Abstract:
A method for controlling an induction motor using an equivalent circuit model, the equivalent circuit having a real component and an imaginary component, is disclosed. The method instead of measuring a plurality of induction motor parameters, the real and the imaginary component of the induction motor impedance are calculated based on the measured phase currents and voltages. The invention calculates a first control function based on the real component of the induction motor impedance, and a second control function based on the imaginary component of the induction motor impedance, and adjusts the induction motor excitation frequency until the first control function is approximately equal to the second control function. After the excitation frequency is determined, the motor torque is calculated by taking the square of motor voltage in the d-q reference frame. Working with a few control parameters, the present invention achieves a desired maximum torque or a desired peak efficiency with a high tolerance of variation in the control parameters.

Description:
TECHNICAL FIELD 
     The present invention relates to systems and methods for controlling induction motors. 
     BACKGROUND 
     One of the most common methods for controlling induction motors is known in the art as indirect rotor flux orientation control. Continuous feedback of motor operation information and various motor parameters are required using this method. For example, rotor position feedback, rotor resistance and inductance are required parameters using this method. Sensor wheels and position sensors are typically used to determine rotor position. Proper slip frequency is maintained based upon rotor resistance, rotor inductance, and phase current. The motor torque can be calculated by measuring the motor current for a given condition. 
     This type of control methodology is simple and crude. One significant problem that arises using this method of control is that rotor resistance and rotor inductance is affected by the temperature and magnetic saturation and thus the motor performance is affected as well. Typically, however, it is assumed that rotor resistance and inductance stays constant for all conditions. This assumption is, of course, incorrect and thus the performance of the motor suffers when the rotor is hot. 
     While there are systems and methods for providing position sensorless control of induction motors, they are typically complicated and their effectiveness varies as motor operating conditions change. Generally, complicated math filters or observers are used to estimate critical motor parameters, such as, rotor resistance, rotor inductance, rotor electrical frequency, etc. As the result, the inaccuracy of estimations greatly effects the motor&#39;s performance. Thus they do not provide optimal dynamic motor control. 
     Therefore, there exists a need for a new and improved method and system for controlling an induction motor. The new and improved method and system should not depend on continuous position sensor feedback and various motor parameters, since these parameters vary with temperature, magnetic saturation, and motor wear. Further, the new and improved system should allow the motor to operate continuously in an optimized range, require minimum calibration, and accommodate for high motor parameter variation tolerance. 
     SUMMARY 
     A method for controlling an induction motor using an equivalent circuit model is provided. The equivalent circuit includes a real resistive component and an imaginary inductive component. The method avoids measuring or estimating individual induction motor parameters, instead, only a few operating parameters, such as phase voltages and phase currents are measured to determine a lump sum of the real and imaginary components of the induction motor impedance. Then, a first control function based on the real component of the induction motor impedance is calculated, a second control function based on the imaginary component of the induction motor impedance is calculated. Then, the induction motor excitation frequency is adjusted until the first control function is approximately equal to the second control function. Finally, the magnitude of the phase voltage is varied to achieve the desired motor/generator performance. 
     In an aspect of the present invention, determining the real component of the induction motor impedance includes calculating the real component of the induction motor impedance using the equation: 
     
       
         Real( Z   in )=( V   ds   i   ds   +V   qs   i   qs )/( i   ds   2   +i   qs   2 ).  
       
     
     In another aspect of the present invention, determining the imaginary component of the induction motor impedance includes calculating the imaginary component of the induction motor impedance using the equation: 
     
       
           Im ( Z   in ) j =( V   qs   i   ds   −V   ds   i   qs )/( i   ds   2   +i   qs   2 ).  
       
     
     In still another aspect of the present invention, when the motor is used to convert electrical power to mechanical power, herein referred to as motoring mode, the first control function is calculated using the equation: 
     
       
         
           A′=K 
           m 
           −A.  
         
       
     
     In still another aspect of the present invention, when motor is used to convert mechanical power to electrical power, herein referred to as generation mode, the first control function is calculated using the equation: 
     
       
         
           A′=K 
           g 
           +A.  
         
       
     
     In still another aspect of the present invention, calculating a second control function further includes calculating using the following equation for both motoring and generation modes: 
     
       
           B′=B /( W   e   K   o ).  
       
