Rotor Temp

34

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004

Determination of the Absolute Rotor Temperature of Squirrel Cage Induction Machines Using Measurable Variables Martin Maximini and Hans-Jürgen Koglin

Abstract—This paper presents a new method for observing the rotor temperature of high-power squirrel cage induction machines using measurable variables. The method is based on the fact that the rotor resistance depends on the actual rotor temperature. The main problem is to separate the changes in the rotor resistance due to temperature and skin effect. By comparing the input impedance with a known circle diagram measured during commissioning, it is possible to calculate changes in the rotor temperature. Further analyses also make it possible to obtain the absolute rotor temperature at any time. Results of procedure testing are demonstrated through computer simulations and evaluations of data recorded on a 75-kW test machine. Index Terms—Differential measurement, induction machine, rotor temperature, thermal protection.

I. INTRODUCTION

D

UE to their high reliability and their robust construction, induction machines with squirrel cage rotors are installed in many areas of industrial practice. In the past decade, research in protection techniques and instrumentation technology have brought some new methods for the measurement of protectionrelevant variables, their link to instrumentation and control technology and, finally, their analysis. Effective supervisory systems have two positive effects: the lifetime of the machine can be prolonged and the operating range of the machine and of the following process can be expanded. Still, a critical variable for induction machines, in particular for those of high power, is the rotor temperature. Direct measurement of the rotor temperature requires considerable effort and it is not very reliable. During the last few years, a number of methods for calculating the rotor temperature have been published. Prediction procedures calculate the actual rotor temperature by using thermal models [1]–[5] or neural networks [6], [7], whereas other procedures use the effects of the rotor temperature on directly measurable variables [8]–[12]. Although some of these ideas are very innovative, they still do not satisfy the practical requirements. The reason for this is on one hand the lack of general applicability of some methods or the complexity of measurement, and, on the other hand, the sensitivity to disturbances or the non-observance of nonlinear effects. The main problem in observing the rotor temperature in measurable variables is to separate the effects due to skin effect and temperature. Thus, even today, a primitive interlocking rule is implemented in most protection devices. The Manuscript received January 13, 2003. The authors are with the Saarland University, Saarbrücken 66123, Germany. Digital Object Identifier 10.1109/TEC.2003.821833

Fig. 1.

Equivalent circuit diagram of an induction machine.

corresponding algorithm was developed on the basis of a very simple first-order thermal model. This kind of modeling is quite conservative, so that the machine and the process are not used optimally. At the Institute of Power Engineering at the Saarland University, a new method for observing changes in the rotor temperature using measured variables has been developed. This new method, called compensation method, was published first in [13]. In Section II, the principle of this method and some new results are presented using a simulation model and data recorded on a 75-kW test machine. Subsequently, a new algorithm using the results of the compensation method for calculating the absolute rotor temperature is explained and the results obtained are presented.

II. COMPENSATION METHOD A. Principle The idea is based on the fact that during the starting operation each induction machine has its own typical impedance circle diagram. This diagram is the fingerprint of the machine. The target of this method is to determine the actual heating status of the rotor by evaluating changes in this circle diagram. Fig. 1 shows the well-known equivalent circuit diagram of the induction machine. depends on the It is obvious that the input impedance values of the model parameters, on the temperature of stator and rotor , and on the slip . An increase in the rotor has the equivalent effect on the input impedance temperature as a reduction of the slip . This fact gives the presented method the name compensation method and it is used in the following

0885-8969/04$20.00 © 2004 IEEE

Authorized licensed use limited to: VELLORE INSTITUTE OF TECHNOLOGY. Downloaded on March 17, 2009 at 05:34 from IEEE Xplore. Restrictions apply.

MAXIMINI AND KOGLIN: DETERMINATION OF THE ABSOLUTE ROTOR TEMPERATURE

35

Fig. 2. Schematic structure of the test machine. TABLE I INDUCTION MACHINE NAMEPLATE DATA Fig. 4.

