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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 2, FEBRUARY 2010

463

A Real-Time Thermal Model of a Permanent-Magnet Synchronous Motor

Georgios D. Demetriades, Member, IEEE, Hector Zelaya de la Parra, Senior Member, IEEE, Erik Andersson, and H? akan Olsson

Abstract—This paper presents a real-time thermal model with calculated parameters based on the geometry of the different components of a permanent-magnet synchronous motor. The model in state-space format has been discretized and a model-order reduction has been applied to minimize the complexity. The model has been implemented in a DSP and predicts the temperature of the different parts of the motor accurately in all operating conditions, i.e., steady-state, transient, and stall torque. The results have been compared with real measurements using temperature transducers showing very good performance of the proposed thermal model. Index Terms—Estimation, modeling, permanent-magnet (PM) machines.

I. INTRODUCTION

M

OTORS are one of the most important parts in energy conversion systems. Failure of the motor can result in failure of the whole system, and in most cases, the economical consequences are quite severe. Motors should be operated and deliver rated power within a speci?ed range of temperature rise without any risk for demagnetization of the magnets and/or stator winding failure. In order to avoid the aforementioned failures, different kinds of thermal protection sensors are used. The most common type of protection available is the positive thermal coef?cient (PTC) sensor. A PTC is a nonlinear resistance that increases dramatically at a certain temperature. This resistance can be measured, and hence, the motor can be stopped before the temperature rise exceeds the prede?ned threshold level. The disadvantage of this method is the inaccuracy as it can only be used as a warning or as a shutdown signal. A plethora of publication on thermal modeling of electrical motors can be found in the literature. Gerling and Dajaku [10] give a good overview on thermal modeling of electrical systems, and the most common equations for thermal analysis are presented. In [6], a water-cooled permanent-magnet synchronous motor (PMSM) has been modeled. Two thermal models are

Manuscript received March 31, 2009; revised June 10, 2009. Current version published February 12, 2010. This paper was presented at the 39th Annual Power Electronics Specialists Conference, Rhodes, Greece, June 15–19, 2008. Recommended for publication by Associate Editor J. O. Ojo. G. D. Demetriades and H. Z. de la Parra are with ABB Corporate Research, V¨ aster? as 721 78, Sweden (e-mail: georgios.demetriades@se.abb.com; hector.zelaya@se.abb.com). E. Andersson is with the Force Measurement, ABB Process Automation, V¨ aster? as 72159, Sweden (e-mail: erik.andersson@se.abb.com). H. Olsson is with the Legal Affairs and Compliance Intellectual, ABB AB, V¨ aster? as 721 83, Sweden (e-mail: hakan.olsson@se.abb.com). Color versions of one or more of the ?gures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identi?er 10.1109/TPEL.2009.2027905

suggested in [4]: one that consists of 107 nodes and a second that employs 7 nodes. The thermal resistances are calculated and empirical formulas for the different thermal resistances are suggested. Mellor et al. [1] developed an extensive lumpedparameter thermal model of an induction motor. As in the model suggested in [4], this model gives both a steady-state solution and a transient solution of the temperature in the motor. Staton and So [5] and Boglietti et al. [9] study the parameters’ sensitivity of the thermal models and some results are presented. In [8], Boglietti et al. developed a simpli?ed thermal model based on [1]. Despite the simplicity of the model, the difference in accuracy of the resistances in [8] compared to the resistances in [1] is only 2.5%. This error is less than the uncertainty in the calculation of a convection resistance [8]. In [1] and [8], most of the components in the motor are approximated with cylinders that make it easier to calculate the resistances. Puranen [12] developed a simpli?ed thermal model of an induction motor. This model was made in order to study the suitability and the characteristics of an induction motor in dynamically demanding drives. Andersson [11] describes two simpli?ed models of a PM motor. One of the models contains components based on real physical parameters and one of the models contains components based on optimized parameters. Further, Chin [19] presented two different methods for thermal analysis of PMSMs employing two different software tools. An extensive study concerning the determination of the critical parameters in electrical machine thermal models is presented in [13]. Parameters such as equivalent thermal resistance between frame and ambient, interface gap between lamination and external frame, forced convection heat transfer coef?cient between end winding and end caps, etc., are discussed and determined. Staton and Cavagnino [21] used empirical dimensionless analysis and formulations to calculate convention heat transfer. Further, in [23] and [24], the behavior of the machines are analyzed by using a combined thermal and electromagnetic analysis where ?nite-element method (FEM) analysis is used. In [24], a minimum set of FE magnetic analyses is carried out to determine the parameters of the induction motor equivalent circuit. In [22], modeling strategies using T-equivalent lumpedparameter blocks as well as conventionally de?ned resistances are discussed. Special attention is paid on the modeling of the convective heat transfer in the air gap of radial-?ux electrical machines at different rotational speeds. Fussel [3] studies the torque–speed performance of a threephase brushless dc motor for both natural and forced convections. Forced convection by means of external air cooling was