     
     In still another aspect of the present invention, adjusting an induction motor operating parameter further includes adjusting an excitation frequency. 
     In still another aspect of the present invention, at the above determined stator excitation frequency, adjusting the amplitude of the voltage applied to motor results in the desired motor torque as described by the equation:                T   e     =       3        P        (       Real   (     Z   in     )     -     R   s       )            (     V   2     )           W   e          (         (     Real   (     Z   in     )     )     2     +       (     Im        (     Z   in     )       )     2       )                 (   3   )                                
     These and other aspects and advantages of the present invention will become apparent upon reading the following detailed description of the invention in combination with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is an illustration of an induction motor with an internal combustion engine forming a hybrid powerplant, in accordance with the present invention 
     FIG. 2 is a schematic diagram illustrating an induction motor, in accordance with the present invention; 
     FIG. 3 is an equivalent electrical circuit model of the induction motor, in accordance with the present invention; 
     FIGS. 4 a  and  4   b  are graphs illustrating a torque output curve, efficiency curve and respective induction motor control signals, wherein the motor is operating in motoring mode at an optimum state, in accordance with the present invention; 
     FIGS. 4 c  and  4   d  are graphs illustrating a torque output curve, efficiency curve and respective induction motor control signals, wherein the motor is operating in generating mode at an optimum state, in accordance with the present invention; 
     FIG. 5 is a flowchart of a control strategy for controlling the operation of an induction motor, in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION 
     The system and method of the present invention will be described and illustrated in a hybrid motor environment. Of course, it should not be construed that this is the only environment or application in which the present invention may be applied. On the contrary, the system and method of the present invention may be used in any application where an induction motor is implemented. 
     With reference to FIGS. 1 and 2, a perspective view of a hybrid automotive engine  10  is illustrated, in accordance with the present invention. Hybrid engine  10  preferably includes an internal combustion engine  12  mechanically coupled to an induction motor  14 . More specifically, induction motor  14  is in rotational communication with the crankshaft of engine  12  and is preferably positioned between the engine block of engine  12  and the transmission. Induction motor  14  advantageously combines the functions of the starter and the alternator. Thus, many benefits and advantages are realized, such as seamless starting and stopping of engine  12 , high efficiency electricity generation, and active damping of powertrain vibrations. 
     More specifically, induction motor  14  has a motor housing  16  which includes mounting features such as through apertures  18  for fixedly securing motor housing  16  to engine  12 . Further, induction motor  14  has a stator  20  fixedly mounted to motor housing  16 , and a rotor  22 , rigidly coupled to the crankshaft (not shown) of engine  12 . A stator winding  24  are disposed about stator  20 . Rotor  22  is concentrically disposed within stator  20  and rotates with the engine&#39;s crankshaft (not shown). Additionally, an air gap  32  is defined by an outer surface  19  of rotor  22  and an inner surface  21  of stator  20 . 
     A transmission (not shown) for transmitting drive torque to a vehicle&#39;s road wheels would be mounted to motor housing  16  and coupled through a driveshaft to a rotor gear spline  30  on rotor  22 . 
     Induction motor  14  operates in at least two modes: a motoring mode, where electrical power is converted to mechanical power, and a generation mode where mechanical power is converted to electrical power. When induction motor  14  is operating in motoring mode, a three-phase alternating current is supplied to stator winding  24  directly and to rotor  22  by induction or a transformer action from the stator winding. The application of this poly-phase signal source to stator winding  24 , produces a magnetic field in air gap  32  between rotor  22  and stator  20 . The magnetic field rotates at a speed determined by the number of poles of stator  20  (a 12 pole machine is utilized in this invention) and the applied stator winding frequency (W e ). The rotor is made of a so-called squirrel cage rotor having windings consisting of conducting bars embedded in slots in the rotor iron and short circuited at each end by conducting end rings. The extreme simplicity and ruggedness of the squirrel cage construction are outstanding advantages of this type of induction motor. 
     The present invention provides a control strategy for controlling the operation of induction motor  14 . The control strategy of the present invention provides sensorless control by measuring the impedance (Z in ) of induction motor  14  to calculate the proper stator winding frequency (W e ) and to achieve the required torque (T e ) to rotate the rotor  22  and thus the crankshaft of engine  12 . The impedance and torque equations below illustrate how the control strategy of the present invention avoids reliance on critical motor parameters, that will change over varying operating conditions, as well as over the operating life of induction motor  14 . Thus, the present invention provides robust motor control whereby the system continuously operates in an optimized torque or efficiency range regardless motor parameter variations. 
     With reference to FIG. 3, an electrical equivalent circuit model  30  of induction motor  14  is illustrated. An impedance (Z in ) of motor  14  includes a stator resistance (R s )  32 , a stator leakage inductance (L 1 )  34 , a rotor leakage inductance (L 2 )  36 , a magnetizing inductance (L m )  38  and a rotor resistance converted to stator side (R r /s)  40 . Furthermore, the impedance (Z in ) of motor  14  is comprised of real Real(Z in ) and imaginary Im(Z in ) components as shown in the equation (1) below: 
     
