IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 49, NO. 6, NOVEMBER/DECEMBER 2013 2487

Compensation of Speed Dependence in SensorlessRotor Temperature Estimation for

Permanent-Magnet Synchronous MotorMartin Ganchev, Student Member, IEEE, Christian Kral, Senior Member, IEEE, and

Thomas M. Wolbank, Member, IEEE

Abstract—This paper proposes an improved method for es-timating the magnet temperature in permanent-magnet syn-chronous machines without using any temperature sensors.Originally, the method implies an intermittent injection of a volt-age pulse in the positive d-axis of the motor while keeping the loadcurrent zero. Thus, the resulting d-current response depends onboth the initial value of the d-current itself and the actual magne-tization level of the permanent magnets. Since the magnetizationof the magnets depends on the temperature, different d-currentslopes are associated with given temperature levels of the magnets.At higher speeds, the current response is additionally affectedby induced voltages of various sources which lead to erroneousestimation of the magnet temperature. By applying a voltage pulsein the positive and negative d-axis of the motor, symmetry of theinduced voltages can be achieved in a manner that the differenceof the current responses from the positive and negative pulses is nolonger affected by the induced voltages.

Index Terms—Condition monitoring, magnet temperature esti-mation, permanent-magnet machines, rotor temperature, satura-tion effects.

I. INTRODUCTION

NOWADAYS, one of the most widely used type of rare-earth magnet in permanent-magnet synchronous ma-

chines (PMSMs) is neodymium–iron–boron (NdFeB). Thegood acceptance of the magnet is justified by its high intrinsiccoercivity (Hci) and big maximum energy product (BHmax).PMSMs manufactured with NdFeB magnets are characterizedwith very high power density. The motor size is significantlyreduced by maintaining an excellent torque capability. How-ever, the resistivity of these magnets is relatively low, givingrise to considerable eddy-current losses particularly when themotor is driven by a pulsewidth-modulated (PWM) inverter.In high-torque and high-speed operation, eddy-current and

Manuscript received October 5, 2012; revised December 22, 2012; acceptedJanuary 15, 2013. Date of publication May 15, 2013; date of current versionNovember 18, 2013. Paper 2012-EMC-516.R1, presented at the 2012 Interna-tional Conference on Electrical Machines, Marseille, France, September 2–5,and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY

APPLICATIONS by the Electric Machines Committee of the IEEE IndustryApplications Society.

M. Ganchev and C. Kral are with the Austrian Institute of Technology, 1210Vienna, Austria (e-mail: martin.ganchev@ait.ac.at; christian.kral@ait.ac.at).

T. M. Wolbank is with the Department of Energy Systems and Electri-cal Drives, Vienna University of Technology, 1040 Vienna, Austria (e-mail:thomas.wolbank@tuwien.ac.at).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIA.2013.2263211

hysteresis losses are responsible for an abundant temperaturerise in the magnets [1]–[8]. When the temperature increases,a partial demagnetization occurs in the magnet. This processis reversible as long as the demagnetizing force, to which themagnet is exposed, does not reach the magnet specific kneevalue. Reversibility means that the flux density will grow toits original value when the temperature is reduced again. A de-crease of the rotor flux linkage in the motor due to temperature-dependent demagnetization effects will lead directly to lowerelectromagnetic torque output [9]. In torque control, this can becompensated either by a flux observer or indirectly when thetemperature of the magnets is known.

The knowledge of the magnet temperature is not only acontrol issue but also a safety issue. The magnet intrinsiccoercivity is a function of the temperature itself, as its abso-lute value decreases while the temperature rises. Therefore,at higher temperatures, excessive currents in the machine canlead to irreversible demagnetization of the magnets [10]. Ingeneral, the machine design should ensure that no irreversibledemagnetization will occur in the machine under the expectedoperating conditions [11]. However, machine overdimensioningcan be avoided, if online magnet temperature estimation isavailable to assure continuous safe operation mode.

Due to rotation, measuring directly the temperature of thepermanent magnets is very cumbersome. The most commontechniques include battery-powered devices [12]–[20], infraredsensors [21]–[24], and slip rings [25], [26]. Carrying out suchmeasurements is rather expensive, and their application is lim-ited to laboratory and experimental setups since specific instru-mentation is normally required. Therefore, significant effortshave been performed recently to develop techniques which donot require any temperature sensors to obtain the rotor temper-ature in PMSMs. Such techniques have been already reportedin various papers. The most common approach is a thermalmodel of the machine. Thermal models imply good knowledgeof the geometry, the cooling system, and, particularly, thematerial specific parameters. Their application is rather limitedto industrial usage with known environmental and operatingconditions. Various issues of PMSM thermal modeling are dis-cussed in [27]–[39]. An algorithm to estimate rotor temperatureby using a flux observer is successfully presented in [40]. Thismethod requires an accurate modeling of the nonlinearities ofthe inverter. The nonlinear relation between current and fluxis defined by a lookup table (LUT). Furthermore, a preciseacquisition of machine and inverter parameters is required. An

0093-9994 © 2013 IEEE

2488 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 49, NO. 6, NOVEMBER/DECEMBER 2013

active parameter estimation method by using high-frequencysignal injection is demonstrated in [23] and [24]. This approachis based on changes in the high-frequency stator and rotor re-sistances due to temperature variation and concludes indirectlythe temperature level in the permanent magnets. The robustnessand accuracy of the method are strongly influenced by thenonideal behavior of the inverter (dead time, dc bus voltagevariation, etc.). A subject of patent [41] is a method comprisingthe estimation of the permanent-magnet temperature based onthe permanent-magnet flux linkage, the q-axis voltage, and theelectrical angular speed.

