTION 
     This invention pertains generally to the field of electric motors and to drives for such motors, and particularly to induction machine drives. 
     BACKGROUND OF THE INVENTION 
     The use of a common magnetic structure which is shared by two sets of stator windings was first introduced in the late 1920s as a way to increase the power capability of large synchronous generators. See, P. L. Alger, et al., “Double Windings for Turbine Alternators, ” AIEE Transactions, Vol. 49, January, 1930, pp. 226-244. Since that time, dual stator machines have been used in many other applications. These include synchronous machines with AC and DC outputs. P. W. Franklin, “A Theoretical Study of the Three-Phase Salient Pole-Type Generator with Simultaneous AC and Bridge Rectified DC Output, ” IEEE Transactions on Power App. and Systems, Vol. PAS-92, No. 2, March/April 1973, pp. 543-557. Dual stator machines have also been used as current source inverters to large pumps, compressors and rolling mills driven by induction machines. T. Kataoka, et al., “Dynamic Control of a Current-Source Inverter/Double-Wound Synchronous Machine System for AC Power Supply, ” IEEE Transactions on Industry Applications, Vol. IA-17, No. , 3May/June 1981, pp. 314-320. Another purpose for the use of dual stators has been to improve reliability at the system level. See, e.g., J. R. Fu, et al., “Disturbance Free Operation of a Multiphase Current Regulated Motor Drive with an Open Phase, ” IEEE Transactions on Industry Applications, Vol. 30, No. 5, September/October 1994, pp. 1267-1274; J. C. Sahnon, et al., “A Split-Wound Induction Motor Design to Improve the Reliability of PWM Inverter Drives, ” IEEE Transactions on Industry Applications, Vol. IA-26, No. 1, January/February 1990, pp. 143-150. 
     Dual stator machines are normally constructed by “splitting ” the stator winding into two displaced but identical windings. See, e.g., E. F. Fuchs, et al., “Analysis of an Alternator with Two Displaced Stator Windings, ” IEEE Transactions on Power App. and Systems, Vol. PAS-93, No. 6, November/December 1974, pp. 1776-1786. However, splitting the stator winding in this manner results in mutual coupling between the stators, causing circulating harmonic currents. K. Gopakumar, et al., “Split-Phase Induction Motor Operation from PWM Voltage Source Inverter, ” IEEE Transactions on Industry Applications, Vol. 29, No. 5, September/October 1993, pp. 927-932. Such split stator winding machines have thus had a major drawback because the circulating currents add extra stator losses and demand larger semiconductor device ratings. In addition, there is coupling between the electromagnetic torques produced by each stator winding. See, T. A. Lipo, “A d-q Model for Six Phase Induction Machines, ” International Conference on Electric Machines, Athens, Greece, 1980, pp. 860-867. 
     SUMMARY OF THE INVENTION 
     A dual stator winding induction machine in accordance with the invention has two polyphase windings with input terminals available to be supplied separately with drive power. The two stator windings are wound with a different number of poles to essentially eliminate the magnetic coupling between the two stator windings and to decouple the torques produced by each set of stator windings. In addition, circulating harmonic currents encountered in conventional dual stator winding machines due to the so called mutual leakage coupling are completely eliminated. Since the output torque corresponds to the algebraic sum of two independent torques, the stator frequency is no longer determined uniquely by the rotor speed and the slip frequency, but also by the added variable of a second torque component, adding an additional degree of freedom to the system for greater control flexibility. 
     The dual stator winding machine supplied with power from two separate variable frequency inverter drives in accordance with the invention provides two independently controllable torque components, thereby allowing the low frequency operation of the machine —including at standstill —to be improved. Such a characteristic is particularly important for constant volts per hertz control operation at zero speed, where the influence of the stator resistance becomes dominant. In the present invention, zero speed operation does not require zero excitation frequency for the two power drives, thus significantly reducing the effect of the resistance voltage drop. The dual stator machine of the present invention can be built with minimal modifications to standard winding configurations, requiring no structural modifications of the stator frame. The provision of the two stator windings also increases the reliability of the machine over standard single stator winding machines, while improving the magnetic material utilization for normal operation. 
