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Induction Motor – Vector Control or Field Oriented Control By M.Kaliamoorthy

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## Induction Motor – Vector Control or Field Oriented Control By M.Kaliamoorthy

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**Induction Motor – Vector Control or Field Oriented Control**By M.Kaliamoorthy Department of Electrical Engineering**Outline**• Introduction • Analogy to DC Drive • Principles of Field Orientation Control • Rotor Flux Orientation Control • Indirect Rotor Flux Orientation (IRFO) • Direct Rotor Flux Orientation (DRFO) • Stator Flux Orientation Control • Direct Stator Flux Orientation (DSFO) • References**Introduction**• Induction Motor (IM) drives are replacing DC drives because: • Induction motor is simpler, smaller in size, less maintenance • Less cost • Capability of faster torque response • Capability of faster speed response (due to lower inertia) • DC motor is superior to IM with respect to ease of control • High performance with simple control • Due to decoupling component of torque and flux**Introduction**Induction Motor Drive • Scalar Control • Control of current/voltage/frequency magnitude based on steady-state equivalent circuit model • ignores transient conditions • for low performance drives • Simple implementation • Inherent coupling of torque and flux • Both are functions of voltage and frequency • Leads to sluggish response • Easily prone to instability • Vector Control or Field Orientation Control • control of magnitude and phase of currents and voltages based on dynamic model • Capable of observing steady state & transient motor behaviour • for high performance drives • Complex implementation • Decoupling of torque and flux • similar to the DC drive • Suitable for all applications previously covered by DC drives**a**f Analogy to DC Drive Te = k fIa Te = k fIa = k’ IfIa sin 90 =k’(If x Ia) In the DC motor: fcontrolled by controlling If Ifsame direction as field f Ia same direction as field a Ia and falways perpendicular and decoupled Hence, Keeping f constant, Te controlled by controlling Ia Ia, If , a and f are space vectors**s**r a b’ c’ b c Analogy to DC Motor Te = krx s In the Induction Motor: s produced by stator currents r produced by induced rotor currents Both s and r rotates at synchronous speed s Angle between s and rvaries with load, and motor speed r Torque and flux are coupled.**Analogy to DC Motor**(1) (2) (3) Induction Motor torque equation : Compared with DC Motor torque equation: Hence, if the angle betweens orr andis is made to be 90, then the IM will behave like a DC motor.**Principles of Field Orientation Control**Achieved through orientation (alignment) of rotating dq frame on r or s Stator-Flux Orientation Control Rotor-Flux Orientation Control Hence, if the angle betweens orr andis is made to be 90, then the IM will behave like a DC motor.**qr**dr ds ds Principles of Field Orientation Control Rotor-Flux Orientation Control Stator-Flux Orientation Control qs qs qs ds**Principles of Field Orientation Control**• Summary of field orientation control on a selected flux vectorf (i.e. either r , s or m):**qr**dr ds Rotor Flux Orientation Control qs (4) (5) r (6) • = torque producing current • = field producing current Similar to ia & if in DC motor Decoupled torque and flux control d- axis of dq- rotating frame is aligned with r . Hence, Therefore,**Rotor Flux Orientation Control**(7) (8) • From the dynamic model of IM, if dq- frame rotates at general speed g(in terms of vsd, vsq, isd, isq, ird, irq): • r rotates at synchronous speed s • Hence, drqr- frame rotates at s Therefore, g = s • These voltage equations are in terms of isd, isq, ird, irq • Better to have equations in terms of isd, isq, rd, rq**Rotor