a speed estimator for high performance sensor less control of im in the field weakening region

8/14/2019 A Speed Estimator for High Performance Sensor Less Control of IM in the Field Weakening Region

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 3, MAY 2002 365

A Speed Estimator for High PerformanceSensorless Control of Induction Motors in the

Field Weakening RegionEmil Levi, Senior Member, IEEE, and Mingyu Wang

AbstractThe paper proposes a modified version of the modelreference adaptive system (MRAS) based speed estimator, whoseoutputs of the reference and the adjustable model are rotor fluxspace vectors. Theestimator is modifiedin such a waythat thevari-ation in the instantaneous level of the main flux saturation duringoperation in the field weakening is recognized and properly com-pensated at alltimes. The speed estimation scheme is equally appli-cable to both vector controlled and direct torque controlled induc-tion machines, since it operates in the stationary reference frameand requires measurement of only stator voltages and currents.Verification of the proposed scheme is provided by simulation and

by experimentation on an indirect feed-forward rotor flux orientedinduction machine for speed references of up to twice the basespeed.

Index TermsField weakening operation, induction motordrives, main flux saturation, sensorless control, speed estimation.

NOMENCLATURE

Voltage, current and flux linkage, respectively.

Magnitude of rotor flux space vector and stator

flux space vector, respectively.

Rotor speed of rotation (electrical) and angular

slip frequency (electrical).

Magnetizing flux and magnetizing current.Magnetizing flux components in the stationary

reference frame.

Magnetizing current components in the

stationary reference frame.

Stator current components in rotor flux oriented

reference frame.

Number of pole pairs.

Rotor time constant.

Stator self-inductance, rotor self-inductance and

magnetizing inductance.

Stator and rotor leakage inductance.

Stator and rotor resistance, respectively.

Stator voltage and stator current space vectors.Rotor flux space vector and magnetizing flux

space vector, respectively.

Manuscript received February 28, 2001; revised January 10, 2002. This paperwas presented in part at the 31st IEEE Annual Power Electronics SpecialistsConferencePESC00, Galway, Ireland, June 1823, 2000. Recommendedby As-sociate Editor G. K. Dubey.

E. Levi is with the School of Engineering, Liverpool John Moores University,Liverpool L3 3AF, U.K.

M. Wangis with the College of Electrical Engineering, ChongqingUniversity,Chongqing 400044, China.

Publisher Item Identifier S 0885-8993(02)04636-7.

Subscripts:

Rated value.

Stator and rotor, respectively.

Base value.

Variables in the stationary two-axis reference

frame.

Superscripts:

Reference values in the controller.

Output of the reference model and the adjustablemodel, respectively.

Magnetizing inductance and speed estimates.

I. INTRODUCTION

ANUMBER of different methods for speed-sensorlessvector and direct torque control of induction machineshave been developed during the last ten years [1], [2]. In

general, two major approaches can be identified. The first one

encompasses the techniques that estimate rotor speed from the

stator current spectrum, while the second one relies on utiliza-

tion of an induction machine model and the speed estimator is

either of open-loop or closed-loop type [2]. The major efforthas been directed toward overcoming the problems encountered

in speed estimation around zero speed. One of the problems

with model based techniques is the sensitivity to induction

motor parameter variation effects and a number of papers

provide experimental and/or simulation comparisons between

the performance of various speed estimation techniques in the

low speed region under tuned and detuned conditions [ 3][8].

It appears that the problem of speed estimation in the field

weakening region has been completely overshadowed by the

interest in solving the zero speed estimation problem.

Many applications require a wide speed range, with the

maximum required speed that significantly exceeds the motor

rated speed. Such is the case in high performance spindle drivesand gearless traction drives [9]. Speed estimation in the field

weakening region presents formidable difficulties regardless of

whether the estimation is model based or spectrum based. In the

spectrum based speed estimation, the time interval during which

speed information has to be extracted by spectrum analysis

reduces as speed increases, thus making good dynamic control

difficult to achieve. The effect on which the speed estimation

relies on in the base speed region may even disappear in the

field weakening region, as the case is with saturation induced

saliencies [10], so that speed estimation becomes impossible.

0885-8993/02$17.00 2002 IEEE
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366 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 3, MAY 2002

The major difficulty in the model based approach stems from

the substantial variation of the magnetizing inductance, caused

by de-fluxing of the machine, as main flux saturation is in

general neglected in the model based speed estimator. Detailed

simulation study, reported in [11] and revisited in Section IV-A

of this paper, shows that if variation in the main flux saturation

level is neglected within the speed estimator, a speed estimation

error of 10 to 20 rpm for a 50 Hz, four-pole machine can beexpected in the field weakening region for speeds between 1

p.u. and 2 p.u. A presently existing attempt to account for the

variable degree of the main flux saturation during the speed

estimation process is the one reported in [12]. A full order

observer is used as the speed estimator and the variation of the

magnetizing inductance is tracked online, by using the reactive

power method. Unfortunately, the reactive power method is

heavily dependent on the correct setting of the rotor resistance

and, in addition, depends on the value of the speed estimate

as well. The speed estimation accuracy reported in [12] is

therefore far from spectacular.A possible solution to the problem of accurate speed estima-

tion in the field weakening region, using model based approach,is to modify the estimator structure in such a way that the vari-ation of main flux saturation is recognized within the estimatorand compensated for. Such an approach is discussed in thispaper. An additional online identifier of the magnetizing induc-tance, such as the one of [12], is therefore not needed. Amongmany different methods that utilize the model based approach,speed estimation based on MRAS [13] has gained substantialpopularity due to its rather simple implementation requirements.This is the technique analyzed in this paper, in conjunction witha current-fed induction machine controlled by means of the in-direct feed-forward rotor flux orientation method. However, itshould be noted that the developed modified speed estimator is

equally applicable to sensorless direct torque control (operatedin the closed loop speed mode) and other methods of sensor-less vector control. MRAS based speed estimation techniquesmutually differ with respect to the quantity that is selected asoutput of the reference and the adjustable model. The type ofthe MRAS speed estimator discussed here is the one with rotorflux space vectors selected as outputs of the reference and theadjustable models [13].

