IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 3, MAY 1998
401
Quasi-Fuzzy Estimation of Stator
Resistance of Induction Motor
Bimal K. Bose, Life Fellow, IEEE, and Nitin R. Patel, Member, IEEE
Abstract— This paper describes a quasi-fuzzy method of online stator-resistance estimation of an induction motor, where
the resistance value is derived from stator-winding temperature
estimation as a function of stator current and frequency through
an approximate dynamic thermal model of the machine. The
estimator has been designed and iterated by simulation study and
then implemented by a digital signal processor on a 5-hp statorflux-oriented direct vector-controlled drive. The experimental
performance of the estimator has been calibrated extensively both
at static and dynamic conditions by a stator-mounted thermistor
network-based estimation and gives excellent performance. The
stator-winding temperature information can also be used for
monitoring, protection, and fault-tolerant control of the machine.
Index Terms—Fuzzy estimation, induction motor, stator resistance, stator temperature.
I. INTRODUCTION
C
URRENTLY, sensorless vector control of induction motor drives is receiving wide attention in the literature.
The estimation of feedback signals (such as flux vector,
speed, and frequency) for both the rotor and stator-fluxoriented vector control methods, which are based on voltage model computation, becomes inaccurate due to statorresistance variation. This error becomes serious near zero
speed (i.e., frequency) when the stator-resistance drop tends to
be comparable with the machine counter electromotive force
(emf). The inaccurate flux vector computation gives error not
only in the flux magnitude, but in the phase angle also, which
affects response of the drive. The direct torque control (DTC)
method of the induction motor drive is similarly affected
by the error in stator-flux estimation. Among all the vector
control methods, the stator-flux-oriented direct vector control
is recently gaining more importance because the feedback
signal estimation accuracy is dependent only on the statorresistance variation, which can be compensated somewhat
easily.
Neglecting the small amount of skin and stray loss effects,
the stator-winding resistance primarily varies with winding
temperature which is given by the following:
C
(1)
Manuscript received November 22, 1996; revised August 1, 1997. This
work was supported by Delphi Energy and Engine Management Systems,
General Motors Corporation. Recommended by Associate Editor, A. Kawamura.
B. K. Bose is with the Department of Electrical Engineering, University of
Tennessee, Knoxville, TN 37996-2100 USA.
N. R. Patel is with Hughes Aircraft-GM Corporation, Torrence, CA 905092923 USA.
Publisher Item Identifier S 0885-8993(98)03355-9.
where
is the resistance at
C,
is the nameplate
resistance (at 25 C ,
is the stator-winding temperature
C , and
is the temperature coefficient of resistance of
10
C).
copper (11.21
If several temperature-sensing thermistors [1], [2] are inserted in a distributed manner in the stator winding, the average
stator-winding temperature can be monitored, and, correspondingly, stator resistance can be estimated fairly accurately by
using (1). However, the use of such temperature sensors in a
sensorless drive is not acceptable.
The question is: is it possible to estimate the stator-winding
temperature with reasonable accuracy from the machine terminal voltage and current signals, i.e., without using any
additional sensors than those required by a sensorless drive?
Basically, the losses in the machine contribute to statorwinding temperature rise, and these losses can be classified
as stator copper loss, rotor copper loss, stator iron loss,
rotor iron loss, and some amount of stray loss [3]. The heat
generated by the losses flow through distributed parameter
thermal equivalent circuit of the motor and cause temperature
rise at different parts. The dynamic thermal model of the
machine is nonlinear, multidimensional, and is extremely
complex. It is influenced by the cooling method used in the
machine. The stator copper and iron losses will dominantly
contribute to stator-winding temperature rise, although the
rotor losses coupled through the machine airgap contribute
to this temperature rise. Fortunately, the iron loss is small
in the rotor, and the rotor copper loss depends on the rotor
current, which is related with the stator current. In the past,
an attempt was made to estimate the stator resistance as a
function of stator current only (using fuzzy logic or neural
network) [4], [5] without considering iron loss and dynamic
thermal model of the machine. Such an estimation is bound
to be highly inaccurate. Unfortunately, the past studies were
based on simulation only and was never corroborated by
experimental work.
