optimal control of traction motor drives under electro-thermal constraints

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/JESTPE.2014.2299765, IEEE Journal of Emerging and Selected Topics in Power Electronics

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Optimal Control of Traction Motor Drives underElectro-Thermal Constraints

Joris Lemmens, Student Member, IEEE, Piet Vanassche, and Johan Driesen, Senior Member, IEEE

Abstract—Peak torque and power density requirements fortraction motor drives continue to increase, while demands onreliability are getting increasingly stringent as well. With theknowledge that most failure mechanisms are related to excessivetemperature (cycling), thermal management is key for increasingperformance, without jeopardizing reliability. This paper pro-poses a control strategy for active thermal management of PMSMdrives, based on real-time estimation and feedback of switchingdevice and motor temperatures. By regulating the switchingfrequency and current control limit, critical components canbe safeguarded from excessive temperature rise. Furthermore,optimal dq-current control vectors are calculated within thetemperature and voltage constraints, to maximize the drive’sefficiency and speed-torque envelope. Hence, the control strategyenables the drivetrain to operate safely at maximum attainableperformance limits. The strategy is experimentally validated onan 11 kW PMSM drive for a number of representative vehicleloads, including a maximum standstill torque test, a maximumacceleration test and a driving cycle test.

Index Terms—Power electronics, PMSM control, thermal man-agement, efficiency optimization, reliability.

I. INTRODUCTION

REQUIREMENTS for traction drives in electric vehiclesinclude a high efficiency, minimal volume and weight,

high starting torque, intermittent overload capability, highspeed operation with a large maximum output power, fastdynamic response, high reliability and low cost [1]. The ever-increasing power density requirements and the challengingthermal environment in automotive applications [2] push thelimits of motor, switching device and thermal managementtechnology [3], [4]. New developments are necessary at thecomponent, packaging, system and control strategy level toimprove performance without jeopardizing reliability [5].

A drive’s reliability is determined by its most vulnerablecomponents, i.e. the electrolytic capacitors and power semi-conductor devices [6]. Due to temperature gradients and dif-fering coefficients of thermal expansion, internal connectionsin the power module are subjected to thermo-mechanical strainduring power or temperature cycling [7]. This can invoke anumber of failure mechanisms such as fatigue of the chip,substrate (DBC) or baseplate soldering and bond-wire lift-offor breakage [8]. Lifetime prediction algorithms based on theaccumulation of damage due to cycling fatigue are given in[9]–[11]. The models contain a Coffin-Manson relationship,directly relating the number of cycles to failure to the device’s

J. Lemmens and J. Driesen are with the Department of Electrical Engi-neering, division ELECTA, KU Leuven, 3001 Heverlee, Belgium (e-mail:[email protected]; [email protected]).

P. Vanassche is with Triphase NV, 3001 Heverlee, Belgium (e-mail:[email protected]).

Fig. 1. Number of cycles to failure as a function of temperature cycleamplitude ∆Tj for different mean Tjm and maximum Tj,max junction tem-peratures. Power cycling lifetime industrial standard (2009), taken from [8].

mean junction temperature Tjm and the temperature cyclingamplitude ∆Tj [8], [12] as shown in Fig. 1. This also appliesto the motor, where excessive temperature rise due to overloadwill damage stator winding insulation and degrade permanentmagnet materials [13]. Temperature-induced damage can beavoided by defining an adequate safety margin in the formof a maximum torque/current rating. However, a conservativerating benefits lifetime on the one hand, but implies a (maybeunnecessary) restriction of performance on the other. Thistrade-off should be optimized to maximize the utilizationof the drivetrain’s thermal capacity, i.e. getting more outputwithout putting reliability at risk.