In this context, this paper focuses on a novel technique forestimating the temperature of the permanent magnets of PMSMwithout using any temperature sensors. The main idea of themethod is to detect changes in the degree of saturation inthe d-axis of the machine which is caused by variation in themagnetization level of the permanent magnets. These changesare distinctively reflected in the slope of the d-current responseupon a voltage pulse applied in the d-axis of the machine.However, the d-current response along the voltage pulse isslightly dependent on the speed. At higher speeds, this wouldlead to erroneous magnet temperature estimation. Although theerror is proportional to the speed, in many cases, it cannot becompensated, as the proportionality is not known or hard toobtain. This paper presents a new approach to reduce the speedinfluence in the d-current response and make it predominantlydependent on the actual magnetization level of the permanentmagnets. The experimental results are validated on an interiorPMSM (IPMSM).

II. BASIC PRINCIPLES

The saturation level of the machine is mostly affected by thepermanent-magnet magnetization in its d-axis. Therefore, thepresented method proposes that, in a rotating machine, a voltagepulse is applied in the d-axis while d-current is measured. Aslong as the initial q-current is set to zero (iq = 0), the resultingd-current response reflects predominantly saturation effects dueto stator flux linkage produced by the d-current excitation itselfand the permanent-magnet flux [42]. Assuming that the magnetmagnetization level depends on the magnet temperature Tm, thefollowing relationship can be derived:

diddt

= fiq=0(id, Tm). (1)

Since this is a strongly nonlinear relationship, identification of(1) has to be done by measurements. The degree of nonlinearitydepends strongly on the construction type and, particularly, onthe size of the effective air gap of the machine.

Using a common three-phase two-level bridge inverter, acorresponding switching pattern can generate a voltage pulsein the pure d-axis of the machine when the angle between thestator and rotor reference frames θel equals one of the six basicspace vector angles (θel = 0◦, 60◦, 120◦, 180◦, 240◦, 300◦). Theproposed method requires the knowledge of the rotor position,either using a rotor position sensor or a sensorless approach,so that the motor d-axis can be continuously traced. For thesake of clarity, for the definition and implementation of the

Fig. 1. Voltage pulse injection in the d-axis of the machine at θel = 0◦.

Fig. 2. Voltage pulse injection in a rotating machine; relative displacement ofthe d-axis along the voltage pulse duration.

method, θel = 0◦ is considered, as shown in Fig. 1. In a rotatingmachine, the voltage pulse is applied in phase a of the machinesuch that the electrical rotor position gets zero (θel = 0◦) in themiddle of the pulse, as depicted in Fig. 2. The angles (θel0 andθel1) between the rotor and stator reference frames at the timeinstant of the beginning t0 and the end t1 of the pulse for agiven machine with p pole pairs depend on the speed n and thevoltage pulsewidth tpw, as follows:

θel0 = θel1 =1

2360◦pntpw. (2)

As long as the θel0 and θel1 are kept small, the followingrelationships for the stator voltage and current components arefulfilled during the voltage pulse:

ud ≈ ua uq ≈ uβ id ≈ ia iq ≈ iβ . (3)

III. SPEED COMPENSATION APPROACH

For further machine analyses upon a voltage pulse genera-tion, the motor voltage equations in the rotor reference framehave to be given first

ud=Rsid+L∗dd

diddt

+L∗dq

diqdt

−ωLqqiq−ωLqdid (4)

uq=Rsiq+L∗qq

diqdt

+L∗qd

diddt

+ωLddid+ωLdqiq+ωψm (5)

where Rs is the stator resistance, ψm is the flux linkageproduced by the permanent magnets, ω is the speed of the rotorreference frame with respect to the stator reference frame, andLdd and Lqq are the inductances in the d- and q-directions of the

GANCHEV et al.: COMPENSATION OF SPEED DEPENDENCE IN SENSORLESS ROTOR TEMPERATURE ESTIMATION 2489

machine, respectively. The inductances L∗ are the differentialinductances with respect to the currents

L∗dd =Ldd +

dLdd

didid (6)

L∗dq =Ldq +

dLdq

diqiq (7)

L∗qq =Lqq +

dLqq

diqiq (8)

L∗qd =Lqd +

dLqd

didid. (9)

Assuming star connection of the motor, the voltage applied tothe motor terminals upon a voltage pulse generation in the d-axis has the following components:

ud ≈ ua =2

3Vdc (10)

uq ≈ uβ =0 (11)

where Vdc is the inverter dc voltage. Thus, from (4), thefollowing relationship for the d-current slope did/dt can beobtained:

L∗dd

diddt

=2

3Vdc−Rsid−

Term 1︷ ︸︸ ︷L∗dq

diqdt

+

Term 2︷ ︸︸ ︷ωLqqiq +

Term 3︷ ︸︸ ︷ωLqdid . (12)

The differential inductance Ldd depends strongly on the d-axissaturation level of the machine which is, in turn, influenced bythe magnetization level of the permanent magnets. Thus, did/dtwill change upon changes in the magnetization level of the mag-nets and can be used as indicator for the magnet temperatureTm. Since did/dt as a function of L∗

dd has a nonlinear character,a distinctive relationship between did/dt and Tm for a givenmachine can be established by a LUT. This is identified duringa commissioning phase either by direct measurements of Tm

and did/dt or by setting reference temperature value levels inthe rotor (e.g., in an environmental chamber).

