An evaluation of model-based stator resistance ... - IEEE Xplore

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 17, NO. 1, MARCH 2002

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An Evaluation of Model-Based Stator Resistance Estimation for Induction Motor Stator Winding Temperature Monitoring Sang-Bin Lee, Student Member, IEEE, Thomas G. Habetler, Fellow, IEEE, Ronald G. Harley, Fellow, IEEE, and David J. Gritter

Abstract—In this paper, the feasibility of using an estimate of the stator resistance ( ) as an indicator of stator winding temperature ( ) is evaluated. The advantages of resistance-based temperature monitoring over conventional thermal model-based methods is critare presented. Since obtaining an accurate estimate of ical for this approach, an investigation of existing estimation schemes, and an analysis showing the sensitivity of model-based estimation due to the uncertainties in motor parameters and variables, are given. It is shown that estimation is difficult during high-speed operation, because estimated becomes sensitive to errors in motor electrical parameters and variables, as the input excitation frequency (speed) increases. A new estimation scheme for the purpose of monitoring the temperature in steady state is proposed. Experimental results on a line-connected induction machine verify the validity of the proposed method and the analysis. Index Terms—Induction motor, rotor resistance estimation, stator resistance estimation, temperature estimation, thermal model, thermal protection.

I. INTRODUCTION

T

HERMAL overheating and cycling degrades the integrity of the organic materials used for stator winding insulation, resulting in acceleration of thermal aging. Gradual deterioration of insulation leads to insulation failure, which eventually causes motor failure. This makes thermal monitoring one of the fundamental protections required for induction motors. Nowadays, motor thermal protection relies on thermal devices (bimetallic strips, eutectic melting alloys), or on microprocessor embedded thermal models, which are based on the thermal heat transfer model of the induction machine. Thermal devices and models, which assume fixed thermal characteristics of the motor, are not capable of providing sufficient thermal protection since they have no means of giving a correct temperature estimate when the thermal characteristics change [1], [2]. The estimate of the can be used as an alternative, and stator winding resistance . more direct measure of stator winding temperature Manuscript received May 12, 2000. This work was supported by Eaton Corporation Innovation Center. S.-B. Lee, T. G. Habetler and R. G. Harley are with the Department of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail: [email protected]; [email protected]; [email protected]). D. J. Gritter is with the American Superconductor Corporation, West Allis, WI 53214 USA (e-mail: [email protected]). He is also with the Eaton Corporation, Milwaukee, WI 53216 USA. Publisher Item Identifier S 0885-8969(02)01508-5.

Resistance-based temperature estimation (RTE) offers many advantages over conventional thermal model-based temperature estimation (TMTE) since RTE uses , which is a direct indicator of stator temperature. The success of RTE, therefore, depends on the accuracy of the stator resistance estimate. There : namely induction maare two approaches for estimating estimation and signal injection-based chine model-based estimation. The proposed methods for these approaches are introduced and compared, but due to the invasive nature of the signal injection approach, the rest of this paper focuses on estimation based on the induction machine model. estimation and its sensiThe feasibility of model-based tivity to errors in machine parameters and variables, are evaluated in this paper. It is shown that the inherent limitation of estimation is its sensitivity to errors in mamodel-based chine parameters, variables and measurements when the excitation frequency (speed) of the machine is high. This paper also proposes a method for minimizing the above errors in estimating in steady both the stator resistance and the rotor resistance state for the purpose of temperature monitoring. The proposed estimation scheme and sensitivity analysis are verified with experimental results on a line-connected 5 hp 4-pole induction motor. II. STATOR WINDING TEMPERATURE MONITORING Temperature rise in the stator winding is caused by power loss inside the machine in which the main contribution comes from the current flowing through the stator winding. The heat generated in the stator winding is proportional to the frequency and the square of the magnitude of the stator current. Other sources of heating include power loss in the rotor conductors, stator core loss, and mechanical losses. There are several conditions under which the temperature rises above the maximum specified temperature: 1) transient overload conditions, 2) running overload conditions, and 3) abnormal cooling situations [1], [2]. Transient overload conditions include motor startup, stall, and jam. Under transient overload conditions, the stator current is typically between two to ten times the full load current, bringing the stator winding to its limiting temperature within a few seconds. Running overload conditions occur when the motor is overloaded and operates at 1–2 times the rated current. Under this condition, the temperature increases or decreases gradually with a time constant that is large compared to the motor mechanical or electrical dynamics.

