31-113

8/13/2019 31-113

1/9

The Online Journal on Electronics and Electrical Engineering (OJEEE) Vol. (3) No. (2)

Reference Number: W10-0113 416

Stator Resistance and Speed Estimation forInduction Motor Drives As Influenced by

SaturationA. M. El-Sawy, Yehia S. Mohamed and A. A. Zaki*Electrical Engineering Department, Faculty of Engineering,

Minia University, EL-Minia, Egypt*[email protected]

Abstract - In this paper, stator resistance and speedestimation for a vector controlled induction motor drivetaking saturation into account is presented. Amathematical dynamic model of an induction motor asinfluenced by magnetic circuit saturation is presented.Moreover, a modified structure of indirect vectorcontroller scheme is proposed which involves thesaturated value of the magnetizing inductance. Parallelstator resistance and rotor speed estimation based onmodel reference adaptive system (MRAS) has been usedto obtain accurate estimation for rotor speed. On-linemagnetizing inductance estimation has been used withinthe speed estimator. Digital simulations have been carriedout in order to evaluate the effectiveness of the proposedsensorless drive system. The results prove excellentsteady-state and dynamic performances of the drivesystem in a wide speed range, which confirms validity of the proposed scheme.

K eywords- Induction Machines, Vector control, Speed Sensorless, Saturation, Stator Resistance, Parameters Estimation.

List of symbols

m L Magnetizing inductance (H)

m L

Estimated Magnetizing inductance (H)

r L Rotor self leakage inductance (H)

s L Stator self leakage inductance (H)

ls L Stator leakage inductance (H)

lr L Rotor leakage inductance (H)

Leakage coefficient

r sm L L L21

lT Load torque (Nm), eT Electromagnetic torque (Nm)

s R Stator resistance () , r R Rotor resistance ()

s R Estimated stator resistance ()

e Synchronous speed (rad/sec), sl Slip speed (rad/sec)*e Command synchronous speed (rad/sec)*sl Command slip speed (rad/sec)

r Actual Rotor speed (rad/sec)*r Reference Rotor speed (rad/sec)

r Estimated Rotor speed (rad/sec)

r T Rotor time constant r r r R LT =

I. INTRODUCTION

Indirect field oriented controlled induction motor drives areincreasingly used in high-performance drive systems.Accurate knowledge of stator resistance is not required inindirect field oriented control scheme [1]. Speed sensorlesscontrol of induction motor drives received great attention toavoid the different problems associated with direct speedsensors. A vast majority of speed estimation schemes rely onutilization of an induction motor model in the process of speed estimation [5] and require an accurate knowledge of all(or the most of) the motor parameters, including the statorresistance and magnetizing inductance.

So, the interest in stator resistance adaptation appearedrecently, with the advances of speed sensorless systems [2].An accurate value of the stator resistance is of crucialimportance for correct operation of a sensorless drive in thelow speed region, since any mismatch between the actualvalue and the set value used within the model of speedestimation may lead not only to a substantial speed estimationerror but to instability as well [6]-[7]. Therefore, there is agreat interest in the research community to develop onlinestator resistance identification schemes for accurate speedestimation in the low speed region.

The available online stator resistance identificationschemes can be classified into a couple of distinct categories.All these methods rely on stator current measurement andchiefly require information regarding stator voltages [1]. Themost famous methods include different types of estimatorswhich often use an adaptive mechanism to update the value of stator resistance [1]-[4]. The stator resistance is determined in[3] by using a reactive power based model reference adaptivesystem (MRAS). The reactive power relies on the accuracy of other parameters such as leakage inductance and rotorresistance which are not necessarily constant and the result isprone to error. Adaptive full-order flux observers (AFFO) forestimating the speed and stator resistance are developed usingPopov's and Lyapunov stability criteria [4]. While thisscheme is not computationally intensive, an AFFO with anon-zero gain matrix may become unstable. Model referenceadaptive system for estimating the speed and stator resistanceis developed using Popov's stability criterion [1]. In suchmethod, the stator resistance adaptation mechanism isdetermined with the difference between the measured andobserved stator currents. In [2], speed estimation with statorresistance algorithm based on a sliding mode current observerwhich combines variable structure control, Lyapunov stability
mailto:*[email protected]:*[email protected]

8/13/2019 31-113

2/9



and Popov's hyper stability theories are used. All of thesemethods assumed that there is no change in the magnetizinginductance during the stator resistance estimation. So theaccuracy of these methods has been affected by the variationof the magnetizing inductance, if the magnetic circuit of theinduction motor has been saturated. Also, these schemescannot be used when the rotor speed is higher than the ratedspeed as in the field weakening region.