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considered. Marcovic et al. [14] study the thermal convection concerning a small motor when natural convection was taken into account. One way to determine the cooling of a motor is to approximate the chassis with a cylinder. Many studies have been found regarding forced, natural, and mixed convection around a cylinder [14]–[18]. These studies investigate horizontal and/or vertical ?ow. Nevertheless, in special applications, robot arms, etc., motors experience cooling where the ?ow is often a superposition of a horizontal ?ow and a vertical ?ow. No studies have been found in the literature when the motor operates in the conditions explained before. The real-time thermal model (RTTM) aims for protection of the motor against thermal stresses and temperature monitoring. In the literature, a considerable number of publications can be found concerning temperature monitoring by means of stator winding resistance estimation. In [25], Lee and Habetler have proposed a resistance estimation scheme based on an injection of a low-power dc bias in the stator winding of an induction motor. The major disadvantage of the aforementioned method is the deviations obtained due to the cable, which connects the drive system with the motor. In [26], Lee and Habetler propose a compensation scheme in order to take account for the existence of cables, fuses and circuit breakers in the system. Further, in [27], Lee et al. study the feasibility of using an estimate of the stator resistance as an indicator of stator winding temperature. The advantages of the resistance-based temperature monitoring over the conventional thermal-model-based methods are presented. It has been shown that the estimation of the stator resistance becomes dif?cult during high-speed operation because the stator resistance becomes sensitive to errors in motors electrical parameters and variables as the speed increases. This could be overcome by the use of sophisticated estimators, e.g., Kalman ?lter, as proposed in [34]. In [28] and [29], neural networks have been used and superiority is claimed compared with the conventional resistance estimation schemes. In [30], Roongsook and Premrudeepreechacharn propose a fuzzy estimator for accurate estimations of the stator resistance. Similarly, a number of publications corresponding to PMSM have been found in the literature. In [31], a reference-modelbased identi?cation scheme is proposed. The estimation scheme is used to compensate for the stator resistance uncertainties and is used in a sensorless control scheme of a PMSM. In [32], a proportional–integral (PI) stator resistance estimator for direct torque control (DTC) PMSM drive is presented. The advantage of this scheme is that it is based on the mathematical model of the interior PMSM and makes use of the current signal only. By means of comparing the actual current and the reference current, the change of stator resistance can be traced and compensated. Only simulation results are presented in this paper. Additionally, in [33], Lee proposes a closed-loop estimation of the PMSM parameters by a PI controller gain tuning. The idea of the proposed method is to tune the controller zero and estimate motor parameters from the tuned controller gains. Furthermore, the induced electromotive force (EMF) is cancelled by

TABLE I ANALOGY BETWEEN THE ELECTRICAL AND THE THERMAL PARAMETERS

a feedforward compensation term. Compared with the conventional methods using system identi?cation or phasor diagrams, the proposed method does not require complex data analysis or test con?guration. The results presented in [33] are for selected operating points and not for the whole speed range. Thus, worst-case studies are not performed as well as sensitivity analysis is absent. On the other hand, the method seems to be relatively simple and a straightforward procedure. In applications where the motor and the drive are not in close proximity with each other, temperature monitoring by employing estimation schemes is quite challenging. Long connection cables are required and the resistance of the cable will certainly affect the accuracy of the estimated temperature. Additionally, the ambient temperatures of the motor and the cable are not identical, thus affecting the results obtained by the estimation scheme. Gao et al. [37] propose a reduced thermal model for real-time temperature estimation. The authors demonstrate that full-order thermal models can be systematically reduced via pole-zero cancellation or Hankel-singular-value-based model reduction techniques without additional physical assumptions. Similarly, in [37], the model reduction method is proposed. In this paper, a reduced RTTM is proposed. The model is based on a lumped-parameter con?guration for a surfacemounted PM motor with distributed windings in the stator. This is the most common con?guration in servo applications. II. THERMAL MODELING The heat can be transported by conduction, if two elements are in contact and in close proximity with each other, and by convection where the heat ?ows between the two elements via a ?uid or gas. Radiation is the third heat transfer mechanism and depends on the emissivity of the elements. Due to the complexity of the electrical machine, i.e., complex geometry, large thermal networks can be obtained. As a result, a high resolution of the temperature distribution can be achieved. Geometrical symmetries can be used resulting in a reducedorder thermal network, which can satisfactorily describe the thermal behavior of the motor. Electrical networks can be used in order to study the thermal behavior of a system. In Table I, the analogy between electrical and thermal parameters is illustrated. Further, Fig. 1 illustrates the analogy between the electrical and the thermal circuits.

