Induction Motor Scalar ControlByMr.M.KaliamoorthyDepartment of Electrical & Electroncis EngineeringPSNA College of Engineering and Technology*

OutlineIntroductionSpeed Control of Induction MotorsPole ChangingVariable-Voltage, Constant FrequencyVariable FrequencyConstant Volts/Hz (V/f) ControlOpen-loop ImplementationClosed-loop ImplementationConstant Airgap Flux ControlReferences

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INDUCTION MOTOR DRIVESThree-phase induction motor are commonly used in adjustable-speed drives (ASD).Basic part of three-phase induction motor : Stator Rotor Air gap

Stator

Three-phase windings

Rotor

Air gap

w

T

Rotor windings

Three-phase supply

w

m

s

w

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 distribution of stator winding so that there is an effect of multiple poles, producing several cycle of magnetomotive force (mmf) or field around the air gap. The speed of rotation of field is called the synchronous speed ws , which is defined by : s is syncronous speed [rad/sec] Ns is syncronous speed [rpm] p is numbers of poles is the supply frequency [rad/sec] f is the supply frequency [Hz] Nm is motor speed

or

Stator

Three-phase windings

Rotor

Air gap

w

T

Rotor windings

Three-phase supply

w

m

s

w

The rotor speed or motor speed is :Where S is slip, as defined as : Or The motor speed

Stator

Three-phase windings

Rotor

Air gap

w

T

Rotor windings

Three-phase supply

w

m

s

w

The rotor speed or motor speed is :Where S is slip, as defined as : Or The motor speed

Stator

Three-phase windings

Rotor

Air gap

w

T

Rotor windings

Three-phase supply

w

m

s

w

Equivalent Circuit Of Induction MotorWhere :Rs is resistance per-phase of stator windingRr is resistance per-phase of rotor windingXs is leakage reactance per-phase of the winding statorXs is leakage reactance per-phase of the winding rotorXm is magnetizing reactance Rm is Core losses as a reactance

Stator

Three-phase windings

Rotor

Air gap

w

T

Rotor windings

Three-phase supply

w

m

s

w

Stator

Air gap

Vs

Is

motor

Im

Ir

Xs

Xr

Rs

Rm

Xm

Rr/s

Performance Characteristic of Induction MotorStator copper loss : Rotor copper loss : Core losses :

Stator

Air gap

Vs

Is

motor

Im

Ir

Xs

Xr

Rs

Rm

Xm

Rr/s

Power developed on air gap (Power fropm stator to rotor through air gap) :Performance Characteristic of Induction Motor Power developed by motor :or Torque of motor :oror

Input power of motor : Performance Characteristic of Induction MotorOutput power of motor : Efficiency :

If and so, the efficiency can calculated as :Performance Characteristic of Induction Motor

Generally, value of reactance magnetization Xm >> value Rm (core losses) and also So, the magnetizing voltage same with the input voltage :Therefore, the equivalent circuit is ;XmPerformance Characteristic of Induction Motor

Stator

Air gap

Vs

Is

motor

Im

Ir

Xs

Xr

Rs

Rm

Xm

Rr/s

Is=Ir

Stator

Air gap

rotor

Vs

Ii

Im

Ir

Xs

Xr

Rs

Rr/s

Pi

Po

Performance Characteristic of Induction MotorXmThe rotor current is :

Is=Ir

Stator

Air gap

rotor

Vs

Ii

Im

Ir

Xs

Xr

Rs

Rr/s

Pi

Po

Torque speed Characteristic

Is=Ir

Stator

Air gap

rotor

Vs

Ii

Im

Ir

Xs

Xr

Rs

Rr/s

Pi

Po

Tst

Tmax

Smax

Td

S=0

ws

Ns

S=1

TL

S=Sm

wm

Nm

Nm =0

Tm=TL

Operating point

Introduction*rsTratedPull out Torque(Tmax)Tes1 0What if the load must be operated here?rotorRequires speed control of motor

Speed Control of IMGiven a load T characteristic, the steady-state speed can be changed by altering the T curve of the motor*Pole ChangingVarying line frequencyVarying voltage (amplitude)231

Speed Control of IMVariable-Voltage (amplitude), Constant FrequencyControlled using:Transformer (rarely used)Thyristor voltage controllerthyristors connected in anti-parallelmotor can be star or delta connectedvoltage control by firing angle control(gating signals are synchronized to phase voltages and are spaced at 60 intervals)Only for operations in Quadrant 1 and Quadrant 3 (requires reversal of phase sequence)also used for soft start of motors

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Speed Control of IMVariable-Voltage (amplitude), Constant FrequencyVoltage can only be reduced from rated Vs (i.e. 0 < Vs Vs,rated)From torque equation, Te Vs2When Vs , Te and speed reduces.If terminal voltage is reduced to bVs, (i.e. Vs = bVs,rated) :

