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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE
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A Review of RFO Induction Motor ParameterEstimation
Techniques
Hamid A. Toliyat, Senior Member, IEEE, Emil Levi, Senior Member,
IEEE, and Mona Raina, Student Member, IEEE
AbstractAn induction motor is the most frequently usedelectric
machine in high performance drive applications. Controlschemes of
such drives require an exact knowledge of at leastsome of the
induction motor parameters. Any mismatch betweenthe parameter
values used within the controller and actualparameter values in the
motor leads to a deterioration in the driveperformance. Numerous
methods for induction machine onlineand offline parameter
estimation have been developed exclusivelyfor application in high
performance drives. This paper aims atproviding a review of the
major techniques used for the inductionmotor parameter estimation.
The paper is illustrated throughoutwith experimental and simulation
examples, related to variousparameter estimation techniques.
Index TermsInduction motor drives, parameter offline
identi-fication, parameter online estimation, vector control.
I. INTRODUCTION
F IELD oriented (or vector) control is the most popularac
machine control method that is widely used in highperformance
industrial applications of electric drives. In thecase of an
induction machine, rotor flux oriented (RFO) controlrequires an
accurate value of at least some of the motorparameters in order to
yield robust control. Which parametersare required depends on the
applied RFO control scheme. Ifthe applied parameter values within
the control system donot match the actual values in the motor,
detuned operationresults. Impact of parameter variations on various
vector controlschemes has been studied in detail in the past and
extensivediscussions are available in many books [1][5].
A vector controlled induction motor can be used within atorque
drive, a speed drive, or a position drive. The type of thedrive
that exhibits the highest sensitivity to the incorrect param-eter
values is the torque drive. Although the motor parametervariations
affect the speed control applications too, existenceof the PI speed
controller considerably reduces negative con-sequences of the
parameter detuning.
Induction motor parameters change with temperature, fre-quency,
and saturation. The consequence of any mismatchbetween the
parameter values used in the controller and thosein the motor is
that the actual rotor flux position does not coin-cide with the
position assumed by the controller. The situationis illustrated in
Fig. 1, [4]. This means that the actual rotor
Manuscript received January 21, 2002.H. A. Toliyat and M. Raina
are with the Department of Electrical En-
gineering, Texas A&M University, College Station, TX
77843-3128 USA(e-mail: [email protected]; [email protected]).
E. Levi is with the School of Engineering, Liverpool John Moores
University,Liverpool, L3 3AF, U.K. (e-mail:
[email protected]).
Digital Object Identifier 10.1109/TEC.2003.811719
Fig. 1. Illustration of commanded (d q ) and actual (dq) rotor
fluxoriented reference frames in detuned operation, caused by a
parametermismatch. Because the commanded reference frame does not
coincide with theactual one, decoupled rotor flux and torque
control does not take place.
flux contains both - and -axis component, leading to a lossof
decoupled flux and torque control. Performance of the
drivetherefore deteriorates from the desired. In order to avoid
sucha situation, it is necessary to provide the vector controller
withaccurate induction motor parameter values. These parametershave
to be obtained somehow from measurements, during ini-tialization of
the drive. Since any vector controlled inductionmotor drive is
inverter fed, numerous tests based on an invertersupply have been
developed in recent past for determinationof the required parameter
values [4][7]. Such methods arefurther on called offline parameter
identification methods.In addition, numerous possibilities exist
nowadays to updatethe parameter values during the drive operation
[3][7]. Thetechniques that enable parameter adaptation during the
driveoperation are further on termed online parameter
estimationmethods.
The aim of this paper is to provide a review of the major
tech-niques used for the induction motor offline and online
parameteridentification and estimation, respectively.
II. INDUCTION MOTOR PARAMETERS
The parameters that may need to be identified offline ortracked
online depend on the vector control scheme underconsideration. If
the drive operates with the constant ratedflux reference, the
required parameters will be some or all ofthe following: rated
magnetizing inductance, stator resistance,rotor resistance, and
stator/rotor leakage inductance or transientstator inductance. If
the drive operates with a variable flux
0885-8969/03$17.00 2003 IEEE
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272 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE
2003
reference (optimal efficiency drives, operation in the
fieldweakening region, etc.), magnetizing curve will usually
berequired as well. Finally, if the drive controller includes
somekind of compensation of the iron losses (that may be
especiallyimportant for torque drives in electric or hybrid
vehicles), onewill need to know the variation of the equivalent
iron loss resis-tance with operating frequency [8]. The most
important offlineidentification and online parameter estimation
techniques arereviewed in the remainder of this paper.
III. OFFLINE PARAMETER IDENTIFICATION TECHNIQUES
It is often the case in practice that one manufacturer
suppliesthe inverter with a vector controller, while the machine
comesfrom another manufacturer. It is then not possible to set the
pa-rameters of the controller in advance and these have to be
setonsite, once when the inverter is connected to the machine.