       
           Z   in =Real( Z   in )+ Im ( Z   in ) j   (1)  
       
     
     
       
         or  
       
     
     
       
           Z   in =( R   s +[(R r   L   m   2   W   e   W   sl )/( R   r   2   +L   r   2   W   sl   2 )])+ j ( L   s   W   e −[( L   m   2   L   r   2   W   sl   2 )])  (2)  
       
     
     The theoretical induction motor torque (T e ) is described by the following equation:          T   e     =       3      P                     L   m   2          (       R   r     /   S     )              W   e          (     V   2     )                        2        [         (       R   s   2     +       L   s   2          W   e   2         )          (       (       R   r   2     /     S   2       )     +       L   r   2          W   e   2         )       +     
            L   m   2            W   e   2          (       2          R   s          (       R   r          /        S     )         -     2        L   s          L   r          W   e   2       +       L   m   2          W   e   2         )           ]                                  
     By substituting Real(Z in ) and Im(Z in ), the torque equation is simplified to:                T   e     =       3        P        (       Real   (     Z   in     )     -     R   s       )            (     V   2     )           W   e          (         (     Real   (     Z   in     )     )     2     +       (     Im   (     Z   in     )     )     2       )                 (   3   )                                
     Where: 
     W e =the excitation frequency; 
     W r =the rotor frequency; 
     W sl =W e −W r  is the slip frequency; 
     V=Phase Voltage; 
     R s =the stator resistance; 
     R r =the rotor resistance; 
     L 1 =the leakage inductance of the stator; 
     L 2  the leakage inductance of the rotor; 
     L m =the magnetizing inductance; 
     L s =L 1 +L m  is the total stator inductance; 
     L r =L 2 +L m  is the total rotor inductance; 
     P=number of pole pairs of the motor; 
     T e =the electromagnetic torque; 
     S=(W e −W r )/W e  is the slip; 
     L σ =(L s L r −L m   2 )/L r  is the total leakage inductance; and 
     λ dr &amp;λ qr  are the flux linkages in the d-q frame. 
     The conventional induction motor (d-q) machine model as described in an article entitled “Control Development and Characterization of the Induction Machine Starter/Alternator Drive Module (IMSAM)”, a Phase III Report for the Ford HEV Program, by Xu, et al, pages 1-7, hereby incorporated by reference is applied. Moreover, the stator current, rotor flux, and rotor frequency are used as the state variables and assuming steady state operation yields the following equations:                  L   σ          (       di   ds     /   dt     )       =     0   =         -     (       R   s     +       (       L   m   2     /     L   r   2       )          R   r         )            i   ds       +     (       L   σ          W   e          i   qs       )     +       (         L   m     /     T   r            L   r       )          λ   dr       +         W   r          (       L   m     /     L   r       )            λ   qr       +     V   ds                 (   4   )                   L   σ          (       di   qs     /   dt     )       =     0   =         -     (       R   s     +       (       L   m   2     /     L   r   2       )          R   r         )            i   qs       -     (       L   σ          W   e          i   ds       )     -         W   r          (       L   m     /     L   r       )            λ   dr       +       (         L   m     /     T   r            L   r       )          λ   qr       +     V   qs                 (   5   )                                
     
       
           T   r ( dλ   dr   /dt )=0= L   m   i   ds −λ dr   +T   r   W   sl λ qr   (6)  
       
     
     
       
           T   r ( dλ   qr   /dt )=0 =L   m   i   qs −λ qr   −T   r   W   sl λ dr   (7)  
       
     
     
       
           T   e (3 PL   m )(λ dr   i   qs −λ qr   i   ds )/(2 L   r )  (8)  
       
     
     Solving Equations (6) and (7) for Xdr and Xqr yields the following: 
     
       
         λ dr =( L   m   i   ds   +T   r   W   sl   L   m   i   qs )/(1 +T   r   2   W   sl   2 )  (9)  
       
     
     
       
         λ qr =( L   m   i   qs   −T   r   W   sl   L   m   i   ds )/(1 +T   r   2   W   sl   2 )  (10)  
       
     
     
       
         Also:  T   r   =L   r   /R   r   (11)  
       
     
     
       
           W   r   =W   e   =W   sl   (12)  
       