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Fig. 1.

Analogy between the electric and the thermal networks.

Fig. 2.

(a) Permanent-magnet synchronous motor. (b) Heat ?ow diagram.

The thermal resistance represents the thermal properties of the different materials used in the structure as well as the thermal connection between different structures. Similarly, the thermal energy stored in a structure can be modeled as a thermal capacitance. The thermal model described in this paper is based on the geometry and the physical properties of the PMSM. Due to the general description, the model can be applied to several PM motors. Heat transfer between two different structures can be modeled by determining the nodes and the thermal impedances of each material. Different characteristics of a speci?c machine part, such as temperature distribution, mechanical complexity, and material properties, were considered when the nodes and their assignments were considered. Ten nodes have been considered, i.e., the ambient, chassis, stator yoke, rotor, end winding, stator winding, shaft, ball bearings, internal air, and the mechanical structure where the motor is attached to. In Fig. 2(a), the PMSM and the geometrical dimensions of the motor used to calculate the thermal resistance and capacitances are shown. Similarly, in Fig. 2(b), heat ?ow between the different parts is illustrated. Additionally, the dimensions of the motor are summarized in Table VII in the Appendix.

The red arrows (Cond) represent the heat transport due to conduction, the green arrows (Conv) the heat ?ow due to convection, and the purple (Rad) due to radiation. Radiation is also present internally, but it has not been considered in this paper. The (Cond) (Conv) and (Rad) are indicated in Fig. 2(b) in the proximity of the arrows. The nodes of interest and the thermal resistances between the nodes are clearly shown. Additionally, in Fig. 3, the power losses in the different parts of the PMSM, such as iron losses, stator winding, and end winding losses, are represented as current sources. The thermal impedances due to conduction and convection have been considered. It must be noted that no ?niteelement (FEM) calculations have been required to obtain the thermal model described in the following paragraphs. Conduction occurs when heat is transferred from one element to another due to a temperature gradient between the two elements. The energy is transferred from a warmer region to a colder region and is described by Fourier’s law q = ?λA ?T ?x (1)

where q is the heat transfer rate, ?T /?x is the temperature gradient in the direction of the heat ?ow, A is the cross-section area, and λ is a positive constant called the thermal conductivity of the

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Fig. 3.

Thermal equivalent network representing a PMSM.

material. The thermal conductivity indicates the ability of the material to conduct heat. The thermal resistance for conduction is de?ned as t (2) Rth = Aλ where t is the thickness of the element [20]. Similarly, convection occurs when heat is transferred to or from an element by a moving ?uid. The heat transfer rate is described by q = hA(Tw ? T∞ ) (3)

calculated by Cth = mCp (5)

where Tw is the temperature of the element, T∞ is the temperature of the ?uid, A is the surface area, and h is a coef?cient called the convection heat transfer coef?cient [2]. The thermal resistance for convection [20] is de?ned as 1 . (4) Ah Two different kinds of convection can be de?ned: the natural convection and the forced convection. Forced convection occurs when an external source, for example, a pump or a fan, is used to move the ?uid. Natural convection, on the other hand, occurs in the absence of an external source, and the driving sources for natural convection are buoyancy and gravity [19]. The stored thermal energy in the different nodes is modeled by thermal capacitance Cth (in joules per kelvin) [20], which is Rth =

where m is the mass of the structure and Cp is the speci?c heat capacity. Some of the convection heat transfer coef?cients have to be determined experimentally and several proposals have been found in the literature [4], [6], [8], [12]. In this paper, the equation de?ned experimentally by Kylander [4] has been used since this equation can be used for a wide range of peripheral velocity of the rotor. The convection heat transfer coef?cients used in order to calculate the thermal resistances due to convection are summarized in Table II. The parameter ur is the rotor peripheral velocity. The convection heat transfer coef?cient in the air gap depends on the characteristics of the ?ow. A turbulent ?ow gives a higher heat transfer coef?cient compared to a laminar ?ow. The modi?ed Taylor number T am is used in order to determine the value of Nusselt number Nu, as given in [1], [4], and [12], which is the factor in the heat transfer coef?cient and depends on the ?ow. T am can be calculated from T am = ω 2 dstator Bore δ 3 2 · υ2 (6)

where ω is the angular velocity and υ is the kinematic viscosity

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TABLE II CONVECTION HEAT TRANSFER COEFFICIENTS

Fig. 4.