Many reasons cause variation in the level of the magneticflux in the induction machine. From these reasons, inductionmotor has been saturated to produce higher torque and thatcauses a variation in the magnetizing inductance value anddetuned in operation of vector control system. Also, if thefield oriented induction motor drive operates in the basespeed region with constant rated rotor flux reference;magnetizing inductance can be regarded as constant and equalto its rated value. But if the vector control drives operate inthe field weakening region with speeds higher than the ratedvalue and the rotor flux reference has to be reduced below itsrated value, the assumption of the constant magnetizinginductance causes detuned in operation of the vector controlsystem. Another reason, to obtain high dynamic performanceof the drive system, it is necessary to keep the magnetizingcurrent at the maximum level. At this level, modern machinesare saturated. Most types of vector control systems aresensitive to errors resulting from non-constant parameters andfurthermore, do not give an accurate representation of themachine under saturated magnetic conditions. Also, theoptimal operation of an induction machine under field-oriented control basically involves the proper selection of theflux level to meet the optimal requirements of the specificapplications. It has been emphasized that the influence of saturation on the selection of this flux is very significant andmust be incorporated in the selection process to obtain validand useful results. If the magnetizing flux is not constant (e.g.field-weakening, optimal operation, incorrect flux control;etc) it is also necessary to incorporate the effect of saturationin the overall control system. Many methods attempt toestimate the magnetizing inductance. Reference [12] suggestsa method for tuning the magnetizing inductance but thismethod uses either the speed sensors or it suffers fromdecoupling problems with the rotor speed. Another methodused in [8]-[9] depends on measured stator voltages andcurrents and the magnetizing curve of the machine and thismethod is characterized with its simplicity. The saturationeffect in the indirect vector control of induction motor hasbeen investigated/compensated by authors [13]-[14]. In thesemethods, the performance of vector controlled inductionmotor drives as influenced by magnetic saturation and itscompensation has been investigated but using speed sensor.On the other hand, no attempt has been made to investigatethe effect of magnetic saturation on the performance of statorresistance estimation for sensorless indirect vector controlledinduction motor drives.

In this paper, the stator resistance identification for a speedsensorless vector controlled induction motor drives takingsaturation into account has been presented. Mathematical

models of an induction motor as influenced by magneticsaturation and saturated indirect vector controller have beenpresented. The modified model reference adaptive system hasbeen used to estimate the stator resistance in parallel withrotor speed for accurate estimation of rotor speed. Theparallel rotor speed and stator resistance estimation algorithmrequires the knowledge of magnetizing inductance whichvaries with saturation level in the machine, so it has beenmodified with an online magnetizing inductance estimator.Digital simulations have been carried out in order todemonstrate the correctness of the proposed drive system. Itis concluded that the consideration of magnetic saturation inthe dynamic model of the machine and the control part of thesystem conform with a real simulation of the drive system.

II. D YNAMIC MODEL OF INDUCTION MOTOR AS INFLUENCEDBY MAGNETIC CIRCUIT SATURATION

To accommodate the effect of magnetic-circuit saturation,the dynamic model of the induction motor in the stationary

ss qd reference frame [13]-[15] has been modified toinclude the saturation of the main flux path as follows:

=dt

di L

dt

di L

dt

di Li RV

Ldt

di s

qr s

sdr

dm

sqs

ssdss

sds

ds

sds

221 (1)

=dt

di L

dt

di Li R

dt

di LV

Ldt

di sqr qm

sdr s

sqss

sdss

sqs

qs

sqs

221 (2)

+

+= sqr dr r ssdr r

sqsmr s

sds

dmdr

sdr i L

dt d

L i Ri L dt d

L dt

di L

L dt

di 22

1(3)