The only currently available discussion of the sensorlessvector control in the field weakening region appears to be thework reported in [14], where the need for compensation ofthe main flux saturation is properly recognized. Although theapplied method of saturation compensation is very approxi-

mate and avoids any change in the speed estimator structure,satisfactory performance is obtained. One interesting proposalof [14] is the application of the field weakening not only inthe high speed region but in the very low speed region as well.Use of field weakening at zero speed leads to an increase in thestator frequency for the given load, so that zero speed operationbecomes possible for all loads down to 20% of the rated [14].The modified speed estimator structure, developed in thispaper for field weakening operation in the high speed region, isequally applicable to field weakening in the low speed regionproposed in [14].

Performance of the developed speed estimator and its accu-racy are verified by performing a series of experiments. These

consist of acceleration tests in the field weakening region, up to2 p.u. speed, under both no-load and loaded conditions. In ad-dition, some simulation results are included as well.

The paper is organized as follows. The experimental rig and

the basic speed estimator structure are described in Section II.

Modified speed estimator for operation in the field weakening

region is proposed in Section III. Simulation and experimental

verification of its performance are provided in Section IV. Con-clusions of the study are summarized in Section V.

II. EXPERIMENTAL RIG AND THE BASIC STRUCTURE

OF THE SPEED ESTIMATOR

A schematic diagram, showing the major components of the

experimental rig, is given in Fig. 1. A PC, through which the

reference speed setting is enabled, controls rotor flux oriented

induction machine with speed sensor. Actual speed is measured

by a resolver and is used for both the speed feedback and

the orientation angle calculation. It is recorded for display

purposes by means of a dynamic signal analyzer (that is used

in oscilloscope mode). The four-pole, 2.3 kW, 50 Hz inductionmotor is coupled to a dc machine, so that loaded operation is

enabled. The current controlled PWM inverter operates with

fixed 10 kHz switching frequency. The industrial, commer-

cially available, DBS 04 vector controller utilizes the indirect

feed-forward field orientation principle and is based on 8051

microcontroller and TMS30C14 digital signal processor. The

vector controller enables operation at speeds up to 8000 rpm

(base speed is normally 1500 rpm, but it can be altered by the

user and set to any desired value up to 1500 rpm). It is equipped

with a modified indirect vector controller of [15], shown in

Fig. 2. Compensation of main flux saturation variation in the

field weakening region is provided within the vector controller,

by inclusion of the inverse magnetizing curve (Fig. 2). Ratio of

magnetizing to rotor inductance is treated as constant and equal

to the one under rated rotor flux conditions. Boost of stator

-axis current reference during rotor flux reference variations

is not present within the controller, since for high inertia drives

variation of the rotor flux reference with speed is rather slow.

Rotor flux reference decreases in inverse proportion to the

speed of rotation in the field weakening region, while it is

constant and equal to rated rotor flux in the base speed region.

The indirect vector controller is at all times operated under

tuned conditions.

Stator line-to-line voltages are measured, attenuated and fil-

tered using analogue circuitry. For current measurement, Halleffect current sensors are used and two phase currents are mea-

sured. Measured line-to-line voltages and stator currents are

converted into two-phase - components of phase voltagesand

currents. The outputs of the voltage card and the current card are

then sent to an A/D card installed in the computer. The sampling

frequency of the A/D card is 20 kHz for each signal. A PC with

LabVIEW software is used for data acquisition and it collects

all the signals. The data obtained in this way are used further on

to investigate the operation of the speed estimator. Speed esti-

mator is implemented in the Simulink/Matlab environment and

is operated at all times in parallel with the sensored drive (that

is, speed estimate is not used for either closed loop speed control
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LEVI AND WANG: SPEED ESTIMATOR FOR HIGH PERFORMANCE SENSORLESS CONTROL 367

Fig. 1. Experimental rig.

Fig. 2. Indirect rotor flux oriented controller with compensation of main fluxsaturation ( S G = R ( L = L ) ; K = ( 3 = 2 ) P L = L ) .

or for orientation angle calculation). It is of course recognized

that this is not an ideal approach to the experimental verifica-

tion. However, the described procedure was devised in order toenable utilization of a commercially available vector controlled

drive, which does not allow for user intervention within the soft-

ware and hardware. The same measured stator voltages and cur-

rents are used as inputs into the speed estimator that would have

been used in true sensorless mode and the estimated and the ac-

tual speed in tuned operation essentially coincide in the base

speed region, as shown shortly. One therefore does not expect

that the operation in true sensorless mode would have been dif-

ferent from the one observed in this way.

The speed estimator is shown in its basic form in Fig. 3, where

the two left-hand side blocks perform integration of (1) and

(2). Speed estimator operates in the stationary reference frame

Fig. 3. Rotor flux based MRAS rotor speed estimator.

and is described with the following space vector equa-

tions [13]:

(1)

(2)

(3)

Index in (1)(2) denotes constant rated values of machine pa-

rameters used in the estimator, symbol denotes differentiation,

stands for rotor time constant and .

Major difficulties in practical implementation of the speed es-

timator described with (1)(3) are related to initial conditionand

drift problems due to pure integration in (1), [13]. In addition,

variation in the stator resistance significantly affects the accu-

racy of the speed estimation at very low frequencies [13].A pos-
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Fig. 4. Implemented structure of the basic (constant parameter) speed estimator of Fig. 3, with tuned values of all the parameters.