In this paper, stator resistance is derived from fuzzy-logicbased estimation of stator-winding temperature, which is defined as a function of stator current and frequency through
an approximate dynamic thermal model of the machine. The
estimation algorithm has been developed on the basis of the
experimental data of a 5-hp induction motor.
II. DESCRIPTION
OF THE
ESTIMATOR
Fig. 1 shows the complete estimation block diagram of
stator resistance, which also includes a thermistor network
(dotted figure) for calibration of the stator-winding temperature
0885–8993/98$10.00  1998 IEEE
402
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 3, MAY 1998
Fig. 1. Quasi-fuzzy estimation block diagram of stator resistance (Rs) (shown with calibrating thermistor network).
Fig. 2. Measured stator temperature rise versus stator current at different frequency (at steady state).
The same thermistor network was also used to generate
experimental data for formulation of the estimator, which
will be described later. In the present project, the estimated
stator resistance provides compensation for correct estimation
of stator-flux vector, torque, and frequency of a stator-fluxoriented sensorless direct vector-controlled induction motor
drive [8]. The torque-controlled electric vehicle (EV)-type
drive was required to operate from zero speed. The fuzzy
estimator, as shown, estimates the steady-state stator-winding
, where
is the
temperature rise
steady-state temperature rise above ambient,
is the steadyis the ambient temstate stator-winding temperature, and
perature. The
signal is defined by the fuzzy relation of
rms stator current
and frequency
Both the
and
signals in a vector-controlled drive can be obtained from
the following relations [9], [10]:
(2)
(3)
(4)
(5)
BOSE AND PATEL: QUASI-FUZZY ESTIMATION OF STATOR RESISTANCE OF INDUCTION MOTOR
403
(a)
(b)
(c)
Fig. 3. Fuzzy estimation membership functions. (a) Stator current
C).
temperature rise Tss ( p.u.
1
1
= 100
Is
1
(
where
stationary frame -axis ( -axis) stator current;
stationary frame -axis ( -axis) stator voltage;
stationary frame -axis ( -axis) stator-flux linkage;
total stator-flux linkage.
can be used approximately as speed
The frequency signal
(electrical rad/s) for the estimation because the slip
signal
frequency is small. Note that (3)–(5) use voltage signals behind
the stator-resistance drops, which require compensation due to
variation. As mentioned before, the compensation becomes
specially important near zero speed (i.e., frequency). On the
other hand, at higher speed, including the field-weakening
region, the compensation may not be needed at all because
of large counter emf. The fuzzy estimator interprets the
signal to represent the copper loss and the
signal (at rated
flux) to represent the core loss. Both these signals are related
nonlinearly to compute the steady-state winding-temperature
through the machine thermal resistance (steady
rise
p.u.
= 12:7
A). (b) Frequency
!e
1
(
p.u.
= 733
r/s). (c) Steady-state
state), which is indirectly embedded in the estimator. A
rigorous estimation of
based on a mathematical model is
extremely complex. The fuzzy estimation, on the other hand,
does not require a mathematical model and is based on the
operator’s and designer’s experience, which will be described
later. In the present machine, cooling or heat transfer to the
ambient occurs by natural convection as well as by a shaftmounted fan. The fan-cooling effect is obviously proportional
to the machine speed. The dynamic thermal model of the
machine can be approximately represented by a first-order low[11], as indicated in the figure, where is
pass filter
a nonlinear function of speed (i.e., frequency). Once the steady
is estimated by the fuzzy estimator, it is converted
state
to dynamic temperature rise through the low-pass filter and
to derive the actual stator
added to ambient temperature
Then, the derivation of
by (1) becomes
temperature
straightforward.