     A particular advantage of the present invention is the ability to drive the machine at zero and low speed operation without the need for a rotor position encoder to provide rotor position and speed feedback. Zero speed operation can be obtained by applying drive power to the two windings at a frequency and power level to provide opposing, balanced torques to the rotor. Implementation of sensorless vector control is thus facilitated since the drive power supplied to the two stator windings is always above zero frequency. 
     The stator of the machine of the present invention is constructed by dividing the normal single polyphase (typically three-phase) winding into two separate (e.g., three-phase) windings wound for a dissimilar number of poles. Although any combination of dissimilar pole numbers may be used, to best utilize the magnetic material, and avoid localized saturation and additional stator losses, in accordance with the invention it is preferred that a 2 pole and 6 pole combination be utilized. For best magnetic material utilization, this pole number configuration provides a nearly trapezoidal magnetomotive force (MMF) distribution while limiting the maximum number of poles to provide good power factor and efficiency. 
    
    
     Further objects, features and advantages of the invention will be apparent from the following detailed description when taken in conjunction with the accompanying drawings. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the drawings: 
     FIG. 1 is a schematic diagram showing the dual stator winding distributions in the machine of the present invention. 
     FIG. 2 is a graph illustrating the 6 pole peak MMF for constant total peak MMF. 
     FIG. 3 is a graph showing speed-torque curves for the two stator windings in a first mode of operation where the torques are added. 
     FIG. 4 is a graph showing speed-torque curves for the two stator windings for low speed operation where the two torques applied by the two stator windings oppose each other. 
     FIG. 5 is another illustrative view of a 2 pole-6 pole dual stator winding induction machine in accordance with the invention. 
     FIG. 6 is a diagram illustrating the winding distribution in the dual stator winding machine for a fractional pitch and variable displacement angle , with a 60° phase belt. 
     FIG. 7 is a diagram as in FIG. 6 illustrating the winding distribution for a fractional pitch and variable displacement angle ξ with a 30° phase belt. 
     FIG. 8 is an illustrative view of a squirrel cage rotor for use on an induction machine of the present invention, illustrating the rotor currents. 
     FIG. 9 is an equivalent circuit schematic diagram for the 2 pole winding of the dual stator winding machine of the invention. 
     FIG. 10 is an equivalent circuit schematic diagram for a “P” pole winding for the dual stator machine of the invention. 
     FIG. 11 is a schematic diagram of a drive system incorporating the dual stator winding machine of the invention which implements constant V/f operation. 
     FIG. 12 is a schematic diagram of a drive system incorporating the dual stator winding machine of the invention which implements field oriented operation. 
     FIG. 13 are graphs illustrating full matrix and complex vector model simulation results for the 2 pole/6 pole dual stator winding machine of the invention. 
     FIG. 14 is a schematic diagram illustrating the use of two separate inverters for driving a dual stator winding induction motor in accordance with the invention. 
     FIG. 15 is a schematic diagram illustrating an inverter having separate sections for driving a dual stator winding induction motor in accordance with the invention. 
     FIG. 16 are diagrams illustrating the winding distribution for a 4 pole winding in a dual stator Winding induction motor in accordance with the invention. 
     FIG. 17 is a diagram illustrating the winding distribution for a 12-pole winding of a dual stator winding motor in accordance with the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The stator of the machine of the invention is constructed by dividing the normal polyphase (e.g., three phase) stator winding into two separate polyphase windings wound for a dissimilar number of poles. Three phase motors are by far the most common type, but it is understood that the present invention may be utilized with machines having two or more phases. Any combination of dissimilar pole number could be used; however, to best utilize the magnetic material, avoid localized saturation and additional stator losses, it is found that the most advantageous configuration is a 2-6 pole combination. Such an arrangement is incorporated in the machine shown generally at  20  in FIG.  1 . The machine  20  in accordance with the invention has a squirrel cage rotor  21  with rotor bar conductors  22  around its periphery in a conventional manner, and is separated by an air gap  24  from the stator  25 . The rotor is mounted for rotation within the stator in a conventional manner. FIG. 1 illustrates the physical arrangement of the dual stator windings, a first, two-pole winding abc and a second, six-pole winding xyz. For simplicity of illustration, the metal frame and magnetic material of the stator, which is entirely conventional, is not shown in FIG.  1 . Each of the windings abc and xyz extend to three external terminals (not shown in FIG. 1) by which power is supplied independently to each of the two windings. 