(a) (b)

Fig. 5. Estimated speed and actual speed for speed commands of 900 rpm and 1500 rpm: (a) no-load operation and (b) loaded operation.

sible solution to the first problem, proposed in [13] and applied

here as well, is to substitute pure integration with low-pass fil-

tering. Such a solution, according to [13], enables good perfor-

mance of the drive down to 2 Hz. As far as the stator resistance

variation problem is concerned, the modified speed estimator

proposed here is aimed at high frequency (field weakening) op-erating region, where variation of stator resistance has practi-

cally no impact on the accuracy of the speed estimation.

The initial tuning of all the filters, machine parameters and

the PI controller of the basic estimator is performed using ex-

perimental data collected for no-load and loaded acceleration

in the base speed region. Since sampling of stator voltages and

currents is not synchronised with the PWM of the inverter, addi-

tional digital filtering is applied, using the second order Butter-

worth filter for each of the four input signals (cut-off frequency

rad/s). Detailed description of the tuning procedure

can be found in [16]. Great care has been taken to ensure good

correspondence between the estimated and the actual speed in

the base speed region, so that subsequent experimental results

for the field weakening are credible although the true sensorless

control has not been implemented. Final structure of the basic

estimator of Fig. 3, as implemented in the experimental rig of

Fig. 1, is shown in Fig. 4.

Performance of the basic speed estimator of Fig. 4, that suf-fices for operation in the base speed region, is illustrated by

comparing the actual speed and the estimated speed during ac-

celeration transient from zero to 900 rpm and from zero to 1500

rpm (with base speed set to 1500 rpm), under both no-load and

loaded conditions. The traces are given in Fig. 5. Estimated

and actual speed are in very good agreement, indicating that

the tuning procedure has been successfully completed. Since

no known problems with this MRAS speed estimator occur at

speeds higher than rated, it is believed that subsequent results

given for the operation in the field weakening region would have

been the same had the true sensorless mode been studied in the

experiment.
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III. MODIFICATION OF THE SPEED ESTIMATOR STRUCTURE FOR

OPERATION IN THE FIELD WEAKENING REGION

Speed estimator described with (1)(2) utilizes the constant,

rated value of the magnetizing inductance. Operation in the field

weakening region requires that the variation in the degree of

main flux saturation be compensated within the speed estimator.

Its structure therefore has to be modified in such a way that

main flux saturation is accounted for in both the reference and

the adjustable model. Hence both the reference and the adaptive

part of the estimator, (1)(2), have to be modified. In order to

do so it is necessary to use as the starting point appropriate state

space models of a saturated induction machine. A number of

saturated machine models have been developed in [17] and the

twothat areparticularly usefulfor thestated purpose here arethe

models with state space variables selected as the stator current

and magnetizing flux space vector, and stator current and rotor

flux space vector, respectively. Both models fully account for

the cross-saturation effect and are therefore complete dynamic

models of a saturated induction machine.

Let the saturated induction machine be described in the sta-tionary - axis reference frame with the general matrix equa-

tion

(4)

where

(5)

If stator current and magnetizing flux space vector components

are selected as state space variables, the state vector of (5) and

matrices and of (4) take the following form as (6) and(7), shown at the bottom of this page [17]. Saturation dependent

inductances in (6) are determined with

(8)

where

(9)

The steady state saturated magnetizing inductance and the dy-

namic inductance, and respectively, are given on the basis

of the known magnetizing curve of the machine with

(10)

Here

(11)

The first two state space equations of the model (4)(7) do not

contain inductances defined in (8) and are therefore suitable

for the use within the reference model. They constitute a re-

duced-order model, that enables straightforward calculation of

the magnetizing flux components from measured stator voltage

and current components. From the first two equations of (4)(7)

it follows that:

(12)

Since the magnetizing flux is now known, it is possible to es-

timate the magnetizing inductance using the known nonlinear

inverse magnetizing curve

(13)

What remains to be calculated are the components of the rotor

flux space vector. These are found by at first determining the

magnetizing current - components, as follows:

(14)

Described procedure shows that estimation of the rotor flux in

the reference model, based on stator voltage and current mea-

surements, contains sufficient information to yield, apart from

the estimates of rotor flux components, the estimate of the mag-

netizing inductance as well. Reference model, described with

(6)

(7)
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Fig. 6. Structure of the saturation adaptive reference model, constructed using (12) and (15), with modified integration algorithm.

(12)(14), fully accounts for variation in the main flux satu-

ration in the calculation of the rotor flux components, and, inaddition, provides an estimate of the magnetizing inductance.

Estimate of the magnetizing inductance, obtained from the ref-

erence model, will be further used in the adaptive model, as ex-

plained shortly. The complexity of (12)(14) can be reduced for

real time applications by suitably re-arranging (13)(14). In par-

ticular, instead of the inverse magnetizing curve ,

the function (directly obtainable from the mag-

netizing curve) can be used, so that the (13)(14) are replaced

with

(15)

Fig. 6 depicts the rotor flux estimator, with simultaneous mag-

netizing inductance estimation, constructed using (12) and (15).

The block Modified integration algorithm of Fig. 6 relies on

the integration method proposed in [18]. The need for this block

will be explained later.