Fig. 2 shows the experimentally determined steady-state
curves as a function of
stator-winding temperature rise
and frequency
for the machine under
stator current
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 3, MAY 1998
Fig. 4. Experimental machine thermal time-constant curve with frequency.
consideration. The machine was connected to a dynamometer
in speed-control mode, and at each speed (i.e., frequency)
setting, the machine was operated with the rated flux, the
torque (i.e., stator current) was varied in steps, and
information was recorded when the steady-state temperature
data was obtained from the
was reached. The average
reading of a set of five thermistors distributed in the stator, and
then subtracting the ambient temperature,
In Fig. 2, note that at higher frequency (i.e., speed), the iron
loss increases tending to a higher temperature rise, but the
dominant cooling effect of the shaft-mounted fan essentially
decreases the temperature. The curves below the minimum
stator current, which corresponds to the magnetizing current
for rated flux, were extrapolated to the vertical axis. The
temperature rise was small at low stator current for the range
of frequency variation.
The experimental curves in Fig. 2 were used to formulate
the fuzzy membership functions shown in Fig. 3 and the
corresponding rule matrix in Table I. Basically, the fuzzy
signal as function
estimator algorithm interpolates the
of stator current and frequency given in Fig. 2. The signals for
membership functions in Fig. 3 are considered on a per-unit
(p.u.) basis so that the same design can be applicable to similar
is defined by nine fuzzy sets
machines. The stator current
with symmetrical membership functions. The frequency
and temperature rise
signals are defined, respectively,
by 8 and 12 fuzzy sets with asymmetrical membership functions. The asymmetry of membership functions introduces the
appropriate nonlinearity in the estimation. The larger number
of membership functions with crowding at low frequency
indicates more accurate estimation of temperature rise and
the corresponding stator resistance near zero speed. A typical
estimation rule from Table I can be defined as follows:
is small–medium (SM)
IF stator current
AND the frequency
is medium (M),
THEN the temperature rise
is
small–small (SS).
From Fig. 3, it is evident that up to four rules can be valid
at the same time. The input signals are converted to p.u.
values, fuzzified through the membership functions, composed
by SUP-MIN composition, defuzzified by the height method,
and then denormalized to actual output values [12], [13].
Fig. 4 gives the experimentally determined approximate
thermal time-constant curve with frequency for the machine
under consideration, where the increased cooling effect of
the shaft-mounted fan at higher speed delays the steady-state
temperature rise, i.e., increases the thermal time constant.
To derive this curve, the machine was connected to a dynamometer with speed-control mode, and at the rated flux,
steps of torque (i.e., stator current) were applied at different
speed setting. The thermal time constant in each case was
determined from the average transient temperature rise data
on the thermistor network, as mentioned before. The time
constant at zero frequency (i.e., zero speed) indicates that if an
operating machine is stopped and restarted, the correct value of
the temperature rise will be stored in the thermal capacitance
giving correct estimation of stator resistance.
III. SIMULATION AND EXPERIMENTAL
PERFORMANCE EVALUATION
Once the fuzzy membership functions and the rule table,
as discussed before, were derived, they were simulated in a
BOSE AND PATEL: QUASI-FUZZY ESTIMATION OF STATOR RESISTANCE OF INDUCTION MOTOR
FUZZY RULE BASE
FOR
405
TABLE I
ESTIMATION OF STEADY-STATE TEMPERATURE RISE
computer and iterated extensively until the calculated temperature rise data matched with the experimental curves given
in Fig. 2. Then, the control block diagram, shown in Fig. 1,
was implemented with C language in a TMS320C30-type
digital signal processor and integrated with the 5-hp drive
control system [8]. The description of drive control system is
beyond the scope of this paper. However, the stator-resistance
compensation gave the desirable performance of the drive.