Current ratings as specified in inverter datasheets are oftenbased on average junction temperature calculations with theassumption of a relatively high electrical frequency comparedto the thermal time constants of the switching devices. Thisimplies that the variation of junction temperature with loadcurrent during a modulation cycle is sufficiently small tobe neglected. However, traction drives frequently operate athigh torque and low speed, for example during repeatedacceleration and regenerative braking in urban traffic. Whenmodulation frequency decreases (<2...5 Hz) at equal torqueoutput, junction temperatures show a larger fluctuation andreach a higher peak value due to the low pass filter charac-teristic of the junction-to-case transient thermal impedance. Inaddition, power modules are generally optimized for inverteroperation with the assumption of a modulation index greaterthan 0.5 [14]. For this type of duty, the majority of loadis on the IGBTs. Therefore, they are generally providedwith a larger chip surface, i.e. a smaller thermal resistance,compared to the freewheeling diodes (FWDIs). The undersizeddiodes are stressed heavily at low speed operation, whendominant load is on the FWDIs. This can become particularlyproblematic for a PMSM drive generating standstill torque. Fora number of distinct rotor positions, one single diode carriesmaximum DC phase current almost continuously, resulting in



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a large elevation of junction temperature. Therefore, the drive’smaximum current rating should be sufficiently low to accountfor this load type and the highest anticipated heatsink/coolanttemperature. However, this implies a sub-maximal utilizationat non-worst-case conditions. Torque is restricted unnecessar-ily, without attaining actual thermal limits.

The key to a better utilization of the drivetrain’s thermalcapacity is taking the actual thermal state into account. Thisrequires a form of temperature feedback of critical componentssuch as permanent magnets, stator windings and semicon-ductor junctions. Unfortunately, readily available measure-ments like heatsink or coolant temperature do not providethe necessary time-critical information. Real-time temperatureestimation with a dynamic thermal model [15]–[19] or thermo-sensitive parameter observation [20]–[23] can offer a solu-tion. Temperature estimates can be used in conjunction withmechanical stress models or physics-of-failure based modelsfor in-service condition monitoring [24], [25]. Applicationsinclude prediction of failure modes, prognosis of remaininglifetime and scheduling of preventative maintenance.

Based on earlier work [26], [27], this paper proposes acontrol strategy using temperature observer feedback for activethermal management, i.e. regulation of drivetrain losses toprevent excessive temperature (cycling). It integrates intoa PMSM field-oriented-control (FOC) algorithm, with theobjective of maximizing performance inside electro-thermalconstraints. Critical component temperatures (amplitude andvariation) follow from a trade-off between performance andlifetime. Applying these thermal constraints to the proposedcontrol algorithm enables operation at maximum attainableperformance limits. Fig. 2 gives an overview of the proposedcontrol algorithm and experimental setup. The thermal stateobserver (Section III) estimates motor and IGBT/FWDI junc-tion temperatures. Depending on the actual margins relativeto the predefined temperature limits, the thermal managementloop performs active loss regulation by setting adaptive con-straints to the current amplitude and switching frequency. Thisis elaborated in Section IV. In order to minimize the error onthe driver’s torque request, the dq-current setpoint calculationis optimized inside the current and voltage constraint region(Section II). Hence, efficiency and torque are maximized atevery operating point, even when thermal limits are reached.This is the added value compared to existing strategies [14],[28]–[30], i.e. combining active thermal management withefficiency optimization and voltage/current limiting in oneglobal control approach.

The strategy is applied to an experimental setup whichmimics a series-hybrid drivetrain topology (without consider-ing battery storage), using modular power electronic convert-ers [31] as shown in Fig. 3. The vehicle’s combustion enginedriven synchronous generator is represented by the grid whichis interfaced through a 17 kVA active frontend. This powermodule facilitates power factor correction and regenerativebraking. A second 17 kVA power module controls the 11 kWinterior PMSM of which the main parameters are given inTable I. This machine is mounted on a test bench including atorque transducer and a DC-machine to emulate dynamic vehi-cle load characteristics. The control algorithm is implemented

Fig. 3. Experimental setup: 3PExpressTM Rapid Prototyping Platform [32]controlling an 11 kW PMSM and a DC-machine for dynamic load emulation.

TABLE IPMSM PARAMETERS

Rated power 11 kWRated torque 70 NmRated speed 1500 RPM

Rated current 20.2 ANumber of pole pairs p 3d-axis inductance Ld 10 mHq-axis inductance Lq 19 mH

Flux linkage Ψ 0.7885 VsStator resistance Rs (24 - 80 C) 0.349 - 0.426 Ω

in Matlab/SimulinkTM, using the Triphase 3PExpressTM rapidprototyping platform [32] to interface both power modules.Extensive experimental results and discussion are given inSection V. The added value of the proposed control strategyis demonstrated for typical vehicle load conditions includingstandstill operation, maximum acceleration and a dynamicdriving cycle. Finally, conclusions are drawn in Section VI.