It is worth noting that the estimate of the magnetizing in-

ductance, obtained as illustrated in Fig. 6, can be used in con-junction with any other model based speed estimation method

(EKFs, observers, other MRAS methods). It is fully applicablein conjunction with the full order observer discussed in [12] as

well. The advantages of the method proposed here over the re-

active power method applied in [12] are significant. First of all,

speed estimate is not involved in the magnetizing inductance

estimation, so that cross-coupling between estimated speed and

the estimated inductance does not take place. Secondly, rotor re-

sistance is not used either. The only parameters required in the

magnetizing inductance online identification are the stator re-

sistance and the stator leakage inductance. However, since the

identification of the magnetizing inductance is required in the

high speed (field weakening) operation, impact of stator resis-

tance variation on the magnetizing inductance estimation is neg-

ligibly small. On the other hand, stator leakage inductance is al-

ways at least ten times smaller than the magnetizing inductance.For the two machines studied in the simulation and experiment,

the rated stator leakage inductance is 3.33% and 5% of the cor-

responding rated magnetizing inductance values, respectively.

The relative value of the stator leakage inductance further de-

creases as field weakening region is entered, due to de-fluxing

of the machine that causes an increase in the magnetizing in-

ductance. Furthermore, the machine always operates in the field

weakening region with a stator current below rated value, so that

no appreciable change in the saturation of the stator core teeth

takes place. It therefore follows that stator leakage inductance

is, first of all, reasonably constant in the field weakening region,

and, secondly, even if it varies the impact of such a variation is

negligibly small with regard to the accuracy of the magnetizing

inductance identification, due to the very small relative value of

the stator leakage inductance with respect to the magnetizing

inductance. It can be stated on the basis of these considerations

that the proposed magnetizing inductance identification proce-

dure is very robust with respect to parameter variation effects. A

proof is provided in Section IV-B, using experimental results.

In order to account for the variable degree of main flux sat-

uration in the adjustable model, induction machine model with

stator current and rotor flux space vector components is selected

asthestarting point.Thestatevector and matrices and of

(4)(5) are, for this selection of the state space variables, given

with (16) and (17), shown at the bottom of the next page [ 17].Variable saturation dependent inductances of matrix in (16)

are now determined with

(18)

where

(19)
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Fig. 7. Implementation of the modified speed estimator that includes compensation of main flux saturation.

and

(20)

Dynamic inductance and steady state saturated magnetizing

inductance remain to be given with (10).

Closer inspection of the model given with (16)(20) shows

that the inductances defined in (18) appear only in the first

two equations. The second two equations constitute another

reduced-order model that is suitable for application within the

adjustable part of the speed estimator with main flux saturation

compensation. From (4) and (16)(17) it follows that

(21)

Equation (21) can be rewritten in the space vector form, analo-

gous to (2), as

(22)

Comparison of (2)and (22) shows that theform of the adjustable

model does not have to be changed at all. It is only necessary to

provide to the adjustable model (22) an additional input, namely

the steady state saturated magnetizing inductance value. This

additional input comes from the reference model, which pro-

vides information on the instantaneous value of the steady statesaturated magnetizing inductance according to Fig. 6.

The complete proposed modified speed estimator is shown in

Fig. 7. The estimator provides full compensation of main flux

saturation in both transient and steady-state operation.

The modified speed estimator of Fig. 7 involves the same

motor parameters as does thebasicestimator of Fig. 3 (stator and

rotor resistance, and stator and rotor leakage inductance). The

modified estimator structure is obtained from (1)(2), so that

the sensitivity to parameter variation effects remains the same

as for the estimator of Fig. 3. As already noted in conjunction

with magnetizing inductance estimation, stator resistance vari-

ation has essentially no impact on the speed estimation when

the proposed estimator is applied in the field weakening region.

Since leakage inductance variation has rather small impact on

accuracy of the speed estimation (provided that it is correctly

identified during the drive commissioning), the only parameter

that will affect the speed estimation process is the rotor resis-

tance. A detailed analytical (for steady states) and simulation

(for transients) analysis of the parameter variation effects in the

speed estimator of Fig. 3 is available in [5], while an insightful

discussion regarding the same issue can be found in [13].

One specific problem, encountered in the implementation of

the modified estimator, is that the pure integration in the refer-

(16)

(17)


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Fig. 8. Modified integration algorithm of [18], applied within the modified reference model of Fig. 6 ( = compensating signal).

ence model applies to the stator flux components, from which

the magnetizing flux components are calculated using (12). Fil-

ters , shown on the right-hand side of Fig. 7 in

the output channels of both the reference and the adjustablemodel, are sufficient to solve the problem of pure integration

when speed estimation is based on (1) and (2), [13]. However,

they are now inadequate. Magnetizing flux components are fur-

ther used to assess the saturation level in the machine and are

involved in estimation of the magnetizing inductance for the

adjustable model. It is therefore mandatory that the amplitude

of magnetizing flux components be not affected by modifica-

tion of the integration algorithm. A solution was found by using

the modified integration algorithm of [18] within the reference

model of Fig. 6 (a suitable cut-off angular frequency is found

to be 100 rad/s, as indicated in Fig. 6). The applied integration

algorithm, developed in [18] specifically for drives with vari-

able flux operation, is reproduced in Fig. 8. It incorporates aquadrature detector that detects the orthogonality between the

estimated flux and the back emf. The algorithm is described in

detail in [18]. All the remaining filter and PI controller parame-

ters in Fig. 7 are the same as those of Fig. 4.

IV. SIMULATION AND EXPERIMENTAL VERIFICATION OF THE

MODIFIED SPEED ESTIMATOR

A. Simulation Study

Operation of the proposed speed estimatoris at firstexamined

by simulation, using a 4 kW, 50 Hz, four-pole induction motor

(the machine data are available in [5]). True sensorless opera-

tion is investigated. Drive is equipped with the indirect vectorcontroller of Fig. 2. The simulations are at first performed using

the constant parameter speed estimator of Fig. 3 with the mag-

netizing inductance set to the constant rated value. The machine

is initially excited at zero speed under no-load conditions. Speed

command is then applied, so that rated speed operation (1 p.u. or

app. 300 rad/s electrical) under no-load conditions is achieved.