Note: b 1*

Speed Control of IMVariable-Voltage (amplitude), Constant FrequencySuitable for applications where torque demand reduces with speed (eg: fan and pump drives where TL m2)Suitable for NEMA Class D (high-slip, high Rr) type motorsHigh rotor copper loss, low efficiency motorsget appreciable speed range

*Practical speed range

Speed Control of IMVariable Voltage (amplitude), Constant FrequencyDisadvantages:limited speed range when applied to Class B (low-slip) motorsExcessive stator currents at low speeds high copper losses Distorted phase current in machine and line (harmonics introduced by thyristor switching)Poor line power factor (power factor proportional to firing angle)Hence, only used on low-power, appliance-type motors where efficiency is not importante.g. small fan or pumps drives*

Speed Control of IMVariable FrequencySpeed control above rated (base) speed Requires the use of PWM inverters to control frequency of motorFrequency increased (i.e. s increased)Stator voltage held constant at rated valueAirgap flux and rotor current decreases Developed torque decreases Te (1/s)For control below base speed use Constant Volts/Hz method

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Constant Volts/Hz (V/f) ControlAirgap flux in the motor is related to the induced stator voltage E1 :

For below base speed operation:Frequency reduced at rated Vs - airgap flux saturates (f ,ag and enters saturation region oh B-H curve):- excessive stator currents flow- distortion of flux wave- increase in core losses and stator copper lossHence, keep ag = rated fluxstator voltage Vs must be reduced proportional to reduction in f (i.e. maintaining Vs / f ratio)*Assuming small voltage drop across Rs and Lls

Constant Volts/Hz (V/f) ControlMax. torque remains almost constantFor low speed operation:cant ignore voltage drop across Rs and Lls (i.e. E1 Vs)poor torque capability (i.e. torque decreased at low speeds shown by dotted lines)stator voltage must be boosted to compensate for voltage drop at Rs and Lls and maintain constant agFor above base speed operation (f > frated):stator voltage maintained at rated valueSame as Variable Frequency control (refer to slide 13)*

Constant Volts/Hz (V/f) Control

*Vs vs. f relation in Constant Volts/Hz drivesVsfLinear offset curve for high-starting torque loadsemployed for most applications

Non-linear offset curve for low-starting torque loadsBoost - to compensate for voltage drop at Rs and Lls

Constant Volts/Hz (V/f) Control For operation at frequency K times rated frequency: fs = Kfs,rated s = Ks,rated (1) (Note: in (1) , speed is given as mechanical speed)

Stator voltage: (2)

Voltage-to-frequency ratio = d = constant:

(3)*

Constant Volts/Hz (V/f) Control For operation at frequency K times rated frequency:Hence, the torque produced by the motor:

(4)

where s and Vs are calculated from (1) and (2) respectively.*

Constant Volts/Hz (V/f) Control For operation at frequency K times rated frequency:The slip for maximum torque is:

(5)

The maximum torque is then given by: (6)

where s and Vs are calculated from (1) and (2) respectively.*

Constant Volts/Hz (V/f) Control

*Field Weakening Mode (f > frated) Reduced flux (since Vs is constant) Torque reducesConstant Power Area(above base speed) Constant Torque Area(below base speed)Rated (Base) frequencyNote: Operation restricted between synchronous speed and Tmax for motoring and braking regions, i.e. in the linear region of the torque-speed curve.

Constant Volts/Hz (V/f) Control

*Constant Power Area Constant Torque Area

ExampleA 4-pole, 3 phase, 400 V, 50 Hz, 1470 rpm induction motor has a rated torque of 30 Nm. The motor is used to drive a linear load with characteristic given by TL = K, such that the speed equals rated value at rated torque. If a constant Volts/Hz control method is employed, calculate:The constant K in the TL - characteristic of the load. Synchronous and motor speeds at 0.6 rated torque. If a starting torque of 1.2 times rated torque is required, what should be the voltage and frequency applied at start-up? State any assumptions made for this calculation.Answers: K = 0.195, synchronous speed = 899.47 rpm & motor speed = 881.47 rpm, At start up: frequency = 1.2 Hz, Voltage = 9.6 V*

Constant Volts/Hz (V/f) Control Open-loop Implementation*PWM Voltage-Source Inverter (VSI)Note: e= s = synchronous speed

Constant Volts/Hz (V/f) Control Open-loop ImplementationMost popular speed control method because it is easy to implementUsed in low-performance applications where precise speed control unnecessarySpeed command s* - primary control variable Phase voltage command Vs* generated from V/f relation (shown as the G in slide 23)Boost voltage Vo is added at low speedsConstant voltage applied above base speedSinusoidal phase voltages (vabc*) is then generated from Vs* & s* where s* is obtained from the integral of s* vabc* employed in PWM inverter connected to motor*