     From the perspective of magnetic material utilization it is convenient to choose a pole number combination that, in the steady state, will tend to produce a nearly trapezoidal MMF distribution. This type of distribution is most efficiently obtained by choosing the number of poles in the ratio 1:3, for example, 2 and 6 poles, 4 and 12 poles, etc. On the other hand, the magnetizing inductance varies inversely proportional to the square of the number of poles, hence a machine with a large number of poles results in low power factor and reduced efficiency. In addition, to achieve a sinusoidal winding distribution the stator winding must be distributed among several slots, and, for a given stator inner diameter, the number of slots per pole decreases in proportion to the number of poles. Also, for a given rotor speed, the stator frequency increases directly proportional to the number of poles. This translates into additional losses, in the machine and in the power converter, further reducing the efficiency. All these factors suggest that the maximum number of poles should be kept to a minimum, and hence the best combination is 2 and 6 poles. However, other pole combinations may be used and are within the scope of the invention. 
     The total MMF distribution in the airgap corresponds to the sum of the MMF&#39;s produced by each stator winding. To avoid the presence of highly saturated points and, at the same time, fully utilize the magnetic core it is desirable to maintain the total peak flux density distribution equal to that created by a two pole winding acting alone. 
     FIG. 2 shows the peak magnitude of the 2 pole MMF as a function of the 6 pole peak MMF, for a constant total peak MMF. The optimum distribution corresponds to choosing a 6 pole MMF equal to approximately 40% that of the 2 pole distribution. In this case the total MMF and the 2 pole MMF have the same peak amplitude, thus preserving the saturation level. 
     The rotor  21  of the machine  20  preferably corresponds to that of a standard squirrel cage type. This construction guarantees that both stator current distributions will simultaneously couple with the rotor flux to produce the desired torque. 
     Because of the decoupling effect produced by the difference in pole number, the dual stator machine 20 behaves as two independent induction machines that are mechanically coupled through the rotor shaft. Therefore, all the known control techniques used in induction machine drives are also applicable to the dual stator winding machine. These include both scalar constant volts per hertz (V/f) control and vector control or field orientation (FO). The basic control method involves generating two torque commands that, when combined, produce the required output torque. By choosing adequate current commands the two individual torques can be added or subtracted, hence providing the ability to control the excitation frequency. Two distinct modes of operation are possible: low speed (below a selected minimum speed) where the two torques produced by the abc and xyz windings are subtracted (opposed to one another), as shown in FIG. 4, and medium to high speed (above the minimum speed), where the torques are added, as shown in FIG.  3 . 
     A detailed, yet simple, dynamic model of the machine can be developed using the following general assumptions: negligible saturation, uniform airgap, stator windings sinusoidally distributed, no electrical interconnection between stators, and negligible inter-bar current. It is also assumed that the two stator windings are wound for 2 and 6 poles, respectively, and that one stator is displaced with respect to the other by a fixed but arbitrary angle ξ. The main stator (2 pole) is denoted as the abc windings and the secondary stator, having 6 poles, the xyz windings, as illustrated in FIG.  1 . The rotor of the machine is a standard squirrel cage type. A simplified diagram showing the relative placement of the windings and their angular relationships is given in FIG.  5 . 
     Since both stators are sinusoidally distributed in space but wound for a different number of poles (and are electrically isolated) there is no mutual coupling due to main flux between them. However, since both windings share common slots and are in close proximity, there is a common leakage flux linking them. This gives rise to the so-called mutual leakage coupling. 