= sqr r sdr qr r s

sqs

qmsdsmr sqr

sqr

i Ri L dt d

L dt

di L i L

dt d

L L dt

di 22

1(4)

The stator and rotor mutual inductance of the d-and q- axesin the above equations are expressed as:

cdm L L L 20 += , cqm L L L 20 =The stator and rotor self inductances of the d- and q-axes in

equations (1)-(4) are defined by:

dmlsds L L L += ,

dmlr dr L L L += ,

qmlsqs L L L += ,

qmlr qr L L L +=Where

( ) 2cos22 L L c = , ( ) 2sin22 L L s = , 20 m L L L += ,

22 m L L L =

mm id d L / = is a dynamic mutual inductance equal tothe first derivative of the magnetization curve.

mmm i L / = is a static mutual inductance and can be alsoobtained directly from the magnetization curve. Evidentlyboth L and m L take account of the fact that mi iscontinuously changing in time. And is the angle of the

magnetizing current space vector with respect to the referenceaxis.The electromagnetic torque can be expressed as:

8/13/2019 31-113

3/9



= sqr sds

sdr

sqsme iiii L

PT

223 (5)

The equation of the motion is:

elr d r T T f

dt d

J =++ (6)

The state form of equation (6) can be written as:

J

T f T

dt d Lr d er = (7)

Thus the dependent variables of the system are sdsi , s

qsi ,

sdr i ,

sqr i and r . The derivatives of these variables are

functions of the variables themselves, motor parameters andstator supply voltage. Simultaneous integration of equations(1)-(5) and (7) predicts the temporal variation of thesevariables.

III. S ATURATED INDIRECT VECTOR CONTROLLER OF THEINDUCTION MOTOR :

The estimation of rotor flux value and its phase angle is

performed in rotor flux oriented ee qd synchronouslyrotating reference frame based on stator currents and speedmeasurement. The rotor flux calculator is derived in such away that nonlinear relationship between the main flux andmagnetizing current is taken into account. In this calculation,the field orientation is maintained, the condition 0=qr issatisfied, the influence of q-axis magnetizing flux on theresultant magnetizing flux can be neglected [14] ( 0=qm ).The approximate saturated rotor flux calculator is given with:

r r

r lr

dm dt d

R

L

+= (8)

r

eqs

r m

sli

T

L

= (9)

+= )( mdmedslr r dm ii L

(10)

r eqs

r

me i L

LPT

43= (11)

Simplified saturated indirect vector controller can beconstructed as shown in Fig. 1 the scheme is described withthe following equations:

**

r r

r lr

dmm dt d

R

L

+= (12)

dt

d

Rii r

r mdm

eds

** 1)(

+= (13)

*

** )(

3

4

r

em

mlr eqs

T

L

L L

Pi

+= (14)

*

**

r

eqs

r m

sli

T

L

= (15)

+= dt slr e )( ** (16)

lr L / 1

+

1

*

dm

*

sl

*

r *dmi

e

dsi *

*

eT

++

e

qsi*

r R

P3 / 4

lr L

dt d / r lr R L /

++

+

Figure (1): Saturated indirect vector controller scheme

IV. P ARALLEL STATOR RESISTANCE AND ROTOR SPEEDESTIMATION :

Accurate knowledge of stator resistance is not required inindirect field oriented control scheme. However, the speedestimation from the machine terminal quantities depends onthe machine model as MRAS technique. The disadvantages of this method are that the stator resistance s R detuning causes arotor speed r and torque response deterioration in the lowspeed range [11].

The basic MRAS rotor speed estimator described in [10]and illustrated in Fig. 2. The reference model and adjustablemodel in this estimator blocks perform integration of (17) and(18). It relies on measured stator currents and measured statorvoltages and is composed of the reference (voltage) and theadjustable (current) model. The estimator operates in thestationary reference frame and it is described with thefollowing equations [10]:

ssss

ssm

r srV i p L RV L

L p )]([ += (17)

srI r

ssr

msrI jT

iT

L p

1

= (18)

e p

I K K p

+= (19)

sdrV

sqrI

sqrV

sdrI

srV

srI e

== (20)

A hat above a symbol in (17) (20) denotes estimatedquantities. All of the parameters in the motor and theestimator are assumed to be of the same value, except for thestator resistance [hence, a hat above the symbol in (17)].Underlined variables are space vectors and subscripts V and I stand for the outputs of the voltage (reference) and current(adjustable) models, respectively. Voltage, current, and fluxare denoted with V , I and , respectively, and subscripts sand r stand for stator and rotor, respectively. Superscript s inspace vector symbols denotes the stationary reference frame.