Block diagram of the compensation method.

In more detailed form, (1) can be rewritten as follows:

(2) is a reference temperature (generally ). In (2), The absolute difference in the electrical rotor frequency between the points and can be neglected, so the following holds: (3) Thus, the parameter is omitted from (2). This implies that the skin effect has no influence on the method. Using the as defined in (4), (2) can be rotor differential temperature converted into (5) (4) Fig. 3.

Principle of the compensation method.

(5) manner: by having two impedance circle diagrams with additional information about the slip, the rotor temperature difference between points of identical slip can be determined. The first impedance circle diagram is called the reference diagram (ref) and the other the measurement diagram (meas). Fig. 2 shows the schematic structure of the test machine. Machine nameplate data are summarized in Table I. The principle of the compensation method is given in Fig. 3: There are the measured impedance circle diagrams of two starts of the test machine presented. The impedance phasor moves clockwise during the starting operation. The points of the measurement diagram and of the reference diagram have idenbut not identical phasors. Because tical slip the rotor temperature during the measurement start was about hotter than during the reference start, the point corresponds to point of the reference. How to use this qualiis shown tative effect to quantify the temperature difference in Section III. B. Derivation The rotor temperature difference between the points with identical slip (points and ) can be evaluated as follows: the input impedance and the rotor resistance are equal at the points and (1)

It is obvious that the calculated rotor differential temperature depends on the measured slip , the temperature coefficient of the rotor material , and the reference rotor temperature . The reference rotor temperature has no essential influence on the differential temperature. This will be shown in the next paper section. Another disturbance, the stator temperature , can be eliminated by using an impedance on which the stator has no influence [see (6) and Fig. 1]. The stator resistance and the stator temperature can easily be measured (6) In Fig. 4, the realization of the compensation method is summarized. During commissioning—for a reference start—the significant variables (slip, input impedance, and stator temperature) are recorded. These data can be called the fingerprint of the machine. Later, during operation, the correspondent measurement data are obtained. With the compensation method, these measurement data are compared with the fingerprint as already explained. The output result of the compensation method is the rotor differential temperature. C. Identification of a Simulation Model To compare practical and theoretical effects of the compensation method, it is necessary to have a simulation model of the test machine. For estimating the parameters of the equivalent circuit

Authorized licensed use limited to: VELLORE INSTITUTE OF TECHNOLOGY. Downloaded on March 17, 2009 at 05:34 from IEEE Xplore. Restrictions apply.

36

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004

Fig. 5. Measured and simulated impedance circle diagram.

Fig. 7. Influence of different reference rotor temperatures (left: theory, right: practice).

TABLE II RESULTS OF THE PARAMETER ESTIMATION

Fig. 8. Influence of the stator temperature (left: theory, right: practice).

Fig. 6.

Used reference rotor temperatures.

diagram of the test machine, a least square algorithm is used. The objective function is the minimum square deviation between the adjusted input impedance during a start measured and the model impedance [14]. The resistance of the stator can be measured directly. The results of the estimation with their 95%confidence-intervals are shown in Table II. Fig. 5 shows the measured impedance circle diagram and the impedance circle diagram of the identified model. The impedance circle diagrams are corresponding very well. This simulation model is used in Section II-D to compare theoretical and practical effects of the compensation method. D. Examinations of Different Influences First, the influence of the reference rotor temperature on the result of the compensation method is examined. Thus, the compensation method is tested with different reference rotor temperatures shown in Fig. 6. is the effectively measured reference rotor temperaand are the reference rotor temperatures ture, simulated for this examination. In Fig. 7, the results obtained by the compensation method are presented. Fig. 7(a) and (c) are the theoretical results obtained with the identified model, and Fig. 7(b) and (d) show the corresponding results using the measured input impedances. Temperatures and

Fig. 9. Influence of errors in the slip (left: theory, right: practice).