In the theoretical approach of the method, it is a subjectto the condition that, at the beginning of the voltage pulse,the q-current is zero (iq = 0), which means that Term 1 andTerm 2 from (12) will be negligible at the beginning of thepulse. However, according to (5), at higher speeds, the absolutevalue of the q-current will change along the voltage pulse. Thischange is produced predominantly by the velocity-dependentinduced inner voltage of the permanent-magnet flux linkage(ωψm) in combination with an outer voltage of zero (uq = 0).Thus, at higher motor speeds, Term 1 and Term 2 from (12) willchange along the voltage pulse duration, affecting the d-currentresponse did/dt.

The dependence of did/dt on the motor speed is seen as adisturbing factor in the proposed method. It introduces a speed-dependent error in the estimation of the magnet temperature.This can be compensated by establishing a LUT at standstilland at nominal speed. In many cases, identifying a LUT for agiven motor at nominal speed is difficult, or in the worst case,it cannot be realized at all. For example, if the identification iscarried out in an environmental chamber, operating the machineat high speeds can be undesirable.

TABLE IPARAMETERS OF THE IPMSM UNDER TEST

By considering a positive and a negative pulse in the d-axisof the machine, symmetry in (12) can be achieved which elim-inates to a great extent the disturbing terms in (12) (Terms 1, 2,and 3) and makes obsolete a LUT at higher speed. Thus, the dif-ference of the resulting d-current responses of the positive andnegative voltage pulses (didP /dt− didN/dt) is less affectedby the motor speed. For the IPMSM under test, the highestinfluence on did/dt among all speed-dependent terms in (12) isrecognized in Term 2, since Lqq � Lqd. Therefore, symmetryis desirable that Term 2 for this particular machine is predom-inantly eliminated in the difference of the d-current responses(didP /dt− didN/dt). This will be the case when the q-currenthas the same values along the positive and negative pulses

iqP = iqN . (13)

Therefore, the negative pulse should be chosen such that (13) isfulfilled. A positive consequence of this symmetry is that Term1 in (12) is eliminated too. Under the assumption that the in-ductances are not changing for the positive and negative voltagepulses, the current responses can be subtracted as follows:

L∗dd

(didPdt

− didNdt

)=

4

3Vdc −Rs(idP − idN )

+ ωLqd(idP − idN ). (14)

The stator resistance voltage drop, together with the speed-dependent term in (14), is neglected in the current investigation.

IV. EXPERIMENTAL VALIDATION OF THE

PROPOSED SPEED COMPENSATION

In this section, the experimental setup and validation of theproposed method are presented. Results obtained for magnettemperature estimation with and without speed compensationare compared.

The motor under test is an IPMSM with parameters listedin Table I. The stator of the motor is depicted in Fig. 3. Thestator winding is a single-layer fractional slot distributed with36 slots and eight poles. The rotor is specially manufacturedto accommodate thermal sensors. Before the magnets wereassembled, holes through the rotor lamination with a diameterof 2 mm were laser drilled in different locations. There aresensors directly fixated to the permanent magnets (Fig. 4). Theused sensors are thermocouples of type K wired to a speciallydesigned battery-powered instrumentation fixated to the hollowmotor shaft, as shown in Fig. 5. The device measures, ampli-fies, and digitalizes the thermocouple voltages. The data aretransmitted to a stationary receiver via infrared optical datalink. With a single battery charge, the temperature of up to 12locations in the rotor of the machine can be measured continu-ously for over 9 h. A detailed description of the instrumentationdesign, implementation, and validation is given in [12].

2490 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 49, NO. 6, NOVEMBER/DECEMBER 2013

Fig. 3. Stator of the IPMSM under test; single-layer fractional-slot distributedstator winding with 36 stator slots and eight poles.

Fig. 4. Rotor of the IPMSM under test equipped with thermocouples oftype K.

Fig. 5. Rotor temperature monitoring instrumentation. (a) Block diagram ofthe assembly parts. (b) Instrumentation enclosure fixated on the hollow shaft ofthe IPMSM under test.

The field-oriented space vector control, together with theproposed voltage pulse generation, is implemented on C6747,a floating-point digital signal processor [43]. The inverter op-erating PWM frequency is set to 20 kHz. The injected voltage

Fig. 6. Current slope difference between two reference temperature valuesupon temperature estimation as a function of the initial d-current value id,ref ;n = 100 r/min.

pulsewidth tpw for the magnet temperature estimation is set to30 μs. Thus, according to (2), the angle between the rotor andstator reference frames upon the beginning of the voltage pulseat nominal speed is θel0 = 1.7◦, which assumes that ia ≈ id forthe time duration of the voltage pulse. Therefore, in order to de-termine the d-current slope, the phase current ia is oversampledsynchronously to the voltage pulse at a sample rate of 500 ns.