Flux Orientation Control**(9) (10) (11) Rotor flux linkage is given by: From (9): Substituting (8) and (10) into (7) gives the IM voltage equations rotating at s in terms of vsd, vsq, isd, isq, rd, rq:**Rotor Flux Orientation Control**(12) (13) (14) Note: Total leakage factor = sl = slip speed (elec.) (15) Important equations for Rotor Flux Orientation Control! Since , hence the equations in rotor flux orientation are:**Rotor Flux Orientation Control**(16) (17) (18) (19) Let Using (16), equation (14) can be rearranged to give: is called the “equivalent magnetising current” or “field current” Hence, from (17): where Under steady-state conditions (i.e. constant flux):**qr**dr ds Rotor Flux Orientation Control qs (20) r dq- reference frame orientation angle • r rotates at synchronous speed s • drqr- frame also rotates at s • Hence, • For precise control, r must be obtained at every instant in time • Leads to two types of control: • Indirect Rotor Flux Orientation • Direct Rotor Flux Orientation**Indirect Rotor Flux Orientation (IRFO)**(21) (22) (23) Orientation angle: Synchronous speed obtained by adding slip speed and electricalrotor speed Slip speed can be obtained from equation (15): Under steady-state conditions ( ):**Indirect Rotor Flux Orientation (IRFO) - implementation**(24) (25) • Closed-loop implementation under constant flux condition: • Obtainisdr* fromr*using (16): Obtainisqr* fromouter speed control loop since isqr* Tm* based on (6): Obtain vsdqr* from isdqr* via inner current control loop.**Indirect Rotor Flux Orientation (IRFO) - implementation**(26) • Closed-loop implementation under constant flux condition: • Determine the angular position r using (21) and (23): where m is the measured mechanical speed of the motor obtained from a tachogenerator or digital encoder. rto be used in the drqr dsqs conversion of stator voltage (i.e. vsdqr* to vsdqs* concersion).**Rotating frame (drqr)**Staionary frame (dsqs) Indirect Rotor Flux Orientation (IRFO) - implementation drqr dsqs transformation 2-phase (dsqs ) to 3-phase (abc) transformation isdr* vsdr* vas* r* vsqs* + Eq. (24) PI PWM VSI vbs* - 2/3 vsqr* ejr isqr* vsds* + + r* vcs* PI PI - - r IRFO Scheme isdr* isqr* slip m r P/2 Eq. (23) + + ias isds isdr NOfield weakening (constant flux) ibs 3/2 e-jr isqs ics isqr**Indirect Rotor Flux Orientation (IRFO) - implementation**vsqs* vsdr* ejr vsds* vsqr* isds isdr e-jr isqs isqr • drqr dsqs transformation • dsqs drqr transformation**Indirect Rotor Flux Orientation (IRFO) - implementation**vas* vsqs* vbs* 2/3 vsds* vcs* ias isds ibs 3/2 isqs ics 2-phase (dsqs )to 3-phase (abc) transformation: 3-phase (abc) to 2-phase (dsqs ) transform is given by: where: and**Example – IRFO Control of IM**An induction motor has the following parameters:**Example – IRFO Control of IM ctd.**The motor above operates in the indirect rotor field orientation (IRFO) scheme, with the flux and torque commands equal to the respective rated values, that is r* = 0.7865 Wb and Te* = 183 Nm. At the instant t = 1 s since starting the motor, the rotor has made 8 revolutions. Determine at time t = 1s: • the stator reference currents isd* and isq*in the dq-rotating frame • the slip speed sl of the motor • the orientation angle r of the dq-rotating frame • the stator reference currents isds* and isqs*in the stationary dsqs frame • the three-phase stator reference currents ias*, ibs* and ics***Example – IRFO Control of IM ctd.