Winding losses and the iron losses of the motor in p.u. of the rated power.

of the air. Nu is given in [1] and [3] and is calculated from Nu = 2, T am < 1740 0 . 241 ?0 . 75 ? 137T am , T am > 1740. 0.409T am (7)

The Nu used in order to calculate the heat transfer coef?cient of the shaft is ?2 ? ? N uL = ?0.825 + 0.387RaL

1/6

The power losses in a PMSM will cause a temperature rise in the different parts of the motor. Power losses consist of winding losses, iron losses, friction losses in the ball bearings, and friction losses due to turbulence caused by the internal air ?ow. The resistive losses of the stator winding can be de?ned as PLoss

Cu

=

Ri i2 i

(9)

1 + (0.492/ Pr)9 / 16

? . 8 / 27 ?

(8)

The thermal resistances and capacitances of the motor are calculated according to (2), (4), and (5), respectively. Nevertheless, a number of thermal resistances are nonlinear, i.e., they are speed dependent or are dependent on the temperature of the component. The thermal resistance used to model the ball bearings is speed dependent. The resistance modeling the convention between the rotor and the stator yoke depends on the temperature of the two parts.

where Ri is the winding resistance at a certain temperature and ii is the rms value of the current in each phase. Stator iron losses can be divided into losses due to hysteresis in the yoke Ph and losses due to the eddy currents ?owing in the laminations of the yoke Pe . The total stator iron losses as well as the hysteresis and eddy current losses are de?ned as

2 2 2 Pf e = kh Bm ax f + ke Bm ax f

(10)

where Bm ax represents the maximum magnetic ?ux density in a PMSM, f is the electrical frequency, and kh and ke are empirically derived parameters. In Fig. 4, the winding and the iron losses of the motor are shown. The winding losses are calculated

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Standstill operation and/or acceleration of the motor under certain loaded conditions can be identi?ed. A. Model-Order Reduction Model-order reduction (MOR) is a branch of systems and control theory, which studies properties of dynamical systems in application for reducing their complexity while preserving (to a certain extent) their input–output behavior. MOR replaces the original large-scale system with a reduced order i.e., much smaller system, yet still retains the original behavior under investigation to high accuracy. As already mentioned, the model is used in order to estimate the temperature of different parts in real time. Consequently, the execution time of the model is limited. The execution time depends on the model complexity. By reducing the model, the execution time is comparably decreased. Model reduction has been reported in [36] and [37]. In the present paper, the balance truncation algorithm [38] has been used but is not discussed, although experimental results and simulations are shown. In Fig. 6, the results obtained by the reduced model are shown. The deviations at three selected points A, B, and C where random perturbations have been added to the speed and torque signals are highlighted. These are summarized in Table III. As shown in the table, the deviations obtained by comparing the results obtained by the full-order model and the reduced model are negligible. IV. THEORETICAL AND EXPERIMENTAL RESULTS A number of simulations have been performed by employing a MATLAB/SIMULINK software in order to verify the thermal behavior of the device under test (DUT). The representation of the discrete-time thermal model is shown in Fig. 7. The calculation of the losses is based on two lookup tables with analytical and experimental data for the motor. In Fig. 7, the inputs of the model are clearly shown, i.e., the torque reference and the speed of the motor. The torque reference and the speed of the motor fully described the operating conditions of the PMSM in combination with the operating temperature. The operating temperature of the motor is introduced to the model as a feedback loop and is shown in Fig. 7. In Fig. 8, the drive cycle used is shown. The motor operates at constant speed and torque for 3800 s. Then, the speed is varied from 1000 to 1500 r/min, as shown in the ?gure, for 4000 s. Further, with the motor operating at constant speed, the torque is varied. In Fig. 9, a comparison between the simulation results obtained by the MATLAB/Simulink model and experimental results is shown. As shown in the ?gure, excellent agreement has been achieved. In Fig. 9, the warm-up and the cooldown periods are shown. When the motor is stopped, the model is still in operation and estimates the temperature of different parts considering that the losses fed into the motor are zero. This feature is quite important since the estimated temperature during cooldown can be used when the motor is restarted. The measured values were obtained with one PT100 sensor located at the end winding of the motor as well as one PT100 located on the housing.