For the validation of a d-current slope did/dt when esti-mating the magnet temperature, the measured phase current iacurve is linearized by polynomial interpolation

y(t) = Sat+ P (15)

where the weighting factor Sa represents the estimated slopeof the curve upon voltage pulse generation and the offset Prepresents iat0 , which is approximately equal to the initiald-current id,ref set by the current controller. Additionally, thefollowing denomination is used here: SaP is the estimated slopeof a d-current response upon a positive voltage pulse, whileSaN is the estimated slope of a d-current response upon anegative voltage pulse.

A. Temperature Estimation Without Speed Compensation

In the following, temperature estimation without speed com-pensation is carried out. This setup implies measurements ofthe d-current response based on a positive voltage pulse inthe d-axis of the motor. The initial d-current id,ref set by thecurrent controller is an important parameter for the proposedmethod since, by varying id,ref , different initial saturation levelsin the d-axis of the motor can be set before the voltage pulse isgenerated. An initial d-current id,ref for a given pulsewidth pro-vides the most sensitivity when the deviation of the estimatedd-current slopes SaP is the highest upon the positive volt-age pulse at two different temperatures. To obtain the initiald-current id,ref for a voltage pulsewidth of 30 μs, the d-currentresponses are evaluated for two reference temperatures (Tm =20 ◦C and Tm = 60 ◦C). The difference of the estimated currentslopes ΔSaP (Tm2−Tm1) is then presented as a function of id,ref .The results are depicted in Fig. 6 which shows that L∗

dd willreveal the best sensitivity with respect to the magnet magne-tization level when id,ref = 0.4 p.u. This is the point aroundwhich the machine stator core starts to saturate in the d-axis.

GANCHEV et al.: COMPENSATION OF SPEED DEPENDENCE IN SENSORLESS ROTOR TEMPERATURE ESTIMATION 2491

Fig. 7. d-current id response upon positive voltage pulse of 30 μs withid,ref = 0.4 p.u. (a) Measured current response at various magnet temperaturesand n = 100 r/min. (b) Linearization of the measured current response bypolynomial interpolation with eliminated offset. (c) Linearized current responsefor n = 100 r/min and n = 4800 r/min at Tm = 60 ◦C.

During a heat-up test, temperature estimation with id,ref =0.4 p.u. and a positive voltage pulse (tpw = 30 μs) is carriedout at low speed n = 100 r/min and at nominal speed n =4800 r/min. The measured current response upon a positivevoltage pulse at n = 100 r/min is shown in Fig. 7(a) for variousmagnet temperatures. Fig. 7(b) demonstrates the same currentresponses linearized according to (15); however, the offset Pis eliminated as it is the same for all curves. The differencebetween the d-current responses at n = 100 r/min and n =4800 r/min is visualized at a constant magnet temperature(Tm = 60 ◦C) in Fig. 7(c). As expected, the slope of the current

Fig. 8. Current slopes SaP upon temperature estimation as a function of themagnet temperature; not compensated setup implying a single positive voltagepulse in the d-axis of the motor.

response at lower speed is smaller compared to the one at higherspeed (SaP,n=100 r/min < SaP,n=4800 r/min). This can easilybe explained with (12), where, at higher speeds, due to theq-current change, Terms 2 and 3 produce additional voltageto the applied voltage pulse. This results in an increase ofdid/dt. The influence of the magnet magnetization on Term 2and Term 3 from (12) is assumed here to be negligible, so theireffect on did/dt is considered to be independent of the magnettemperature. This can be seen in Fig. 8 where the estimatedcurrent slopes SaP at n = 100 r/min and n = 4800 r/min aredepicted as a function of the magnet temperature. As expected,the curves reveal a speed-dependent offset (SaP,n=4800 r/min −SaP,n=100 r/min > 0), which can be considered, to a greatextent, constant along the magnet temperature. As stated before,this offset is undesirable since it will lead to erroneous temper-ature estimation when considering a LUT solely identified atstandstill.

B. Temperature Estimation With Speed Compensation

The main idea of the proposed speed compensation is toeliminate the q-current influence on the d-current response,as seen in (12). This is realized by applying a positive and anegative voltage pulse in the d-axis of the motor whereby theq-current is kept at the same value along the pulses. Thed-current response evaluation is carried out upon the slopedifference between the current responses from the positive andnegative pulses, respectively,

SaPN = SaP − SaN . (16)

It should be noted here that the voltage pulse durations for thepositive and negative pulses are the same (tpw = 30 μs). Theinitial d-current for the positive pulse is kept id,ref,P = 0.4 p.u.,while the initial d-current for the negative pulse id,ref,N variesunder the condition that the q-current has the same valuesalong the positive and negative pulses (13). The compensationprinciple is demonstrated in Fig. 9, where the q-current iq isplotted upon positive and negative voltage pulses at low speed(n = 100 r/min) and at high speed (n = 4800 r/min). For agood compensation, the deviation between the q-current iqresponses along the positive and negative voltage pulses shouldbe as small as possible.