II. OPTIMAL PMSM CONTROL UNDER VOLTAGE ANDCURRENT CONSTRAINTS

A. PMSM Torque and Voltage Equations

In the dq-framework rotating synchronously with electricalangular frequency ωel, PMSM electromagnetic torque Tel isexpressed by (1), with p the number of pole pairs, id and iqthe direct and quadrature motor currents, Ψ the permanentmagnet flux linkage, Ld the d-axis inductance and Lq theq-axis inductance. Note that the iron loss resistance RFe asshown in the equivalent scheme of Fig. 4 is assumed infinitefor calculation of Tel. The resulting motor voltages ud and uqare given by (2), with Rs the stator winding resistance.

Tel = p iq (Ψ− (Lq − Ld) id) (1)ud = Rsid − ωelLqiquq = Rsiq + ωelLdid + ωelΨ

(2)

+ -

+-

+-

Fig. 4. PMSM steady-state equivalent scheme.



3

NNOkWOinteriorOPMSM

DC

ActiveOfrontend Inverter

DynamicOLoadOEmulator

DC6link

GridGrid

LCL6filter

Experimental setup

FieldOOrientedOControl

Thermal managementTemperatureOprotectionOofOdrivetrainOcomponentsObyOactiveOlossOcontrol

Loss modelReal6timeOmotorOandOinverterOlossOcalculation

Thermal modelReal6timeOmotorOandOinverterOtemperatureOestimation

Thermal state observer

VehicleOmodel

SpeedTorque

Control algorithm

N . 3

4 5 6

3PExpressTMOPowerOModules

Torquerequest

AdaptiveOcurrentOlimit

VoltageOlimit

dq6currentOsetpoints

AdaptiveOswitchingOperiod

PWM TemperatureOmeasurements

Encoder

Voltage/Current limiting

MEPNmcontrol

RotorOposition

OptimalOd6axisOcurrentOsetpx

frequency

PreviousOiterationOd6axisOcurrentOsetpx

Fig. 2. Block diagram of the proposed control algorithm and experimental setup.

B. Maximum Efficiency per Nm Control

According to the PMSM torque equation (1), the requestedtorque T ∗

el can be generated with an infinite number of possibledq-current setpoint combinations i∗d and i∗q . However, theallowable operating area in the dq-current plane is restricted bya current limit circle and a voltage limit ellipse (Section II-C).Making abstraction of these limitations, the d-axis currentcan be chosen freely to obtain a desired operating regime.Examples include 90-degree current angle (id = 0), MaximumTorque per Ampere (MTPA) or unity power factor opera-tion. This paper implements a Maximum Efficiency per Nm(MEPNm) strategy, a model-based approach to generate dq-current setpoints yielding minimal overall motor and inverterlosses. First, approximate analytical loss expressions for thePMSM-inverter combination of Fig. 3 are derived.

Due to the stator winding resistance, motor currents give riseto copper loss PCu according to (3). Note that the dependencyof Rs on winding temperature Twinding is taken into accountin (4) by thermal model feedback (Section III-A).

PCu = Rs (i2d + i2q) (3)

Rs = 0.349(1 + 3.93e−3(Twinding − 24)

)(4)

Iron loss PFe is given by (5) as the dissipated power in anequivalent iron loss resistance RFe. The latter is a functionof ωel and was experimentally determined according to [33]as shown in Fig 5. With a least-squares data-fit, an analyticalexpression for RFe was derived.

PFe =(ud −Rsid)2 + (uq −Rsiq)2

RFe

=(ωelLqiq)

2 + (ωelLdid + ωelΨ)2

RFe(5)

Losses in the hard-switching voltage-source inverter (VSI)can be subdivided into switching and conduction loss. Ac-cording to [8], the conduction loss in a single IGBT or FWDI

Fig. 5. Equivalent iron loss resistance (RFe = 2.1182ωel + 42.427),experimentally determined according to [33].

device, averaged over one electrical period is calculated as:

P c,igbt =1

2π

π∫0

Vce i sin(x)1 + δ ·m(x+ ϕ)

2dx (6)

P c,fwdi =1

2π

2π∫π

Vec

∣∣∣i sin(x)∣∣∣ 1 + δ ·m(x+ ϕ)

2dx (7)

with i =√

23 (i2d + i2q) the line current amplitude, ϕ the phase

angle between voltage and current and δ the maximum dutycycle (from 0 to 1) in a fundamental period. Multiplying δwith the modulation function m(x + ϕ) gives an expressionfor the modulation index. Note that m(x+ϕ) equals sin(x+ϕ)in case of sinusoidal PWM. In this paper, space-vector modu-lation (SVM) is applied. Hence, the modulation function is asuperposition of a sine wave and a third harmonic triangularwave, limited between -1 and +1. The current and temperaturedependent IGBT and FWDI voltage drops Vce (as shown inFig. 6) and Vec are provided in the power module’s data sheetgraphs [34].