slip data are the same for the theoretical and the practical examinations; in both cases, the measured data were used. The indexes specify the used reference rotor temperature. It can be concluded that theory and practice correspond very well. The influence of the used reference rotor temperature on the result is not essential. The influence depends on the mechanical speed (i.e., slip) of the machine and on the size of the rotor differential temperature for theory and practice in the same manner. In Fig. 8, the influence of the stator temperature on the result of the compensation method is presented, in Fig. 8(a) the theoretical effect is seen, in Fig. 8(b) the practical effect, respecbeing designated, the differential temperature tively. With is calculated calculated with the adjusted impedances (6), with the original impedances, including the stator influences. Theory and practice show the same effect: the influence of the stator temperature diminishes with the mechanical speed. The last effect examined is the influence of errors in the slip on the compensation method. These results are shown in Fig. 9. The slip of the measurement is changed for one evaluation: the is changed from 50.018 to 50 Hz. It is electrical frequency

Authorized licensed use limited to: VELLORE INSTITUTE OF TECHNOLOGY. Downloaded on March 17, 2009 at 05:34 from IEEE Xplore. Restrictions apply.

MAXIMINI AND KOGLIN: DETERMINATION OF THE ABSOLUTE ROTOR TEMPERATURE

Fig. 11.

37

Thermal transfer function.

Fig. 10. Measured and calculated rotor differential temperature for different operating conditions.

visible that theory and practice correspond once again, errors in the electrical frequency (i.e., in the slip) show the same in: an effect fluence on the calculated differential temperature can only be observed in the range of higher mechanical speed. It can be summarized that all of the presented studies have shown that theory and practice correspond excellently and that the examined disturbances have no essential influence on the result of the compensation method. Finally, the compensation method is tested for different operating conditions of the machine. The machine must run under load, because running at no load, the rotor temperature is not observable in the input impedance. The results of the analyses are presented in Fig. 10. The evaluated start was a start with the motor initially at ambient temperature. Therefore, the rotor differential temperature during this time is about 0 . After start, a load application of 21 kW was made. Due to the machine runduring ning with rated speed, the rotor is cooling off by 50 16 min. After that, a load change to 69 kW was made and the rotor is warming up by 20 . Subsequently, a load change to 29 kW was made. It can be concluded that the presented method gives excellent results under all tested operating conditions of the machine. Only for a short period after load changes, differential temperature cannot be observed. This is due to the electromechanical transient reactions which are caused by these load changes. Under these conditions, the equivalent circuit diagram does not describe the machine. The method is applicable during steady states or quasi-steady states. If the absolute reference temperature is known in advance, it would be also possible to calculate the actual absolute rotor temperature by summation of the actual differential temperature and reference temperature at points of identical slip. In Section III, an algorithm for absolute reference temperature estimation is presented. The data measured during two similar starts represent the data basis of this algorithm. III. DETERMINATION OF THE ABSOLUTE ROTOR TEMPERATURE As shown in Fig. 11, the thermal transfer function in the Laplace-domain is the starting point of the algorithm for reference rotor temperature reconstruction. Here, the input variable which is proportional to is a current dependent power loss

Fig. 12. Algorithm for reference temperature reconstruction (a) Model parameter for the heating of the machine during the starting operation. (Stator temperature directly measurable) (b) Model parameter for the cooling of the machine during the steady-state operation, identified with the differential temperatures. (Rotor differential temperature from the compensation method).