Fig. 5. RTTM of a PMSM. Electrical measurements are fed back to the thermal model in order to estimate the losses.

values that have been corroborated with actual measurements; the iron losses come directly from measurements. III. REAL-TIME THERMAL MODEL IMPLEMENTATION As in the case of an electrical network, a thermal network with n + 1 nodes can be represented by n coupled algebraic equations. In this paper, the thermal network representing a PMSM is expressed in the state-space domain and is de?ned by x (t) = Ax (t) + Bu (t) y (t) = Cx (t) + Du (t)

?

(11) (12)

where x (t) denotes the state vector, u (t) the input vector, y (t) the output vector, and the matrices A, B, C, D are the state coef?cient matrix, source coef?cient matrix, output matrix, and the feedforward matrix, respectively. The model has been implemented in a DSP, and the thermal parameters of the PMSM are calculated in real time. This implies that the model has to be described in the discrete form. Thus, x [k + 1] = Ad x [k ] + Bd u [k ] y [k ] = Cd x [k ] + Dd u [k ] where Ad = eA T s a m p l i n g Cd = C and

Tsa m p lin g

(13) (14)

Bd =

0

eA σ Bdσ (15)

Dd = D.

In Fig. 5, the RTTM of the PMSM studied in this paper is illustrated. Electrical measurements such as the speed of the motor ω and the output instantaneous torque T are used in order to estimate the losses in the different parts of the PMSM. Additionally, and with knowledge of the operating condition of the motor, vital decisions can be taken concerning the thermal behavior of the motor.

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Fig. 6.

Results obtained by the reduced model (three selected points A, B, and C are shown for comparison). TABLE III DEVIATIONS COMPARING THE FULL-ORDER MODEL WITH THE RESULTS OBTAINED BY THE REDUCED MODEL

The model has been tested when the motor is operating under stall torque. During stall torque, the current is distributed unevenly in the winding of the motor. In Fig. 10, the current through the phase winding is shown. The vertical lines indicate different stall torque cases. When the motor operates, as indicated by the second vertical line (green), the current through phase U is zero and 0.9 p.u. and ?0.9 p.u. through phases V and W, respectively. This implies that phases V and W are thermally stressed and phase U is cooled down. In Fig. 11, the results obtained by simulations and experiments are plotted. The results correspond to phase W. As shown in the ?gure, the agreement is excellent considering the measured and the simulated temperatures of the chassis. On the other hand, the results obtained for the phase end winding temperature is fairly acceptable. The deviation is up to 8 ? C. As shown in the ?gures, good agreement between simulation and experimental results has been obtained when the motor is operating at steady state and during transient operating conditions. On the other hand, during stall torque operation, the agreement is fairly good since at this working point, only one phase carries the full current, which makes it dif?cult to obtain an accurate estimation. However, the results obtained could still be used to protect the motor effectively.

Fig. 7.

Real-time thermal model.

V. IMPLEMENTATION OF THE RTTM AND EXPERIMENTAL RESULTS The RTTM has been implemented in the DSP of the inverter of the motor. As already mentioned and due to the execution time limitations, a reduced model has been considered.

Different drive cycles have been considered in order to prove the feasibility of the model. The experimental setup is shown in Fig. 12, where it is shown that the speed of the motor is controlled by an inverter and the torque by the load machine. PT100 elements have been used in order to measure the temperature of the different parts of the motor that are of interest, i.e., the end and stator winding temperature, the stator yoke temperature, and the shaft and chassis temperature. In Fig. 13, the examined drive cycle and a comparison between the estimated and the measured temperatures are shown.

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Fig. 8.

Drive cycle.

Fig. 10. Stall torque operation. Observe that the vertical lines are determining the current through the windings of the motor.

Fig. 11. Obtained results by simulations and experiments when the motor is operated at stall torque.

Fig. 9.

Comparison between measured and simulated results.

The examined cycle is a high-speed, high-torque drive cycle. Therefore, the motor losses are comparably high. Observe that the iron losses are proportional to the square of the speed, as de?ned in (10). Similarly, the winding losses are proportional to the square of the current, as given by (9). As shown in the ?gure, the results are in good agreement, though the deviations are not constant. A summary of the results is given in Table IV. The presented values correspond to the maximum deviation at steady state. Similarly, the plus sign indicates that the temperature is overestimated by the RTTM. In Fig. 14, the examined drive cycle and a comparison between the estimated and the measured temperatures are shown. The speci?c drive cycle is a mixture of stall torque, transient, and steady-state operations. The speed of the motor is not very high compared with the drive cycle presented in Fig. 13(a). On the other hand, the motor experience intermittent high peak

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Fig. 12.