2492 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 49, NO. 6, NOVEMBER/DECEMBER 2013

Fig. 9. q-current iq response upon positive and negative voltage pulses of30 μs for n = 100 r/min and n = 4800 r/min at Tm = 60 ◦C.

Fig. 10. Current differences idP − idN upon positive and negative voltagepulses of 30 μs with id,ref,P = 0.4 p.u. (a) Linearized current responsewith eliminated offset at various magnet temperatures and n = 100 r/min.(b) Linearized current response for n = 100 r/min and n = 4800 r/min atTm = 60 ◦C.

The difference from the positive and negative voltage cur-rent responses idP − idN for various magnet temperaturesat speed n = 100 r/min is depicted in linearized form inFig. 10(a). In an analogical manner, the current response dif-ference at n = 100 r/min and n = 4800 r/min is demonstratedin Fig. 10(b) for a constant magnet temperature (Tm = 60 ◦C).As it can be observed, the slope of the current response dif-ference at n = 100 r/min is almost the same as that at n =4800 r/min (SaPN,n=100 r/min ≈ SaPN,n=4800 r/min). The es-timated slope differences SaPN of the current responses are

Fig. 11. Current slope differences SaPN as a function of the magnet temper-ature; compensated setup implying a positive and a negative voltage pulse inthe d-axis of the motor.

Fig. 12. Distribution of 25 measurements for SaPN for each referencemagnet temperature; n = 100 r/min.

depicted in Fig. 11 as a function of the magnet temperature forn = 100 r/min and n = 4800 r/min.

Regarding the initial d-current id,ref , the demonstrated setupis not optimal as it implies only maximum sensitivity for SaP

but not maximum sensitivity for SaN upon magnet temperaturevariation. This is because, for comparison, the same initiald-current for the positive voltage pulse is used, as estimatedfrom Fig. 6 (id,ref = 0.4 p.u.). However, the overall maximumsensitivity can be estimated by measuring the deviation ofSaPN at two different reference temperatures and drawing thedifference ΔSaPN as a function of id,ref,P , as in Fig. 6.

C. General Measuring Conditions

The demonstrated temperature estimation is conducted forreference temperatures from 20 ◦C to 120 ◦C with steps of10 ◦C. A set of 25 measurements is carried out for every refer-ence temperature. Thus, the estimated current slope for a givenreference temperature and speed is the mean value over 25measurements. The time interval between two sequential mea-surements for the same reference temperature is set to 100 ms.In the case of speed compensation, the distribution of the 25measurements of SaPN for each rotor reference temperatureat n = 100 r/min is shown as a histogram in Fig. 12, where asingle SaPN,1 measurement consists of a measurement of SaP,1

and a consequent measurement of SaN,1. The time interval be-tween the two measurements SaP,1 and SaN,1 is set to 100 ms.

GANCHEV et al.: COMPENSATION OF SPEED DEPENDENCE IN SENSORLESS ROTOR TEMPERATURE ESTIMATION 2493

Fig. 13. Temperature sensor locations in the rotor of the IPMSM under test.

TABLE IIROTOR TEMPERATURE SENSORS (SEE FIG. 13)

TABLE IIIROTOR TEMPERATURE SENSOR OUTPUTS FOR 60 ◦C

REFERENCE TEMPERATURE IN DEGREE CELSIUS

The gray lines in Fig. 12 indicate the mean values of SaPN over25 measurements.

The current sensors used in the presented setup are factoryintegrated in the inverter. According to the data sheets, thesensors have a temperature coefficient of 0.003%/◦C and anaccuracy of ±0.65%.

The thermocouples are of tolerance class 1, which implies arelative tolerance of ±0.36 ◦C for the investigated temperaturerange. The calibration of the temperature sensors, together withcircuitry of the rotor temperature measuring device (see Fig. 5),is carried out using a high-precision environmental chamber.The overall tolerance of the measured temperature signals istested to be around 1 ◦C [12]. For a given reference temperature,the average output of six temperature sensors is considered. Thelocation of the sensors is depicted in Fig. 13 and summarizedin Table II. The winding currents are controlled in a waythat a constant reference temperature is established across themagnets. This is interrupted for short-period test measurementsonly. The outputs of the sensors for measurements carried outat a reference temperature of 60 ◦C are listed in Table III.

V. DISCUSSION

Temperature estimation based solely on evaluation of thed-current response of a positive voltage pulse is influencedby the speed. The estimated d-current slope reveals a speed-dependent offset which is predominantly attributed to the volt-

Fig. 14. Magnet temperature estimation error at n = 4800 r/min with andwithout speed compensation.

age in the d-axis generated by the q-current component (Fig. 8).To identify this offset, the relationship between the d-currentresponse and the magnet temperature (did/dt ∼ Tm) shouldbe known at standstill and at the maximum expected operatingspeed. In case the offset cannot be identified, an additionalnegative pulse can be considered, which creates symmetry in(12) and reduces speed-dependent terms in (12). Dependingon the type of symmetry, the resulting temperature estimatedvalues can be considered, to a great extent, speed independent(see Fig. 11). The errors in the estimated magnet temperaturevalues at n = 4800 r/min derived from the presented exper-imental results are depicted in Fig. 14. In the case of speedcompensation, the absolute error could be reduced to less than4 ◦C. Although this is a relatively good value, in practice, theoverall accuracy and sensitivity of the proposed method dependstrongly on the topology of the motor, the temperature coef-ficient of the permanent magnets, the accuracy of the currentsensors, the number of measurements that can be carried outfor the estimation of a single magnet temperature level, and theavailable current oversampling capability of the control system[44]. Furthermore, not uniform temperature distribution acrossthe magnet is not considered in the current investigation. Allmeasurements are carried out at uniform magnet temperaturedistribution (see Table III).