0885–8969/02$17.00 © 2002 IEEE

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In addition to the above conditions, there are emergency or abnormal situations when the cooling of the machine is obstructed by a broken cooling fan or accidentally blocked air vents, which leads to rapid motor failure.

A. Thermal Model-Based Temperature Estimation (TMTE) Most of the motors used in industrial applications rely on electromechanical or thermal devices for protection in the overload range. These devices are characterized by an overload class, which is the time in seconds that it takes the device to trip at six times the rated current [2]. Thermal devices provide low cost protection of the stator winding and have been used for many years. However, these devices have limitations because the thermal element does not emulate the thermal characteristics of the motor accurately. Therefore, these devices are subject to false tripping or under-protection. Recently, software based thermal protection, which is based on a thermal heat transfer model of the motor, is being provided as a standard feature of some motor drives [1]. In this method, the power loss inside the machine is calculated based on terminal measurements, and temperature at specific locations of the machine are estimated based on a thermal model that represents the heat flow inside the machine. TMTE provides a more than traditional overload reliable and accurate estimate of relays. It also allows the user to have greater flexibility in responding to overload conditions, since there are situations when protection of the entire process is more critical than the motor itself. However, the TMTE method suffers from the following drawbacks. • The thermal model assumes fixed parameters although they vary under the following conditions. — The thermal time constant changes significantly under abnormal cooling situations such as a broken cooling fan, blocked vents, or obstruction or leakage in the cooling duct. — The thermal time constant of the stator winding is a function of speed because the effect of the cooling fan is proportional to its speed. — The heating and cooling time constants are different. — The thermal resistance changes when the cooling fins of the motor are clogged. and are constant. How• It implicitly assumes that is approximately 0.75–1.7 times ever, the variation of is even larger its nominal value, and the variation of because of its strong dependency on than that of the frequency [6]. • At least one temperature sensor is required in order to obtain an absolute temperature estimate. Unless these drawbacks are compensated for, an error will result in the estimated temperature. The value of the error can be acceptable in some cases, but becomes too large when an abnormal cooling situation occurs. This will lead to rapid motor failure and there is no means of detecting this when using the thermal model.

B. Stator Resistance Based Temperature Estimation For small induction machines 50 hp , the maximum temperature limit of the stator is reached before that of the rotor (stator limited) in both transient and running overload condi100 hp are stator tions, whereas large induction machines limited under running overload conditions, and rotor limited under transient overload conditions [3]. In either case, the stator winding temperature must be monitored for thermal protection. Once the stator resistance is estimated, the stator temperature can be calculated using

(1) represents the reference temperature of the stator C , , are the resistances at temperature , , respecC. tively, and is the temperature coefficient of resistivity can also be calculated from the esThe rotor temperature timated , using a relationship similar to (1), and taking skin effect into account. is a direct indicator of , RTE provides certain Because advantages over TMTE. First of all, RTE provides a more accan be escurate estimate of the temperature than TMTE if timated accurately, since it is possible to respond to all of the situations where the thermal model parameters change. This is is a direct indicator of , whereas TMTE calculates because indirectly using terminal measurements and predetermined thermal parameters based on experimental data. In contrast to TMTE, the temperature rise due to abnormal cooling situations can be detected by RTE. The RTE method is also a software-based method that uses a microprocessor, so it carries all the advantages of the TMTE method such as networking capabilities and flexibility in responding to overload conditions. Furthermore, RTE does not require a temperature sensor for estimation of the absolute temperature. In addition, the thermal time constant information can be exestimate, and this can be used for monitoring tracted from the the condition of the overall motor cooling system [1], if combined with a trend analysis. Again, this is not possible if TMTE is used because a fixed thermal time constant is assumed. III. STATOR RESISTANCE ESTIMATION METHODS The key to success of the RTE method is an accurate esti. Most of the proposed estimation schemes are mate of intended for either improving the performance of field oriented drives [4]–[6], or obtaining a better estimate of shaft speed for speed sensorless control [10]–[12] at low speed. This is because most of the methods used for achieving field orientation, or estimating speed, are based on the induction machine model and must therefore be known. There are not the variation of estimation scheme for the many publications that propose an purpose of thermal monitoring [13], [14]. The two approaches estimation, model-based estimation and signal injecfor estimation, are summarized and evaluated in this tion-based section.