The fuzzy estimator can be translated into a feedforward
neural network [14], if desired. Table II gives the parameters
of the machine under test. Once the stator temperature and
the corresponding stator-resistance estimator were designed
and iterated by simulation study, they were calibrated extensively with the thermistor generated data at different stator
current and frequency under both steady state and dynamic
conditions, and estimation accuracy was found to be very
good. After calibration, the thermistor network can be removed
from the machine, if desired. Fig. 5(a) shows the temperature
estimation accuracy at different stator current, but constant
speed of 357 rpm, and Fig. 5(b) shows the corresponding
resistance estimation performance. Figs. 6 and 7 give similar
results, but at speeds 725 and 918 rpm, respectively. The
general performance of the estimator was found to be very
good.
The validity of the proposed estimator for different sizes
and types of machines and in different operating conditions
require some explanation. Although the fuzzy estimator was
designed on the basis of a particular machine, it should be
generally valid for similar machine of different sizes. The
variation of machine parameters will alter the scale factors
TABLE II
INDUCTION MOTOR PARAMETERS
for normalization and denormalization of the variables in the
fuzzy estimator. The thermal time-constant curve of every
machine may have differences and requires individual test
data for merging with the fuzzy estimator. For any difference
in the electrical and thermal features of the machine, or
for other classes of machines, the same algorithm is valid,
but the estimator is to be designed separately with the test
406
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 3, MAY 1998
(a)
(b)
Fig. 5. (a) Stator temperature estimator performance with dynamically varying stator current, but at a constant speed of 357 rpm. (b) Corresponding
resistance estimator performance.
data of the machine. Comprehensive tests of the estimator
performance and design iteration are recommended in case of
any doubt for the validity of the estimator for other machines.
Again, note that precision estimation of stator resistance is
needed at low-speed range, but at higher speed (including
field-weakening region), the resistance compensation can be
totally ignored.
The proposed estimator is designed for the rated flux condition, and the results of the estimator should be valid for all
driving conditions at the rated flux. However, the estimator
BOSE AND PATEL: QUASI-FUZZY ESTIMATION OF STATOR RESISTANCE OF INDUCTION MOTOR
407
(a)
(b)
Fig. 6. (a) Stator temperature estimator performance with dynamically varying stator current, but at a constant speed of 725 rpm. (b) Corresponding
resistor estimator performance.
will not be valid with any flux programming control in the
constant torque region or in the field-weakening mode of
operation. In such a case, the flux parameter should be used as
an additional input signal of the fuzzy estimator. The thermal
capacitor in the low-pass filter will store the temperature and
give correct estimation in case the machine is stopped and
restarted, as mentioned before. At any speed, the machine is
assumed to be energized with the rated flux. If the statorwinding temperature information is used for other purposes
(such as monitoring, protection, and fault-tolerant control),
then accurate fuzzy estimation is required at all operating
conditions.
408
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 3, MAY 1998
(a)
(b)
Fig. 7. (a) Stator temperature estimator performance with dynamically varying stator current, but at a constant speed of 918 rpm. (b) Corresponding
resistance estimator performance.
IV. CONCLUSION
This paper describes an on-line method of induction-motor
stator-resistance estimation, where fuzzy and nonfuzzy approaches have been mixed. The fuzzy algorithm estimates
the stator-winding temperature rise at steady state as a function of stator current and frequency, and then the signal
is processed through a low-pass filter with an approximate
thermal time constant to determine the transient temperature
BOSE AND PATEL: QUASI-FUZZY ESTIMATION OF STATOR RESISTANCE OF INDUCTION MOTOR
information. It is then added with the ambient temperature, and
the stator resistance is calculated in precision as a function
of stator temperature. Calibration with a thermistor network
data indicates the excellent performance of the estimator. The
results of the estimation have been used in a stator-fluxoriented sensorless vector-controlled induction motor drive,
which is described in a separate paper [8]. The principle of
the estimator can be extended to rotor-resistance estimation.
The stator-resistance estimation, as discussed in this paper,
exemplifies possibly one of the best applications of fuzzy
logic.
ACKNOWLEDGMENT
The authors would like to acknowledge the help of Dr.