A load torque of 1 p.u. is applied next at s. At

s load torque is stepped down to 0.5 p.u. and this value is not

changed any more. Finally, at s speed command is fur-

ther increased in a ramp-wise manner, so that field-weakening

region is entered. Transients for two different final speeds, 1.5

p.u. and 2 p.u., are illustrated in Fig. 9, where the actual and

the estimated angular speed (electrical) and the speed error (de-

fined as difference between the actual and the estimated speed

and expressed in mechanical rpm) are depicted (more detailed

sets of simulation results can be found in [11]). As can be seenfrom Fig. 9, estimated speed tracks the actual speed very well in

the base speed region (except during the first part of the accel-

eration, for the reasons explained in [11]). However, once when

field weakening region is entered (at s) a significant

speed estimation error occurs due to variation of the magne-

tizing inductance that is neglected in the speed estimator. The

already mentioned speed estimation error of 10 to 20 rpm can

be observed in the two final steady states in Fig. 9.The same simulation study is performed once more. The

proposed modified speed estimator of Section III is now usedinstead of the constant parameter one. As there are not anyobservable differences in the traces of the actual and the es-

timated speed when compared to those of Fig. 9, only thespeed estimation error is shown in Fig. 10 for final speeds of

1.5 p.u. and 2 p.u. Comparison of the speed estimation errorin Figs. 9 and 10 shows that the application of the proposedmodified speed estimator essentially eliminates the speed esti-

mation error (note the difference in the scales in Figs. 9 and10; the residual speed estimation error in Fig. 10 is less thanone rpm in both cases). The existence of a very small residual

speed estimation error is explained as follows. The speed es-timator requires an analytical approximation of the function

, as shown in Fig. 6. The saturated inductionmachine model, used in simulations, is the current state spacemodel, that asks for an analytical approximation of the inverse

magnetizing curve . Since the analytical expres-sions for the two functions are created using least-squaresfitting technique, an ideal one-to-one correspondence is not

achieved. This leads to a residual speed estimation error ofaround 1 rpm for the final speed of 1.5 p.u. in Fig. 10(a).For the final speed setting of 2 p.u. in Fig. 10(b) the residual

speed estimation error is practically zero. This speed and allthe higher speeds apply to the motor operation on the linearpart of the magnetizing curve. Results of the simulation study

in Figs. 9 and 10 confirm the capability of the modified speedestimator to adapt to the actual saturation level in the machine

and therefore provide an accurate speed estimate for any op-erating point in the field weakening region.
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(a) (b)

Fig. 9. Sensorless drive operation with constant parameter speed estimator of Fig. 3: estimated and actual speed, and speed estimation error for the final speedsof (a) 1.5 p.u. and (b) 2 p.u.

(a)

(b)

Fig. 10. Drive operation with the modified speed estimator: speed estimationerror for the final speeds of (a) 1.5 p.u. and (b) 2 p.u.

B. Experimental Verification

In order to verify theaccuracyof themodifiedspeed estimator

of Fig. 7 for operation in the field weakening region experimen-

tally, a series of tests are performed, for both no-load and loaded

operation. As the maximum speed of the dc machine is 1500

rpm, base speed at which the field weakening operation is initi-

ated is set in all the tests to 650 rpm. DC generator load setting

was determined in such a way that the output power of the in-

duction motor in loaded operation becomes approximately rated

at 1500 rpm. All the parameters of the indirect vector controllerof Fig. 2 are set to correct values, so that the drive with speed

sensor operates at all times without any detuning induced by

parameter variation effects. Magnetizing curve of the machine,

required in both the indirect vector controller of Fig. 2 and in the

modified reference model of Fig. 6 for calculation of the func-

tion , was determined for the 2.3 kW machine

under consideration using the procedure detailed in [19].

Before proceeding further, it seems appropriate to address an

apparent drawback of the proposed modified speed estimator,

namely the requirement that the magnetizing curve of themachine has to be known and therefore identified during thedrive commissioning. First of all, it has to be pointed out that

operation of an indirect vector controlled current fed inductionmachine in the field weakening region requires knowledge ofthe magnetizing curve anyway, since the inverse magnetizing

curve has to be incorporated in the indirect vector controller,as shown in Fig. 2 (the controller of Fig. 2 is a part of theindustrial, commercially available drive used in this work).

Secondly, although the knowledge of the magnetizing curvedoes require additional effort during the drive commissioningor existence of sophisticated software routines for the drive

self-commissioning, many different methods are nowadaysavailable that can be used for this purpose. Identification of

the magnetizing curve, using a vector control system and aPWM inverter, has been discussed extensively in recent past
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[19][25]. A method, ideal for self-commissioning, should

enable identification at standstill with either single-phase acor dc supply, it should require measurement of stator currents

and dc voltage only, and it should be accurate. Additionally,an important consideration is the complexity of the algorithm.As it is aimed at on-site commissioning, it should be possibleto add the algorithm within the existing digital controllers, so

that its implementation needs to be simple. Unfortunately, amethod that satisfies all these requirements is not available atpresent. If identification is performed at standstill, statisticalmethods, such as recursive least squares [21], [22], have tobe used in data processing. As voltages are reconstructed

rather than measured, it is necessary to pre-determine inverternonlinear characteristic by appropriate tests, prior to the

magnetizing curve identification [21], [22]. Accuracy of themethod significantly deteriorates below certain magnetizingcurrent value [21], [22], due to the pronounced impact of the

inverter lock-out time on identification results. This techniqueis therefore regarded as inappropriate for magnetizing curveidentification [23]. If the measurement of the stator voltages

is allowed, it is possible to avoid the use of statistical methodsand to perform identification purely from the measurement

data [24], [25]. These methods are applicable during thedrive commissioning if the voltage sensors are available. Thesimplest situation results if fundamental harmonic voltage

measurement is available and the machine is allowed to rotateunder no-load conditions during the commissioning. In such

a case the procedure described in [19] enables, in its simplestform, an essentially calculation-free identification of the mag-netizing curve. The inverse magnetizing curve is represented

in per unit form within the controller of Fig. 2 (a very specificfunctional approximation, detailed in [19], is used for thispurpose), its parameters are guessed and the test is performed.