8/13/2019 31-113

4/9



Referance Model(Sta tor Equat ions)

AdaptationM e c h a n i s m

e

s

r V

sus

i

r

m

m

mi

L =

Satura tedInduct ion Motor

M o d e l

Adjus table Model(Rotor Equat ions)

-

s

r I

Figure (2): Basic configuration of saturated MRAS speedestimation

The accuracy of estimated speed depends on the fluxessrV derived from stator model of the induction motor. This

flux estimation is dependent on the stator resistance s R of theinduction motor as shown by equation (17). At low speeds,the low voltages and variations in the stator resistance due totemperature rise and switch voltage drops, dead times tend toreduce the accuracy of the estimated signals. The error in

srV estimation due to variation in s R is known to introduce

significant error in speed estimation for speed sensorlessdrive. These provide the incentive stator resistance s Restimation. [1].

As is evident from (17) (20) and Fig. 2, the adaptivemechanism (PI controller) relies on an error quantity thatrepresents the difference between the instantaneous positionsof the two rotor flux estimates. The second degree of freedomand the difference in amplitudes of the two rotor fluxestimates is not utilized. The parallel rotor speed and statorresistance MRAS estimation scheme will make use of thissecond degree of freedom to achieve simultaneous estimationof the two quantities. The role of the reference and theadjustable model will be interchanged for this purpose, sincethe rotor flux estimate of (18) is independent of statorresistance.

Parallel rotor speed and stator resistance estimation schemeis designed based on the concept of hyperstability [10] inorder to make the system asymptotically stable. For thepurpose of deriving an adaptation mechanism, it is valid toinitially treat rotor speed as a constant parameter, since itchanges slowly compared to the change in rotor flux. Thestator resistance of the motor varies with temperature, butvariations are slow so that it can be treated as a constantparameter, too. The configuration of the proposed parallelrotor speed and stator resistance is shown in Fig. 3.

Let s R and denote the true values of the stator resistancein the motor and rotor speed, respectively. These are ingeneral different from the estimated values. Consequently, amismatch between the estimated and true rotor flux spacevectors appears as well. The error equations for the voltageand the current model outputs can then be written as

ssssmr V i R R L

L p )

( = , qV dV srV srV V j +==

(21)

srI I r I

jT

j p )()1

( += , qI dI srI srI I j +==

(22)Symbols srV ,

srI in the above equations stand for true

values of the two rotor flux space vectors. Equations (21),(22) can be rewritten in matrix notation as

W AW T

T

p

qV dV

qI dI

r

r

qV dV

qI dI

=

=

.

0000

0000

001

001

(23)

where [ ] == T V T I qV dV qI dI T and W isthe nonlinear block, defined as follows:

=

=ss

srI

smr

sqs

sds

sqrI

sdrI

smr R L

L

i

i R

L L

W i

.

I0

0J

.

1001

0000

0000

0110

(24)

where = , sss R R R

= ,T s

qrI sdrI

srI =

,

T sqs

sds

ss iii = ,

=01

10J , = 10

01I

The system is hyperstable if the input and output of thenonlinear block W satisfies Popovs criterio n [10]:

=1

0

t T dt W .s

dt i R L

Ldt ss

T V s

t

mr s

rI

t T I ).()

.J.(

11

00

+=2

21 += S L L

S m

r (25)

).()

.J.(. ssT V sm

r srI

T I

T i R L

LW += (26)

The validity of eq. (25) can be verified using inequality eqs.(27), (28) with adaptive mechanisms eqs. (29), (30) for rotorspeed estimation and stator resistance identification,respectively:

21

0

1 )

.J.(

1

= dt S srI t

T I (27)