LEE et al.: EVALUATION OF MODEL-BASED STATOR RESISTANCE ESTIMATION

A.

Estimation Based on the Induction Machine Model

estimation provides a Induction machine model-based ; however, it has been obnoninvasive way of estimating served in [7]–[9], [15] and [16] that it is very difficult to obtain when using the induction machine an accurate estimate of is poorly estimated model. For example, [15] states that from the steady state induction machine model from available measurements, and that this phenomenon has not been fully estimation explained. In [16], it is observed that separating from estimation of other parameters leads to better behaved estimates, and the authors state that they are working toward is understanding the reason. References [7]–[9] state that is included in the parameter estimated with poor accuracy if vector in recursive least square (RLS) estimation. The phenomestimation has, enon of the poor accuracy in model-based therefore, been empirically observed in many publications, but the reasons have not been explained. Because of the difficulty , it was suggested in [10] and [13] that of estimating could be obtained from the estimate of , assuming that the and is constant. If this is assumed for ratio between -based temperature monitoring, then the estimated is no longer a direct indicator of temperature and will not provide the has a strong advantages listed in Section II. Furthermore, dependency on rotor frequency, especially for NEMA class B is not a function of rotor frequency. The and C designs, but is due to both the temperature and frequency of variation of estimation. the rotor, making it inappropriate for esOn the other hand, successful results of model-based timation are shown in [4]–[6] and [10]–[12] for improving field orientation performance or speed estimation accuracy in the low speed range. In stator flux field oriented drives, the estimate of the stator flux linkage is obtained by integrating the stator voltage equation, given by

(2) , are the stator voltage and current vectors, and where is the estimated stator flux linkage vector. This creates a ), since the term is a nonproblem at low speed (low estimate depends negligible term, and the accuracy of the estimate. In [4], the estimate is on the accuracy of the calculated from the rotor flux linkage estimate obtained from the rotor voltage equation when the motor is operated at low based on (2). At high speed, and it is used for estimating estimate is calculated using (1) and the estispeed, the is mate obtained during low speed operation. In [5] and [6], and the estimated from the error between the measured command that corresponds to the flux and torque commands for is updated only during low direct torque control. In [4]–[6], speed operation, and excellent tracking capability of the estimators is shown in the results. In speed estimation schemes based on the induction machine becomes relatively large at model, the term that includes low speed making the accuracy of the speed estimate dependent on . In [10] and [11], Lyapunov’s direct method is used for and based on the error beobtaining an update rule for

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tween the measured and estimated . A mutual model reference adaptive system (MRAS) approach for estimating , , is proposed in [12]; the error between the interchangeand able reference and adjustable models that are derived using the stator and rotor equations, respectively, is used for tuning the three quantities. The experimental results shown in [10]–[12] estimators work well in the low verify that the proposed speed range. In [4]–[6] and [10]–[12], the estimator performance is only verified in the low speed range, and the proposed schemes are is only applicable to field oriented drives [4]–[6], [12]. If to be used for stator temperature monitoring, a more general estimation that is successful over the entire speed method for range, and is independent of the motor control method, is required. B.