Sucha situation has led to the development of the so-called
self-com-missioning procedures for vector controlled induction
machines[9], [10]. The main idea behind this concept is that the
controllerautomatically determines all of the parameters of an
inductionmachine, required for vector control. The automated
procedureof testing and calculation is done following the first
enabling ofthe controller. As the induction machine may already be
cou-pled to a load, the tests aimed at self-commissioning have
toidentify the required parameters at standstill. The
identificationis therefore performed with single-phase supply to
the machine.In principle, two types of excitation may be applieddc
or ac.The one ideal for true self-commissioning is dc. From
applieddc voltage and resulting dc steady state current, one finds
thevalue of the stator resistance. Determination of the
remainingparameters is then based most frequently on transient
current re-sponse that follows application of the dc voltage.
Self-commis-sioning schemes that rely on this approach are those
describedin [11][16].
The methods regarded as suitable for commissioning
butinappropriate for self-commissioning are those that
eitherrequire some special conditions to be satisfied during
thecommissioning (for example, the machine is allowed to rotate)or
they require substantially more complicated mathematicalprocessing
of the measurement results, when compared tothe self-commissioning
methods. For example, proceduresdescribed in [17][19] are all based
on some tests withsingle-phase supply to the machine. However, the
methoddescribed in [17] involves application of
pseudo-randombinary-sequence voltage excitation and requires an
adaptiveobserver. The procedure of [18] relies on maximum
likelihoodmethod to obtain transfer function parameters. A step
voltage isapplied at the stator terminals and the stator voltage
and statorcurrent responses are recorded. The Laplace
transformationis used to get the transfer function along with the
maximumlikelihood estimation. The method of [19] requires
applicationof the recursive least squares algorithm, this being the
same asfor the procedure of [20].
The second possible excitation for parameter identificationat
standstill is single-phase ac. Standstill frequency responsetest
forms in this case the basis for the parameter identifica-tion
[21][24]. A particularly interesting procedure based on
single-phase ac excitation is the rotor time constant
identifica-tion method of [25]. It is based on trial-and-error and
essentiallydoes not require any computations.
Some of the offline identification procedures surveyed so
farenable identification of the machines magnetizing curve in
ad-dition to other rated parameter values. Such is the case for
themethods described in [13], [15], [21][23]. It should be
notedthat the requirement for magnetizing curve identification
oftenadds to the complexity of the commissioning procedure
sincemore than one test needs to be performed. A significant
stepforward in this sense is the method of [26], where
magnetizingcurve is identified at standstill using only one test
with single-phase ac supply. Other possibilities of the magnetizing
curveidentification for self-commissioning purposes have been
ex-plored in [27][30].
If the conditions of the commissioning are less stringent,
thedrive may be allowed to rotate for the purposes of
parameteridentification. A whole array of additional parameter
determi-nation methods opens up in this case. For example, an
extremelysimple procedure for rotor time constant tuning [31] is
based onthe tests performed while the machine is rotating. The
drive isoperated in the torque mode for the purposes of the rotor
timeconstant tuning, with rated rotor flux reference. An
alternatingsquare-wave torque reference is applied at certain speed
of rota-tion. If the rotor time constant value used in the
controller is cor-rect, the actual torque is an alternating
square-wave as well, sothat the speed response follows a triangular
function. If the rotortime constant setting is not correct,
situation of Fig. 1 resultsand the actual torque response is not
the same as the torque ref-erence. Speed response then deviates
from triangular. An exper-imental illustration of this
trial-and-error method of rotor timeconstant tuning is given in
Fig. 2.
Standard no-load test and locked rotor test may be performedwith
a PWM inverter supply if the commissioning situation al-lows for
such testing. Parameters that are calculated are the sameas those
obtained with sinusoidal supply, provided that the cal-culations
are based on the fundamental components [32]. Thisfeature is
exploited in [33], where the parameters are identi-fied using the
dc, no-load and the pseudo-locked rotor tests. Amethod for
pseudo-locked rotor test is presented since the me-chanical locking
of the rotor is undesirable in any onsite com-missioning
scenario.
Identification of the machines magnetizing curve becomesa simple
and straightforward task if the machine is allowedto rotate under
no-load conditions during the onsite commis-sioning. By defining
the magnetizing curves analytical approx-imation in a suitable
functional form and by performing a seriesof steady state
fundamental harmonic voltage measurements inthe field weakening
region, it becomes possible to determinethe correct magnetizing
curve approximation purely by visualinspection of the measurement
results [34]. An experimentalillustration of this method is given
in Fig. 3, where measuredline-to-line fundamental voltage component
is shown, togetherwith the reconstructed magnetizing curve.
Another magnetizing curve identification procedure isdescribed
in [35]. It relies on the signals that are alreadypresent within
the drive controller (stator currents and the dclink voltage), so
that additional measurements are not required.