22

0

2 ).(1

= dt i R L LS ssT V st

mr (28)

)

(

.J.( s

rV

s

rI

I

p

s

rI

T

I

I

p p

K K

p

K K

+=

+=

8/13/2019 31-113

5/9



e p

I K K p

+= (29)

where sdrV sqrI sqrV sdrI e

=

+=

+= srI

srV

ss

IRs pR

ss

T V

IRs pRs i p

K K i

p

K K R ss .).(

Rs IR

s pRs e p

K K R s

+= (30)

where )

()

( s

qrI sqrV

sqs

sdrI

sdrV

sds Rs iie +=

where pK , I K , s pRK and s IRK are PI parameters of

and s R adaptation mechanisms. The and s R can beestimated by eq. (29) and eq. (30) parallel at any . Theadaptation mechanism eq. (29) is the same as in customaryMRAS speed estimator, having only the speed estimationmechanism eq. (20).

R e f e r a n c e M o d e l( S t a t o r E q u a t io n s )

A d a p t a t io nM e c h a n is m

e

s

r V

sus

i

r

)(

)(mm

mmm

i L

=

S a t u r a t e dI n d u c t io n M o t o r

M o d e l

A d ju s t a b le M o d e l( R o t o r E q u a t io n s )

_

s

r I

A d a p t a t io nM e c h a n is m

R se

s R

+

Figure (3): Structure of saturated MRAS system for parallelrotor speed and stator resistance estimation

V. O NLINE IDENTIFICATION ALGORITHM OF MAGNETIZINGINDUCTANCE

The accuracy of speed estimation depends on the precisemagnetizing inductance which varies due to the main fluxsaturation. Magnetizing inductance of an induction motormay vary significantly when the main magnetic flux issaturated. Standard assumption of constant magnetizing

inductance is no longer valid and it becomes necessary tocompensate for the nonlinear magnetizing inductancevariation. Therefore, the structure of the speed estimatorshould be modified in such a way that the variation of mainflux saturation is recognized within the speed estimationalgorithm. This requires online identification algorithm of themagnetizing inductance [8]-[9].

The magnitude of magnetic flux vector is calculated fromits components as:

22 sqm

sdmm += (31)

The air-gap magnetizing flux components can be obtainedin the stationary reference frame [9] as:

sdsls

sdss

sds

sdm i Ldt i RV = )( (32)

sqsls

sqss

sqs

sqm i Ldt i RV = )( (33)

The magnetizing curve of the machine is identified offlinein the laboratory from no-load test and is represented with asuitable polynomial relating the magnetizing flux with themagnetizing current. Since the magnetizing flux is known, itis possible to estimate the magnetizing inductance using theknown non linear inverse magnetizing curve.

)( mm f i = (34)

)(

mmm

m i L

= (35)

VI. P ROPOSED SENSORLESS VECTOR CONTROLLEDINDUCTION MOTOR DRIVE

Figure 4 shows the block diagram of the proposed

sensorless indirect vector controlled induction motor drivetaking saturation into account. It consists mainly of a loadedinduction motor model taking saturation into account, ahysteresis current-controlled PWM (CCPWM) inverter, asaturated vector control scheme followed by a coordinatetransformation (CT) and an outer speed loop. In addition tothe machine and inverter the system include speed controllertogether with a parallel stator resistance and motor speedestimator based on MRAS. To compensate the effect of nonlinear magnetizing inductance due to saturation in theaccuracy of rotor speed estimation, an online magnetizinginductance estimator has been constructed and used withinrotor speed estimator. The magnetizing inductance is

estimated based on the measured stator voltages and currentsand the inverse magnetizing curve of the machine. The speed

controller generates the command eq components of stator

currente

qsi* from the speed error between the estimated

motor speed and the command speed. The rotor flux referencedecreases in inverse proportion to the speed of rotation in thefield weakening region, while it is constant and equal to ratedrotor flux rn in the base speed region as also shown in Fig.4 and is used to fed the saturated vector controller scheme for

obtaining the command of stator currente

dsi* .