IGBT switching loss and FWDI reverse recovery loss can becalculated from (8) and (9) with Ts the switching period, Udc



4

Fig. 6. IGBT collector-emitter voltage drop Vce [34].

the DC-link voltage, Eon, Eoff the IGBT turn-on and turn-off energy loss and Err the FWDI reverse recovery energyloss. Switching energy loss graphs as a function of current areprovided in [34], at reference DC-bus voltage Uref .

Psw,igbt =1

Ts· (Eon + Eoff ) · Udc

Uref(8)

Prr,fwdi =1

Ts· Err ·

UdcUref

(9)

In what follows, a strategy to generate optimal d-axiscurrent setpoints using the previous loss equations is described(MEPNm control block in Fig. 2). To simplify the calculations(see further), a number of assumptions are made. First, a fixedvalue of 1.5 V is assigned to the IGBT and FWDI voltage drop.Hence, because Vce = Vec, the sum of average IGBT (6) andFWDI (7) conduction losses becomes independent of δ and ϕand simplifies to:

P c,igbt + P c,igbt ≈Vceπ

√2

3

(i2d + i2q

)(10)

In addition to the previous assumption, switching energy lossesEon, Eoff and Err are also considered constant (no currentdependency). It should be noted that polynomials expressingthe temperature and/or current dependency of switching deviceparameters, allowing more accurate power loss calculations forjunction temperature estimation, are used in Section III-B.

The copper (3), iron (5) and inverter conduction losses (10)are functions of both id and iq . Solving the torque equation (1)to iq and substituting into these loss expressions results insingle variable (id) equations. Doing so, the total (average)inverter conduction loss P c,inv is expressed by (11). The samesubstitution of iq needs to be applied applied in the copper andiron loss equations (3) and (5).

P c,inv =2√

6

πVce

√i2d +

T 2el

p2(Ψ− (Lq − Ld)id)2(11)

The d-axis current corresponding to minimal overall lossesfor a given torque request T ∗

el and actual (measured) motorfrequency ωel can be found with a Newton iteration. Eachiteration, a step adjustment did,opt is calculated with (12)and applied to the previous iteration d-axis current setpointid,0 (13). Note that (12) only includes loss componentsdependent on d-axis current, i.e. excluding switching losses(simplification). Taking into account the voltage and/or currentconstraints of the motor drive, i∗d,opt can be overruled by thevoltage/current limiting block of Fig. 2 (discussed in Sec-tion II-C). For example, if field-weakening operation becomes

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0800

850

900

950

1000

1050

1100

1150

1200

Fig. 7. Combined motor and inverter losses (measured) as a function ofd-axis current with indication of the MTPA and MEPNm operating points.

necessary at high speed to limit motor voltage, a larger (morenegative) field-weakening current than i∗d,opt will be applied.If no voltage or current limitations are attained, i∗d,opt willconverge to the optimal value, i.e. the minimum of the convexoverall loss curve as shown in Fig. 7.

did,opt = −

d

did

(PCu + PFe + P c,inv

)d2

di2d

(PCu + PFe + P c,inv

)∣∣∣∣∣∣∣∣∣id=id,0

(12)

i∗d,opt = id,0 + did,opt (13)