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TOLIYAT et al.: A REVIEW OF RFO INDUCTION MOTOR PARAMETER
ESTIMATION TECHNIQUES 273
Fig. 2. An experimental trial-and-error method of rotor time
constant tuningin indirect vector controller: speed response to
alternating square-wave torquecommand with correct rotor time
constant and with 1.7 times correct rotor timeconstant (0.75-kW
machine). Speed response is a triangular function of timewhen the
rotor time constant is correctly set (upper figure). The method
wasoriginally proposed in [31] and the results shown are from
[4].
A special identification function, proposed in [35],
ensuresprecise acquisition of the magnetizing curve, robust
againstthe stator resistance variation, and the inverter lock-out
time.The algorithm does not require any test signals. It is
sufficientto perform the measurements during running of the
unloadedmotor at around 100 r/min. Performing measurements at such
alow speed enables the impact of iron and mechanical losses
onidentification accuracy to be minimized. This, in turn,
enablesaccurate identification down to 10% of the rated
magnetizingflux, including the point of infliction. An illustration
of theresults of the procedure of [35] is given in Fig. 4.
Some other approaches to the magnetizing curve identifica-tion,
described in [36][38] are more involved and therefore lesssuitable
for onsite commissioning of the drive. Method of [36]performs
identification at standstill and only current measure-ments are
needed. However, all the three phases of the machineare energized
and standstill condition is achieved by means ofclosed loop speed
control. The method requires that the vectorcontrolled induction
motor is coupled to a controllable load andis therefore not
suitable for onsite commissioning. Similar con-clusion applies to
the broad-band excitation method [37], whichrequires injection of
multiple frequency supply into the ma-chines stator terminals.
Method of [38], although apparentlyvery accurate, is rarely
applicable in practice since it requiresthat the neutral point of
the stator star connected winding isaccessible.
Fig. 3. Measured fundamental stator voltage for different
settings of theparameter a of the inverse magnetizing curve
per-unit analytical approximationi = a + (1 a) and reconstructed
magnetizing curve(2.3-kW machine, field-weakening starts at 1150
r/min; results taken from[34]). The correct value is a = 0:9 since
it gives the flattest voltage behaviorin the field-weakening
region.
Fig. 4. Experimentally identified magnetizing curve and
magnetizinginductance (100 r/min, no-load conditions, 7-kW machine,
method of [35]).
It is worth noting that offline magnetizing curve (or
magne-tizing inductance) identification suffices for saturation
compen-sation schemes and that identification of dynamic
(differential)inductance is usually not required. However, there
are methodsthat enable identification of the dynamic inductance as
well, forexample [37] and [39].
Compensation of iron losses in vector controlled
inductionmachines usually requires knowledge of the equivalent iron
loss
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274 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE
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resistance for the fundamental harmonic, which is a function
ofthe fundamental frequency [8]. The equivalent iron loss
resis-tance can be identified during the drive commissioning
usingthe procedure outlined in [40]. A series of no-load tests
areperformed at various fundamental frequencies, using the samePWM
voltage source inverter that will be subsequently used forthe
normal drive operation. Fundamental harmonic input powerneeds to be
measured, mechanical losses are separated fromthe fundamental iron
losses using the customary no-load testprocedure, and equivalent
iron loss resistance is eventually cal-culated. The procedure
requires that rotation is permitted andthat no-load condition is
available. An illustration of the ex-perimental results related to
fundamental iron loss componentand the corresponding equivalent
iron loss resistance is givenin Fig. 5. Tests at standstill, which
would enable identificationof the equivalent iron loss resistance,
do not seem to exist atpresent.
It should be noted that accuracy of parameter determination
inall offline identification techniques depends on the sample
rateselection, quantization errors, resolution and accuracy of
sen-sors, etc. [41]. Identified parameter values will therefore
alwaysbe characterized with certain error margin. The major
problemencountered in offline parameter identification at
standstill isundoubtedly the inverter lock-out time and
nonlinearity, whichmake the accurate parameter determination on the
basis of re-constructed voltages very difficult without prior
knowledge ofthe inverter voltage drop characteristics [42]. A
technique forovercoming this problem has recently been proposed,
based onrecursive least squares [43].
Further important works describing various approaches
toself-commissioning and commissioning are those of [44][55].
IV. ONLINE ROTOR TIME CONSTANT ESTIMATION TECHNIQUES
The major effort has been put into development of rotor
timeconstant (rotor resistance) online estimation methods. Due toa
huge number of proposed solutions of very different nature,these
are further classified into four subgroups.