VI. CONCLUSION

A method to estimate the permanent-magnet temperaturein IPMSM has been proposed. The method is characterizedwith relatively high accuracy along a wide motor speed range.While at low-speed or constant-speed applications, a singlevoltage pulse in the d-axis of the motor can be considered;in applications with a larger speed range, the accuracy of themethod can be clearly improved by applying an additionalnegative voltage pulse. The method can be adopted and tuned toalmost every type of PMSM and easily integrated in a commonfield-oriented control scheme. As presented, the method can becurrently applied only in applications where the load currentcan be set to zero for a time duration bigger or equal to three tofive times the electrical motor constant. The subject of ongoingresearch is to define method applicability under load conditionsby investigating the inherent influence of the q-current iq on thed-current response due to cross-saturation effects.

2494 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 49, NO. 6, NOVEMBER/DECEMBER 2013

REFERENCES

[1] K. Yoshida, Y. Hita, and K. Kesamaru, “Eddy-current loss analysis in PMof surface-mounted-PM SM for electric vehicles,” IEEE Trans. Magn.,vol. 36, no. 4, pp. 1941–1944, Jul. 2000.

[2] K. Yamazaki, M. Shina, Y. Kanou, M. Miwa, and J. Hagiwara, “Effect ofeddy current loss reduction by segmentation of magnets in synchronousmotors: Difference between interior and surface types,” IEEE Trans.Magn., vol. 45, no. 10, pp. 4756–4759, Oct. 2009.

[3] K. Yamazaki and A. Abe, “Loss investigation of interior permanent-magnet motors considering carrier harmonics and magnet eddy currents,”IEEE Trans. Ind. Appl., vol. 45, no. 2, pp. 659–665, Mar./Apr. 2009.

[4] K. Yamazaki, Y. Kanou, F. Yu, S. Ohki, A. Nezu, T. Ikemi, andR. Mizokami, “Reduction of magnet eddy-current loss in interiorpermanent-magnet motors with concentrated windings,” IEEE Trans. Ind.Appl., vol. 46, no. 6, pp. 2434–2441, Nov./Dec. 2010.

[5] J. D. Ede, K. Atallah, G. W. Jewell, J. B. Wang, and D. Howe, “Effectof axial segmentation of permanent magnets on rotor loss in modularpermanent-magnet brushless machines,” IEEE Trans. Ind. Appl., vol. 43,no. 5, pp. 1207–1213, Sep./Oct. 2007.

[6] K. Atallah, D. Howe, P. H. Mellor, and D. A. Stone, “Rotor loss inpermanent-magnet brushless AC machines,” IEEE Trans. Ind. Appl.,vol. 36, no. 6, pp. 1612–1618, Nov./Dec. 2000.

[7] M. Kamiya, Y. Kawase, T. Kosaka, and N. Matsui, “Temperature dis-tribution analysis of permanent magnet in interior permanent magnetsynchronous motor considering pwm carrier harmonics,” in Proc. ICEMS,Oct. 2007, pp. 2023–2027.

[8] A. Fukuma, S. Kanazawa, D. Miyagi, and N. Takahashi, “Investigation ofAC loss of permanent magnet of SPM motor considering hysteresis andeddy-current losses,” IEEE Trans. Magn., vol. 41, no. 5, pp. 1964–1967,May 2005.

[9] R. Krishnan and P. Vijayraghavan, “Fast estimation and compensation ofrotor flux linkage in permanent magnet synchronous machines,” in Proc.ISIE, 1999, vol. 2, pp. 661–666.

[10] T. Sebastian, “Temperature effects on torque production and efficiency ofPM motors using NdFeB magnets,” IEEE Trans. Ind. Appl., vol. 31, no. 2,pp. 353–357, Mar./Apr. 1995.

[11] J.-W. Jung, S.-H. Lee, J.-P. Hong, K.-N. Kim, H.-J. Cho, and S.-H. Moon,“Optimum design for eddy current reduction in permanent magnet toprevent irreversible demagnetization,” in Proc. ICEMS, Oct. 2007,pp. 949–954.

[12] M. Ganchev, H. Umschaden, and H. J. Kapeller, “Rotor temperaturedistribution measuring system,” in Proc. 37th Annu. IEEE IECON,Nov. 2011, pp. 2006–2011.

[13] D. J. T. Siyambalapitiya, P. G. McLaren, and P. P. Acarnley, “A rotorcondition monitor for squirrel-cage induction machines,” IEEE Trans.Ind. Appl., vol. IA-23, no. 2, pp. 334–340, Mar. 1987.