Table II compares the proposed MEPNm strategy withtwo more straightforward alternatives; i.e. MTPA and 90-degree current angle (id = 0) control. While applying aconstant 71 Nm load to the PMSM at speeds between 400 and1400 RPM, the combined inverter and motor loss is measuredwith a Voltech PM6000 power analyzer and a torque/speedtransducer. In addition, SVM signal amplitude δ and cosϕare recorded for each operating point. Switching frequencyis set at 10 kHz and Udc = 650 V. As a reference, wetake the power losses at 90-degree current angle control. TheMTPA strategy is able to lower the current-dependent lossesconsiderably by exploiting the interior PMSM’s reluctancetorque component (Ld < Lq). The MEPNm strategy reduceslosses further, because it optimizes overall loss, including ironand inverter losses. The additional field-weakening current ofMEPNm compared to MTPA reduces iron loss at elevatedspeed. In absolute numbers, the benefit is quite small for theconsidered PMSM due to the relatively low speed and lowspecific core losses. In Fig 7, the measured motor and inverterpower loss is plotted as a function of the optimized variable id.This illustrates that, despite the numerous simplifications, theMEPNm-generated d-axis current approximates the minimumof the convex loss curve. As speed increases, the differencebetween MTPA and MEPNm becomes more significant dueto the larger share of iron losses.



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TABLE IIMEASURED MOTOR + INVERTER LOSSES AT CONSTANT TORQUE WITH THREE DIFFERENT D-AXIS CURRENT CONTROL STRATEGIES

id = 0 MTPA MEPNm

Speed Torque Ploss δ cosϕ id ∆Pid=0 δ cosϕ id ∆Pid=0 δ cosϕ[RPM] [Nm] [W] [-] [-] [A] [W] [-] [-] [A] [W] [-] [-]

400 71 956 0.33 0.83 -9.1 -144 0.32 0.93 -9.9 -148 0.31 0.94600 71 1016 0.46 0.81 -9.1 -156 0.44 0.92 -10.4 -164 0.43 0.93800 71 1068 0.60 0.79 -9.1 -168 0.56 0.91 -10.9 -179 0.55 0.931000 71 1123 0.73 0.77 -9.1 -177 0.68 0.91 -11.2 -190 0.66 0.931200 71 1182 0.86 0.76 -9.1 -187 0.80 0.90 -11.6 -206 0.78 0.931400 71 1226 0.98 0.76 -9.1 -173 0.92 0.90 -12.1 -194 0.89 0.93

C. Voltage and Current Limiting

The voltage/current limiting block in Fig. 2 generates cur-rent setpoints i∗d and i∗q to maximize efficiency and torque,without violating current or voltage constraints. A maximumallowable current amplitude |I|lim is imposed by the thermalmanagement loop (Section IV) to prevent thermally-inducedfailure of motor and/or inverter components. Hence, the dq-current setpoints must satisfy:

|I| =√i2d + i2q ≤ |I|lim (14)

In addition, maximum achievable voltage amplitude |U |limdepends on the DC-link voltage Udc and the PWM method. Incase of space vector modulation, the voltage limit is calculatedfrom the measured Udc, with ∆U a small control margin:

|U |lim =Udc√

2−∆U (15)

Hence, the resulting dq-voltages must satisfy:

|U | =√u2d + u2q ≤ |U |lim (16)

These limitations are represented in graphical form in Fig. 8,with motor parameters according to Table I. The allowableoperating range is determined by the overlapping area of thecurrent limit circle and the voltage limit ellipse. Maximumtorque within the 35 A current limit equals 88.45 Nm (MTPApoint A). Due to the dependency of motor voltage magnitudeon electrical frequency, the voltage limit ellipse shrinks withincreasing speed and/or decreasing DC-link voltage. Field-weakening operation, i.e. injecting an additional negative id,becomes necessary from a certain speed to limit the motorvoltage at |U |lim. Hence, the operating point shifts away fromthe MTPA curve and the maximum feasible torque duringfield-weakening operation is determined by the intersectionof ellipse and circle. Assuming a 500 V DC-link voltage anda ∆U of 0 V in Fig. 8, the maximum torque point shiftsfrom A to B along the current limit circle above 1178 RPM.The maximum attainable (theoretical) speed for the consideredPMSM is finite (2568 RPM), because point B on the d-axiscorresponding to full field-weakening is not encircled by thecurrent limit circle, i.e. Ψ/Ld > |I|lim. Note that this speedlimit does not take mechanical constraints into account.

An ideal PMSM current vector control strategy should gen-erate dq-current setpoints i∗d and i∗q according to the followingorder of priority:

1) Satisfy the voltage limit (16). This constraint is con-sidered more stringent than the current limit because

-80 -60 -40 -20 0 20 40-40

-30

-20

-10

0

10

20

30

40

Fig. 8. Theoretical torque curves, voltage limit ellipses, MTPA trajectory andcurrent limit circle calculated with PMSM parameters according to Table I.

a broken voltage constraint eventually leads to loss ofcontrol, yielding unwanted currents anyway.