A. Spectral Analysis TechniquesThis group of methods encompasses
all of the cases where
online identification is based on the measured response to a
de-liberately injected test signal or an existing characteristic
har-monic in the voltage/current spectrum [56][66]. Stator
currentsand/or voltages of the motor are sampled and the parameters
arederived from the spectral analysis of these samples. In the
caseof spectral analysis, a perturbation signal is used because
underno-load conditions of the induction motor, the rotor induced
cur-rents and voltages become zero, so slip frequency becomes
zero,and hence, the rotor parameters cannot be estimated. In [56]
and[57], the disturbance to the system is provided by injecting
nega-tive sequence components. An online technique for
determiningvalue of the rotor resistance by detecting the negative
sequencevoltage is proposed in [56]. Special precautions need to be
takento circumvent the torque-producing action when an
inductionmotor, equipped with this system, is used as a torque
drive; oth-erwise, the outer loop might prevent the perturbation
from beinginjected into the system. The main drawback of this
method is
Fig. 5. Fundamental component of the iron loss identified using
the procedureof [40] and the corresponding equivalent iron loss
resistance (4-kW machine).
Fig. 6. Rotor inductance and rotor resistance identification
using the methodof [57] (simulation results).
that the strong second harmonic torque pulsation is induced
dueto the interaction of positive and negative rotating
componentsof MMF.
In [57], an online estimation technique is proposed, based onthe
model in the frequency domain. The -axis componentof the injected
negative sequence component is kept at zero, sothat the machine
torque is undisturbed. The -axis componentaffects the flux of the
machine. FFT is used to analyze thecurrents and voltages and the
fundamental components of thesampled spectral values are used to
determine the parameters.Average speed is used for the
identification of parameters.The simulation results, obtained using
this method, for rotorresistance and rotor inductance
identification are given in Fig. 6[57].
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TOLIYAT et al.: A REVIEW OF RFO INDUCTION MOTOR PARAMETER
ESTIMATION TECHNIQUES 275
In [58], an attempt to create online tests similar to the
no-loadand full-load tests is made. In [59], a pseudo-random binary
se-quence signal is used for perturbation of the system by
injectingit into the -axis and correlating with -axis stator
current re-sponse. The sign of correlation gives the direction for
rotor timeconstant updating. This method however does not work
satisfac-torily under light loads. In [60], a sinusoidal
perturbation is in-jected into the flux producing stator current
component channel.Though rotor resistance can be estimated under
any load andspeed condition, the cost is high due to the
installation of twoflux search coils.
Solutions described in [61][63] all belong to the samecategory.
A very different approach is the one described in[64][66], where
rotor slot harmonics in stator current aretracked and used for
online updating of the rotor time constant.
B. Observer-Based TechniquesIn [67], Loron and Lalibert describe
the motor model and
the development and tuning of an extended Kalman filter (EKF)for
parameter estimation during normal operating conditionswithout
introducing any test signals. The proposed method re-quires
terminal and rotor speed measurements and is useful forautotuning
an indirect field-oriented controller or an adaptivedirect
field-oriented controller. In [68], Zai, DeMarco, and Lipopropose a
method for detection of the inverse rotor time con-stant using the
EKF by treating the rotor time constant as thefifth state variable
along with the stator and rotor currents. Thisis similar to a
previously mentioned method that injected per-turbation in the
system, except that in this case, the perturbationis not provided
externally. Instead, the wide-band harmonicscontained in a PWM
inverter output voltage serve as an excita-tion. This method works
on the assumption that when the motorspeed changes, the machine
model becomes a two-input/two-output time-varying system with
superimposed noise input. Thedrawbacks are that this method assumes
that all other parame-ters are known and the variation in the
magnetizing inductancecan introduce large errors into the rotor
time constant estima-tion. The application of the EKF for slip
calculation for tuningan indirect field oriented drive is proposed
in [69]. Using theproperty that in the steady state the Kalman
gains are asymptot-ically constant for constant speeds, the Riccati
difference equa-tion is replaced by a look-up table that makes the
system muchsimpler. The disadvantage is that, although the
complexity ofthe Riccati equation is reduced, the full-order EKF is
computa-tionally very intensive as compared to the reduced
order-basedsystems.
In [70], an online estimation of rotor resistance and the
mag-netizing inductance, using continuous form of the Kalman
filteris proposed, though the actual estimation is done offline
usingthe discrete form of the KF. For using the KF online, it is
im-portant to estimate the magnetizing inductance accurately as
aninaccurate magnetizing inductance gives improper value of
therotor time constant. The method is based on the assumption
thatsince the value of the magnetizing inductance follows the
motorflux level, the magnetizing inductance can be estimated
alongwith the rotor resistance and the rotor time constant using
theKF. Other solutions, based on the Kalman filter, are those
de-scribed in [71][76].
An extended Luenberger observer (ELO) for joint state
andparameter estimation was developed in [77][79]. In [78] and[79],
the authors have provided a comparison of the operationof the ELO
and the EKF. In [78], a deterministic approach todesigning the ELO
with joint online estimation of motor statesand parameters is
presented. In [79], Du and Brdys implementedthe scheme using three
different full-order ELOs. The first ELOwas used for rotor time
constant and rotor flux estimation. Thesecond one was used for
shaft speed and rotor flux estima-tion and the third for shaft
speed, load torque, and rotor fluxestimation.