     The total flux linked by the stator windings and due only to the stator currents is abc and is xyz can be written, in matrix form as                [           Λ   ssabc               Λ   ssxyz           ]     =         [           L   s1           L   s12               L   s21           L   s2           ]          [           i   sabc               i   sxyz           ]                       where               (   1   )                       [           Λ   ssabc               Λ   ssxyz           ]     =     [           λ   ass               λ   bss               λ   css               λ   xss               λ   yss               λ   zss           ]       ;          [           i   sabc               i   sxyz           ]       =     [           i   as               i   bs               i   cs               i   xs               i   ys               i   zs           ]             (   2   )                                
     L s1  and L s2  represent the self inductance matrices of the abc and xyz windings, respectively. They are of the form:                L   si     =     [             L   lsi     +     L   msi             -       L   msi     2             -       L   msi     2                 -       L   msi     2               L   lsi     +     L   msi             -       L   msi     2                 -       L   msi     2             -       L   msi     2               L   lsi     +     L   msi             ]             (   3   )                                
     The magnetizing inductance L msi  is known to be:                L   msi     =           πμ   0        lτ     g            (       N   si     P     )     2               (   4   )                                
     Where N si  is the total number of turns per phase of each winding set and P is the number of poles. L lsi  represents the total per-phase self leakage inductance of each winding and it can be calculated by traditional methods. 
     The sub-matrices L s12  and L s21  account for the mutual leakage coupling between the two stator windings. In general, the leakage flux can be divided into slot, end winding, belt and zig-zag components and each one of them will contribute to the self and mutual leakage inductance. For simplicity, however, the mutual leakage due to the zig-zag and belt leakage components will be neglected and it will be assumed that they only contribute to the self leakage. Therefore, it will be assumed that only the slot and end winding components contribute to the mutual leakage. Furthermore it will be assumed that the end winding leakage varies as the slot leakage. 
     The winding distributions of FIGS. 6 and 7 may be used to study the mutual leakage. The illustrative winding distribution shown in FIG. 6 corresponds to fractional pitch due to the displacement ξ between stators, 60% phase belt, and in the distributions FIG. 7 corresponds to fractional pitch, 30% phase belt. Since the two sets of windings have 2 and 6 poles respectively, their pitch angles α 1  and α 2  are in the ratio 6/2. In FIG. 6, defining p 1  and p 2  as the pitch of the abc and xyz windings respectively, for a variation of ξbetween zero and 20°, the corresponding pitch factors vary as 8/9&lt;p 1 &lt;1 and 2/3&lt;p 2 &lt;1. 
     The slot leakage can be divided into self leakage and mutual leakage. The self leakage represents that part of the flux produced by the in-phase current component (i.e., slots with coil sides belonging to the same phase). The mutual leakage accounts for the leakage flux due to having conductors from different phases sharing common slots. In general, for a two layer winding self, (L sls ), and mutual, (L slm ), components of the slot leakage inductance can be expressed, as a function of the pitch p, by 
     
       
         L sls =L IT +L IB + 2 k s (p)L lTB   (5) 
       
     
     
       
         L slm =k m (p) L lTB   (6) 
       
     
     where L IT  and L lB  are the slot leakage inductances associated to the coils in the top and bottom halves of the slots. They are calculated for the case of unity pitch and do not depend on winding pitch. The term L lTB  represents the mutual inductance between coils in the top and bottom halves of the slot. The quantities k s  and k m  are called slot factors and they correspond to proportionality constants that depend on the pitch. 
     For the dual stator machine of the invention, it can be demonstrated that both stator windings are fully decoupled and the total flux linked by the stator windings can be written as 
     
       
         Λ sabc =L s1 i sabc +L sr1 i r    (7) 
       
     
     for the primary winding and 
     
       
         Λ sxyz =L s2 i sxyz +L sr2 i r    (8) 
       
     
     for the secondary winding. The matrices L sr1  and L sr2  describe the mutual coupling between the stator and rotor circuits and they can be determined using winding functions. Using complex vector representation, the stator flux associated to the abc winding can be written as                  λ   _     sabc     =         (       L   ls1     +       3   2          L   ms1         )            i   _     s1       +         2      n                 sin                 δ       π                   N   s1              L   ms1               j        (       θ   r     +   δ     )                i   _     r1                 (   9   )                                
     where n is the number of rotor bars, δ is ½ the angle between rotor bars, and the complex vector currents  i   s1  and  i   r1  are defined by                  i   _     s1     =       2   3          (       i   as     +       a   _          i   bs       +         a   _     2          i   cs         )               (   10   )                   i   _     r1     =         2   n          [       1        b   _       ,       b   _     2     ,     …                     b   _       n   -   1           ]            [           i   r1               i   r2             ⋮             i   rn           ]               (   11   )                                
     With  a =e j2π/3 and  b =e j2π/n . The vector [i r1 , i r2  . . . i rn ] T  represents the instantaneous rotor currents, defmed according to FIG. 8, which illustrates the currents flowing in the rotor bars  22  and in the end rings  27  that connects the bars  22 . 