2) Satisfy the current limit (14) to protect components fromthermal damage.

3) Minimize error on requested torque T ∗el.

4) Minimize error on MEPNm/MTPA d-axis current set-point i∗d,opt.

Numerous PMSM current vector control strategies includingflux-weakening operation were proposed in literature [35].Feedforward approaches [36] apply analytically or experimen-tally determined current vectors for each speed and torqueoperating point. This yields fast transient response, but requireslookup tables or solving complex equations online. Further-more, motor parameters are subject to variation with tempera-ture and/or saturation which leads to a significant discrepancybetween model and reality. Consequently, feedforward controlcould result in a violation of current or voltage limitationsor sub-maximal performance. On the other hand, feedbackmethods [37] are more robust, but are generally less dynamic.In this paper, an enhanced feedback current vector controlmethod is applied, combining a high degree of robustness withfast transient response. A detailed description of this algorithmis out of the scope of this paper, but is available in [38]. Itshould be noted that alternative PMSM current vector controlstrategies available in literature [35]–[37] could be integratedin the global control loop of Fig. 2 as well.

In what follows, the experimental results of Fig. 9 andFig. 10 are discussed to analyze the behaviour of the volt-age and current limiting block shown in Fig. 2. During the



6

Fig. 9. Experimental validation of the PMSM current vector control blockperforming voltage and current limiting (dq-current plot).

experiment, DC-link voltage is maintained constant at 300 Vby the active front-end. Taking into account a voltage margin∆U of 20 V, the voltage limit |U |lim equals 192 V. First,the current limit |I|lim is gradually increased from 0 to 25 Awhile the rotor is held stationary by the load machine. Hence,the dq-current operating point shifts from A along the MTPAcurve until the 40 Nm torque request is satisfied. Note thatat standstill operation, MTPA is equivalent to MEPNm asiron losses are zero. Next, the speed-controlled load machineramps up from 0 to 1500 RPM. To obtain MEPNm operation,the negative d-axis current amplitude is slightly increased tocounteract the increasing iron losses. At a speed of 670 RPM,the voltage limit is reached in operating point B. As speedincreases further, deeper field weakening is required, shiftingthe operating point from B to C along the 40 Nm torque line.Note that in this operating mode, the MEPNm d-axis currentsetpoint i∗d,opt can not be satisfied. In C (870 RPM), |I|limis reached and T ∗

el can not be delivered any longer as speedincreases further. Hence, the drive operates on the current andvoltage limit between C and D. In D, the maximum allowablespeed (1315 RPM) according to the current and voltage limitis reached. Operation beyond this point is not allowed becauseit implies a violation of the current constraint. However, thestrategy will still maintain control of the PMSM drive, tocontinue satisfying |U |lim with minimum current overshoot.

III. MOTOR AND CONVERTER THERMAL STATEOBSERVATION

Active thermal management requires real-time feedbackof IGBT/FWDI junction and motor temperatures, which areoften difficult to access and measure directly. Therefore, thecontrol strategy in Fig. 2 includes online loss calculations incombination with lumped-parameter thermal models.

A. Motor Temperature Estimation

Copper loss PCu is calculated with (3), iron loss PFewith (5), while rotor loss Pr is neglected. Note that thedependency of Rs on winding temperature Twinding is takeninto account by thermal model feedback. Furthermore, motor

Fig. 10. Experimental validation of the PMSM current vector control blockperforming voltage and current limiting (time plot).

voltages ud and uq in (5) are obtained directly from theFOC-block PI current control loops. All loss components aresupplied to a lumped-parameter thermal model of the TEFC(Totally Enclosed Fan Cooled) motor, which was implementedaccording to [39]. Fig. 11 shows the structure of the thermalmodel in a simplified form. The nodes represent averagetemperatures of the frame Tframe, stator core Tcore, statorwinding Twinding and rotor Trotor. Thermal resistances andcapacitances were calculated from material properties, motorgeometry and basic experimental data according to [19], [39],[40]. Note that the thermal resistance between motor frameand ambient is dependent on the rotor speed due to theshaft-mounted fan. The cooling air speed and correspondingconvection coefficient were determined experimentally, butremain a large source of uncertainty. Therefore, the PMSMthermal model is implemented as a Kalman filter. This offersthe possibility to include weighted information of a PT100temperature sensor mounted on the motor frame to improveaccuracy of the estimates. As shown in Fig. 12, estimated(solid lines) and measured (dots) temperatures are in goodagreement. Frame and core temperatures were measured with



7

Fig. 11. PMSM (TEFC-design) lumped-parameter thermal model (shown ina simplified form).

