Abstract:
A method for limiting the torque of a permanent magnet AC motor includes a torque limit controller. The torque limit controller at least in part bases the torque limit on a selected direct voltage limit. The selected direct voltage limit may be used in combination with other torque limit conditions to generate the torque demand for the AC motor.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a non-provisional application which claims priority from U.S. provisional application No. 61/974,168, filed Apr. 2, 2014, which is incorporated by reference herein in its entirety. 
    
    
     TECHNICAL FIELD/FIELD OF THE DISCLOSURE 
     The present disclosure relates generally to control of electric motors, and specifically to controlling torque in permanent magnet AC motors. 
     BACKGROUND OF THE DISCLOSURE 
     Alternating current (AC) electric motors rely on alternating currents passed through induction windings within the stator to cause rotation of the rotor. So-called three phase AC motors include three matched sets of windings positioned radially about the stator. By supplying sinusoidal AC power to each of the sets of windings such that each set receives an alternating current offset by 120 degrees, a torque can be imparted on the rotor as it rotates. 
     Unlike a brushed DC motor, output speed in an AC motor is controlled by the frequency of the current sent to the stator windings. In order to control output torque, and thus speed, a variable frequency drive (VFD) is used to vary the current fed to the AC motor. Because the inductive reactance of the stator windings is proportional to the frequency applied to the winding, increased voltage is necessary to maintain a relatively constant current within the windings, and thus a relatively constant output torque. Additionally, in a permanent magnet AC motor, as the permanent magnetic field of the permanent magnets of the rotor rotates, a voltage known as a back EMF or counter EMF is induced into the stator windings. The current supplied to the windings of the AC motor is thus dependent on the voltage supplied to the motor less the back EMF voltage. 
     In order to properly drive the AC motor, VFD&#39;s often operate using one of two control methods. In a volts/Hz control or flux control scheme, the VFD varies the output speed of the motor by supplying AC power to the stator windings at a particular frequency and voltage. For a given desired torque, voltage is proportionally related to the frequency by a so-called “voltage-to-frequency” or “volts/Hz” ratio. By using closed-loop feedback, a VFD using volts/Hz can maintain motor speed in changing conditions. This simple control scheme, however, is inherently slow in its response to rapid changes in demand speeds, as it relies on control of voltages and frequencies rather than current directly. Additionally, this simple form of volts/Hz may not be usable in a permanent magnet motor control system. 
     With the rapid advancement in low-cost, high speed microprocessor technology, VFDs utilizing field-oriented control (FOC) models are increasingly popular. In FOC, the current supplied to the phases of the AC motor is decoupled into torque and flux components acting on the rotor in a rotating reference frame. Thus, each of these currents can be independently controlled. Current supplied to the phases of the motor are measured or derived and transformed into the torque-flux space (utilizing, for example, a Clarke/Park transformation), a closed-loop feedback model can be created to control each of these currents continuously. The processor then back-transforms the torque and flux components into three phase currents. The three phase currents are fed to a three phase inverter which outputs pulse-width modulated signals to each set of windings in the motor. 
     In an AC motor, even under FOC, as the speed of the permanent magnet motor is increased, the voltage generated by the fixed magnetic field (EMF) increases proportionally. At some speed, the voltage generated by the motor exceeds the maximum voltage that can be produced by the drive that is controlling the motor. If operation above this speed is desired, it is necessary to modify the current vector applied to the motor to maintain the desired torque, and control the terminal voltage of the motor to a value less than the maximum drive output voltage, thus operating in a flux weakening mode. In such a situation, the EMF may interfere with the operation of the VFD in the flux weakening mode. 
     SUMMARY 
     The present disclosure provides for a method for limiting torque demand of a three phase permanent magnet AC motor having a rotor and stator driven by a three phase current generated by a variable frequency drive. The method may include measuring the three phase current supplied to the permanent magnet AC motor. The method may include transforming the measured three phase current signal into a two-phase signal projected onto a two-axis rotating reference frame The phase components of the two-phase signal may define a feedback quadrature current and a feedback direct current. The method may include calculating an estimated rotor speed and estimated rotor position. The method may include calculating a speed error signal by subtracting the estimated rotor speed from a target speed. The method may include calculating, using a speed controller, a torque demand from the speed error signal. The method may include calculating, using a torque limit controller, a limited torque demand. The limited torque demand may be calculated at least in part with respect to a selected maximum direct voltage. The method may include calculating a quadrature current error signal by subtracting the feedback quadrature current from a quadrature demand current. The method may include calculating, using an I q  controller, a quadrature voltage from the quadrature current error signal. The method may include calculating a direct current error signal by subtracting the feedback direct current from a demand direct current. The method may include calculating, using an I d  controller, a direct voltage from the direct current error signal. The method may include transforming the quadrature and direct voltages into a three phase voltage signal. The method may include modulating a DC voltage with a three phase inverter to supply three phase current corresponding to the three phase voltage signal to the permanent magnet AC motor. 
     The present disclosure also provides for a method for limiting torque demand of a permanent magnet AC motor having a rotor and stator driven by a current supplied to each phase of the permanent magnet AC motor generated by a variable frequency drive. The method may include measuring the current supplied to the permanent magnet AC motor. The method may include transforming the measured current signal into a two-phase signal projected onto a two-axis rotating reference frame. The phase components of the two-phase signal may define a feedback quadrature current and a feedback direct current. The method may include calculating an estimated rotor speed and estimated rotor position. The method may include calculating a speed error signal by subtracting the estimated rotor speed from a target speed. The method may include calculating, using a speed controller, a torque demand from the speed error signal. The method may include calculating, using a torque limit controller, a limited torque demand. The method may include calculating a quadrature current error signal. The method may include calculating a quadrature voltage from the quadrature current error signal. The method may include calculating a direct current error signal. The method may include calculating a direct voltage from the direct current error signal. The method may include transforming the quadrature and direct voltages into a voltage signal corresponding to each phase of the permanent magnet AC motor. The method may include modulating a DC voltage with a three phase inverter to supply current to each phase of the permanent magnet AC motor corresponding with the voltage signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure is best understood from the following detailed description when read with the accompanying figures. It is emphasized that, in accordance with the standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion. 
         FIG. 1  depicts a block diagram of a three phase permanent magnet AC motor controlled by a VFD utilizing torque limiting consistent with embodiments of the present disclosure. 
         FIG. 2  depicts a block diagram of a VFD utilizing torque limiting consistent with embodiments of the present disclosure. 
         FIG. 3  depicts a block diagram of the torque limit calculator of  FIG. 2 . 
     