Measurements of two stator phase voltages and currents aretransformed to sd - and sq components and are used in theparallel stator resistance, speed and online magnetizingestimators. The coordinate transformation (CT) in Fig. 4 isused to transform the stator currents components command

(e

qsi* and

e

dsi* ) to the three phase stator current command

( *asi , *bsi and *csi ) by using the field angle *e . The hysteresiscurrent control compares the stator current to the actualcurrents of the machine and switches the inverter transistorsin such a way that the commanded currents are obtained.

8/13/2019 31-113

6/9



VII. S IMULATION RESULTS AND D ISCUSSIONS

Computer simulations have been carried out in order to

validate the effectiveness of the proposed scheme of Fig. 4.The Matlab / Simulink software package has been used forthis purpose.

The induction motor under study is a 3.8 HP, four polesmotor, whose nominal parameters and specifications arelisted in table 1. The actual value of the magnetizinginductance in the motor model is considered to account forthe magnetic circuit saturation as measured in the laboratory.It is represented as a function of the magnetizing current m I by a suitable polynomial in the Appendix.

The transient performance of the conventional sensorlessdrive system is investigated for step change of the statorresistance when the motor is running at 100 rpm with nominalload torque. Figure 5a, 5b, 5c, 5d, 5e and 5f show the vectorcontrol response when the stator resistance is increased by 33% from its nominal value at t = 2.5 sec. From figures 5a, 5cand 5d, it seen that, the estimated motor speed, motor torque,

ee qd axes rotor flux components are oscillating anddeviate from their command values during the statorresistance variation. These deviations and oscillations maycause the vector control drive system to become unstable.

IMPWMinverter

Rectifier

hysteresiscurrent

controller

Coordinatetransformation

speedcontroller Limeter

saturatedvector

controller

Rotor Speed andStator

ResistanceEstimator MRAS

r

++

+

*qsi

*dsi

*ai

*ci

*bi

phase3 C

L

sds

sds iV ,

sqs

sqs iV ,

*sl

*e

3-phasecurrents

inversecoordinatetranslator

*r

3-phasevoltages

)( mm L

r

*r

Magnatizing

InductanceEstimator

s R

Figure (4): Overall block diagram of the proposed sensorlessvector controlled induction motor drive

Table (1): Parameters and data specificationsof the induction motor

Rated power (HP) 3.8 Rated voltage (V) 380Rated current (A) 8 Rated frequency (Hz) 50

Rs () 1.725 Rr () 1.009Ls (H) 0.1473 Lr (H) 0.1473Lm (H) 0.1271 Rated rotor flux, (wb) 0.735

J (kg.m2) 0.0400 Rated speed (rpm) 1450

In order to improve the drive performance, the statorresistance estimation in parallel with the rotor speed schemeis introduced with the control system. The estimated statorresistance is able to track the change in stator resistanceadequately as shown in Fig. 6e. Also, the estimated statorresistance converges and tracks its actual after a short delaytime. With stator resistance estimator, the estimated speed,

motor torque and ee qd axes rotor flux components arekept constant and matched with their commands as shown infigures 6b, 6c and 6d.

Figure (5): Effect of stator resistance variation on the motordrive performance.

The transient performance of the proposed sensorless drive

system is investigated for step-change of the load torquewhen the actual stator resistance equals its nominal value.Figures 7a, 7b, 7c and 7d show the motor speed,

electromagnetic torque, stator phase current and ee qd axes rotor flux components, when the motor subjects to a loaddisturbance from 10 to 20 N.m (about rated torque) at 10 rpm.Figure 7a shows the dip and overshoot of the estimated motorspeed following the application and removal of the loadtorque disturbance. The speed dip and overshoot aredetermined by the gains of the speed controller of motorspeed loop, as indicated in Fig. 7a. Figure 7b shows fast andgood response of the motor torque. However, this torqueexhibits high-frequency pulsations of large magnitude due tovoltage source inverter pulse width modulation. Figure 7cshows that the phase stator current is sinusoidal. The rotorflux components are unchanged during the load disturbanceas shown in Fig. 7d. This proves that the decoupled control of the torque producing current from the magnetizing current isevident at low speed.

8/13/2019 31-113

7/9



Figure (6): Motor drive performance with the parallel statorresistance and motor speed estimation.