the square of the stator current . The output variables are the ). stator and the rotor temperatures ( , The key idea of the algorithm is to estimate the parameters of by using the result of the compensation the rotor model . The stator model can be method and the stator model easily identified by means of the measured stator temperature. The principle of the algorithm for the reference rotor temperature reconstruction is shown in Fig. 12. It is assumed that the proportions of the model parameters for the heating of the machine during the starting operation and for the cooling of the machine during the steady-state operation are identical. For identifying the thermal models, a least square algorithm is used. In the next step, the dependency of the differential rotor temperature on the reference rotor temperature, given by (5) and in Fig. 7, can be used to estimate the reference rotor temperature. By combining the algorithm shown in Fig. 12 with the compensation method described in Section II, it is possible to obtain an algorithm for adaptive calculation of the reference rotor temperature. As already mentioned, the measured data of two similar starts represent the data basis of the algorithm. In Fig. 13, the principle of this adaptive reference rotor temperature reconstruction is shown. The compensation method is initialized with a random ref. The result of the compensation erence rotor temperature method, the differential rotor temperature , is used as an input

Authorized licensed use limited to: VELLORE INSTITUTE OF TECHNOLOGY. Downloaded on March 17, 2009 at 05:34 from IEEE Xplore. Restrictions apply.

38

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004

Fig. 15.

Fig. 13.

Principle for adaptive reference temperature reconstruction.

Measured and calculated absolute rotor temperature.

method. As an example, the result of such a calculation—using the differential temperature from Fig. 10—is given in Fig. 15. It can be concluded that it is possible to calculate the rotor temperature very exactly, the difference between the calculated and the measured rotor temperature averages less than 10 . IV. CONCLUSION

Fig. 14. Result of the adaptive reference temperature reconstruction k : iteration counter.

variable for the algorithm described in Fig. 12. The result of . This this procedure is again the absolute rotor temperature loop is repeated until the calculated rotor temperature does not change anymore. For testing the algorithm reliability, it is necessary to check whether the finally calculated rotor temperature is independent of the algorithm initialization. In Fig. 14, the results of two runs with different initializations of the reference temperature are presented. The first calculation (A) started with a reference temperature ramp from , the second calculation (B) started with a ramp 20 to 30 temperature from 20 to 200 . The simulations showed that the calculated rotor reference temperatures converge to the same result after three iterations, independent of the selected initial values (see Fig. 14). Thus, the fingerprint of the machine is complete and it is possible to calculate the absolute rotor temperature by adding the rotor reference temperature and the result of the compensation

In this paper, a new method for observing the rotor temperature using the input impedance, the slip, and the stator temperature of an induction machine is presented. In the first step, the temperature difference between the actual rotor temperature and a reference temperature is detected by using the rotor temperature dependency of the input impedance. This method is called compensation method. Because this method has the characteristic of a differential measurement, the main problem, separating the changes in the rotor resistance due to skin effect and temperature, can be solved. In the second step, the dependency of the result of the compensation method on the reference rotor temperature and the measured stator temperature are used in an algorithm for reference rotor temperature reconstruction. Here, the assumption was established that the proportions of the thermal stator and rotor model parameters for the heating of the machine during the starting operation and for the cooling of the machine during the steady-state operation are equal. By combining these two procedures, it is possible to adaptively reconstruct the reference rotor temperature. Thus, the absolute rotor temperature can be obtained by addition at any time. The methods are tested by simulations and evaluations of data recorded on a 75-kW test machine. In both cases, the efficiency of the methods is shown. REFERENCES [1] A. Eltom and N. Moharai, “Motor temperature estimation incorporating dynamic rotor impedance,” IEEE Trans. Energy Conversion, vol. 6, pp. 107–113, Mar. 1991. [2] A. Bousbaine, “Thermal modeling of induction motors based on accurate loss density distribution,” Elect. Mach. Power Syst., vol. 27, no. 3, pp. 311–324, 1999. [3] E. G. Egorov, V. S. Genin, and N. M. Mikhailov, “Microprocessor thermal-safety relay for induction motors with short-circuit rotor,” Russian Elect. Eng., vol. 68, no. 1, pp. 68–71, 1997. [4] M. S. Rajagopal and K. N. Seetharamu, “Transient thermal analysis of induction motors,” IEEE Trans. Energy Conversion, vol. 13, pp. 62–69, Mar. 1998.