    
    
     DETAILED DESCRIPTION 
     It is to be understood that the following disclosure provides many different embodiments, or examples, for implementing different features of various embodiments. Specific examples of components and arrangements are described below to simplify the present disclosure. These are, of course, merely examples and are not intended to be limiting. In addition, the present disclosure may repeat reference numerals and/or letters in the various examples. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. 
       FIG. 1  depicts a block diagram of three phase AC motor  10  controlled by VFD  101 . Although described herein as a three phase AC motor, one having ordinary skill in the art with the benefit of this disclosure will understand that three phase AC motor  10  may instead be a polyphase AC motor without deviating from the scope of this disclosure. One having ordinary skill in the art with the benefit of this disclosure will understand that the specific methods and equations described herein may be modified to account for other numbers of motor phases. VFD  101  may be positioned to output three phase AC power to the stator windings (not shown) of AC motor  10  in response to input parameters  103 . Input parameters  103  may include, without limitation, at least one of torque demand, speed demand, and maximum drive voltage. 
     In the case of a permanent magnet motor, the interaction of current, flux, voltage, and speed are defined by the model voltage equation as follows:
 
 v   s   =R   s   ·i   s   +l   s   ·{dot over (i)}   s   +jω   0   l   s   ·i   s +{dot over (φ)} r   +jω   0 ·φ r ,
 
     where v s  is the stator voltage vector, R s  is the stator resistance, is i s  the stator current vector, is l s  the stator leakage inductance, φ r  is the total rotor flux vector, and ω 0  is the synchronous frequency given by:
 
φ 0   =P   p ×ω r ,
 
     Where P p  is the number of pole pairs per phase, and ω r  is the speed of the rotor. Total rotor flux φ r  may be given by:
 
φ r =φ pm   +L   m   ·i   s  
         where φ pm  is the permanent magnet flux (the reference frame is chosen such that the permanent magnet flux is entirely real), and L m  is the mutual stator-rotor inductance. As used in the equations, “_” indicates a vector quantity, and the “·” operator is the first order time derivative.       