Figure (7): Performance of the proposed sensorless drivesystem for load torque disturbance.

Figure 8 shows the performance of the conventional MRASspeed estimator for speed sensorless induction motor driveswhen operating in the field weakening region. Figures 8a, 8b,8c and 8d show the actual and estimated motor speed,electromagnetic torque, error between actual and estimated

speeds and ee

qd axes rotor flux components, when themotor speed command changed from 1500 rpm to 1800 rpmin step change fashion at t = 3 second with nominal statorresistance. The rotor flux reference decreases in inverseproportion to the speed of rotation in the field weakeningregion, while it is constant and equal to rated rotor flux in thebase speed region. From the figure it is seen that due tooperation in the field weakening region with reduced rotorflux command and using the nominal value of magnetizinginductance in MRAS estimator, an error between theestimated speed and actual rotor speed has been found asshown in Fig 8a. Also figure 8d shows that there exist steady-state errors between the rotor flux vector and its reference

value. These performances can be improved by introducingthe proposed control system scheme with using online

magnetizing inductance estimation that gives an accuratevalue of magnetizing inductance at every level of magnetizingflux.

Figure 9 shows the performance of the control system withthe proposed MRAS speed estimator. From this figure, theactual and estimated speeds have the same track as shown inFig 9a. The rotor flux components are taken the same track ascommanded value during the field weakening region asshown in Fig. 9d. This proves that the decoupled control of the torque producing current from the magnetizing current isevident at speed higher than rated speed with reduced rotorflux command.

Figure (8): Performance of the conventional sensorless drivesystem for operation in the field weakening region.

Figure (9): Performance of the proposed sensorless drivesystem for operation in the field weakening region.

VIII. C ONCLUSIONS :

This paper investigates the stator resistance estimation forspeed sensorless vector controlled induction motor drivesystem based on the model reference adaptive systemtechnique taking magnetic saturation into account. Aneffective on-line estimation method for magnetizing

inductance has been proposed to improve the driveperformance. The superiority of the modified MRAS over the

8/13/2019 31-113

8/9



constant parameter one for operation with saturated main fluxor stator resistance variation due to temperature variation hasbeen proved. Simulations results are provided to demonstratesmooth steady state operation and high dynamic performanceof the proposed drive system in a wide range of motor speed.The main conclusions that can be inferred from the results aresummarized as follows:1. The variation of stator resistance degrades the

performance of the sensorless drive by introducingerrors, in the estimated motor speed, motor torque and

ee qd axes rotor flux components.2. The parallel speed and stator resistance estimator scheme

is capable of tracking the stator resistance variation verywell. Then, the proposed drive scheme can be operated invery low speed range.

3. The transient performance of the proposed sensorlessdrive is presented when the motor is subjected to a loadtorque disturbance. The estimated speed response gives adesired dynamic performance which is not affected bythe load torque disturbance and the variation of motorparameters. Fast and good response of the motor torquedisturbance is achieved following the application andremoval of load torque disturbance, this in addition torotor flux components which are kept constant during theload disturbance.

4. Good and stable operation during field weakening underfull load torque is obtained by the proposed sensorlessdrive system.

5. The estimation of the motor speed and stator resistancesimultaneously results in accurate speed estimation andgood performances are obtained in wide speed rangefrom very low speed to speeds higher than the ratedspeeds. Consideration of magnetic saturation in thedynamic model of the machine and controller with statorresistance estimation scheme serve to make the motorcontrol accurate. Therefore, the proposed sensorless driveis robust against the motor parameter variations.

APPENDIX I

The non-linear relationship between the air-gap voltage and themagnetizing current was measured from no-load test of the induction

motor neglecting core losses. Then, the relationship between themagnetic flux and the magnetizing current (i.e. magnetizing curve)has been obtained. The data of the magnetizing curve was fitted by asuitable polynomial which is expressed as:

0.00290.150.0820.037-0.00580.00041-100001.0 m2m

3m

4m

5m

6mm ++++= I I I I I I

The static magnetizing inductance m L is calculated from the

above polynomial as mmmm I I L / )( = and the dynamicmagnetizing inductance L is calculated from the first derivative of this polynomial as mmm I d I d L / )( = . Figure Appendix I shows therelationship between the magnetizing flux and the magnetizingcurrent.