In the case of joint state and parameter estimation, ELO
turnsout to be the advantageous solution. Since the induction motor
isa nonlinear system, the observations from the EKF at
individualtime instants do not lead to an overall optimal
observation. Forthe ELO, there is a great deal of flexibility in
choosing the gain,unlike the EKF and the rate of convergence can be
tuned withoutadversely affecting the steady state accuracy of the
observer.The main advantage of the ELO over the EKF is that the
ob-server performance can be greatly enhanced by simply
adjustingthe gain matrix for rapid convergence of the estimates,
whichgives an unbiased estimation in the case of the ELO.
The major problems related to EKF and ELO applications
arecomputational intensity and the fact that all the inductances
aretreated as constants in the motor equations. In order to
improvethe accuracy of the EKF-based rotor resistance
identification, itis suggested in [68], [70], and [73] to
simultaneously identifythe magnetizing inductance. Another
possibility of improvingthe accuracy is the inclusion of the iron
loss into the model [72].
C. Model Reference Adaptive System-Based TechniquesThe third
major group of online rotor resistance adaptation
methods is based on principles of model reference
adaptivecontrol. This is the approach that has attracted most of
theattention due to its relatively simple implementation
require-ments. The basic idea is that one quantity can be
calculated intwo different ways. The first value is calculated from
referencesinside the control system. The second value is calculated
frommeasured signals. One of the two values is independent of
therotor resistance (rotor time constant). The difference
betweenthe two is an error signal, whose existence is assigned
entirelyto the error in rotor resistance used in the control
system. Theerror signal is used to drive an adaptive mechanism (PI
or Icontroller) which provides correction of the rotor
resistance.Any method that belongs to this group is based on
utilizationof the machines model and its accuracy is therefore
heavilydependent on the accuracy of the applied model. The numberof
methods that belong to this group is vast [80][100] andthey
primarily differ with respect to which quantity is selectedfor
adaptation purposes. Reactive power-based method is notdependent on
stator resistance at all and is probably the mostfrequently applied
approach [80][85]. A method based onspecial criterion function,
derived again from stator voltageand current measurement, is
described in [86]. Next, air gappower can be selected as the
quantity on which adaptationis based [87], [88]. The reference air
gap power is calcu-lated from reference torque and frequency
values, while theactual one has to be calculated from measured
input power
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276 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE
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and estimated stator losses in the machine. Alternatively,
dclink power can be measured instead of the machines inputpower. In
both cases, the accuracy of the method is heavilyundermined by the
need to estimate stator loss (and inverterlosses if dc link power
is measured). Other possibilities includeselection of torque [83],
[89], rotor back emf [90], [91], rotorflux magnitude [83], rotor
flux -, and -components [92],stored magnetic energy [93], product
of stator -axis currentand rotor flux [94], stator fundamental rms
voltage [95], stator
-axis or -axis voltage components [94], or stator -axis cur-rent
component [96]. There are a couple of common featuresthat all of
the methods of this group share. First, rotor resis-tance
adaptation is usually operational in steady-states onlyand is then
disabled during transients. Thus, the adaptationcan be based on
steady-state model of the machine. Second,in the vast majority of
cases, stator voltages are required forcalculation of the adaptive
quantity and they have either to bemeasured or reconstructed from
the inverter firing signals andmeasured dc link voltage. Third, in
most cases, identificationdoes not work at zero speed and at zero
load torque. Finally,identification heavily relies on the model of
the machine, inwhich, most frequently, all of the other parameters
are treatedas constants. This is at the same time the major
drawback ofthis group of methods. Indeed, an analysis of the
parametervariation influence on accuracy of rotor resistance
adaptation[101] shows that when rotor flux magnitude method is
appliedand actual leakage inductances deviate by 40% from the
valuesused in the adaptation, rotor resistance is estimated with
suchan error that the response of the drive becomes worse than
withno adaptation at all. Similar study, with very much the
sameconclusions, is described in [102] where parameter
sensitivityis examined for -axis stator voltage method, -axis
statorvoltage method, air gap power method, and reactive
powermethod.
Due to high sensitivity of the model-based methods to
otherparameter variation effects, it is desirable to account for at
leastsome of these in the process of rotor resistance
adaptation.Variation of the magnetizing inductance with saturation
is forthis reason sometimes taken into account, so that the
accu-racy of rotor resistance identification is improved [84],
[86],[103], [104]. The other drawback of this group of
methods,impossibility of adaptation at zero speed and zero load
torque,is successfully eliminated in certain cases. For example,
theschemes of [86] and [96] are operational at zero speed and
atlight loads although they do fail at zero load.