**Answers:**Indirect Rotor Flux Orientation (IRFO) – field weakening**imrd* imrd (rated) r r (base) • Closed-loop implementation under field weakening condition: • Employed for operationsabove base speed • DC motor: flux weakened by reducing field current if • Compared with eq. (17) for IM: • IM: flux weakened by reducing imrd (i.e. “equivalent magnetising current” or “field current)**Rotating frame (drqr)**Staionary frame (dsqs) Indirect Rotor Flux Orientation (IRFO) – field weakening implementation With field weakening Same as in slide 20 vsdr* imrd r * vsqs* isdr* + r* + PI PI - - vsqr* isqr* ejr vsds* imrd r + r* + PI PI - - imrdr* r isqr* r slip Eq. (22) + + isds isdr e-jr isqs isqr**Indirect Rotor Flux Orientation (IRFO) – Parameter**sensitivity • Mismatch between IRFO Controller and IM may occur • due to parameter changes with operating conditions (eg. increase in temperature, saturation) • Mismatch causes coupling between T and producing components • Consequences: • r deviates from reference value (i.e. r*) • Te deviates in a non-linear relationship from command value (i.e. Te*) • Oscillations occurs in r and Te response during torque transients (settling time of oscillations = r)**Direct Rotor Flux Orientation (DRFO)**(27) (28) • Orientation angle: obtained from: • Direct measurements of airgap fluxes mdsand mqs • Estimated from motor’s stator voltages vsdqs and stator currents isdqs Note that:**Direct Rotor Flux Orientation (DRFO) – Direct measurements**mds& mqs (29) • Direct measurements of airgap fluxes mdsand mqs • mdsand mqs measured using: • Hall sensors – fragile • flux sensing coils on the stator windings – voltages induced in coils are integrated to obtain mdsand mqs • The rotor flux r is then obtained from: • Disadvantages: sensors are inconvenient and spoil the ruggedness of IM.**Rotating frame (drqr)**Stationary frame (dsqs) Direct Rotor Flux Orientation (DRFO) – Direct measurements mds& mqs Flux sensing coils arranged in quadrature isdr* vsdr* vas* r* vsqs* + Eq. (24) PI PWM VSI vbs* - 2/3 vsqr* isqr* ejr vsds* + + r* vcs* PI PI - - r DRFO Scheme mds rds Eq. (29) tan-1 mqs rqs m r P/2 r ias isds isdr NOfield weakening (constant flux) ibs 3/2 e-jr isqs ics isqr**Direct Rotor Flux Orientation (DRFO) – Estimated from**vsdqs& isdqs (30) (31) • Estimated from motor’s stator voltages and currents • sdsand sqs obtained from stator voltage equations: • The rotor flux r is then obtained from: • Disadvantages: dc-drift due to noise in electronic circuits employed, incorrect initial values of flux vector components sdq(0)**Direct Rotor Flux Orientation (DRFO) – Estimated from**vsdqs& isdqs • Estimated from motor’s stator voltages and currents • This scheme is part of sensorless drive scheme • using machine parameters, voltages and currents to estimate flux and speed • sdqscalculations (eq. 30) depends on Rs • Poor field orientation at low speeds ( < 2 Hz), above 2 Hz, DRFO scheme as good as IRFO • Solution: add boost voltage to vsdqs at low speeds • Disadvantages: Parameter sensitive, dc-drift due to noise in electronic circuits employed, incorrect initial values of flux vector components sdq(0)**Rotating frame (drqr)**Stationary frame (dsqs) Direct Rotor Flux Orientation (DRFO) – Estimated from vsdqs& isdqs isdr* vsdr* vas* r* vsqs* + Eq. (24) PI PWM VSI vbs* - 2/3 vsqr* isqr* ejr vsds* + + r* vcs* PI PI - - r DRFO Scheme sds rds vsdqs Eq. (31) Eq. (30) tan-1 isdqs rqs sqs m r P/2 r ias isds isdr NOfield weakening (constant flux) ibs 3/2 e-jr isqs ics isqr**Rotating frame (drqr)**Stationary frame (dsqs) Direct Rotor Flux Orientation (DRFO) – field weakening implementation With field weakening Same as in slide 26 or 29 vsdr* imrd r * vsqs* isdr* + r* + PI PI - - vsqr* isqr* ejr vsds* imrd r + r* + PI PI - - r rds tan-1 rqs r r isds isdr e-jr isqs isqr**ds**Stator Flux Orientation Control qs (32) qs (33) ds (34) • = torque producing current • = field producing current Similar to ia & if in DC motor Decoupled torque and flux control d- axis of dq- rotating frame is aligned with s. Hence, Therefore,**Stator Flux Orientation Control**(7) (8) • From the dynamic model of IM, if dq- frame rotates at general speed g (in terms of vsd, vsq, isd, isq, ird, irq): • s rotates at synchronous speed s • Hence, dsqs- frame rotates at s Therefore, g = s • These voltage equations are in terms of isd, isq, ird, irq • Better to have equations in terms of isd, isq, sd, sq**Stator Flux Orientation Control**(35) (36) (37) Stator flux linkage is given by: From (9): Substituting (8) and (36) into (7) gives the IM voltage equations rotating at s in terms of vsd, vsq, isd, isq, sd, sq:**Stator Flux Orientation Control**(38) (39) (40) (41) Important equations for Stator Flux Orientation Control! Since , hence the equations in stator flux orientation are:**Stator Flux Orientation Control**(42) Varying to control torque causes change in Torque will not react immediately to Equation (40) can be rearranged to give: should be independent of torque producing current From (42), is proportional to and . Coupling exists between and .**Stator Flux Orientation Control – Dynamic Decoupling**(43) • De-coupler is required to • overcome the coupling between and (so that has no effect on ) • Provide the reference value for • Rearranging eq. (42) gives: • can be obtained from outer speed control loop • However, eq. (43) requires**Stator Flux Orientation Control – Dynamic Decoupling**(44) can be obtained from (41): in (43) and (44) is the reference stator flux vector Hence, equations (43) and (44) provide dynamic decoupling of the flux-producing and torque-producing currents.**Stator Flux Orientation Control – Dynamic Decoupling**+ s* isds* + isqs* isqs* x from speed controller x sl* Dynamic decoupling system implementation:**ds**Stator Flux Orientation Control qs qs ds s dq- reference frame orientation angle • dsqs- frame also rotates at s • For precise control, s must be obtained at every instant in time • Leads to two types of control: • Indirect Stator Flux Orientation • Direct Stator Flux Orientation • s easily estimated from motor’s stator voltages vsdqsand stator currents isdqs • Hence, Indirect Stator Flux Orientation scheme unessential.**Direct Stator Flux Orientation (DSFO) - implementation**(45) • Closed-loop implementation: • Obtainisds* fromscontrol loop and dynamic decoupling systemshown in slide 38. Obtainisqs* fromouter speed control loop since isqr* Te* based on (34): Obtain vsdqs* from isdqs* via inner current control loop.**Direct Stator Flux Orientation (DSFO) - implementation**(46) (47) (48) • Closed-loop implementation: • Determine the angular position s using: sdsand sqs obtained from stator voltage equations: Note that: Eq. (48) will be used as feedback for the s control loop**Direct Stator Flux Orientation (DSFO) - implementation**• Closed-loop implementation: • sto be used in the dsqs dsqs conversion of stator voltage (i.e. vsdqs* to vsdqs* concersion). • sestimated from pure integration of motor’s stator voltages equations eq. (47) which has disadvantages of: • dc-drift due to noise in electronic circuits employed • incorrect initial values of flux vector components sdqs(0) • Solution: A low-pass filter can be used to replace the pure integrator and avoid the problems above.**Rotating frame (dsqs)**Stationary frame (dsqs) Direct Stator Flux Orientation (DSFO) - implementation r m P/2 isqs* vsqs* - vas* vsqs* + + r* PI PI PWM VSI vbs* - 2/3 vsds* ejs s* vsds* Decoupling system vcs* PI + s isds* sds vsdqs Eq. (47) + tan-1 isdqs sqs + - s + PI ias isqs isqs - |s| ibs 3/2 e-js Eq. (48) isds ics isds sds sqs**References**Trzynadlowski, A. M., Control of Induction Motors, Academic Press, San Diego, 2001. Krishnan, R., Electric Motor Drives: Modeling, Analysis and Control, Prentice-Hall, New Jersey, 2001. Bose, B. K., Modern Power Electronics and AC drives, Prentice-Hall, New Jersey, 2002. Asher, G.M, Vector Control of Induction Motor Course Notes, University of Nottingham, UK, 2002.