Authorized licensed use limited to: VELLORE INSTITUTE OF TECHNOLOGY. Downloaded on March 17, 2009 at 05:34 from IEEE Xplore. Restrictions apply.

MAXIMINI AND KOGLIN: DETERMINATION OF THE ABSOLUTE ROTOR TEMPERATURE

[5] A. Boglietti, M. Lazzari, G. Luparia, and V. Hollo, “A simplified thermal model for the power derating prediction of variable speed self-cooled induction motor,” in Proc. Int. Conf. Elect. Mach., Espoo, Finland, Aug. 28–30, 2000, pp. 348–352. [6] R. Busch and S. Hilfert, “On-line bestimmung der temperatur von elektrischen maschinen mittels neuronaler netze,” ELEKTRIE, vol. 52, no. 1–2, pp. 56–61, 1998. [7] E. Aviolio and C. Dias, “Development of a thermal-electric mathematical model, to analyze and specify induction motors using artificial neural networks,” in Proc. Int. Conf. Elect. Mach., Espoo, Finland, Aug. 28–30, 2000, pp. 363–367. [8] B. Amin, “Principle of the direct determination of the temperature-dependant rotor and stator resistance of an induction motor,” Eur. Trans. Elect. Power, vol. 8, no. 1, pp. 69–71, 1998. [9] M. Schrödel, “Identifikation der rotortemperatur einer käfigläufer-asynchronmaschine,” E&I, vol. 105, no. 7/8, pp. 315–318, 1998. [10] O. V. Thorsen and M. Dalva, “Methods of condition monitoring and fault diagnosis for induction motors,” Eur. Trans. Elect. Power, vol. 8, no. 5, pp. 383–395, 1998. [11] C. Ghita and H. G. Schuster, “Short-circuit/overload protection of induction motors using a calorimetric method,” in Proc. 31st Int. Intell. Motion Conf., Nürnberg, Germany, 1997, pp. 317–321. [12] Th. Vetter, “Überwachung Und Prädiktion Des Erwärmungsverhaltens Einer ASM Mit Käfigläufer Mittels Parameterschätzung,” Ph.D. dissertation, Technical Univ. Darmstadt, Darmstadt, Germany, 1998. [13] M. Maximini, H.-J. Koglin, and M. Igel, “New method for rotor temperature estimation,” in Proc. Int. Measure. Confederation, Vienna, Austria, Sept. 25–28, 2000, pp. 393–398.

39

[14] S. Spannhake, “Eine Methode Zur Identifikation Der Parameter Der Asynchronmaschine mit Doppelkäfigläufer Zur Verlustleistungsberechnung,” Ph.D. dissertation, Berlin, T. Univ., Germany, 1994.

Martin Maximini received the Dipl.-Ing. and Dr.-Ing. degrees from the Saarland University, Saarbruecken, Germany, in 1995 and 2001, respectively. Currently, he is Senior Consulting Engineer in the Electrical System Consulting Group of ABB Utilities GmbH, Mannheim, Germany. He is responsible for the planning of power systems. His main research interests include reliability of power systems, protection, and electrical machines.

Hans-Jürgen Koglin was born in 1937. He received the Dipl.-Ing. and Dr.-Ing. degrees from the Technical University Darmstadt, Darmstadt, Germany, in 1964 and 1972, respectively. Currently, he is a Full Professor at Saarland University, Saarbruecken, Germany, where he has been since 1983. From 1973 to 1983, he was a Professor at Saarland University. His main research interests include the planing and operation of power systems and specially optimal MV and LV networks, visibility of overhead lines, state estimation, reliability, corrective switching, protection, and fuel cells.

Authorized licensed use limited to: VELLORE INSTITUTE OF TECHNOLOGY. Downloaded on March 17, 2009 at 05:34 from IEEE Xplore. Restrictions apply.