Operation of a MRAS rotor resistance adaptation scheme
isillustrated in Fig. 7 by means of experimentally recorded
traces.The method based on special criterion function of [86],
whichenables rotor resistance adaptation at zero speed and under
lightloading conditions, is implemented. The error function,
whichserves as the input into the PI controller, is shown together
withthe rotor resistance estimate in per unit (i.e., ratio of rotor
re-sistance in the controller to the actual one in the machine).
Thedrive operates at zero speed with 0.2 per unit load torque.
Theadaptation mechanism operation is illustrated for step
variationof rotor resistance used in the controller, of 50 . As can
beseen from Fig. 7, rotor resistance adaptation works well as
theresistance in the controller always returns, after the
introduceddisturbances, to the previous value (i.e., to ).
Fig. 7. Experimental recording of the operation of the rotor
resistanceadaptation in indirect rotor flux oriented induction
machine, using the methodof [86] (scales: time10 s/div, error
function0.5 p.u./div, rotor resistanceestimate0.4 p.u./div; 0.75-kW
machine). Figure provided courtesy of theauthor, Dr. S.N.
Vukosavic.
Other methods of online rotor resistance adaptation, that donot
belong to any of the three main groups, are reviewed next.
D. Other MethodsThere exist a number of other possibilities for
online rotor
resistance (rotor time constant) adaptation, such as those
de-scribed in [105][107]. For example, the method of [107] doesnot
require either a special test signal or complex computations.It is
based on a special switching technique of the current regu-lated
PWM inverter, which allows measurement of the inducedvoltage across
the disconnected stator phase. The rotor time con-stant is then
identified directly from this measured voltage andmeasured stator
currents. The technique provides up to six win-dows within one
electric cycle to update the rotor time constant,which is
sufficient for all practical purposes. A simulation il-lustration
of the method is given in Fig. 8, where estimated andactual rotor
time constant are shown. The updating is performedonly twice
(rather than six times) during one electrical cycle.
Another possibility, opened up by the recent developmentsin the
area of artificial intelligence (AI), is the application
ofartificial neural networks for the online rotor time
constant(rotor resistance) adaptation. Such a possibility is
exploredin [108][112]. The other AI technique that can be
utilizedfor online rotor time constant adaptation is the fuzzy
logic[113][120].
Recent emphasis on sensorless vector control has led to a
de-velopment of a number of schemes for simultaneous rotor speedand
rotor time constant online estimation, that are applicable
inconjunction with the appropriate speed estimation
model-basedalgorithms [121][134]. These methods of rotor time
constantestimation belong in vast majority of cases to one of the
groupsalready reviewed in this section.
An excellent review of the rotor resistance compensationschemes,
available at the time, is the one of [135].
V. ONLINE ESTIMATION OF STATOR RESISTANCE
An industrially accepted standard for sensored rotor flux
ori-ented control has become the indirect rotor flux oriented
control(IRFOC), which does not require the knowledge of the stator
re-sistance. Since the rotor time constant is of crucial
importance
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TOLIYAT et al.: A REVIEW OF RFO INDUCTION MOTOR PARAMETER
ESTIMATION TECHNIQUES 277
Fig. 8. Estimated and actual rotor time constant using the
procedure of[107]. The estimate is updated twice per electrical
cycle, on the basis of themeasurement of the voltage across a
disconnected phase.
for decoupled flux and torque control in IRFOC, the major
ef-fort was directed toward development of online techniques
forrotor time constant identification, as shown by the review in
Sec-tion IV. The situation has however dramatically changed withthe
advent of sensorless vector control, which requires rotorspeed
estimation. Vast majority of speed estimation techniquesare based
on the induction machine model and involve the statorresistance as
a parameter in the process of speed estimation. Anaccurate value of
the stator resistance is of utmost importancein this case for
correct operation of the speed estimator in thelow speed region. If
stator resistance is detuned, large speed es-timation errors and
even instability at very low speeds result. Itis for this reason
that online estimation of stator resistance hasreceived
considerable attention during the last decade, as wit-nessed by a
large number of publications devoted to this subject[136][163]. The
other driving force behind the increased in-terest in online stator
resistance estimation was the introductionof direct torque control
(DTC), which in its basic form relieson estimation of stator flux
from measured stator voltages andcurrents. The accuracy of DTC,
especially in the low frequencyregion, therefore heavily depends on
the knowledge of the cor-rect stator resistance value.
In general, methods of stator resistance estimation are sim-ilar
to those utilized for rotor time constant (rotor
resistance)estimation and include application of observers,
extendedKalman filters, model reference adaptive systems, and
artificialintelligence.