     A similar analysis can be performed for the xyz winding. 
     It can further be demonstrated that the stator current  i   s1  depends only on the applied voltage  v   s1  and the rotor current  i   r1 . Similarly, the stator current  i   s2  depends only on the applied voltage  V   s2  and the rotor current  i   r2 . This result is consistent with the fact that, for a sinusoidally distributed winding, there only exists coupling between current distributions of the same number of poles. 
     Although the instantaneous rotor current distribution simultaneously contains two components of different frequencies and pole number, each stator field is capable of interacting only with that part of the rotor field with the “correct ” number of poles. This is true not only on an average basis but also instantaneously. It is well known that sinusoidally distributed windings only couple with fields wound for the same number of poles; however, the rotor cage is clearly not a sinusoidal winding and one might expect that the presence of two superimposed flux distributions would give rise to pulsating torques. However, this is not the case for the dual stator winding machine. An equivalent circuit, using d-q notation, is shown in FIGS. 9 and 10 for the 2-pole and P-pole windings, respectively. 
     Neglecting saturation, the electromagnetic torque can be expressed as the partial variation of the co-energy with respect to position                T   e     =       [       i   sabc   T          i   sxyz   T       ]            ∂     ∂     θ   r              [           L   sr1               L   sr2           ]            i   r               (   12   )                                
     which can be written as the separate sum of the torques produced by each set of stator currents          T   e     =         i   sabc   T            ∂     L   sr1         ∂     θ   r              i   r       +       i   sxyz   T            ∂     L   sr2         ∂     θ   r              i   r                                
     Substituting the corresponding matrices and carrying out the differentiation yields the torque as:                T   e     =       -     (       3      n                 sin                 δ       π                   N   s1         )            L   ms1        Im        {              j        (       θ   r     +   δ     )                i   _     s1   *            i   _     r1       +            j3        (       θ   r     +   δ   -   ξ     )                  N   s2          sin        (     3      δ     )           3        N   s1        sin                 δ              i   _     s2   *            i   _     r2         }               (   14   )                                
     where P=6 is used. Since  i   r1  and  i   r2  are orthogonal vectors the two torque components can be controlled independently by the stator currents. 
     As noted above, because the machine of the invention behaves as two independent induction machines, mechanically coupled through the shaft, all the known control techniques used in induction machine drives are also applicable to the dual stator winding machine. 
     In general, there are two distinct modes of operation, the low speed range (i.e., frequencies below a minimum frequency, e.g., few hertz) and the medium to high speed range. In the low speed range, the goal is to maintain the frequency of the 2 pole winding above a minimum level (typically about 3 Hz) and the torque is controlled by adjusting the frequency of the 6 pole winding. By keeping the frequency above this pre-set limit, the influence of the stator resistance is minimized, hence simplfying the control. In this mode the two MMFs rotate asynchronously, but because of the reduced frequency the additional losses caused by saturation are minimal. 
     In the medium to high speed range, the negative effect of the stator resistance is not a concern and the frequencies are kept in the same ratio as the number of poles, e.g., ratio 1:3. This constraint guarantees a nearly trapezoidal flux distribution, and the torque is controlled by adjusting the magnitude of the applied voltages. The trapezoidal shape, in turn, allows for slightly greater 2 pole flux than when only the 2 pole winding is excited, thereby producing slightly more torque per ampere. 
     The operation and control may be explained with reference to FIGS. 3 and 4. For high speed, the stators are fed with voltages with frequencies in 1:3 ratio to produce the torque-speed curves of FIG.  3 . The output torque for a given rotor speed corresponds to the algebraic sum of the torques T 1  and T 2  produced by each of the stator. The torque produced by each winding can be controlled by adjusting the magnitude of the stator voltages supplied to each winding. 
