Speed Sensorless Induction Motor Drive

with Magnetizing Reactance Estimation

Mateusz Dybkowski, Teresa Orlowska-Kowalska, Senior Member IEEE

Wroclaw University of Technology, Institute of Electrical Machines, Drives and Measurements, Wroclaw, Poland

E-mail: teresa.orlowska-kowalska@pwr.wroc.pl, mateusz.dybkowski@pwr.wroc.pl

Abstract — The paper deals with the speed sensorless in-

duction motor drive with MRAS type speed and flux estima-

tor. The proposed control structure has been equipped with

additional estimator of the magnetizing reactance recon-

struction. Methodology is based on the well known mathe-

matical interpolation of the inverse magnetizing curve.

Dynamical performances of the vector control system with

the current-type MRAS estimator with magnetizing reac-

tance estimator are tested in simulation and in the labora-

tory set-up. Control structure is checked in the low speed

and in the field weakening regions.

Keywords — Variable speed drive, induction motor, vector

control, sensorless control.

I. INTRODUCTION

One of the most popular solutions of the speed and

flux reconstruction is the MRAS (Model Reference Adap-

tive System) methodology presented first in [1], [2].

However, a classical estimators based on the MRAS con-

cept are sensitive to motor parameter changes due to the

high sensitivity of rotor flux current and voltage models

used for rotor flux vector estimation. Nevertheless this

methodology is still developed. The novel MRAS type

speed and flux estimator [3] id less sensitive to the motor

parameters changes than classical solutions and is stable

for the whole reference speed changes. Universal speed sensorless induction motor drive

should work stable for starting from the standstill, for low speed region and in the regenerating mode [4] – [7]. Con-trol structure should assure good dynamical performance in the wide speed reference changes (including a field weakening region).

It was proved however, that all speed estimators are sensitive to changes of the magnetizing reactance of the induction motor. Magnetizing reactance of the induction motor depends on the magnetizing flux and current. This value is not constant during the motor operation in the control structure [8], so the speed estimator should be ex-tended with the estimator of this parameter.

In this paper the sensorless Direct Field Oriented Con-trol structure of the induction motor is tested. The speed and rotor flux reconstruction is the MRAS

CC [3] estimator

equipped with magnetizing reactance estimator, according to the methodology presented in [8], [9]. Sensitivity of the drive system to the magnetizing reactance for different speed values is checked. Dynamical performances are in-vestigated in the whole speed range, including the field weakening and low speed regions (typical for the traction and Electrical Vehicle (EV) drives).

II. IDENTIFICATION ALGORITHM

OF MAGNETIZING REACTANCE

Parameters of the induction motor are not constant un-der the drive system operation and they depend on the temperature, current and motor speed. One of the most important parameter in the sensorless induction motor drive, which influences its behavior, is a magnetizing reac-tance. This parameter is not constant, especially in the field weakening region. So the structure of the speed and flux estimator used in sensorlees drive should be modified by estimated magnetizing reactance.

The magnetizing reactance can be calculated from the equation (in stator coordinate system):

m

mm

ix

Ψ= (1)

where the magnetizing flux vector can be obtained from:

22

βα mmm Ψ+Ψ=Ψ (2)

and:

( )

( ) βσβββ

ασααα

sssssm

sssssm

ixdtiru

ixdtiru

−−=Ψ

−−=Ψ

∫

∫. (3)

The magnetizing current depends on the rotor current and can be calculated as follows:

βββ

ααα

rsm

rsm

iii

iii

+=

+=. (4)

Rotor current cannot be measured in the control structures, so the magnetizing current can be estimated using the known nonlinear inverse magnetizing curve:

)( mm fi Ψ= (5)

m

mestm

ix

Ψ= . (6)

Magnetizing curve can be represented in per unit as in [8]:

( ) b

mmm aai Ψ−+Ψ= 1 , (7)

where a and b are determined as constant coefficients cha-racteristic for the given induction motor.

14th International Power Electronics and Motion Control Conference, EPE-PEMC 2010

978-1-4244-7855-2/10/$26.00 ©2010 IEEE T5-120

As it is presented in [8], estimated magnetizing current depends on the coefficients a and b. Proper choice of those values guaranties the good reconstruction of this current ver-sus magnetizing flux. In the Fig. 1 the magnetizing curves for different values of parameters a and b are shown.

Fig. 1. The magnetizing curves of an induction motor for different values of parameters a and b

It was presented in [8], [9] that for low and medium power induction motors, parameter b should be equal to 7 and parameter a should be set between 0.6 and 0.9.

The magnetizing curve and the magnetizing reactance variation of the induction motor tested in this paper (with parameters presented in detail in Appendix) are shown in Fig. 2. The calculated curves are compared with the meas-ured characteristics. Coefficients a and b were determined as a=0.7 and b=7. The measured points are marked with cross, while the calculated ones are marked by dot. It is seen from this comparison, that a very good accuracy of the measured magnetizing curve is obtained with the char-acteristic given by (7), according to the methodology pro-posed in [8].

a)

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 0,2 0,4 0,6 0,8 1 1,2

i m/i

mN

[

p.

u.]