[14] H. Yahoui and G. Grellet, “Measurement of physical signals in rotatingpart of electrical machine by means of optical fibre transmission,” in Proc.IMTC, Jun. 1996, vol. 1, pp. 591–596.

[15] H. Zhe and G. Guobiao, “Wireless rotor temperature measurement systembased on MSP430 and nRF401,” in Proc. ICEMS, Oct. 2008, pp. 858–861.

[16] X. Xue, V. Sundararajan, and W. P. Brithinee, “The application of wire-less sensor networks for condition monitoring in three-phase inductionmotors,” in Proc. Elect. Insul. Conf. Elect. Manuf. Expo, Oct. 2007,pp. 445–448.

[17] H. Hafezi and A. Jalilian, “Design and construction of induction motorthermal monitoring system,” in Proc. Univ. Power Eng. Conf., Sep. 2006,vol. 2, pp. 674–678.

[18] G. Jianzhong, G. Hui, and H. Zhe, “Rotor temperature monitoring tech-nology of direct-drive permanent magnet wind turbine,” in Proc. ICEMS,Nov. 2009, pp. 1–4.

[19] Z. Lazarevic, R. Radosavljevic, and P. Osmokrovic, “A new thermalobserver for squirrel-cage induction motor,” in Proc. IMTC, Jun. 1996,vol. 1, pp. 610–613.

[20] M. Kovacic, M. Vražic, and I. Gašparac, “Bluetooth wireless communica-tion and 1-wire digital temperature sensors in synchronous machine rotortemperature measurement,” in Proc. 14th Int. EPE/PEMC, Sep. 2010,pp. T7-25–T7-28.

[21] C. Kral, A. Haumer, M. Haigis, H. Lang, and H. Kapeller, “Comparisonof a CFD analysis and a thermal equivalent circuit model of a TEFCinduction machine with measurements,” IEEE Trans. Energy Convers.,vol. 24, no. 4, pp. 809–818, Dec. 2009.

[22] S. Stipetic, M. Kovacic, Z. Hanic, and M. Vrazic, “Measurement ofexcitation winding temperature on synchronous generator in rotation us-ing infrared thermography,” IEEE Trans. Ind. Electron., vol. 59, no. 5,pp. 2288–2298, May 2012.

[23] D. Reigosa, F. Briz, P. Garcia, J. M. Guerrero, and W. Degner, “Magnettemperature estimation in surface PM Machines using high-frequencysignal injection,” IEEE Trans. Ind. Appl., vol. 46, no. 4, pp. 1468–1475,Jul./Aug. 2010.

[24] D. Reigosa, F. Briz, M. W. Degner, P. Garcia, and J. M. Guerrero,“Magnet temperature estimation in surface PM machines during six-step operation,” IEEE Trans. Ind. Appl., vol. 48, no. 6, pp. 2353–2361,Nov./Dec. 2012.

[25] C. Mejuto, M. Mueller, M. Shanel, A. Mebarki, M. Reekie, and D. Staton,“Improved synchronous machine thermal modelling,” in Proc. ICEM,Sep. 2008, pp. 1–6.

[26] W. T. Martiny, R. M. McCoy, and H. B. Margolis, “Thermal relationshipsin an induction motor under normal and abnormal operation,” Trans.Amer. Inst. Elect. Eng. Power App. Syst., Part III, vol. 80, no. 3, pp. 66–76,Apr. 1961.

[27] E. Odvarka, N. L. Brown, A. Mebarki, M. Shanel, S. Narayanan, andC. Ondrusek, “Thermal modelling of water-cooled axial-flux perma-nent magnet machine,” in Proc. 5th IET Int. Conf. PEMD, Apr. 2010,pp. 1–5.

[28] Y. Chun, W. Keying, and W. Xiaonian, “Coupled-field thermalanalysis of high-speed permanent magnetic generator applied inmicro-turbine generator,” in Proc. 18th ICEMS, Sep. 2005, vol. 3,pp. 2458–2461.

[29] A. Boglietti, A. Cavagnino, and D. Staton, “Determination of criticalparameters in electrical machine thermal models,” IEEE Trans. Ind. Appl.,vol. 44, no. 4, pp. 1150–1159, Jul./Aug. 2008.

[30] A. Boglietti, A. Cavagnino, D. Staton, M. Shanel, M. Mueller, andC. Mejuto, “Evolution and modern approaches for thermal analysis ofelectrical machines,” IEEE Trans. Ind. Electron., vol. 56, no. 3, pp. 871–882, Mar. 2009.

[31] C. Lim, J. Bumby, R. Dominy, G. Ingram, K. Mahkamov, N. Brown,A. Mebarki, and M. Shanel, “2-D lumped-parameter thermal model-ing of axial flux permanent magnet generators,” in Proc. 18th ICEM,Sep. 2008, pp. 1–6.

[32] C. Jungreuthmayer, T. Bauml, O. Winter, M. Ganchev, H. J. Kapeller,A. Haumer, and C. Kral, “A detailed heat and fluid flow analysis ofan internal permanent magnet synchronous machine by means of com-putational fluid dynamics,” IEEE Trans. Ind. Electron., vol. 59, no. 12,pp. 4568–4578, Dec. 2012.