Estimation Based on Signal Injection

estimation problem is to Another approach to solving the by injecting a signal derive additional models for estimating on-line. One of the proposed methods is to inject a dc bias into the stator supply voltage and to use the dc components of the [8], [14]. Anvoltage and current measurements to calculate other method is to use the zero sequence stator voltage equation [9], whereby the neutral of a Y-connected infor estimating duction machine is connected to the center of the dc supply so that the current has a zero sequence component. Although these methods [8], [9], [14] are capable of giving a more reliable estimate of , they are invasive methods that disturb the motor esperformance to a certain degree. The dc injection based timation is independent of the speed and motor parameters, but induces negative torque and causes torque pulsation. The zero sequence method injects zero sequence and/or triplen harmonic current components that will result in additional heating of the winding. Because of its noninvasive nature, only the induction estimation method is considered furmachine model-based ther. IV. SENSITIVITY ANALYSIS OF MODEL-BASED

ESTIMATION

It can be concluded from the prior research that, in general, from the it is very difficult to obtain an accurate estimate of induction machine model except when the motor is operated at low speed. This phenomenon has been empirically observed, but not fully explained. This section reviews those problems and presents a thorough physical and analytical explanation of the estimation sufphenomenon. It is shown that model-based fers from sensitivity to the errors in machine parameters and estimavariables as the speed increases, independent of the tion scheme. In the following analysis, it is assumed that the stator voltage, stator current, rotor speed, and stator input electrical frequency are known. It is also assumed that the magnetizing and leakage inductances are known and constant, and that is being estimated. In practical situations, these assumptions are not entirely valid since it is difficult to keep track of the exact values of the parameters, and there are situations where the speed cannot be measured. Nevertheless, these assumptions enable the paper to focus solely on the stator resistance estimation problem.

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A. Analysis Based on the Induction Machine Steady State Equivalent Circuit The steady state equivalent circuit of the induction machine can be used for a simple and intuitive analysis of parameter senestimation. The stator winding resissitivity of model-based tance can be obtained from the steady state equivalent circuit, as shown in (3), if the measurements of the voltage phasor , , , are current phasor , speed and the values of , available. (3) , , are the magnetizing and the stator and rotor is the input electrical freleakage inductances, respectively, quency, is the slip, and denotes a parallel connection. When is large, as in line-connected machines, is negligibly small compared to the stator per phase input impedance of the . Therefore, it is difficult to determine from (3) machine using terminal measurements, because the value of estimated becomes very sensitive to errors in measurements and , an accurate estimate parameters. For a good estimate of is required because an error in is amplified since of it is being divided by the slip , which has a small value. , , and Moreover, accurate values of the inductances and accurate measurements of the stator voltage, current and rotor speed are also required for obtaining a good estimate of , as can be seen in (3). This gives an intuitive explanation of in the high-speed range. It will the difficulty in estimating be shown in Section IV-B that even small errors in the machine estimate parameters or variables cause a large error in the at high-speed. remains When the speed decreases with constant V/Hz, is scaled down the same whereas the rest of the impedance by the decreasing frequency. Therefore, the relative magnitude compared to increases, making the estimate less of sensitive to errors in other parameters. This explains the accurate estimates obtained in the low-speed range in [4]–[6] and [10]–[12]. B. Analysis Based on the Induction Machine Dynamic Equations The dynamic equations of the induction machine can be expressed in an arbitrary reference frame as [18] (4) (5) (6) (7) is the rotor current vector. Among (4)–(7), the only where is (4), the stator voltage equation. All equation that includes estimation methods [4]–[7], [10]–[12], of the model-based is the parameter [15]–[17] are based on this equation, since being estimated. If it is assumed that all the other machine pavalue would be esrameters are known, then the estimated sentially the same, independent of the method used in finding from (4)–(7), because the same information is estimated