K. Rajashekara and D. R. Crecelius of Delphi Energy and
Engine Management System for their help in supplying the
experimental data for the project.
REFERENCES
[1] B. K. Bose, M. G. Simoes, D. R. Crecelius, K. Rajashekara, and R.
Martin, “Speed sensorless hybrid vector controlled induction motor
drive,” in Conf. Rec. IEEE-IAS Annu. Meet., 1995, pp. 137–143.
[2] Delphi Energy and Engine Management System, private communication,
Apr. 1992.
[3] G. C. D. Sousa and B. K. Bose, “Loss modeling of converter induction
machine system for variable speed drive,” in Conf. Rec. IEEE-IECON,
1992, pp. 114–120.
[4] S. A. Mir, D. S. Zinger, and M. E. Elbuluk, “Fuzzy controller for inverter
fed induction machines,” in Conf. Rec. IEEE-IAS Annu. Meet., 1992,
pp. 464–471.
[5] L. A. Cabrera and M. E. Elbuluk, “Tuning the stator resistance of
induction motors using artificial neural network,” in Conf. Rec. IEEEPESC, 1995, pp. 421–427.
[6] B. K. Bose and N. R. Patel, “A programmable cascaded low-pass filterbased flux synthesis for stator flux-oriented vector-controlled induction
motor drive,” IEEE Trans. Ind. Electron., vol. 44, pp. 140–143, Feb.
1997.
[7] B. K. Bose, N. R. Patel, and K. Rajashekara, “A start-up method
for a speed sensorless stator flux oriented vector controlled induction
motor drive,” IEEE Trans. Ind. Electron., vol. 44, pp. 587–590, Aug.
1997.
[8] B. K. Bose and N. R. Patel, “A sensorless stator flux oriented vector
controlled induction motor drive with neuro-fuzzy based performance
enhancement,” in Conf. Rec. IEEE-IAS Annu. Meet., 1997, pp. 393–400.
[9] B. K. Bose, Power Electronics and AC Drives. Englewood Cliffs, NJ:
Prentice-Hall, 1986.
[10] X. Xu and D. W. Novotny, “Implementation of direct stator flux
orientation control on a versatile DSP based system,” IEEE Trans. Ind.
Applicat., vol. 27, pp. 694–700, July/Aug. 1991.
[11] B. K. Bose, “A high performance drive control system of an interior
permanent synchronous machine,” IEEE Trans. Ind. Applicat., vol. 24,
pp. 987–997, Nov./Dec. 1988.
[12]
, “Expert system, fuzzy logic, and neural network applications
in power electronics and motion control,” Proc. IEEE, vol. 82, pp.
1303–1323, Aug. 1994.
[13] B. K. Bose, Ed., Power Electronics and Variable Frequency Drives.
New York: IEEE Press, 1997.
[14] B. K. Bose, N. R. Patel, and K. Rajashekara, “A neuro-fuzzy based online efficiency optimization control of a stator flux oriented direct vector
controlled induction motor drive,” IEEE Trans. Ind. Electron., vol. 44,
pp. 270–273, Apr. 1997.
[15] B. K. Bose, “Intelligent control and estimation in power electronics
and drives,” in Conf. Rec. IEEE Int. Electric Machines and Drives,
Milwaukee, WI, , 1997, pp. TA2-2.1–TA2-2.6.
[16]
, “High performance control and estimation in ac drives,” in Conf.
Rec. IEEE-IECON, 1997, pp. 377–385.
[17]
, “Energy, environment and progress in power electronics” in IEE
Japan Conf. Industry Applications, Nagaoka, Japan, Aug. 1997.
409
Bimal K. Bose (S’59–M’60–SM’78–F’89–LF’96)
received the B.E. degree from Calcutta University,
Calcutta, India, the M.S. degree from the University of Wisconsin, Madison, and the Ph.D. degree
from Calcutta University in 1956, 1960, and 1966,
respectively.