Constant Volts/Hz (V/f) Control Open-loop ImplementationProblems in open-loop drive operation:Motor speed not controlled precisely primary control variable is synchronous speed s actual motor speed r is less than s due to slsl depends on load connected to motorsl cannot be maintained since r not measuredcan lead to operation in unstable region of T- characteristicstator currents can exceed rated value endangering inverter-converter combinationProblems (to an extent) can be overcome by:Open-loop Constant Volts/Hz Drive with Slip CompensationClosed-loop implementation - having outer speed loop with slip regulation*

Constant Volts/Hz (V/f) Control Open-loop Implementation*Open-loop Constant Volts/Hz Drive with Slip Compensation- Slip speed is estimated and added to the reference speed r*

Note: e= s = synchronous speed

Constant Volts/Hz (V/f) Control Open-loop ImplementationHow is sl estimated in the Slip Compensator?Using T- curve, sl Te sl can be estimated by estimating torque where:

(8)

(9)

*Open-loop Constant Volts/Hz Drive with Slip CompensationNote: In the figure, slip= sl = slip speedsyn= s = synchronous speed(7)

Constant Volts/Hz (V/f) Control Closed-loop Implementation*Open-loop system (as in slide 23) Slip ControllerNote: e= s = synchronous speed

Constant Volts/Hz (V/f) Control Closed-loop ImplementationReference motor speed r* is compared to the actual speed r to obtain the speed loop errorSpeed loop error generates slip command sl* from PI controller and limiterLimiter ensures that the sl* is kept within the allowable slip speed of the motor (i.e. sl* slip speed for maximum torque)sl* is then added to the actual motor speed r to generate synchronous speed command s* (or frequency command)s* generates voltage command Vs* from V/f relationBoost voltage is added at low speedsConstant voltage applied above base speedScheme can be considered open loop torque control (since T s) within speed control loop*

Constant Airgap Flux ControlConstant V/f control employs the use of variable frequency voltage source inverters (VSI)Constant Airgap Flux control employs variable frequency current source inverters or current-controlled VSIProvides better performance compared to Constant V/f control with Slip Compensationairgap flux is maintained at rated value through stator current controlSpeed response similar to equivalent separately-excited dc motor drive but torque and flux channels still coupledFast torque response means:High-performance drive obtainedSuitable for demanding applicationsAble to replace separately-excited dc motor drivesAbove only true is airgap flux remains constant at rated value*

Constant Airgap Flux ControlConstant airgap flux in the motor means:

For ag to be kept constant at rated value, the magnetising current Im must remain constant at rated valueHence, in this control scheme stator current Is is controlled to maintain Im at rated value

*maintain at ratedControlled to maintain Im at ratedAssuming small voltage drop across Rs and Lls

Constant Airgap Flux ControlFrom torque equation (with ag kept constant at rated value), since ss = sl and ignoring Rs and Lls,

By rearranging the equation:

*Te sl sl can be varied instantly instantaneous (fast) Te response

Constant Airgap Flux ControlConstant airgap flux requires control of magnetising current Im which is not accessibleFrom equivalent circuit (on slide 31):

From equation (10), plot Is against sl when Im is kept at rated value. Drive is operated to maintain Is against sl relationship when frequency is changed to control speed.Hence, control is achieved by controlling stator current Is and stator frequency:Is controlled using current-controlled VSIControl scheme sensitive to parameter variation (due to Tr and r)*(10)

Constant Airgap Flux Control - Implementation*rCurrent controller options: Hysteresis Controller PI controller + PWMEquation (10) (from slide 33)i*ai*bi*cCurrent Controlled VSI

Current-Controlled VSI ImplementationHysteresis Controller*

Current-Controlled VSI ImplementationPI Controller + Sinusoidal PWM*Due to interactions between phases (assuming balanced conditions) actually only require 2 controllersVoltage Source Inverter (VSI)

Current-Controlled VSI ImplementationPI Controller + Sinusoidal PWM (2 phase)

*Motori*ai*bi*cabcdqPWMVoltage Source Inverter (VSI)id*iq*idiq

ReferencesKrishnan, 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.Trzynadlowski, A. M., Control of Induction Motors, Academic Press, San Diego, 2001.Rashid, M.H, Power Electronics: Circuit, Devices and Applictions, 3rd ed., Pearson, New-Jersey, 2004.Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008.Ahmad Azli, N., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008.*

*Dr. Ungku Anisa, July 2008Dr. Ungku Anisa, July 2008