     Substituting the flux equation into the voltage equation, and the definition that φ m  is entirely real (direct or d-axis), the voltage equation evaluates to: 
     
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               v 
                               d 
                             
                           
                         
                         
                           
                             
                               v 
                               q 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     R 
                                     s 
                                   
                                   + 
                                   
                                     pL 
                                     d 
                                   
                                 
                               
                               
                                 
                                   
                                     - 
                                     
                                       ω 
                                       0 
                                     
                                   
                                   ⁢ 
                                   
                                     L 
                                     q 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     ω 
                                     0 
                                   
                                   ⁢ 
                                   
                                     L 
                                     d 
                                   
                                 
                               
                               
                                 
                                   
                                     R 
                                     s 
                                   
                                   + 
                                   
                                     pL 
                                     q 
                                   
                                 
                               
                             
                           
                           ] 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   i 
                                   d 
                                 
                               
                             
                             
                               
                                 
                                   i 
                                   q 
                                 
                               
                             
                           
                           ] 
                         
                       
                       + 
                       
                         [ 
                         
                           
                             
                               0 
                             
                           
                           
                             
                               
                                 
                                   ω 
                                   0 
                                 
                                 ⁢ 
                                 
                                   Φ 
                                   m 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                   , 
                 
               
               
                 
                     
                 
               
             
           
         
       
         
         
           
             where p is the d/dt operator, L d  is the total inductance in the d-axis, L q  is the total inductance in the quadrature or q-axis, each given by:
 
 L   d =( l   s   +L   dm )
 
 L   d =( l   s   +L   qm )
 
             where L dm  is the d-axis component of L m  and L qm  is the q-axis component of L m . 
           
         
       
    
     Torque supplied by the motor may be given by:
 
 T   e =3 P   p (φ r   ×i   s ),
         which, from the definition that φ m  is entirely real, can be expressed as:
 
 T   e =3 P   p (φ m   ·i   q +( L   d   −L   q ) i   d   ·i   q )
       

     Thus, speed can be expressed by the following equation: 
     
       
         
           
             
               
                 
                   ω 
                   . 
                 
                 r 
               
               = 
               
                 
                   1 
                   
                     ( 
                     
                       
                         J 
                         m 
                       
                       + 
                       
                         J 
                         L 
                       
                     
                     ) 
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       T 
                       e 
                     
                     - 
                     
                       
                         T 
                         m 
                       
                       ⁡ 
                       
                         ( 
                         
                           ω 
                           r 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         T 
                         L 
                       
                       ⁡ 
                       
                         ( 
                         
                           ω 
                           r 
                         
                         ) 
                       
                     
                   
                   ) 
                 
               
             
             , 
           
         
       
         
         
           
             where J m  and J L  are the motor and load inertias respectively, T m (ω r ) is the motor loss torque as a function of speed, and T L (ω r ) is the load torque as a function of speed. 
           
         
       
    
     The voltage and flux equations can thus be combined into the following extended state-space format: 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       
                         i 
                         . 
                       
                       d 
                     
                   
                 
                 
                   
                     
                       
                         i 
                         . 
                       
                       q 
                     
                   
                 
               
               ] 
             
             = 
             
               
                 
                   [ 
                   
                     
                       
                         
                           ( 
                           
                             
                               - 
                               
                                 R 
                                 s 
                               
                             
                             
                               L 
                               d 
                             
                           
                           ) 
                         
                       
                       
                         
                           ( 
                           
                             
                               ω 
                               0 
                             
                             ⁢ 
                             
                               
                                 L 
                                 q 
                               
                               
                                 L 
                                 d 
                               
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         
                           ( 
                           
                             
                               - 
                               
                                 ω 
                                 0 
                               
                             
                             ⁢ 
                             
                               
                                 L 
                                 d 
                               
                               
                                 L 
                                 q 
                               
                             
                           
                           ) 
                         
                       
                       