ΨΨΨΨm /ΨΨΨΨmN [p. u.]

Measurement

Estimation

b)

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 0,2 0,4 0,6 0,8 1 1,2

xm

/xm

N

[p

. u

.]

ΨΨΨΨm /ΨΨΨΨmN [p. u.]

Estimation

Measurement

Fig. 2. Magnetizing curve (a) and magnetizing reactance (b) variation of

the machine used in simulation and experiments (a=0.7 and b=7)

III. MATHEMATICAL MODEL OF THE MRASCC

ESTIMATOR

The MRASCC

estimator was presented in detail in a paper [4]. This estimator is based on the two well known simulators [6] (voltage model and current model of rotor flux) transformed to the stator current estimator and to the rotor flux estimator based on a current model.

Current estimator used in MRASCC

is obtained by the equation:

i

r

rs

e

m

i

r

rs

r

s

s

e

s

rs

srre

sxxT

xj

xxT

rx

xTxxT

rxxr

dt

d

N

m

N

m

NN

mΨΨuii

σω

σσσ−++

+−=

22

221 .(8)

where: ωme – estimated rotor angular speed, rs, rr, xs, xr, xm

– stator and rotor resistances, stator and rotor leakage reac-tances, us, is

e, ΨΨΨΨr

i – stator voltage, estimated stator current

and rotor flux vectors respectively, σ=1-xm2/xsxr.

TN=1/2πfsN

Current model can be calculated from the equation:

N

i

r

e

m

i

rsm

r

ri

rT

jxx

r

dt

d 1)(

+−= ΨΨiΨ ω . (9)

Both stator current model (8) and rotor flux model (9) are adjusted by the estimated rotor speed [10]:

( ) ( )∫ Ψ−Ψ+Ψ−Ψ= dteeKeeK i

ri

i

riI

i

ri

i

riP

e

m ssss αβαβ βαβαω . (10)

where e

ssi iies βαβαβα ,,,

−= - error between the estimated and

measured stator current.

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a) b) c)

Fig. 4.Pole placement of the transfer function of the MRASCC speed estimator depending on magnetizing reactance changes (±100% xm)

for ωm = 0.01ωmN (a), ωm = ωmN (b), ωm = 2ωmN (c)

The MRASCC

estimator can be extended with the mag-netizing reactance estimator presented in the Chapter II. The general scheme of the MRAS

CC estimator with on-line

magnetizing reactance estimation algorithm is presented in Fig. 3.

αsu

βsu

e

mωe

si α

e

si β

mω

αsi

βsi

e

mω

i

rβΨ

i

rαΨ

αsie

si α

βsi

e

si β

i

rαΨ

i

rβΨ

( ) b

mmm aai Ψ−+Ψ= 1

( )

( ) βσβββ

ασααα

sssssm

sssssm

ixdtiru

ixdtiru

−−=Ψ

−−=Ψ

∫

∫αsu

βsu

αsi

βsi

m

mestm

ix

Ψ=

estmx

estmx

Fig. 3. MRASCC estimator with magnetizing reactance estimator

The MRAS

CC speed and rotor flux estimator is robust to

the all motor parameters changes and is stable in the whole speed reference changes [3]. Stability and sensitivity anal-ysis were presented in detail in [11], using the transfer function given by (11).

( )

( )

sNs

rsmNrsNI

IPrmmIrr

rsmNrsrIr

NIrImr

IPPrmr

m

e

m

σxsTrbwith

xσxxsTxrTTs

sTbKxxsxTxr

xσxxsTxrsxTr

TsωsbTxsTxrsMwhere

sM

sTKKbxxr

s

ssW

+=

+++

++++

++++

+++=

+==

:

)))2(2(

)1((

))2((

)(:

)(

)(

)()(

22

0

22

0

2

22

222

0

423

0

3

ωω

ω

ω

ω

(11)

In this paper the pole placement of the MRASCC

estimator in the function of magnetizing reactance changes is pre-sented in Fig. 4, for different values of speed reference.

IV. SIMULATION TESTS OF THE DRIVE SYSTEM

Direct Field Oriented Control structure with MRASCC

estimator and reactance estimator used in simulation and experimental set up is presented in Fig. 5. In this chapter chosen simulation results are shown.

refω

e

mω

e

mω

e

rΨ

e

Ψγ

e

Ψγ

βα ,si

βα ,su

c

xV

c

yV

Fig. 5. Sensorless speed control structure

In the following figures the performances of the sensor-

less drive without magnetizing reactance updating in the field weakening region are shown.

a)

b)

Fig. 6. Transients of the sensorless IM drive for the field weakening

and in the small speed region

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The sensorless IM drive works properly. But in the steady state, for the speed references bigger than nominal,