     
     Substituting into Equations (9)-(12) into Equations (4) and (5):              0   =         -     (       R   s     +     [       (       R   r          L   m   2          W   e          W   sl       )     /     (       R   r   2     +       L   r   2          W   sl   2         )       ]       )            i   ds       +       (       L   s            W     e   -            [       (       L   m   2          L   r          W   e          W   sl   2       )     /     (       R   r   s     +       L   r   2          W   sl   2         )       ]         )          i   qs       +     V   ds               (   13   )               0   =           -     (       L   s            W     e   -            [       (       L   m   2          L   r          W   e          W   sl   2       )     /     (       R   r   2     +       L   r   2          W   sl   2         )       ]         )            /     ds   -            (       R   s     +     [       (       R   r          L   m   2          W   e          W   sl       )     /     (       R   r   2     +       L   r   2          W   sl   2         )       ]       )            i   qs       +     V   qs               (   14   )                                
     
       
         Let:  A =( R   s +[( R   r   L   m   2   W   e   W   sl )/( R   r   2   +L   r   2   W   sl   2 )])  (15)  
       
     
     
       
           B =( L   s   W   e −[( L   m   2   L   r   W   e   W   sl   2 )/( R   r   2   +L   r   2   W   sl   2 )])  (16)  
       
     
     Then Equations (13) and (14) become: 
     
       
           V   ds =( A ) i   ds −( B ) i   qs   (17)  
       
     
     
       
           V   qs =( B ) i   ds −( A ) i   qs   (18)  
       
     
     
       
         And:  A =( V   ds   i   ds   +V   qs   i   qs )/( i   ds   2   +i   qs   2 )  (19)  
       
     
     
       
           B =( V   qs   i   ds   −V   ds   i   qs )/( i   ds   2   +i   qs   2 )  (20)  
       
     
     Substituting Equations (15) and (16) into (2) suggests: 
     
       
           A→ Real( Z   in )=( V   ds   i   ds   +V   qs   i   qs )/( i   ds   2   +i   qs   2 )  (21)  
       
     
     
       
           B→Im ( Z   in ) j =( V   qs   i   ds   −V   ds   i   qs )( i   ds   2   +i   qs   2 )  (22)  
       
     
     Since V ds , V qs  are controlled parameters, l qs , l ds  are the motor phase currents converted to d-q frame, the motor impedance is calculated without using individual motor parameters, such as R s , L s , R r , L r  and Slip. Since the variation of motor parameters affects motor phase voltage and phase current, the impedance calculated in (21) and (22) represents the actual motor operation condition and the effect of parameter changes due to motor speed, temperature change, and magnetic saturation are also included. 
     With reference to FIGS. 4 a  and  4   b , a plot of induction motor control signals or functions  52 ,  54  are illustrated for motoring mode operation. More specifically, FIG. 4 a  illustrates how K m  may be adjusted to achieve maximum torque. While FIG. 4 b  illustrates how K m  may be adjusted to achieve maximum efficiency as represented by efficiency curve  58 . In motor motoring mode, the control signals or functions  52  and  54  are defined by equations (23a) and (24) below: 
     
       
           A′=K   m −A  (23a)  
       
     
     
       
           B=B /( W   e   K   o )  (24)  
       
     
     Where K m  is a motor performance control constant, introduced purposely to cause the motor to operate in the desired range, such as optimized torque generation or maximum efficiency, and K o  is a unit conversion constant used to optimize motor control as will be discussed hereinafter. Control signal  52 , as indicated by equation (23a), is derived from the real part of induction motor impedance (Z in ). Induction motor control signal  54 , as indicated by equation (24), is derived from the imaginary part of the induction motor impedance (Z in ). The stator winding excitation frequency W e , is controlled so that control function  52  approximately equals control function  54 , thus allowing the motor to operate in the desired operating range (i.e. maximum torque output or maximum efficiency). 
     The torque generated by induction motor  14  is shown in FIGS. 4 a  and  4   b  and is represented by reference numeral  56 . Control signals  52  and  54  cross at two points, namely CP 1  and CP 2 . As is clear from FIGS. 4 a  and  4   b , crossing point CP 1  does not correspond with a desired torque output (maximum torque) or maximum efficiency of induction motor  14 . Accordingly, CP 1  is not used to judge whether the motor is in a desirable operating range. Further, K m  is adjusted such that CP 2  corresponds with the maximum output torque of induction motor  14  or peak efficiency which depends on motor operating requirements. There always exists a relationship between CP 2  and the maximum torque point over the motor excitation speed range. 
     By evaluating the magnitude of motor impedance |Z in | or |I ds   2 +l qs   2 |/( V   ds   2   +V   qs   2 ) and the polarity of torque (T e ), the difference between crossing point CP 1  and CP 2  is easily distinguishable. Whereby only crossing point CP 2  is selected to achieve sensorless motor control. 
     With reference to FIGS. 4 c  and  4   d , a plot of induction motor control signals or functions  62 ,  64  are illustrated in generating mode. More specifically, FIG. 4 c  illustrates how K g  may be adjusted to achieve maximum torque. While FIG. 4 d  illustrates how K g  may be adjusted to achieve maximum efficiency as represented by efficiency curve  68 . In motor generation mode, the control signals or functions  62  and  64  are defined by equations (23b) and (24) below: 
     