from the same set of equations [(4)–(7)] using the same measurements . Update Rule for Sensitivity Analysis: In order to focus 1) the present discussion solely on the stator resistance estimation problem, it is assumed that the rotor resistance is known. In this case, in the stationary reference frame, the rotor flux linkage estimate can be obtained by integrating (8), and using this result, the stator flux linkage estimate can be estimated from (9), where ; finally, can be obtained using (10). Equations (8) and (9) can be derived by combining (5), (7) and (6), (7), respectively, and (10) can be obtained by rearranging is only updated the -axis equation of (4). When using (10), , has a value large enough to avoid when the denominator, singularity problems. It should be noted that (8)–(10) form an for the purpose of analyzing the sensitivity update rule for of model-based estimation to uncertainties in the motor, and is not an update rule that can actually be used for updating since it is assumed that is known. It should be noted here estithat the results of the following analysis applies to all mation schemes based on the induction machine model shown in (4)–(7). (8) (9) (10) is a result of taking Equation (10) shows that estimating and , and dividing the difference between the two terms, estiit by the current, . Therefore, the sensitivity of the and , depends on the mate, due to uncertainties in terms term. When the machine is operating relative size of the term in (10) is small at high speed or is line-supplied, the and terms. In order to illustrate this, the compared to three terms of (10) are plotted separately in Fig. 1 by simulating a line-connected 3 hp 4-pole induction motor for rated load. This simulation is repeated at low speed (Fig. 2), where the input frequency is 10 Hz, assuming that the ratio between stator voltage and frequency is constant. The results of Figs. 1 and 2 show that , compared to the other terms in the relative magnitude of (10), changes significantly, and it is predictable that estimating would be more sensitive to errors in and at high and are large and almost equal. Even a speed, where and , therefore, results in an unacceptsmall error in at higher speed. Possible ably large error in the estimate of estimate are evaluated below. sources of error in the Due to Errors in Parameters 2) Sensitivity of Estimated , , , : In Section IV-B-1, it was assumed that all the machine parameters (except ) are known, but in practice this is not true. In addition, values of currents, voltages, speed, and flux linkages are needed, and while some can be measured, flux linkage is estimated because it is difficult and impractical using (4), an estimate of the stator to measure. To estimate or rotor flux linkage is therefore required. Equations (8) and (9) show that estimating the stator or rotor flux linkage requires in, formation of all the electrical parameters of the machine


Fig. 1. Plot of R

i

, v , and p

terms in steady state at 60 Hz.

Fig. 2. Plot of R

i

, v , and p

terms in steady state at 10 Hz.

, , . An error in the estimated stator flux linkage is amplified by the input electrical frequency due to the differentiation operation in (10). Therefore, it is expected that even a small error in the estimated stator or rotor flux linkage, caused , , , , by an error in any of the motor parameters will cause a large error in estimated , especially at high speed. estimation, due To illustrate the sensitivity of model-based , , and , (8)–(10) are simto errors in parameters , ulated for a 3 hp test motor. Figs. 3 and 4 show the result of error for values of , , , and ranging estimated from 90% to 110% of their nominal values for 60 and 10 Hz operation, respectively. To focus on the effect of parameter error, it is assumed in the simulation that the error in estimated flux linkages are only due to the errors in the parameters. Figs. 3 and estimate is 4 show that in both the 60 and 10 Hz cases, the and it is therefore critical to continuously most sensitive to caused by changes in temperature update the variation of or rotor frequency. It is also important to know the inductance can values with high accuracy, since even a small error in cause an unacceptable error in , particularly when the motor is operating at high speed. Due to Errors in Estimated 3) Sensitivity of Estimated Flux Linkage: In addition to errors in machine parameters, er-

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Fig. 3.

Error in R due to error in parameters R , L , L , and L

at 60 Hz.

Fig. 4.

Error in R due to error in parameters R , L , L , and L

at 10 Hz.

rors in estimated stator or rotor flux linkage can be caused by the integration used for estimating the flux linkages. In many induction motor applications [4] that involve estimation of parameters is usually updated by integrating (8) using or flux linkages, Euler’s method for simplicity, because it is a first-order approximation of the Taylor series. When numerical integration is performed, the result becomes more accurate as the step length of integration is decreased. For practical sampling rates used in motor applications, the estimated rotor flux linkage using (8) contains an error that depends on the step length of integration, even if the parameters and measurements are precise. In other words, the integration operation itself causes an error in the rotor flux linkage estimate. Figs. 5 and 6 show the error in estimated when the error in the magnitude of estimated is between 1 and 1% of its actual value, and when the error in the phase is between 0.01 rad and rad at 60 and 10 of Hz, respectively. These results confirm that an error in estimated rotor flux linkage has a much smaller impact on the accuracy of at low frequency than at rated frequency. estimated Error: In addition to errors in 4) Additional Causes of parameters and estimated flux linkages, the accuracy of the mea, , and , also have a large impact on obsurements

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Fig. 5.