The test is repeated for different values of the parameters ofthe functional approximation. The assumed parameters of

the functional approximation attain correct values once whenthe measured fundamental voltage in the field weakeningregion becomes practically constant at all speeds. As alreadynoted, this procedure was used here in order to identify the

magnetizing curve of the machine.

A series of acceleration transients are recorded, all starting

from standstill. Figs. 11 and 12 compare the actual speed and the

estimated speed for speed commands equal to 900, 1050, 1200,and 1350 rpm for no-load and loaded operation. The speed set-ting of 1350 rpm corresponds to approximately twice the base

speed, so that rotor flux reference setting is just below one halfof the rated flux. Operation for this speed and all the higherspeeds essentially takes place on the linear portion of the mag-

netizing curve of the machine. The cases illustrated in Figs. 11and 12 therefore encompass the complete nonlinear region ofthe magnetizing curve through which the drive will pass during

operation in the field weakening region.

A very good agreement between the actual and the estimated

speed is achieved for all the operating conditions, as is evi-dent from inspection of Figs. 11 and 12. This is further con-firmed in Fig. 13 where zoomed extractsfrom Fig. 11, that apply

to no-load transients, are given. The average speed estimationerror is negligibly small. One observes however in Fig. 13 rel-

Fig. 11. Actual speed and estimated speed using speed estimator of Fig. 7in no-load acceleration transient, for speed commands of 900 rpm, 1050 rpm,1200 rpm, and 1350 rpm (base speed = 650 rpm).

atively substantial noise, especially in the trace of the actualspeed (the actual speed trace was obtained from an existing ana-

logue output of the drive). This noise therefore limits the accu-racy of theupper andlower bounds of thespeed estimation error,that is discussed next in conjunction with the acceleration tran-

sients of the loaded machine (Fig. 12). Speed estimation erroris extracted for all the four speed settings in Fig. 12 in vicinity

of the steady state and is shown in Fig. 14(a). It can be seen thatthe average value of the speed estimation error is confined to
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Fig. 12. Actual speed and estimated speed using speed estimator of Fig. 7

during acceleration transient with connected load, for speed commands of900 rpm, 1050 rpm, 1200 rpm, and 1350 rpm (base speed = 6 5 0 rpm).

a small value for all speed settings. This is contrasted with re-sults obtained in exactly the same way and for exactly the same

transients, shown in Fig. 14(b). The results of Fig. 14(b) apply tothe case when the constant parameter speed estimator, describedwith (1)(3) and with the magnetizing inductance set to the con-

stant rated value, is used instead of the modifiedspeed estimator.The speed estimation error is averaged for all the cases illus-

trated in Fig. 14 and the results are summarized in Table I.

Typical reduction of the speed estimation error, achieved by

means of the proposed speed estimator, is of the order of 6 rpm.

(a)

(b)

Fig. 13. Zoomed extracts from Fig. 11 in vicinity of steady-state operation forset speeds of (a) 900 rpm and (b) 1200 rpm (no-load operation).

This is somewhat smaller than the improvement achieved in

simulations, where a different machine was studied. The reason

for this apparent discrepancy will be explained shortly, in con-

junction with the results of the magnetizing inductance identi-

fication.

Achievable levelof improvement in the drive operation by the

application of the modified speed estimator can be evaluated by

direct comparison of experimental results in Fig. 14(a) and (b),

by means of Table I, and by comparison of simulation results in

Figs. 9 and 10.

The lack of compensation of themagnetizinginductance vari-

ation within the speed estimator predominantly manifests itself

through a steady state speed estimation error in the field weak-

ening region, while the transient part of the speed response is

affected to a much lesser extent. This remark applies provided

that the indirect vector controller of Fig. 2, with compensationof the main flux saturation, is used. In this case the setting of

the stator -axis current reference is hardly affected by an error

in the speed estimate (since the error is rather small). Similarly,

setting of the stator -axis current reference is hardly affected

as well since the input into the speed controller is large during

acceleration/deceleration transients and the output is likely to

be in the limit anyway. Speed estimation error will have some

impact on the orientation angle, so that torque response will be

affected to some extent, as shown by simulation in [ 11]. In the

experimental work described here it was not possible to detect

any improvement in the transient speed response behavior when

the modified speed estimator was used.
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(a) (b)

Fig. 14. Speed estimation error in vicinity of steady state operation for speed commands of 900 rpm, 1050, rpm, 1200 rpm, and 1350 rpm: (a) results obtainedwith the modified speed estimator and (b) results obtained with the constant parameter estimator with magnetizing inductance set to constant rated value.

The last set of experimental results illustrates the process of

the magnetizing inductance identification using the proposed

scheme of Fig. 6 and proves the robustness of the procedure

with respect to parameter variation effects. The transient already

illustrated in Figs. 12 and 14(a), acceleration of the loaded ma-

chine from standstill to 1350 rpm, is selected for this purpose.