                         
                           ( 
                           
                             
                               - 
                               
                                 R 
                                 s 
                               
                             
                             
                               L 
                               q 
                             
                           
                           ) 
                         
                       
                     
                   
                   ] 
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       
                         
                           i 
                           d 
                         
                       
                     
                     
                       
                         
                           i 
                           q 
                         
                       
                     
                   
                   ] 
                 
               
               + 
               
                 
                   [ 
                   
                     
                       
                         
                           ( 
                           
                             
                               V 
                               d 
                             
                             
                               L 
                               d 
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         
                           ( 
                           
                             
                               
                                 V 
                                 q 
                               
                               - 
                               
                                 
                                   ω 
                                   0 
                                 
                                 ⁢ 
                                 
                                   ϕ 
                                   m 
                                 
                               
                             
                             
                               L 
                               q 
                             
                           
                           ) 
                         
                       
                     
                   
                   ] 
                 
                 . 
               
             
           
         
       
     
       FIG. 2  depicts a block diagram of VFD  101  of  FIG. 1 . In this embodiment, input parameters  103  shown are maximum drive voltage  105  and target speed  107 . Maximum drive voltage  105  may be, as the name suggests, the maximum voltage available to VFD  101  to output to AC motor  10 . Since AC motor  10  is driven by PWM signals from three phase inverter  109 , maximum drive voltage  105  is a DC voltage. Maximum drive voltage  105  may be determined by the AC voltage available to be rectified by a rectifier into the DC voltage used to drive VFD  101 . 
     As VFD  101  drives AC motor  10 , VFD  101  measures the currents i a , i b , i c  supplied to each of the stator windings phases using, for example, ammeters  111   a - c . In some embodiments wherein AC motor  10  is ungrounded and supplied with balanced three phase currents, the current supplied to one of the three windings may be derived from measurements of the other two windings. The three current signals i a , i b , i c  are transformed into a two-phase projection of the currents in a rotating reference frame, namely feedback quadrature current i q FB  and feedback direct current i d FB . This transformation may be accomplished by, for example, Park/Clarke transformation  113 . Park/Clarke transformation  113  uses estimated position θ 0  generated by position estimator  114 . Position estimator  114  may calculate estimated position θ 0  from a signal generated by resolver/encoder  116 , which may be attached to the output shaft of AC motor  10 . 
     The signal generated by resolver/encoder may also be used by speed estimator  118  to calculate estimated rotor speed ω r . In other embodiments, the two-phase projected currents may be used to calculate estimated position θ 0  and rotor speed ω r . In other embodiments, two-phase projected currents in a stationary reference frame as calculated by a Clarke transformation alone may be used to calculate estimated position θ 0  and rotor speed ω r . In some embodiments, an open loop controller may be utilized to estimate rotor speed ω r , using, for example, feedback from voltage supplied to AC motor  10 . 
     Furthermore, in some embodiments, one or more of position estimator  114  and speed estimator  118  may incorporate feedback into the position and rotor speed calculations. In such embodiments, parameters including but not limited to direct voltage v d , quadrature voltage v q , feedback direct current i d FB , and/or feedback quadrature current i q FB  (as discussed below) may be utilized in the estimation of estimated position θ 0  and rotor speed ω r . 
     Rotor speed ω r  is subtracted from target speed  107  at  115  to generate a speed error signal ε ω  which may be used by speed controller  119  to generate a torque demand Trq*. However, the above equations used to determine torque demand Trq* imply no intrinsic limit to the maximum torque that AC motor  10  is capable of producing in the given implementation. In reality, the actual maximum torque is affected by, for example and without limitation, the mechanical constraints of AC motor  10 , the maximum current available to AC motor  10 , and the maximum power available to AC motor  10 . Thus, torque demand Trq* as calculated by speed controller  119  may demand a greater torque from AC motor  10  than AC motor  10  is capable of producing. 
     To account for such an eventuality, torque limit controller  122  is positioned to calculate a limited torque demand Trq* LIM .  FIG. 3  depicts a block diagram for torque limit controller  122 . Torque limit controller  122 , as depicted, may account for each of the above listed factors which affect maximum torque of AC motor  10 . Torque limit controller  122  may determine limited torque demand Trq* LIM  by selecting the smallest torque value calculated among each of the above listed factors and torque demand Trq*. For example, torque limit controller  122  calculates a first torque limit Trq 1  by dividing the maximum power  201  available to AC motor  10  by rotor speed ω r . 
     In order to account for other factors, an i q  limit may be calculated by selecting the smallest i q  calculated with respect to the factor. For example, the maximum current  203  and i d  may be used to calculate an i q  limit according to:
 
 i   q.lim =√{square root over ( I   lim   2   −i   d   2 )},
         where I lim  is the maximum current  203  available to AC motor  10 .       