     When both stators are fed with different effective frequencies, the result is that shown in FIG.  4 . By fixing the frequency ƒ 1  of power supplied to one of the stator windings, say abc, the total output torque can be adjusted by controlling the frequency ƒ 2  (and voltage) supplied to the xyz winding. As shown in FIG. 4, an increase in torque requires an increase in ƒ 2 , and vice versa. In this case, the first one of the stator windings (abc) operates in the motoring region while the other (xyz) operates as a generator. Note that this operating mode corresponds to the one required to operate at zero speed, and that the torque can be controlled from zero to rated value. 
     A simplified block diagram of the control scheme for constant V/f operation is shown in FIG.  11 . As illustrated in this figure, the abc winding receives 3-phase power on input terminals  30  from a first 3-phase PWM voltage source inverter  31 , while the xyz windings receive power on terminals  32  from a separate 3-phase PWM voltage source inverter  34 . The commanded speed, ω*, is provided to a summing junction  35  where it is compared with the estimated speed, {circumflex over (ω)}, and the difference is provided to a speed controller  37 , e.g., a proportional-integral (PI) controller. The output of the speed controller is provided to a frequency limit detection circuit  38 , which is provided with a selectable minimum frequency, ƒ min . The circuit  38  is connected by lines  39  to provide control signals to switches  40 ,  41 , and  42 . If the input frequency is greater than ƒ min , the output of the circuit  38  on a line  43  is the same as the input and the switches  40 ,  41 , and  42  are in the positions shown in FIG. 11 ( 40  open,  41  and  42  closed). If the input frequency to the circuit  38  is less than ƒ min , the output frequency from the circuit is clamped at the value ƒ min , and the switches are activated so that the switch  40  is closed and the switches  41  and  42  are opened. The output ƒ 1 * of the circuit  38  is used as the reference frequency for a V/f modulation function  43  and a carrier frequency function cos ((ω 1 t)  44 , the outputs of which are multiplied together and applied as the input to the voltage source inverter  31  to provide the abc (e.g., two pole) winding drive power on the terminals  30 . The output of the speed controller  37  is also provided to the switch  40  and thence to a summing junction  46 , which also receives from a gain unit  47  through the switch  41  an input equal to 3 ƒ 1 *. The output ƒ 2 * of the summing junction  46  is equal to 3ƒ 1 * when the switch  41  is closed, and is equal to the output of the speed controller  37  when the switch  40  is closed and the switch  41  is opened. The signal ƒ 2 * is provided to a circuit composed of a V/f function  50  and a cos (ω 2 t +θ) function  51 , the outputs of which are multiplied and applied to the voltage source inverter  34  to provide the xyz winding (e.g., 6 pole) drive power on the terminals  32 . The power applied to the machine  20  on the input terminals  30  and  32  is fed back by lines  55  and  56  to speed and flux estimators  57  and  58 , respectively. The estimator circuit  58 , of conventional design, provides an estimate {circumflex over (ω)} of motor speed on a line  60  back to the summing junction  35 . The estimator circuits  57  and  58  also provide signals indicative of the flux applied by the two stator windings, which signals are passed through phase angle measurement circuits  61  and  62  and added at a summing junction  63 . The estimated flux of the xyz winding (6 pole) has three times the frequency of the flux from the abc winding; for this reason a frequency divider block  64  is used on the flux estimate from the estimator  58 . The phase difference from the junction  63  is provided through the switch  42  to a control circuit  66  (e.g., PI), the output of which is provided as a phase difference ø to the circuit  51 . 