Experimental setup. TABLE IV SUMMARY OF THE RESULTS AT STEADY STATE

torque. This implies that the winding losses might be the dominant power loss mechanism. As shown in the ?gure, the results are in good agreement. From Table V, the RTTM underestimates the temperature by 2? . As shown in Fig. 15, the motor is operated at stall torque. Thus, the speed is zero and the average torque is around 30 N·m. By examining Fig. 15(b), two of the phase windings have the same temperature meanwhile the temperature of the third winding is comparably lower. This implies, and as shown in Fig. 10, that the current through the warm winding, phase U, and the current through phase V are comparable with each other. Assuming a symmetrical three-phase system, the current through phase W equals to iW = iV + iU . (16)

Fig. 13. Examined drive cycle and a comparison between the estimated temperature by the RTTM and the measured temperature. (a) Examined drive cycle, speed, and torque. (b) Estimated and measured temperature.

A summary of the obtained results is shown in Table VI. As shown in the table, the RTTM underestimates the temperature of the end windings and the chassis by 1? . Observe that the RTTM estimates the highest temperature of the motor that is critical in order to avoid motor failure due to high thermal stresses.

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Fig. 14. Examined drive cycle and a comparison between the estimated temperature by the RTTM and the measured temperature. (a) Examined drive cycle, speed, and torque. (b) Estimated and measured temperature. TABLE V SUMMARY OF THE RESULTS AT STEADY STATE

Fig. 15. Examined drive cycle and a comparison between the estimated temperature by the RTTM and the measured temperature. (a) Examined drive cycle, speed, and torque. (b) Estimated and measured temperature. TABLE VI SUMMARY OF THE RESULTS AT STEADY STATE

VI. CONCLUSION In this paper, an RTTM concerning a PMSM has been presented. The modeling procedure was brie?y presented. The thermal resistances and capacitances of the model are calculated based on the geometry of the different parts of the motor. The model is then expressed in a matrix form, represents a state-space model, and is discretized. Since the model is expressed in state space, conventional control theory techniques,

e.g., MOR, have been applied in order to reduce the complexity of the model. Simulation results have been compared with experimental results in order to study the performance and the feasibility of the concept. Additionally, the RTTM has been implemented in a DSP, and the estimated results have been compared with experimental results. An overall good agreement has been achieved between estimated and experimental results. The deviations obtained can be due to discretization of the model, though it is evident that the model discretization can cause minor problems.

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473

TABLE VII MOTOR PARAMETERS

TABLE VIII MOTOR DIMENSIONS

ACKNOWLEDGMENT The authors would like to kindly acknowledge Dr. X. Feng at ABB for his valuable contribution and inputs during the work process.

REFERENCES

[1] P. H. Mellor, D. Roberts, and D. R. Turner, “Lumped parameter thermal model for electrical machines of TEFC design,” Proc. Inst. Electr. Eng. Electr. Power Appl., vol. 138, no. 5, pp. 205–2018, Sep. 1991. [2] J. P. Holman, Heat Transfer, 7th ed. New York: McGraw-Hill, 1992. [3] B. K. Fussel, “Thermal effect on the torque-speed performance of a brushless DC motor,” in Proc. Electr. Electron. Insul. Conf. Electr. Manuf. Coil Winding Conf., Oct. 1993, no. 4–7, pp. 403–411. [4] G. Kylander, “Thermal modelling of small cage induction motors,” Ph.D. dissertation, School Electr. Comput. Eng., Chalmers Univ. Technol., G¨ oteborg, Sweden, Tech. Rep. 265, Feb. 1995. [5] D. A. Staton and E. So, “Determination of optimal thermal parameters for brushless permanent magnet motor design,” in Proc. IEEE Ind. Appl. Soc. Conf., St. Luis, MO, 1998, pp. 41–49. [6] J. Lindst¨ om, “Thermal model of a permanent-magnet motor for a hybrid electric vehicle,” Dept. Power Eng., Chalmers Univ. Technol., G¨ oteborg, Sweden, Internal Rep., Apr. 1999. [7] F. P. Incropera and D. P. DeWitt, Heat and Mass Transfer, 5th ed. New York: Wiley, 2002. [8] A. Boglietti, A. Cavagnino, M. Lazzari, and M. Pastorelli, “A simpli?ed thermal model for variable-speed self-cooled industrial induction motor,” IEEE Trans. Ind. Appl., vol. 39, no. 4, pp. 945–952, Jul./Aug. 2003. [9] A. Boglietti, A. Cavagnino, and D. A. Staton, “TEFC induction motors thermal model: A parameter sensitivity analysis,” IEEE Trans. Ind. Appl., vol. 41, no. 3, pp. 756–763, May/Jun. 2005. [10] D. Gerling and G. Dajaku, “Novel lumped-parameter thermal model for electrical systems,” presented at the Eur. Conf. Power Electron. Appl., Dresden, Germany, 2005. [11] E. Andersson, Real Time Thermal Model for Servomotor Applications, ABB AB Corporate Research, V¨ aster? as, Sweden, Feb. 2006. [12] J. Puranen, “Induction motor versus permanent magnet synchronous motor in motion control applications: A comparative study,” Ph.D. dissertation, Lappeenranta Univ. Technol., Lappeenranta, Finland, Dec. 2006. [13] A. Boglietti and A. Cavagnino, “Determination of critical parameters in electrical machine thermal models,” IEEE Trans. Ind. Appl., vol. 44, no. 4, pp. 1150–1159, Jul./Aug. 2008. [14] M. Marcovic, L. Saunders, and Y. Perriard, “Determination of the thermal convection coef?cient for a small electric motor,” in Conf. Rec. Annu. Meeting 2006 IEEE Ind. Appl. Conf., Oct., 2006, pp. 58–61. [15] A. Joda, I. Cuesta, and A. Vernet, “Numerical study of forced convection ?ow around rectangular cylinders with different aspect ratios,” in Proc. Int. Conf. Thermal Issues Eng. Technol.: Theory Appl. (THETA 2007), Jan., pp. 227–233. [16] W. Nowak and A. Stachel, “Convection heat transfer during an air ?ow around a cylinder at low Reynolds number regime,” J. Eng. Phys. Thermodyn., vol. 78, no. 6, pp. 1214–1221, Nov. 2005.