Fig. 12. Motor thermal model validation at nominal load (1500 RPM, 70Nm).

thermocouples with the PMSM operating at nominal load.Winding temperature was derived from an offline stator re-sistance measurement (indicated with an X on Fig. 12).

B. IGBT/FWDI Junction Temperature Estimation

Real-time junction temperature estimation requires calcula-tion of the instantaneous loss in each IGBT and FWDI deviceof the voltage-source inverter. Therefore, the device-specificconduction and switching losses per switching timecycle Tsare calculated online. This approach neglects the detailedbehaviour of the semiconductor devices within one switchingcycle but gives sufficient detail to include power cycling atfundamental frequency.

The relation between IGBT collector-emitter voltage dropVce and collector current, based on datasheet [34] values at25 and 125 C, is shown in Fig. 6. In order to includethis non-linear dependency in the calculation of the IGBTconduction loss, each current value in the datasheet graph ismultiplied with the according voltage drop. This procedure[17] has the advantage that the resulting conduction loss curvesas a function of current can easily be approximated with asecond order polynomial. The IGBT conduction loss surface inFig. 13 is described by (17). Note that the current dependencyand temperature dependency are described respectively by asecond and first order polynomial. A similar function (18) isderived for the FWDI conduction loss. Note that it does notinclude a temperature dependency as this is not provided inthe datasheet Vec-graph.

Pc,igbt(i, T ) = 1.149 · |i|+7.35e−3 · i2 +1.81e−3 · |i| ·T (17)

Pc,fwdi(i) = 1.496 · |i|+ 10.37e−3 · i2 (18)

For each IGBT-FWDI combination in the power module,the conduction current (for the part of the switching periodwhere the PWM command signal to the considered deviceis on) can be derived from the measured phase currents iabc.Depending on the sign (direction) of current s(i), the IGBT or

Fig. 13. IGBT conduction loss current and temperature dependency derivedfrom Fig. 6 by directly multiplying current and voltage drop.

the anti-parallel FWDI (paired together) will conduct. For thefirst inverter leg, device currents are given by (19) and (20).Similar equations are used for phase b and c.[

iigbt,1iigbt,4

]=

1

2·[

1 + s(ia)1− s(ia)

]· ia (19)[

ifwdi,1ifwdi,4

]=

1

2·[

1− s(ia)1 + s(ia)

]· ia (20)

The average conduction loss over one switching cycledepends on the actual modulation index δ of the consideredphase, with −1 ≤ δ ≥ 1. The ratio between conduction timeand switching period (duty cycle) equals (1 + kδ)/2, withk = 1 for the devices at the upper side (IGBT/FWDI 1-2-3)and k = −1 for the devices at the lower side (IGBT/FWDI4-5-6) of the inverter legs. For example, δ = 0.5 correspondsto a 75% duty cycle for the upper and and a 25% duty cyclefor the lower IGBT. Consequently, the average conduction lossover one switching cycle Ts, for IGBT-FWDI pair 1 (phasea) can be calculated with (21) and (22). Similar equations canbe derived for the other devices.

Pc,igbt,1 = Pc,igbt(iigbt,1, Tigbt,1) · 1 + kδa2

∣∣∣∣k=1

(21)

Pc,fwdi,1 = Pc,fwdi(ifwdi,1) · 1 + kδa2

∣∣∣∣k=1

(22)

IGBT switching energy losses Eon and Eoff and diodereverse recovery loss Err are provided in datasheet graphs as afunction of current at reference DC-link voltage Uref = 600 V.Third order polynomials are fitted to this data to describe thecurrent dependency:

Eon(i) = −9.56e−8 · i2 + 6.89e−8 · |i|+ 6.70e−4 (23)

Eoff (i) = −1.96e−7 · i2 + 1.20e−4 · |i|+ 6.68e−4 (24)

Err(i) = −2.33e−7 · i2 + 1.26e−4 · |i|+ 2.90e−4 (25)

With these polynomials, switching and reverse recovery lossin IGBT-FWDI pair 1 can be calculated by (26) and (27).It should be noted that these equations are only valid if thecurrent through the considered device is different from zero.If not, switching loss falls to zero.