Figure App. I: Magnetizing curve of the induction machineused in simulation.

REFERENCES :

[1] Veran Vasic, Slobodan N. Vukosavic, and Emil Levi, "Astator resistance estimation scheme for speed sensorlessrotor flux oriented induction motor drives," IEEE Trans.on Energy Conversion, Vol. 18, No. 4, December 2003,pp. 476-483.

[2] M. S. Zaky, M. M. Khater, H. Yasin, and S. S. Shokralla,"Speed and Stator Resistance Identification Schemes fora Low Speed Sensorless Induction Motor Drive ", IEEEConf. MEPCON, Aswan, Egypt, 2008, PP. 103-108.

[3] Gregor Edelbaher, Karel Jezernik, and Evgen Urlep,"Low-speed sensorless control of induction machine,"IEEE Trans. on Ind. Electr., Vol. 53, No. 1, February2006, PP. 120-129.

[4] Hossein Madadi Kojabadia, and Liuchen Changb,"Comparative study of pole placement methods inadaptive flux observers," Control Engineering Practice,Elsevier, Vol. 13, 2005, pp. 749 757.

[5] M. S. Zaky, M. M. Khater, H. Yasin, and S. S. Shokralla,A. El-Sabbe, "Speed-sensorless control of inductionmotor drives (Review Paper)", Engineering ResearchJournal (ERJ), Faculty of Engineering, MinoufiyaUniversity, Egypt, Vol. 30, No. 4, October 2007, PP.433-444.

[6] Hirokazu Tajima, Giuseppe Guidi, and Hidetoshi Umida,"Consideration about problems and solutions of speedestimation method and parameter tuning for speed-sensorless vector control of induction motor drives,"IEEE Trans. on Ind. Applicat., Vol. 38, No. 5,September/October 2002, pp. 1282-1289.

[7] Joachim Holtz, and Juntao Quan, "Sensorless vectorcontrol of induction motors at very low speed using anonlinear inverter model and parameter identification,"IEEE Trans. on Ind. Applicat., Vol. 38, NO. 4,July/August 2002, pp. 1087-1095.

[8] Emil Levi, Matija Sokola, and Slobodan N. Vukosavic,"A method for magnetizing curve identification in rotorflux oriented induction machines," IEEE Trans. OnEnergy Conversion, Vol. 15, No. 2, June 2000, pp. 157-162.

[9] Emil Levi, and Mingyu Wang, "Online Identification of the Mutual Inductance for Vector Controlled Induction

8/13/2019 31-113

9/9



Motor Drives," IEEE Trans. on Energy Conversion, Vol.18, No. 2, June 2003, pp. 299-305

[10] C. Schauder, Adaptive speed identification for vecto rcontrol of induction motors. without rotationaltransducers, IEEE Trans . Ind. Applicat., vol. 28, pp.1054 1061, Sept. /Oct. 1992

[11] Peng, Z.; Fukao, T.; "Robust speed identification forspeed sensorless vector control of induction motors".IEEE Trans. on Ind. Appl. 30 (1994) no. 5, pp. 1234-1240.

[12] J. C. Moreira and T. A. Lipo, A new method for rotor time constant tuning in indirect field orient control, inIEEE Conf. PESC 90,VA, June 1990, pp. 573 580.

[13] Hossam A. Abdel Fattah, Kenneth A. Loparo, HassanM. Emara, Induction motor control magnetic system

performance under Saturation Proceedings of theAmerican Control Conference, San Diego, California, lJune-1999, PP 1668-1672.

[14] E.Levi, S.Vukosavic, V.Vuckovic, "Saturationcompensation schemes for vector controlled inductionmotor drives", IEEE Power Electronics SpecialistsConference PESC, San Antonio, TX, 1990, pp. 591-598.

[15] J. E Brown, K. P Kovacs and P. Vas, "A method of including the effect of main flux path saturation in thegeneralized Equations of Ac machines", IEEE, Trans.Power Appar. and Sys., Vol. PAS 102, no.1, pp. 96-103,1983.

Documents

31-113