Since the base speed is 650 rpm, the machine will operate in

the final steady state at the linear part of the magnetizing curve,

since reference flux setting will be 0.48 per unit. Time interval

in vicinity of final steady state (from 2.6 till 3 s) is examined

using the following procedure. All the parameters of the speed

estimator are at first tuned to the correct (rated values) and the


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TABLE IROUNDED AVERAGE SPEED ESTIMATION ERROR WITH THE PROPOSEDSATURATION ADAPTIVE SPEED ESTIMATOR AND WITH THE CONSTANTPARAMETER SPEED ESTIMATOR (MAGNETISING INDUCTANCE SET TO

THE RATED VALUE) FOR THE TRACES OF Fig. 14 (TIME INTERVAL: 2.6TO 3 SECONDS; BASE SPEED = 6 5 0 rpm)

(a)

(b)

Fig. 15. Magnetizing inductance identification of the loaded inductionmachine in vicinity of final steady state with speed setting of 1350 rpm (basespeed = 6 5 0 rpm). (a) L = L and trace 1 0 R = R , trace2 0 R = 1 : 2 5 R , trace 3 0 R = 0 : 7 5 R . (b) R = R and trace1 0 L = L , trace 2 0 L = 1 : 2 5 L , trace 3 0 L = 0 : 7 5 L .

magnetizing inductance is identified. Next, stator resistance is

detuned by % and the magnetizing inductance is identified

under detuned conditions. The same is repeated for % vari-

ation in the stator leakage inductance. The results are plottedin Fig. 15. The value of the magnetizing inductance with cor-

rect parameter tuning is around 86.56 mH. Detuning of stator

resistance or stator leakage inductance by % introduces an

error in the identified magnetizing inductance of no more than

0.02 mH, which is well below 0.05%. It should be noted that

the value of the magnetizing inductance of 86.56 mH closely

corresponds to the value that can be calculated using the results

of [19] (87 mH). The rated magnetizing inductance for this ma-

chine is 78 mH [19]. The variation of the magnetizing induc-

tance from saturated to unsaturated value is relatively small, in-

dicating that the rated operated point is close to the linear part

of the magnetizing curve. This is the reason why the observed

improvement in the accuracy of the speed estimation by means

of the proposed estimator is smaller than in simulation (where

a different machine, with much more pronounced saturation ef-

fect in the rated operating point, was used).

V. CONCLUSION

The paper discusses application of a MRAS based speedestimator of rotor flux type for sensorless high performance

control of induction machines in the field weakening region.

When model based approach to speed estimation is used,

it becomes necessary to compensate the variation in the

magnetizing inductance for operation at speeds above rated,

caused by de-fluxing of the machine. It is shown that the

correct speed estimation in the field weakening region can be

achieved by appropriately combining the two modified rotor

flux estimators, that both account for the variable degree of the

main flux saturation. Simple modifications of the rotor flux

estimation from measured stator voltages and currents enable

not only calculation of the rotor flux component estimates that

fully account for variation in the level of saturation, but an iden-tification of the magnetizing inductance as well. Magnetizing

inductance, estimated in this way, is further utilized within

the adjustable model, so that the second pair of the rotor flux

component estimates (output of the adjustable model) fully

account for the main flux saturation variation as well.

Some simulation results that illustrate the superiority of the

proposed modified speed estimator over the constant parameter

one for operation in the field weakening region are provided.

The modified structure of the speed estimator is further verified

by performing experiments in the field weakening region, under

no-load and loaded conditions, up to twice the base speed. Very

good agreement between actual and estimated speed is achieved

in both transient and steady-state operation.Developed speed estimator is equally applicable to both sen-

sorless vector and sensorless direct torque controlled induction

machines (provided that closed loop speed control is required),

since it operates in the stationary reference frame. In addition,the estimation of the magnetizing inductance from the stator

voltage equation, that is essentially insensitive with respect to

parameter variation effects, can be utilized in conjunction with

other methods of model-based speed estimation, such as a full

order observer, to provide an accurate speed estimate during op-

eration in the field weakening region.

REFERENCES

[1] K.Rajashekara,A. Kawamura,and K.Matsuse,Eds., Sensorless Controlof AC Motor Drives. Piscataway, NJ: IEEE Press, 1996.

[2] P. Vas, Sensorless Vector and Direct Torque Control. Oxford, U.K.:Oxford Univ. Press, 1998.

[3] G. J. Armstrong and D. J. Atkinson, A comparison of model referenceadaptive system and extended Kalman filter estimators for sensorlessvector drives, in Proc. Eur. Conf. Power Electron. Applicat. EPE97Conf., Trondheim, Norway, 1997, pp. 1.4241.429.

[4] K. Ohyama, G. M. Asher, and M. Sumner, Comparison of the practicalperformance and operating limits of a sensorless induction motor driveusing a closedloop flux observer anda full order observer, in Proc. Eur.Conf. Power Electron. Applicat. EPE99, Lausanne, Switzerland, 1999.

[5] M. Wang and E. Levi, Evaluation of steady-state and transient behaviorof a MRAS based sensorless rotor flux oriented inductionmachine in thepresence of parameter detuning, Elect. Mach. Power Syst., vol. 27, no.11, pp. 11711190, 1999.


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[6] C. Ilas, A. Bettini, G. Griva, and F. Profumo, Comparison of differentschemes without shaft sensors for field oriented control drives, inProc. IEEE Ind. Electron. Soc. Annu. Meeting IECON94, Bologna,Italy, 1994, pp. 15791588.

[7] M.N. Marwali andA. Keyhani, A comparativestudyof rotor flux basedMRAS andbackemf based MRAS speed estimators forspeed sensorlessvector control of induction machines, in Proc. IEEE Ind. Applicat. Soc.

Annu. Meeting IAS97, New Orleans, LA, 1997, pp. 160166.[8] R. Blasco-Gimenez, G. M. Asher, M. Sumner, and K. J. Bradley, Dy-

namic performance limitation for MRAS based sensorless inductionmotor drives. Part 1: Stability analysis for the closed loop drive, Proc.Inst. Elect. Eng., vol. 143, no. 2, pp. 113122, 1996.