APPENDIX A. Motor Data Tables VII and VIII describe the motor parameters and motor dimensions, respectively.

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[17] S. J. D. D’Alessio, M. G. Saunders, and D. L. Harmsworth, “Forced and mixed convective heat transfer from accelerated ?ow past an elliptic cylinder,” Int. J. Heat Mass Transf., vol. 46, no. 16, pp. 2927–2946, Jul. 2003. [18] S. Sanitjai and R. J. Goldstein, “Forced convection heat transfer from a circular cylinder in cross ?ow to air and liquids,” Int. J. Heat Mass Transf., vol. 47, no. 22, pp. 4795–4805, Oct. 2004. [19] Y. K. R. Chin “A permanent magnet traction motor for electric forkliftsdesign and iron loss analysis with experimental veri?cation,” Ph.D. dissertation, Div. Electr. Mach. Power Electron., R. Inst. Technol., Stockholm, Sweden, 2006. [20] D. Staton, Thermal Analysis of Electric Motors and Generators, Training Course. Shropshire, U.K.: Motor Design Ltd., Apr. 2007. [21] D. Staton and A. Cavagnino, “Convection heat transfer and ?ow calculations suitable for electric machines thermal models,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3509–3516, Oct. 2008. [22] J. Nerg, M. Rilla, and J. Pyrh¨ onen, “Thermal analysis of radial-?ux electrical machines with a high power density,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3543–3554, Oct. 2008. [23] D. G. Dorrell, “Combined thermal and electromagnetic analysis of permanent-magnet and induction machines to aid calculation,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3566–3574, Oct. 2008. [24] L. Alberti and N. Bianchi, “A coupled thermal-electromagnetic analysis for a rapid and accurate prediction of IM performance,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3575–3582, Oct. 2008. [25] S. B. Lee and T. G. Habetler, “An online stator winding resistance estimation technique for temperature monitoring of the line-connected induction machines,” IEEE Trans. Ind. Appl., vol. 39, no. 3, pp. 685–694, May/Jun. 2003. [26] S. B. Lee and T. G. Habetler, “A remote and sensoreless thermal protection scheme for small line-connected AC machines,” IEEE Trans. Ind. Appl., vol. 39, no. 5, pp. 1323–1332, Sep./Oct. 2003. [27] S. B. Lee, T. G. Habetler, R. G. Harley, and D. J. Gritter, “An evaluation of model-based stator resistance estimation for induction motor stator winding temperature monitoring,” IEEE Trans. Energy Convers., vol. 17, no. 1, pp. 7–15, Mar. 2002. [28] M. Ebrahimi, E. Rezaei, B. Vaseghi, and M. Danesh, “Rotor resistance identi?cation using neural networks for induction motor drives in the case of insensitivity to load variations,” Iranian J. Sci. Technol., Trans. B, Eng., vol. 30, no. B2, pp. 223–236, 2006. [29] M. Summer, J. Campel, and M. Curtis, “A stator resistance estimator for sensoreless vector controlled drives using arti?cial neural networks,” in Proc. Eur. Power Electron. (EPE) Conf., Lausanne, Switzerland, 1999. [30] K. Roongsook and S. Premrudeepreechacharn, “Speed sensorless induction motor drive using adaptive stator ?ux observer,” in Proc. Int. Conf. Intell. Technol. (InTech), Chiang Mai, Thailand, 2003. [31] B. N. Mobarakeh, F. M. Tabar, and F. M. Sargos, “Mechanical sensorless control of PMSM with online estimation of stator resistance,” IEEE Trans. Ind. Appl., vol. 40, no. 2, pp. 457–471, Mar./Apr. 2004. [32] L. Tang and M. F. Rahman, “A novel PI stator resistance estimator for direct torque controlled permanent magnet synchronous machine drive,” in Proc. IEEE Electr. Mach. Drives Conf. (IEMDC 2003), Jun., vol. 1, no. 1–4, pp. 382–388. [33] S.-B. Lee, “Closed loop estimation of permanent magnet synchronous motor parameters by PI controller gain tuning,” IEEE Trans. Energy Convers., vol. 21, no. 4, pp. 863–870, Dec. 2006. [34] E. Foulon, C. Forgez, and L. Loron, “Resistance estimation with an extended Kalman ?lter in the objective of real-time thermal monitoring of the induction machine,” IET Electr. Power Appl., vol. 1, no. 4, pp. 549–556, 2007. [35] R. J. Kerkman, B. J. Seibel, T. M. Rowan, and D. Sclegel, “A new ?ux and stator resistance identi?er for AC drive system,” in Conf. Rec. 13th IEEE IAS Annu. Meeting (IAS 1995), Oct., vol. 1, no. 8–12, pp. 310–318. [36] N. Jaljal, J.-F. Trigeol, and P. Lagonotte, “Reduced thermal model of an induction machine for real-time thermal monitoring,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3535–3542, Oct. 2008. [37] Z. Gao, R. S. Colby, T. G. Habetler, and R. G. Harley, “A model reduction perspective on thermal models for induction machine overload relays,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3525–3534, Oct. 2008. [38] G. F. Franklin, J. D. Powel, and A. Emani-Naeini, Feedback Control of Dynamic Systems, 3rd ed. Reading, MA/White Plains, NY: AddisonWesley/Longman, 1993.