       
           A′=K   g   +A.   (23b)  
       
     
     
       
           B′=B /( W   e   K   o )  (24)  
       
     
     Where K g  is a motor performance control constant, introduced purposely to cause the motor to operate in the desired range, such as optimized torque generation or maximum efficiency, and K o  is a unit conversion constant used to optimize motor control, as will be discussed hereinafter. Control signal  62 , as indicated by equation (23b), is derived from the real part of induction motor impedance (Z in ). Induction motor control signal  64 , as indicated by equation (24), is derived from the imaginary part of the induction motor impedance (Z in ). The stator winding excitation frequency W e , is controlled so that control function  62  approximately equals control function  64 , thus allowing the motor to operate in the desired operating range (i.e. maximum torque output or maximum efficiency). 
     The torque generated by induction motor  14  is shown in FIGS. 4 c  and  4   d  and is represented by reference numeral  66 . Control signals  62  and  64  cross at two points, namely CP 1  and CP 2 . As is clear from FIGS. 4 c  and  4   d , crossing point CP 1  does not correspond with a desired torque output (maximum torque) or maximum efficiency of induction motor  14 . Accordingly, CP 1  is not used to judge whether the motor is in a desirable operating range. Further, K g  is adjusted such that CP 2  corresponds with the maximum output torque of induction motor  14  or peak efficiency which depends on motor operating requirements. There always exists a relationship between CP 2  and the maximum torque point over the motor excitation speed range. 
     By evaluating the magnitude of motor impedance |Z in | or |l ds   2 +l qs   2 |/(V ds   2 +V qs   2 ) and the polarity of torque (T e ), the difference between crossing point CP 1  and CP 2  is easily distinguishable. Whereby only crossing point CP 2  is selected to achieve sensorless motor control. 
     Therefore, the sensorless induction motor control of the present invention is achieved by: adjusting the stator frequency W e  until equation (23a) or (23b) equals equation (24) and by varying V ds  and V qs  in equation (3) to control the magnitude of the motor torque. 
     Referring now to FIG. 5, a flow chart illustrating an induction motor control strategy is illustrated, in accordance with the present invention. Control strategy  100  is initiated at block  102 , and at block  104  induction motor phase currents and phase voltages are directly measured and converted to the d-q reference frame. At block  106 , the real component of the motor impedance is calculated. The imaginary component of the motor impedance is calculated at block  108 . At block  110 , control functions A′ and B′ are calculated according to the mode the motor is operating in, whereby A′ is determined by (23) or (23a). The control function B′ is calculated by taking the imaginary component of the induction motor impedance and dividing by the product of the excitation frequency (W e ) and a unit conversion constant (K o ). Next, the difference of the control functions A′ and B′ are calculated, at block  112 . At block  114  a selection of the correct crossing point (CP 2 ) is made. At block  116 , the excitation frequency (We) is adjusted until the control function A′ approximately equals the control function B′. In practice however, the excitation frequency will be adjusted so that control function A′ is approximately equal to control function B′ within a predefined and specified range. With W e  selected, the motor torque may then be calculated from (3) where V ds  and V qs  are the inputs. 
     Thus, the present invention provides a sensorless induction motor control with voltages in the d-q frame as the only inputs for achieving the desired motor performance. Instead of employing individual motor parameters, the aforementioned sensorless induction motor control strategy relies on measuring motor phase voltage and phase current, and the continuous calculation of control functions (23a), (23b), and (24), accounting for operating condition changes, temperature changes, magnetic saturation, and motor wear. 
     The present invention has many advantages and benefits over the prior art. For example, the impedance and torque equations described above illustrate how the control strategy of the present invention avoids reliance on critical motor parameters, that will change over varying operating conditions, as well as over the life of induction motor  14 . Still, the control parameters, K m , K g , and K 0  provide an easy means for adjusting motor operation in the desired operation range. Thus, the present invention provides a robust motor control whereby the system continuously searches for the optimized torque/efficiency range to operate the motor.