Error in R due to error in estimated rotor flux linkage at 60 Hz.

5) Summary: From the results shown in Figs. 3–6, it can be concluded that model based estimation of the stator resistance is a difficult problem to solve when the speed is high. With the errors of parameter, measurement, and integration combined, the error of can be even worse than those shown in Figs. 3–6. This is an inherent limitation that applies to all model-based estimation schemes. In cases where all the electrical parameters are simultaneously estimated [7], it is, therefore, even more difat high speed, because all ficult to obtain a good estimate of estiof the estimated parameters must be precise. All of the mation schemes, introduced in the references that are described in Section III, show good experimental results in the low speed range, since errors in the inductance parameters are not critical at low speed. If the stator winding temperature is to be monitored using estimated from the dynamic equations of the machine model, accurately at high speed unless the it is difficult to estimate parameters and measurements are accurate. If the machine is applied to run only in the low speed range, the performance estimator that uses model-based estimation is exof the pected to be superior to the TMTE method of Section II. A posestimation over the entire speed range, sible solution for is therefore to use a hybrid estimator in which a model-based method is used during low speed operation, and the dc injection method is used during high speed operation. This will provide a good estimate of the stator resistance over the entire speed range, although torque pulsation due to a dc bias will be present during high-speed operation. However, since signal inestimation degrades motor performance, a new jection-based error due to simple model-based method that minimizes the machine uncertainties is proposed in Section V. V. STATOR AND ROTOR RESISTANCE ESTIMATOR

Fig. 6.

Error in R due to error in estimated rotor flux linkage at 10 Hz.

taining a good estimate of , especially at high speed. This is because an error in measured stator voltage affects the estimated directly in (10), and an error in stator current or speed affects the accuracy of estimated flux linkage. There are additional problems under light load and saturation, estimation for stator temperature when using model-based monitoring. In both the 10 and 60 Hz cases, the accuracy of affects the accuracy of the most, among all the parameters, as shown in Figs. 3 and 4. Unfortunately, it is difficult to estiwhen the motor is lightly loaded. The reason is similar mate estimation problem. As can be seen from (5), to that of the term bewhich is the only equation that includes , the comes smaller and approaches 0, as the load decreases. Thereis difficult to estimate accurately from the model, before, becomes very sensitive to errors in other parameters as cause the load (rotor current) decreases. However, this is not a major problem for -based thermal monitoring since the temperature does not rise significantly under light load conditions. Another estimation is when the machine is concern in model based operating under saturation. This causes a significant decrease in , which will result in an estimate of with a large error, particularly during high-speed operation.

The analysis in Section IV shows that the accuracy of estiis significant for obtaining an accurate estimate of mated . Thus, a simple method for estimating both and in and estimasteady state is proposed for the purpose of tion. Considering that the temperature (resistance) variation of and estimathe stator and rotor is slow, a steady state and monitoring is sufficient for motor tion scheme for protection purposes. The update rule can be derived using the induction machine dynamic (4)–(7). In the synchronous refer, and assuming steady state ence frame , and that the current vector is aligned to the -axis , (4)–(7) reduce to (11) (12) (13) (14) where by eliminating

. These equations can be further reduced and to yield (15) (16)


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TABLE I PARAMETERS OF TEST MACHINE

Fig. 7. Overall structure of R and R estimator.