ωm = 1.5ωmN, the small error between the measured and estimated speed is visible (Fig. 6 a, Fig. 7 b). This error is

connected with the wrong magnetizing reactance value, used in the speed estimator mathematical model. This val-ue increases for such high motor speed due to a flux weak-ening.

a) b)

c) d)

Fig. 7. Simulation results of the sensorless IM drive with MRASCC estimator without magnetizing reactance estimator

for the field weakening region

a) b)

c) d)

Fig. 8. Simulation results of the sensorless IM drive with MRASCC estimator with magnetizing reactance estimator

for the field weakening region

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Dynamical properties are good. If the magnetizing reac-tance is not estimated, speed reconstruction error oscillates around zero only for the rotor speed smaller than its nominal value; for higher speed, especially for the loaded motor, the steady state error is visible. Components isx and isy of the stator current vector depend respectively on the rotor flux vector magnitude and electromagnetic torque (see Fig. 7).

In the control structure with MRASCC

speed and flux es-timator, extended with the magnetizing reactance estima-tor, the rotor speed is reconstructed in the whole speed reference properly (Fig. 8). Speed estimation error oscil-lates around zero value (see Fig. 8 b).

V. CHOSEN EXPERIMENTAL RESULTS

Proposed estimation algorithm and DFOC control struc-ture was implemented in the laboratory set-up with PC computer, using the dSPACE software. The schematic diagram of the experimental test bench is shown in Fig. 9.

The experimental set-up is composed of the IM motor fed by the voltage inverter with Space Vector Modulator (SVM). The motor is coupled to a load machine (AC mo-tor supplied from an AC inverter).

The driven motor has the nominal power of 1.1 kW. The speed and position of the drive are measured by the incremental encoder (5000 imp./rev), only for the com-parison with the estimated speed in the sensorless drive system. The control and estimation algorithms are imple-mented in DS1103 card.

Fig. 9. Schematic diagram of the laboratory test bench

In the Fig. 10 – Fig. 12 the chosen experimental result

of the sensorless IM drive under different condition are demonstrated.

First, the operation of sensorless DFOC system based on MRAS

CC estimator without additional magnetizing

reactance adaptation is shown. The steady state error is visible under field weakening region (Fig. 10b). This error is connected, like in simulation results, with the magnetiz-ing reactance changes, which are not taken into account in the algorithm of the speed estimator.

Next sensorless drive with MRASCC

estimator equipped with the proposed magnetizing reactance estima-tion algorithm is tested and results are shown in Fig. 11. Drive system works properly in the field weakening region and an average value of the speed estimation error (Fig. 11b) is now close to zero.

a) b) c)

Fig. 10. Experimental results of the sensorless IM drive with MRASCC speed and flux estimator for the field weakening and small speed region

without magnetizing reactance estimator

a) b) c)

Fig. 11. Experimental results of the sensorless IM drive with MRASCC speed and flux estimator for the field weakening and small speed region

with magnetizing reactance estimator

In Fig. 12 a very long reverse operation under load torque in a small speed region of the sensorless drive is shown. It can be seen that the sensorless drive works prop-erly. Small speed error is visible only for a speed reference

close to zero. It proves that the updating of the magnetiz-ing reactance improves the drive system operation in the whole speed range, from very low, through nominal value, to much higher than nominal one.

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a) b) c)

Fig. 12. Experimental results of the sensorless IM drive with MRASCC speed and flux estimator for the reverse operation from the speed

reference ωref =-0.0035ωmN to ωref =0.0035ωmN,, moL=0.25mN

VI. CONCLUSION

The MRASCC

speed and flux estimator, which uses the

current model and current estimator, performs very well

in the wide range of the speed reference, in the sensorless

DFOC drive system.

Proposed estimation algorithm of the magnetizing reac-

tance can be easily implemented in this speed estimator, im-

proving its behavior in the field weakening region. Control

structure with the analyzed estimator can be implemented in

the drive working with very low and high speeds.

ACKNOWLEDGMENT

This research work was supported by the Ministry of Science

and Higher Education, Poland, under Grant N510 334637 (2009-2011)

APPENDIX

Motor rated data PN = 1.1 [kW] UN = 230/400 [V] IN = 5.0/2.9 [A]

nN = 1380 [rpm] fN = 50 [Hz] pb = 2

Parameters of the IM equivalent circuit

Rs Rr Xs Xr Xm

5.9 4.5 131.1 131.1 123.3 [Ω]

0.07 0.06 1.725 1.725 1.62 [p.u.]

Per unit system calculation methodology (reference values):

Ub= 2 UNf, Ib= 2 IN, Zb=Ub/Ib, ωb=2πfN, Ψb=Ub/ωb,

Sb=(3/2)UbIb,, Mb=Sb pb/ωb, Parameters in per unit system:

rs=Rs/Zb, rr=Rr/Zb, xs=ls=Xs/Zb, xr=lr=Xr/Zb, xm=lm=Xm/Zb

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