     At the same time, inherent mechanical constraints may be accounted for as well. For example, when operating in a field weakening mode, the voltage developed by quadrature inductance may, for example, prevent a field weakening controller to operate normally and maintain terminal voltage control. By limiting this direct voltage v d ″ to a selected value, terminal voltage control may be maintained. In some embodiments, v d ″ may be limited to approximately half of the available drive output voltage. The i q  limit associated with the limited direct voltage v d.lim ″ may be calculated according to: 
     
       
         
           
             
               i 
               
                 q 
                 · 
                 lim 
               
             
             = 
             
               
                 
                   v 
                   
                     d 
                     · 
                     lim 
                   
                   ″ 
                 
                 
                   
                     3 
                   
                   ⁢ 
                   
                     ω 
                     r 
                   
                   ⁢ 
                   
                     L 
                     q 
                   
                 
               
               . 
             
           
         
       
     
     Torque limit calculator  122  may then use the smaller of the i q  limits with the following torque calculation to determine a second torque limit Trq 2 :
 
 T   e =3 P   p (φ m   ·i   q +( L   d   −L   q ) i   d   ·i   q )
 
     as above. 
     Torque limit calculator  122  may then select the smallest of the first torque limit Trq 1 , second torque limit Trq 2 , and the calculated torque demand Trq* to determine limited torque demand Trq* LIM . 
     The calculated limited torque demand Trq* LIM  which is subsequently used by I q  calculator  120  to calculate demand quadrature current i q *. Quadrature current can be described as the component of current which induces the component of the stator magnetic field separated by 90 degrees from the rotor. Likewise, direct current can be described as the component of current which induces the component of the stator magnetic field aligned with the rotor. Thus, the quadrature component generally has a greater effect on rotor torque than the direct component. However, the direct component may contribute to torque in, for example, salient machines where L d  and L q  are significantly different. Thus demand direct current i d * may also be taken into account by I q  calculator  120  in determining demand quadrature component i q *. 
     Feedback quadrature current i q FB  is subtracted from demand quadrature current i q *, and the calculated error may be fed into I q  controller  123 . I q  controller  123 , which may operate as a PI controller or “bang-bang” controller as understood in the art, thus calculates quadrature voltage v q , i.e. the quadrature component of the voltage to be supplied to AC motor  10 . 
     In a similar manner, I d  feed forward calculator  121  generates a demand direct current i d *. In typical operation, it may be desired to maintain demand direct current i d * at zero since maximum torque results from a magnetic field aligned 90 degrees offset from the rotor. Feedback direct current i d FB  is then subtracted from demand direct current i d * to generate an error to be fed into I d  control  125 . I d  control  125 , which may operate as a PI controller or “bang-bang” controller as understood in the art, then generates direct voltage v d . 
     Direct and quadrature voltages v d , v q  are then reverse transformed by inverse Park/Clarke transformation  129  from the rotating reference frame to the three phase voltages v a , v b , v c . The three phase voltages v a , v b , v c  are fed into three phase inverter  109 , which using, for example, PWM, modulates the supplied DC voltage into variable frequency AC current to AC motor  10 . 
     The foregoing outlines features of several embodiments so that a person of ordinary skill in the art may better understand the aspects of the present disclosure. Such features may be replaced by any one of numerous equivalent alternatives, only some of which are disclosed herein. One of ordinary skill in the art should appreciate that they may readily use the present disclosure as a basis for designing or modifying other processes and structures for carrying out the same purposes and/or achieving the same advantages of the embodiments introduced herein. One of ordinary skill in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the present disclosure and that they may make various changes, substitutions, and alterations herein without departing from the spirit and scope of the present disclosure.