VI. ONLINE COMPENSATION OF SATURATION AND IRON LOSS
In contrast to temperature-related resistance variation that
isslow, change in machines inductances is very rapid. Compen-sation
of such variations is therefore most easily accomplishedby means of
modified nonlinear machine models that accountfor the variable
degree of saturation and invariably ask for theknowledge of an
appropriate magnetizing curve. Compensationof main flux saturation,
that will simultaneously yield onlinemagnetizing inductance
estimation, requires that the basic ma-chine model is modified in
such a way that the nonlinearity ofthe magnetizing curve is
accounted for. The standard assump-tion is that leakage flux and
main flux components of the statorand rotor flux can be treated
independently. It is assumed fur-ther on that leakage inductances
are constants and that only mainflux saturates.
Derivation of the complete dynamic axis models thataccount for
main flux saturation is rather involved and thefinal form depends
on the selected set of state space variables[164][166]. However, if
one is interested only in modifyingthe rotor flux estimators or the
indirect vector controller in sucha way that the main flux
saturation is compensated, then thistask can be accomplished in a
relatively simple way, becauseall of the estimators and the
indirect vector controller are basedon the reduced order models of
an induction machine [1],[167][170]. Very much the same applies to
the utilization of afull order observer for rotor flux estimation,
provided that theobserver is constructed using stator current and
rotor flux axis components as state space variables [171]. In all
of thesecases, knowledge of the induction machines magnetizing
curveis a prerequisite, since this characteristic has to be
incorporatedinto the control system. Magnetizing curve has
therefore to beidentified offline during the commissioning of the
drive.
The other existing approaches to online magnetizing induc-tance
estimation are predominantly based on standard axismachine model
and they do not require a-priori knowledge ofthe magnetizing curve.
Such is the situation with methods re-ported in [103], [172][178].
While the estimation is sufficientlygood in steady state, it is
usually of limited accuracy during tran-sients, since the schemes
are based on the induction machinemodel that accounts for the main
flux saturation in a very ap-proximate way (only through continuous
variation of the steadystate magnetizing inductance). A couple of
theoretical/ simula-tion attempts were made recently to apply AI
techniques (ANNsand FL) in the estimation of the saturated
magnetizing induc-tance [179], [180].
Online magnetizing inductance estimation is illustrated inFig. 9
for a model-based method, described in [181], whichrequires
knowledge of the magnetizing curve of the machine.An experimental
recording of the start-up transient, withset speed of 1350 r/min,
is shown. The machine is initiallypremagnetized and the field
weakening operation starts at650 r/min by means of the IRFOC scheme
described in [34].The magnetizing inductance exhibits substantial
variation, fromunsaturated value in premagnetized state to rated
saturatedvalue and then back toward unsaturated value as the speed
ofrotation in the field weakening region increases.
Rotor leakage flux saturation can be included in the model ofthe
machine by making rotor leakage inductance a variable pa-rameter,
dependent on the rotor current. Frequency-related vari-ation of
rotor parameters can be accounted for by representingthe rotor
winding with two branches. A scheme with air gapflux oriented
control, that includes both compensation of rotorleakage flux
saturation and frequency dependent variation ofrotor parameters,
derived from a modified induction machinemodel that accounts for
both of these phenomena, is described indetail in [182][184]. It is
demonstrated in [182][184] that, forthe chosen machine in which
both of these effects are severelypronounced, vector control scheme
derived from such a mod-ified model provides superior performance
when compared tothe performance obtainable with vector control
scheme based onthe constant parameter model. It is worth noting
that the schemeof [182][184] additionally compensates for main flux
satura-tion as well. The intrinsic difficulty in implementation of
sucha vector control scheme is that the number of rotor
parameters
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278 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE
2003
Fig. 9. Online estimated magnetizing inductance and speed of
rotation forthe accleration transient of a loaded machine, using
the method of [181]. Fieldweakening starts at 650 r/min.
that have to be determined during the commissioning is now
fiverather than two. One possibility is to use finite element
calcu-lations, as suggested in [182]. Alternatively, a series of
lockedrotor tests, executed for different current values at various
oper-ating frequencies, can be used to experimentally identify
offlinethe parameters of this modified model.
Compensation of iron loss is nowadays almost exclusivelydone
using the model-based approach, which consists of de-velopment of a
modified vector control scheme on the basisof a machines model that
takes into account the existence ofthe iron loss. Iron loss is
represented within the machine modelwith either a parallel or a
series equivalent iron loss resistanceand a modified vector control
strategy is then derived. This ap-proach requires equivalent iron
loss resistance offline identifica-tion at the commissioning stage.
The examples of utilization ofthis compensating strategy are
numerous and include [8], [40],[185][205].
A very different approach to equivalent iron loss
identifica-tion and adaptive iron loss compensation is described in
[206],[207]. It is based on the fact that an error in the rotor
flux po-sition estimate is inevitably introduced by the existence
of theiron loss [8]. This error can be brought down to zero only
ifthe iron loss-compensating signal relies on the correct value
ofthe equivalent iron loss resistance for the given operating
condi-tions. An online tuning scheme is hence developed, which
pro-vides quasi steady state tuning of the equivalent iron loss
resistoron the basis of the stator -axis voltage error signal. The
methodrequires stator voltage and current measurement but avoids
theneed for offline equivalent iron loss resistance
identification.
