IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 3, MAY 1998

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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

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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

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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

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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.

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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.

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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.