[33] T. Bauml, C. Jungreuthmayer, and C. Kral, “An innovative parameteriza-tion method for a thermal equivalent circuit model of an interior perma-nent magnet synchronous machine,” in Proc. 37th Annu. IEEE IECON,Nov. 2011, pp. 1746–1751.

[34] B.-H. Lee, K.-S. Kim, J.-W. Jung, J.-P. Hong, and Y.-K. Kim, “Tempera-ture estimation of IPMSM using thermal equivalent circuit,” IEEE Trans.Magn., vol. 48, no. 11, pp. 2949–2952, Nov. 2012.

[35] R. Wrobel, P. H. Mellor, and D. Holliday, “Thermal modeling of a seg-mented stator winding design,” IEEE Trans. Ind. Appl., vol. 47, no. 5,pp. 2023–2030, Sep./Oct. 2011.

[36] D. M. Ionel, M. Popescu, M. McGilp, T. J. E. Miller, S. J. Dellinger, andR. J. Heideman, “Computation of core losses in electrical machines usingimproved models for laminated steel,” IEEE Trans. Ind. Appl., vol. 43,no. 6, pp. 1554–1564, Nov./Dec. 2007.

[37] D. M. Ionel and M. Popescu, “Finite-element surrogate model for electricmachines with revolving field-application to IPM motors,” IEEE Trans.Ind. Appl., vol. 46, no. 6, pp. 2424–2433, Nov./Dec. 2010.

[38] P. Milanfar and J. H. Lang, “Monitoring the thermal condition ofpermanent-magnet synchronous motors,” IEEE Trans. Aerosp. Electron.Syst., vol. 32, no. 4, pp. 1421–1429, Oct. 1996.

[39] G. D Demetriades, H. Z. de la Parra, E. Andersson, and H. Olsson, “A real-time thermal model of a permanent-magnet synchronous motor,” IEEETrans. Power Electron., vol. 25, no. 2, pp. 463–474, Feb. 2010.

[40] A. Specht and J. Böcker, “Observer for the rotor temperature of IPMSM,”in Proc. 14th Int. EPE/PEMC, Sep. 2010, pp. T4-12–T4-15.

[41] J. Wu, F. Leonardi, F. Liang, W. Degner, and D. Luedtke, “Permanentmagnet temperature estimation,” U.S. Patent 7 979 171, Jul. 12, 2011.

[42] M. Ganchev, C. Kral, H. Oberguggenberger, and T. Wolbank, “Sensorlessrotor temperature estimation of permanent magnet synchronous motor,”in Proc. 37th Annu. IEEE IECON, Nov. 2011, pp. 2018–2023.

[43] M. Ganchev, C. Kral, and T. Wolbank, “Hardware and software imple-mentation of sensorless rotor temperature estimation technique for per-manent magnet synchronous motor,” in Proc. IEEE Int. Conf. ESARS,Oct. 2012, pp. 1–6.

[44] M. Ganchev, C. Kral, and T. Wolbank, “Identification of sensorless ro-tor temperature estimation technique for permanent magnet synchronousmotor,” in Proc. Int. SPEEDAM, Jun. 2012, pp. 38–43.

GANCHEV et al.: COMPENSATION OF SPEED DEPENDENCE IN SENSORLESS ROTOR TEMPERATURE ESTIMATION 2495

Martin Ganchev (S’12) received the Dipl.-Ing de-gree from the Vienna University of Technology,Vienna, Austria, in 2005. He is currently workingtoward the Ph.D. degree in the field of rotor temper-ature estimation of permanent-magnet synchronousmotors at the Austrian Institute of Technology (AIT),Vienna, and at the Vienna University of Technology.

Since 2004, he has been with AIT. His main re-search interests and activities are focused on electricmachine diagnostic algorithms, motor digital controlprogramming, motor control optimization, and hard-

ware design of motor test benches.

Christian Kral (M’00–SM’05) received the Dip-loma and Ph.D. degrees from the Vienna Universityof Technology, Vienna, Austria, in 1997 and 1999,respectively.

From 1997 to 2000, he was a Scientific Assistantwith the Institute of Electrical Drives and Machines,Vienna University of Technology. Since 2001, he hasbeen with the Austrian Institute of Technology (theformer Arsenal Research), Vienna. From January2002 to April 2003, he was a Visiting Professor at theGeorgia Institute of Technology, Atlanta, GA, USA.

His current research interests include diagnostics and monitoring techniquesand the modeling and simulation of electric machines and drives with aparticular focus on nonlinear effects, thermal behavior, and faulty machineconditions.

Dr. Kral is a member of the Austrian Electrotechnical Association (OVE) andthe Modelica Association.

Thomas M. Wolbank (M’92) received the Ph.D. de-gree and the Habilitation from the Vienna Universityof Technology, Vienna, Austria, in 1996 and 2004,respectively.

He is currently with the Department of EnergySystems and Electrical Drives, Vienna University ofTechnology. He has coauthored some 100 papersin refereed journals and international conferenceproceedings. His research interests include saliency-based sensorless control of ac drives, dynamicproperties and condition monitoring of inverter-fed

machines, transient electrical behavior of ac machines, and motor drivesand their components and controlling them by the use of intelligent controlalgorithms.