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**INDUCTION MOTOR Scalar Control (squirrel cage)**

MEP 1523 ELECTRIC DRIVES INDUCTION MOTOR Scalar Control (squirrel cage)

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Scalar control of induction machine: Control of induction machine based on steady-state model (per phase SS equivalent circuit): Is Lls Ir’ Llr’ Rs + Vs – + Eag – Lm Rr’/s Im

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**Scalar control of induction machine**

Te Pull out Torque (Tmax) rotor TL Te Intersection point (Te=TL) determines the steady –state speed sm rated Trated r s s

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**Scalar control of induction machine**

Given a load T– characteristic, the steady-state speed can be changed by altering the T– of the motor: Pole changing Synchronous speed change with no. of poles Discrete step change in speed Variable voltage (amplitude), frequency fixed E.g. using transformer or triac Slip becomes high as voltage reduced – low efficiency Variable voltage (amplitude), variable frequency Using power electronics converter Operated at low slip frequency

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**Variable voltage, fixed frequency**

e.g. 3–phase squirrel cage IM V = 460 V Rs= 0.25 Rr=0.2 Lr = Ls = 0.5/(2*pi*50) Lm=30/(2*pi*50) f = 50Hz p = 4 Lower speed slip higher Low efficiency at low speed

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**Variable voltage, variable frequency**

Constant V/f operation At low slip

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**If Φag is constant Te α slip frequency**

Variable voltage, variable frequency – Constant V/f If Φag is constant Te α slip frequency

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**Approximates constant air-gap flux when Eag is large**

Variable voltage, variable frequency – Constant V/f How do we make constant ? Approximates constant air-gap flux when Eag is large Eag = k f ag = constant Speed is adjusted by varying f - maintaining V/f to approximate constant air-gap flux

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**Characteristic with constant**

Variable voltage, variable frequency – Constant V/f Characteristic with constant

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**Constant constant V/f**

Variable voltage, variable frequency Constant constant V/f Vs Vrated Constant slope frated f

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**Constant V/f – open-loop**

Variable voltage, variable frequency Constant V/f – open-loop Rectifier 3-phase supply VSI IM C f Ramp Pulse Width Modulator V s* + rate limiter is needed to ensure the slip change within allowable range (e.g. rated value)

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**Constant V/f – open-loop**

Variable voltage, variable frequency Constant V/f – open-loop Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2

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**Constant V/f – open-loop**

Variable voltage, variable frequency Constant V/f – open-loop Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2 constant_vhz_withoutBoost/Signal Builder : Group 1 Signal 1 50 40 30 20 10 0.5 1 1.5 2 2.5 3 3.5 Time (sec) 13

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**Constant V/f – open-loop**

Variable voltage, variable frequency Constant V/f – open-loop Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2 14

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**Constant V/f – open-loop**

Variable voltage, variable frequency Constant V/f – open-loop Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2 With almost no rate limiter 15

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**Constant V/f – open-loop**

Variable voltage, variable frequency Constant V/f – open-loop Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2 With 628 rad/s2 16

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**Constant V/f – open-loop low speed problems**

Variable voltage, variable frequency Constant V/f – open-loop low speed problems Problems with open-loop constant V/f At low speed, voltage drop across stator impedance is significant compared to airgap voltage - poor torque capability at low speed Solution: (i) Voltage boost at low frequency (ii) Maintain Im constant stator current control

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**Constant V/f – open-loop low speed problems (i) voltage boost**

Variable voltage, variable frequency Constant V/f – open-loop low speed problems (i) voltage boost Torque deteriorate at low frequency – hence compensation commonly performed at low frequency In order to truly compensate need to measure stator current – seldom performed

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**Constant V/f – open-loop low speed problems (i) voltage boost**

Variable voltage, variable frequency Constant V/f – open-loop low speed problems (i) voltage boost With voltage boost of Irated*Rs Torque deteriorate at low frequency – hence compensation commonly performed at low frequency In order to truly compensate need to measure stator current – seldom performed

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**Constant V/f – open-loop low speed problems (i) voltage boost**

Variable voltage, variable frequency Constant V/f – open-loop low speed problems (i) voltage boost Voltage boost at low frequency Vrated Linear offset Boost Non-linear offset – varies with Is frated

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**Constant V/f – open-loop low speed problems (i) voltage boost**

Variable voltage, variable frequency Constant V/f – open-loop low speed problems (i) voltage boost Idc Rectifier + Vdc - 3-phase supply VSI IM C f Ramp Pulse Width Modulator s* + V + Vboost

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**Constant V/f – open-loop low speed problems (i) Constant Im**

Variable voltage, variable frequency Constant V/f – open-loop low speed problems (i) Constant Im ag, constant → Eag/f , constant → Im, constant (rated) Controlled to maintain Im at rated Is Lls Llr’ Ir’ Rs + Vs – Lm + Eag – Rr’/s maintain at rated Im

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**Constant V/f – open-loop low speed problems (i) Constant Im**

Variable voltage, variable frequency Constant V/f – open-loop low speed problems (i) Constant Im From per-phase equivalent circuit, Current is controlled using current-controlled VSI The problem of stator impedance drop is solved Dependent on rotor parameters – sensitive to parameter variation

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**Current reference generator**

Variable voltage, variable frequency Constant V/f – open-loop low speed problems (i) Constant Im 3-phase supply VSI Rectifier IM C Current controller Tacho slip * + |Is| PI - + s r Current reference generator +

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**Problems with open-loop constant V/f**

Variable voltage, variable frequency Constant V/f Problems with open-loop constant V/f Poor speed regulation Solution: (i) Slip compensation (ii) Closed-loop control

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**Constant V/f – poor speed regulation: (i) slip compensation**

Variable voltage, variable frequency Constant V/f – poor speed regulation: (i) slip compensation Motor characteristic AFTER slip compensation T ωr (rad/s) ωs1* Tload ωs2*=ωs1*+ωslip1 ωslip1 Motor characteristic BEFORE slip compensation ωr2≈ωs1* T2 ωr1 T1 ωslip1

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**Constant V/f – poor speed regulation: (i) slip compensation**

Variable voltage, variable frequency Constant V/f – poor speed regulation: (i) slip compensation Idc Rectifier + Vdc - 3-phase supply VSI IM C f Ramp Pulse Width Modulator s* + + V + + Vboost Slip speed calculator Vdc Idc

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**Constant V/f – poor speed regulation: (i) slip compensation**

Variable voltage, variable frequency Constant V/f – poor speed regulation: (i) slip compensation How is the slip frequency calculated ? + Vdc Idc INV Pdc= VdcIdc Pmotor,in= Pdc – Pinv,losses Pmotor,in Stator Copper lossess Stator Core losses ROTOR STATOR Pair-gap 28

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**Constant V/f – poor speed regulation: (i) slip compensation**

Variable voltage, variable frequency Constant V/f – poor speed regulation: (i) slip compensation How is the slip frequency calculated ? Pair-gapc = Tesyn Te = Pair-gap/syn For constant V/f control, 29

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**Constant V/f – poor speed regulation: (i) closed-loop speed**

Variable voltage, variable frequency Constant V/f – poor speed regulation: (i) closed-loop speed Require speed encoder Increase complexity 30

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The stator winding are supplied with balanced three-phase AC voltage, which produce induced voltage in the rotor windings. It is possible to arrange the.

The stator winding are supplied with balanced three-phase AC voltage, which produce induced voltage in the rotor windings. It is possible to arrange the.

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