He was a Faculty Member at Calcutta University
for 11 years. In 1971, he joined Renasselaer Polytechnic Institute, Troy, NY, as a Faculty Member. In
1976, he joined General Electric Corporate Research
and Development, Schenectady, NY, as a Research
Engineer and served there for 11 years. He currently holds the Condra Chair
of Excellence in Power Electronics at the University of Tennessee, Knoxville,
where he has been responsible for organizing the power electronics program
for the last ten years. His research interests are spread over the whole spectrum
of power electronics and specifically include power converters, ac drives,
microcomputer control, EV drives, expert systems, fuzzy logic, and neuralnetwork-based intelligent control of power electronic and drive systems. He
has published more than 130 papers and holds 19 U.S. patents. He is the
author of Power Electronics and AC Drives (Englewood Cliffs, NJ: PrenticeHall, 1986) and Editor of Adjustable Speed AC Drive Systems (New York:
IEEE Press, 1981), Microcomputer Control of Power Electronics and Drives
(New York: IEEE Press, 1987), Modern Power Electronics (New York: IEEE
Press, 1992), and Power Electronics and Variable Frequency Drives (New
York: IEEE Press, 1997).
Dr. Bose was awarded the Premchand Roychand Scholarship and Mouat
Gold Medal by Calcutta University in 1968 and 1970, respectively, for
his research contributions. He received the IEEE Industry Applications
Society’s Outstanding Achievement Award for “outstanding contributions
in the application of electricity to industry” (1993), the IEEE Industrial
Electronics Society Eugene Mittelmann Award in “recognition of outstanding
contributions to research and development in the field of power electronics
and a lifetime achievement in the area of motor drives” (1994), the IEEE
Region 3 Outstanding Engineer Award for “outstanding achievements in
power electronics and drives technology” (1994), the IEEE Lamme Gold
Medal for “contributions in power electronics and drives” (1996), and the
IEEE Continuing Education Award for “exemplary and sustained contributions
to continuing education (1997). He received the GE Publication Award, Silver
Patent Medal, and a number of IEEE prize paper awards. He is a Distinguished
Scientist of the EPRI-Power Electronics Applications Center, Knoxville, and
an Honorary Professor of Shanghai University and China University of Mining
and Technology, China. He was the Guest Editor of the PROCEEDINGS OF THE
IEEE Special Issue on Power Electronics and Motion Control (August 1994).
He has served the IEEE in various capacities. He has been the Chairman of
the IAS Industrial Power Converter Committee, an IAS Member in the Neural
Network Council, Chairman of the IE Society Power Electronics Council, and
Associate Editor of IE Transactions and various professional committees. He is
on the Editorial Board of PROCEEDINGS OF THE IEEE and has served on many
national and international conference committees. He was a Distinguished
Lecturer in the IEEE IA and IE Societies.
Nitin R. Patel (S’96–M’97) was born in Gujarat,
India. He received the B.S. degree in instrumentation and control from the University of Poona,
India, and the M.S. degree in electrical engineering
at University of Tennessee, Knoxville, in 1991 and
1997, respectively. His Master’s thesis dealt with
the sensorless ac drive application for EV’s using
neuro-fuzzy control.
From 1992 to 1993, he attended Apple computer
classes to learn “C” and UNIX. He worked as an
Assistant Computer Engineer from 1993 to 1994.
His research interests include fuzzy logic and neural-network applications to
power electronics, drives, and sensorless machine control. He was a Research
and Development Engineer at Dover Elevator Systems, Horn Lake, MS, from
January 1997 to August 1997, where he conducted research in sensorless drive
systems for elevator application using TMS320C50 a digital signal processor
and IGBT inverter. He is currently a Member of Technical Staff at Hughes
Aircraft-GM Corporation, Torrence, CA, where he is involved in development
of ac drives control for EV application. He has authored several publications
in IEEE conferences. There are two patents pending for the new strategies
presented in his M.S. thesis in the control and performance enhancement of
induction motor drives.