[9] F. Profumo, G. Griva, A. Tenconi, M. Abrate, and L. Ferraris, Stabilityanalysis of Luenberger observers for speed sensorless high performancespindle drives, in Proc. Eur. Conf. Power Electron. Applicat. EPE99,Lausanne, Switzerland, 1999.

[10] P. L. Jansenand R. D. Lorenz, Transducerless fieldorientation conceptsemploying saturation-induced saliencies in induction machines, IEEETrans. Ind. Applicat., vol. 32, pp. 13801393, Nov./Dec. 1996.

[11] M. Wang, Parameter Variation Effects in Sensorless Vector ControlledInduction Machines, Ph.D. thesis, Liverpool John Moores Univ., Liv-erpool, U.K., 1999.

[12] Y. J. Kim, J. S. Choi, and Y. S. Kim, Speed sensorless control of sat-urated induction motor using a hybrid speed estimator, in Proc. IEEETENCON99 Multimedia Technol. Asia-Pacific Inform. Infrastruct.,Cheju Island, South Korea, 1999, pp. 367370.

[13] C. Schauder, Adaptive speed identification for vector control of induc-tion motors without rotational transducers, IEEE Trans. Ind. Applicat.,vol. 28, pp. 10541061, Sept./Oct. 1992.

[14] R. Blasco-Gimenez,G. M. Asher, M. Sumner, J. Cilia, andK. J. Bradley,Field weakening at high and low speed for sensorless vector controlledinduction motor drives, in Proc. IEE Int. Conf. Power Electron. Vari-able Speed Drives PEVD96, Nottingham, U.K., 1996, pp. 258261.

[15] E. Levi, S. Vukosavic, and V. Vuckovic, Saturation compensationschemes for vector controlled induction motor drives, in Proc. IEEEPower Electron. Spec. Conf. PESC90, San Antonio, TX, 1990, pp.591598.

[16] M. Wang and E. Levi, Experimental tuning of a MRAS based speed es-timator for sensorlessvector controlledinductionmotor drives, in Proc.

Int. Conf. Elect. Mach. ICEM00, Helsinki, Finland, 2000, pp. 822826.[17] E. Levi and Z. Krzeminski, Main flux saturation modeling in d - q axis

models of induction machines using mixed current-flux state-spacemodels, Eur. Trans. Elect. Power ETEP, vol. 6, no. 3, pp. 209215,

1996.[18] J. Hu and B. Wu, New integration algorithms for estimating motor fluxover a wide speed range, IEEE Trans. Power Electron., vol. 13, pp.969977, Sept. 1998.

[19] E. Levi, M. Sokola, and S. N. Vukosavic, A method of magnetizingcurve identification in rotor flux oriented induction machines, IEEETrans. Energy Conv., vol. 15, pp. 157162, June 2000.

[20] E. Levi and S. N. Vukosavic, Identification of the magnetizing curveduring commissioning of a rotorflux oriented induction machine, Proc.

Inst. Elect. Eng., vol. 146, no. 6, pp. 685693, 1999.

[21] M. Ruff and H. Grotstollen, Off-line identification of the electrical pa-rameters of an industrial servo drive systems, in Proc. IEEE Ind. Ap-

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drive system, in Proc. IEEE Ind. Applicat. Soc. Annu. Meeting IAS94 ,Denver, CO, 1994, pp. 616623.

[23] M. Beroluzzo, G. Buja, and R. Menis, Identification techniques of in-duction motorparametersfor self-commissioning field-oriented drives,

Automatica, vol. 38, no. 34, pp. 103115, 1997.

[24] N. R. Klaes, Parameters identification of an induction machine withregard to dependencies on saturation, in Proc. IEEE Ind. Applicat. Soc.Annu. Meeting IAS91, Dearborn, MI, 1991, pp. 2127.

[25] W. H. Kwon, C. H. Lee, K. S. Youn, and G. H. Cho, Measurement ofrotor timeconstant takinginto accountmagnetizing flux in theinductionmotor, in IEEE Ind. Applicat. Soc. Annu. Meeting IAS94, Denver, CO,1994, pp. 8892.

Emil Levi (S89M92SM99) was born in Zren-janin, Yugoslavia in 1958. He received the Diplomadegree from the University of Novi Sad, Yugoslavia,and the M.Sc. and the Ph.D. degrees from the Uni-versity of Belgrade, Yugoslavia, in 1982, 1986, and1990, respectively, all in electrical engineering.

In 1982, he joined the Department of ElectricalEngineering, University of Novi Sad, where hebecame Assistant Professor in 1991. He joinedLiverpool John Moores University, U.K., in May1992 as a Senior Lecturer. From 1995 to 2000, he

was a Reader in Electrical Power Engineering. Since September 2000, he hasbeen Professor of electric machines and drives. His main areas of researchinterest are modeling and simulation of electric machines, control of highperformance drives, and power electronic converters. He has published over130 papers, including more than 30 papers in major international journals.

Mingyu Wang was born in 1960. He receivedthe B.Eng. degree in electrical engineering fromChongqing University, China, in 1982 and the Ph.D.

degree from the Liverpool John Moores University,U.K., in 1999.He became a Member of the Academic Staff,

Department of Automation Engineering, ChongqingUniversity, in 1982, and was a Lecturer there from1988 to 1993. He was a Visiting Scholar in theDepartment of Electrical Engineering, Universityof Manchester, U.K., from 1993 to 1995. He is

currently with Chongqing University, China. His research interests are in powerelectronics, adjustable speed drives, and vector control of induction machines.

a speed estimator for high performance sensor less control of im in the field weakening region

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