VII. CONCLUSIONHigh performance control schemes of an induction
motor in-
variably rely on the knowledge of at least some of the motor
pa-
rameters. Parameter values are used within the drive
controllerand they have therefore to be identified offline, during
the drivecommissioning. However, since all of the parameters
inevitablyvary during the drive operation, it is often desirable to
improvethe performance of the drive by adding an online parameter
esti-mator. Such a situation has led to development of a large
numberof offline parameter identification and online parameter
estima-tion methods during the last two decades. An attempt is made
inthis paper to review the existing methods and to provide a
com-prehensive bibliography on the subject.
The attention is at first focused on self-commissioning
andcommissioning techniques that serve the purpose of the
offlineparameter identification at the stage of the drive
initialization.Available methods for induction motor equivalent
circuit param-eter identification are reviewed, along with the
possibilities forthe magnetizing curve and equivalent iron loss
resistance deter-mination. Since an accurate value of the rotor
time constant isof utmost importance for tuned operation of the
vast majorityof vector controlled induction motor drives, a
substantial spaceis further devoted to the methods that enable
online rotor timeconstant estimation. This is followed by
discussion of the onlinestator resistance estimation methods, since
the exact knowledgeof the stator resistance is of paramount
importance in a numberof sensorless vector and direct torque
control schemes.
In contrast to the resistance variations that are slow,
varia-tions in the magnetizing inductance and iron loss are rapid
andare therefore most easily compensated by utilizing a
modifiedvector controller, that is developed using an appropriately
mod-ified motor model (that accounts for the flux saturation
and/oriron loss) as the starting point. Methods aimed at online
estima-tion and compensation of the magnetizing inductance
variationand the iron loss are surveyed in the last section of the
paper.
The paper is illustrated throughout with numerous experi-mental
and simulation results, related to different offline param-eter
identification and online parameter estimation techniques,taken
from various publications of the authors.
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Hamid A. Toliyat (S87M91SM96) received thePh.D. degree in
electrical engineering from the Uni-versity of Wisconsin-Madison in
1991.
Currently, he is an Associate Professor in theDepartment of
Electrical Engineering at Texas A&MUniversity, College Station.
Dr. Toliyat is an Editorof IEEE TRANS. ENERGY CONVERSION, an
AssociateEditor of IEEE TRANS.POWER ELECTRONICS, anda member of the
Editorial Board of Electric PowerComponents and Systems Journal.
His main researchinterests and experience include multiphase
variable
speed drives, fault diagnosis of electric machinery, analysis
and design ofelectrical machines, and sensorless variable speed
drives. He has publishedover 150 technical papers in these fields.
He is actively involved in presentingshort courses and consulting
in his area of expertise to various industries.
He has received the Texas A&M Select Young Investigator
Award in 1999,Eugene Webb Faculty Fellow Award in 2000, NASA Space
Act Award in 1999,and the Schlumberger Foundation Technical Award
in 2000 and 2001. He is alsoVice-Chairman of IEEE-IAS Electric
Machines Committee, and is a memberof Sigma Xi. He is the recipient
of the 1996 IEEE Power Eng. Society PrizePaper Award for his paper
on the Analysis of Concentrated Winding InductionMachines for
Adjustable Speed Drive ApplicationsExperimental Results.
Emil Levi (S89M92SM99) was born in 1958 inZrenjanin, Yugoslavia.
He received the Diploma de-gree from the University of Novi Sad,
Yugoslavia,and the M.Sc. and Ph.D. degrees in electrical
engi-neering from the University of Belgrade, Yugoslavia,in 1982,
1986, and 1990, respectively.
Currently, he is Professor of Electric Machinesand Drives in the
School of Engineering at LiverpoolJohn Moores University,
Liverpool, U.K. In 1982,he joined the Department of Electrical
Engineeringat the University of Novi Sad, where he became
Assistant Professor in 1991. He joined Liverpool John Moores
University,U.K., in May 1992 as a Senior Lecturer. From 1995 till
2000, he was a Readerin Electrical Power Engineering. His main
areas of research interest aremodeling and simulation of electric
machines, control of high performancedrives, and power electronic
converters. He has published over 130 papers,including more than 30
papers in major international journals.
Mona Raina (S00) received the Bachelors degreein electrical
engineering from the University ofMadras, India. She is currently
pursuing the M.Sc.degree in electrical engineering at Texas
A&MUniversity, College Station.
She is currently with Novellus Systems, Inc., SanJose, CA. Her
research interests are in the fields ofpower electronics and motor
drives and they includethe parameter estimation of induction
motors.
Index:
CCC: 0-7803-5957-7/00/$10.00 2000 IEEE
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