Georgios D. Demetriades (M’06) was born in Famagusta Cyprus. He received the M.Sc. degree in electrical engineering from the Democritus University of Thrace, Xanthi, Greece, and the Tech. Licentiate and Ph.D. degrees in power electronics from the Royal Institute of Technology (KTH), Stockholm, Sweden. He worked in Cyprus for two years. In 1995, he joined ALSTOM Power Environmental Systems, Sweden. In 2000, he joined ABB Corporate Research, V¨ aster? as, Sweden, where he is currently a Research and Development Engineer. His current research interests include power electronics, voltage-source converter HVdc, ?exible ac transmission system devices, high-frequency dc–dc power resonant converters, and high-frequency electromagnetic modeling.

Hector Zelaya de la Parra (SM’02) was born in Mexico City, Mexico, in 1953. He received the B.Sc. degree in electrical engineering from the Universidad Iberoamericana, Mexico City, in 1976, the M.Sc. degree from Loughborough University, Leicestershire, U.K., in 1981, and the Ph.D. degree from Bradford University, Bradford, U.K., in 1987. From 1989 to 1997, he was a member of the Power Electronics and Traction Systems Group, Birmingham University, Birmingham, U.K. For the past 11 years, he has been with ABB Corporate Research, V¨ aster? as, Sweden, where he is currently a Senior Principal Scientist. His current research interests include power electronics, switched-mode power supplies, motor drives, and control strategies. Dr. de la Parra is a Registered Charter Engineer in the U.K.

Erik Andersson received the M.Sc. degree in engineering physics from Uppsala University, Uppsala, Sweden. He was with ABB Corporate Research, where he was working with thermal models for servomotors. Since 2006, he has been with the Force Measurement, ABB Process Automation, V¨ aster? as, Sweden, where he is involved in the research and development on torque sensors for automotive applications.

H? akan Olsson received the M.Sc. degree in information technology engineering from Uppsala University, Uppsala, Sweden, in 2005. In 1994, he joined the ABB Corporate Research as a Laboratory Engineer at the High-Power Laboratory. After completing his studies, he was involved with thermal modeling of servomotors. He is currently with the Legal Affairs and Compliance Intellectual, ABB AB, V¨ aster? as, Sweden.

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