     A simplified block diagram of a vector controller is given in FIG.  12 . As in the constant V/f method, the vector control operation is divided into two operating regions: a high speed range defmed by frequencies above a minimum frequency ƒ min  and a low speed range for frequencies below ƒ min . For the high speed region, the controller divides the output torque among the two windings to yield similar stator currents and a nearly trapezoidal flux distribution. In the low speed range, a negative torque command is given to the secondary (e.g., xyz) winding, hence increasing the torque produced by the primary winding which yields an increased stator frequency. The goal is to maintain the primary stator frequency at a constant value equal to ƒ min . The torque command input T* and the minimum frequency ƒ min  . are provided to a torque divider control circuit  70 , which provides output command signals for the two windings T 1 * and T 2 *, for the abc and xyz windings, respectively. The torque command T 1 * is provided to a summing junction  71 , which also receives a torque feedback estimate {circumflex over (T)} 1  on line  72 , and the difference is provided to a torque controller  74 . A flux command signal and a flux feedback signal are provided to a summing junction  75 , the output of which is provided to a flux controller  76 . The outputs of the flux controller  76  and torque controller  74  are supplied to a transformation circuit  77 , which also receives a signal that is an estimate of the rotor flux angle from an estimater circuit  80 . The ransformation circuit  77  provides current command signals to a current controlled hree-phase PWM inverter  81 , which provides output power on the lines  30  to the bc winding. The power signals on the lines  30  are also supplied to a torque ontroller feedback circuit  83 , the output of which is provided to a torque calculator  84  to provide the torque estimate on the line  72 . Similar components, designated by similar numerals with a prime notation, “′”, are utilized in the control circuit to rovide the drive power on lines  32  to the xyz winding. 
     The torque divider used in the control loop for the field oriented control strategy of FIG. 12 works as follows: given the external torque command and the limit frequency ƒ min  it adjusts the torque commands T 1 * and T 2 * such that the two supplied frequencies are in the ratio 1:3 and the lowest frequency (2-pole winding) is above ƒ min . If the required frequency is less than the minimum value, the commanded frequency to the 2-pole winding is fixed at the value ƒ min  and the torque command T 2 * is adjusted such that the resulting torque corresponds to the externally commanded torque. 
     The results obtained from a space vector model of the machine  20  and those obtained from a full matrix model of the machine are shown in FIG. 13 for a free acceleration run at 60 Hz (f 2 =180 Hz). The complex vector and full matrix model traces are superimposed. Both simulations provide essentially identical results, demonstrating the validity of the complex vector model. As shown in FIG. 13, the rotor currents contain two different frequencies dictated by the frequency of each of the stator currents and the rotor mechanical speed. Although the rotor currents simultaneously produce two field distributions that rotate at different speeds, because of the different number of poles and the sinusoidal characteristic of the stator windings, they do not give rise to harmonic torques. 
     The present invention may be implemented utilizing two separate inverters  31  and  34  for providing the drive power to the two windings of the induction motor  20 , as illustrated in FIG.  14 . The first inverter  31 , providing drive power to the input lines  30  of the abc winding, receives power across DC bus lines  100  and  101 , with an illustrative DC bus capacitor shown at  102 . Semiconductor switches S 1 ∝S 3  and S 7 -S 9  are appropriately controlled to provide the desired drive power to the dual stator induction motor. The second inverter  34  receives drive power from separate DC bus lines  104  and  105  with a DC bus capacitor illustratively shown at  106 . Semiconductor switches S 4 -S 6  and S 10 -S 12  are operated to provide the power to the xyz windings on the input lines  32 . Although not necessary in accordance with the invention, it is convenient to utilize inverters of the so-called current regulated pulse width modulated type (CRPWM). Alternatively, as shown in FIG. 15, the inverters  31  and  34  can be implemented utilizing a single set of DC bus lines  110  and  111  with a DC bus capacitor illustratively shown at  112 . Switches S 1 -S 3  and S 7 -S 9  are operated across the DC bus lines  110  and  111  to provide the drive power to the input lines  30 , while switches S 4 -S 6  and S 10 -S 12  are operated to provide drive power on the input lines  32  to the xyz windings. The two inverter sections  31  and  34  can thus be operated independently of each other even though utilizing the same DC bus lines. 
     The present invention may be implemented utilizing winding combinations other than 2-pole to 6-pole, for example, 4-pole to 12-pole and higher. FIG. 16 illustrates at  120  the 4-pole winding distribution for a 4-pole to 12-pole machine, and in the top diagram labeled  121  the corresponding distribution of the abc windings in the top of the slots (air-gap side). FIG. 17 illustrates the 12-pole winding distribution at  130 , and the diagram  131  illustrates the distribution of the xyz windings in the bottom of the slot (yoke side) of the machine. 
     It is understood that the invention is not confined to the particular embodiments set forth herein as illustrative, but embraces all such forms thereof as come within the scope of the following claims.