(17) (18) and vary with temperature, the update rule Since both must be independent of . Therefore, (15), (17), and for (18) are used for deriving an update rule for . By eliminating from these three equations, expressions for estimates of and , that are independent of , can be derived as

(a)

(19) (20)

can be used to calculate , as previously menEstimated are derived based on the tioned. Similar update rules for same procedure of aligning the voltage or current vector to a synchronously rotating axis in [13] and [17]. In addition to (20), can be derived using (16), (18), (19) and an update rule for (20) as (21) and estimator for each The overall structure of the sampling interval is shown in Fig. 7. Since the proposed new method is used in steady state, an error in the intermediate flux in this case, is caused only by linkage estimate, which is is also errors in the machine parameters. Furthermore, since estimate is due only to the inbeing updated, the error in the , , and , provided that the meaductance parameters, surements of voltage, current, and speed are accurate. The poor due to the difficulty in estimation under light accuracy in load conditions is not a problem since the temperature does not rise significantly. is much It is shown in Figs. 3 and 4 that the accuracy of and for obtaining a good esmore important than that of using timate of . Therefore, the accuracy of the estimated . Although it is assumed (21) depends on the preciseness of is constant in the derivation of (19)–(21), actually that varies due to magnetic saturation. In some applications where field oriented drives are used to control the flux linkage to be can be tuned depending on the flux linkage refconstant, varies due to magnetic saturation, eserence. In general, must be pecially when the motor is overloaded, therefore, tuned at the operating point of the motor. A possible solution

Fig. 8.

(b) Estimated R and R using the proposed method.

for tuning during saturation is to use a method for obtaining in steady state using the magnetization curve [19]. VI. EXPERIMENTAL RESULTS The proposed new estimation scheme was tested on a 5-hp 4-pole induction motor, where the motor ratings and parameters given by the manufacturer are shown in Table I. The supply frequency (60 Hz) was chosen because this is when model-based estimation is most sensitive to parameter errors. Voltage, and current, and speed measurements and calculations of were performed at 5 kHz in steady state. Estimated and were low pass filtered using a fourth order digital elliptic filter, to eliminate high frequency noise. and estimators Fig. 8 shows the performance of the shown in at different loads. The average values of estimated Fig. 8(a) are 0.903 , 0.85 , and 0.34 at 80% load, half load, and no load, respectively, where the value at full load, given by the manufacturer, is 0.987 . The rotor of this machine is a has a strong frequency deNEMA class B design; therefore, estimate at no load was explained pendency. The error in the term in (6) being small in Section IV, and is due to the due to small rotor current when the machine is lightly loaded. shown in Fig. 8(b) are 1.493 , The average of estimated 1.487 , and 5.95 at 80% load, half load, and no load, respectively, where the value given by the manufacturer is 1.4865 . The large error at no load is caused by the error in (esis very sensitive to error in at high speed). The timated

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(60 Hz), which is when model-based estimation is most sensitive to parameter errors. Experimental results have verified the is predetermined validity of the new scheme provided that with good accuracy. The proposed estimation scheme can also be extended to motor control problems where estimation of the stator and/or rotor resistance is required. Resistance-based thermal monitoring is expected to yield more reliable thermal protection compared to conventional thermal model based monitoring. However, further study into estimation method that is not only insensitive developing an to uncertainties in the motor parameters, but also does not influence the motor performance, is necessary for further improving the reliability of resistance-based thermal protection. REFERENCES Fig. 9. Average of estimated R and R with error in inductance.

estimates of both and are accurate when the machine is , , and loaded, provided that the electrical parameters are known with high accuracy. and at 80% load Fig. 9 shows the average of estimated for a line-connected induction motor, when errors in parameters , , and are introduced simultaneously. The values of , , and are intentionally varied from 90–110% of their and nominal values to observe their effects on the estimated . The estimator is clearly insensitive to errors in the paestimate matches that rameters. The trend of the error in the of the analysis for 60 Hz excitation shown in Fig. 3.

VII. CONCLUSION This paper has shown the possibility of using model-based estimation for stator winding temperature estimation. The advantages of resistance-based temperature estimation (RTE), over conventional thermal-model-based temperature estimation (TMTE), have been reviewed. In addition to providing an accurate temperature estimate that responds to changing thermal conditions, RTE is capable of detecting abnormal cooling conestimate is further processed. ditions if the The main contributions of this paper are the analysis and estimation for stator temperature evaluation of model-based estimation scheme. The monitoring, and the proposed new reason for the phenomenon of poor accuracy in model-based estimation during high-speed operation has been fully explained estimain this paper. It has been shown that all model-based , tion methods are very sensitive to errors in parameters, , , , intermediate estimate of flux linkage, and measurements during high-speed operation. Understanding the inherent estimation under high-speed and limitation of model-based light load conditions is expected to be very helpful for all inducestimate is needed. tion machine applications where the estimaBased on the sensitivity analysis of model-based estimation scheme, that minimizes the error in tion, a new caused by uncertainties in the measurements and motor parameters, has been proposed for temperature monitoring in steady state. The proposed scheme has been tested at rated frequency

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Sang-Bin Lee (S’99) was born in Korea in 1971. He received the B.S. and M.S. degrees in electrical engineering from Korea University, Seoul, South Korea, in 1995 and 1997, respectively. He is currently pursuing the Ph.D. degree at the Georgia Institute of Technology, Atlanta. His research interests include diagnostics and control of electrical machines.

Thomas G. Habetler (S’82–M’83–SM’92–F’02) received the B.S.E.E. and M.S. degrees in electrical engineering from Marquette University, Milwaukee, WI, and the Ph.D. degree in electrical engineering from the University of Wisconsin, Madison, in 1981, 1984, and 1989, respectively. From 1983 to 1985, he was with the Electro-Motive Division of General Motors, LaGrange, IL, as a Project Engineer. While there, he was involved in the design of switching power supplies and voltage regulators for locomotive applications. Currently, he is a Professor of Electrical Engineering at Georgia Institute of Technology, Atlanta. His research interests are in switching converter technology and electric machine protection and drives. Dr. Habetler was Corecipient of the 1989 First-Prize Paper Award and the 1991 Second-Prize Paper Award of the Industrial Drives Committee, and the 1994 Second-Prize Paper Award of the Electric Machines Committee of the IEEE Industry Applications Society. He serves as the President of the IEEE Power Electronics Society and Chair of the Industrial Power Converter Committee of the IEEE Industry Applications Society.

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Ronald G. Harley (M’77–SM’86–F’92) received the M.Sc.Eng. degree in electrical engineering from the University of Pretoria, South Africa, and the Ph.D. degree from Imperial College, London, U.K., in 1965 and 1969, respectively. In 1971, he was appointed Professor of Electric Machines and Control at the University at Natal, Durban, South Africa. He was a Visiting Professor at Iowa State University, Ames, in 1977, Clemson University, Clemson, SC, in 1987, and the Georgia Institute of Technology, Atlanta, in 1994. Currently, he is the Duke Power Company Distinguished Professor of Electrical Engineering at the Georgia Institute of Technology, Atlanta. His areas of research include power system dynamics, electrical machines, power electronics, and control of ac variable-speed drives. Dr. Harley is a member of the IEEE Power Engineering Society and Industrial Applications Society (IAS). He is also a fellow of the British IEE and SAIEE, South Africa.

David J. Gritter received the B.S.E.E. degree in electrical engineering from Michigan Technological University, Houghton, in 1973. Currently, he is a Senior Technical Fellow of the Power Electronics Business Unit of American Superconductor Corporation, West Allis, WI, where he is responsible for the simulation, design, and specification of power conversion systems and their associated control algorithms. He began his career with Eaton’s Corporate Research Group, Milwaukee, WI, where he was involved in product development for the Electric Drives Division and DOE funded electric vehicle programs. After moving to the Electric Drives Division in 1978, he was the Principal Designer of several adjustable frequency drive products, which included “clean power” multipulse rectifiers and four-quadrant drives using active PWM rectifiers. He also participated in motor and magnetic circuit design activities for the division. He was employed by Eaton Corporation as a Principal Engineer with a specialization in power conversion. He has over twenty years experience in the design and control of static inverters for power quality and motor drive applications. Moving back to Corporate Research in 1998, he participated in Cutler-Hammer’s power quality and electric machinery diagnostics programs.