Psw,igbt,1 =1

Ts· (Eon(iigbt,1) + Eoff (iigbt,1)) · Udc

Uref(26)

Prr,fwdi,1 =1

Ts· Err(ifwdi,1) · Udc

Uref(27)



8

Heatsink

IGBT

Diode

DBC substrateBase plate

PT100

Fig. 14. Layout of a three-phase power module mounted on a heatsink.

X 6 X 6

Fig. 15. Per-component IGBT and FWDi junction temperature estimation,with 12 junction-case thermal networks linked to a case-ambient thermalobserver incorporating an optional heatsink temperature measurement Tfin.

Fig. 14 shows the internal layout of the three-phase powermodule. It consists of six IGBT-FWDI pairs soldered toa direct bonded copper (DBC) substrate. The substrate issoldered to a copper base plate which is mounted on aheatsink. In order to estimate the junction temperatures, thedevice losses are supplied to a lumped-parameter thermalnetwork. Fig. 15 shows the thermal model which is splitinto twelve separate Cauer (ladder type) equivalent circuitsrepresenting the junction-case transient thermal impedanceof each FWDi and IGBT. The circuits are implemented indiscrete state space form with three states corresponding tothe nodes of a Cauer-type RC-network. Inputs are the device’sswitching and conduction losses and the baseplate temperatureTcase obtained from the underlying case-ambient thermalnetwork. Because these circuits describe the three-dimensionalstructure as one-dimensional, temperature estimation errorsare inevitable. Another simplification is the assumption of auniform baseplate and heatsink temperature.

IGBT power module manufacturers usually provide ajunction-case transient thermal impedance (Zjc) curve asshown in Fig. 16 from which the RC elements of a Fosternetwork (chain-type) can be extracted. Applying a curve-fittingresults in a finite series of exponential terms of the form:

Zjc(t) =

n∑i=1

Ri(1− e−t/τi) (28)

Transformation to the Laplace domain gives:

Zjc(s) =

n∑i=1

Ri1 + τis

(29)

with τi = RiCi and the total steady-state junction-case thermalresistance Rjc equal to the sum of resistances Ri. It was foundthat using three terms provides an acceptable fit. Table III gives

Fig. 16. Junction-to-case transient thermal impedance Zjc of IGBT andFWDi. Curve-fitting of datasheet values results in a three-element Foster-typeRC-network.

the time constants and resistances for the IGBT and FWDijunction to case thermal networks.

TABLE IIIFOSTER-TYPE JUNCTION-CASE RC-NETWORK PARAMETERS EXTRACTED

FROM THE TRANSIENT THERMAL IMPEDANCE CURVE (FIG. 16)

τ1 τ2 τ3 R1 R2 R3

[s] [s] [s] [K/W] [K/W] [K/W]IGBT 0.0020 0.0280 0.4424 0.0470 0.1256 0.1026FWDi 0.0020 0.0280 0.4424 0.0788 0.2108 0.1723

The junction-case state-space model of Fig. 15 requires theCauer equivalent R and C element values, which were derivedby applying a continuous-fraction expansion [41] to (29)resulting in Table IV.

TABLE IVCAUER-TYPE JUNCTION-CASE RC-NETWORK PARAMETERS

C1 C2 C3 R1 R2 R3

[J/K] [J/K] [J/K] [K/W] [K/W] [K/W]IGBT 0.0359 0.2090 4.7154 0.0671 0.1191 0.0888FWDi 0.0214 0.1245 2.8092 0.1126 0.2000 0.1491

The case-ambient thermal model estimates the baseplatetemperature Tcase and the heatsink temperature Tfin. With theassumption of a uniform base plate temperature, losses in onecomponent influence other component temperatures as wellthrough the baseplate coupling. The case-heatsink interface isassumed purely resistive, with Rca,fi = 0.015 K/W accordingto the datasheet (thermal grease applied). The transient thermalimpedance curve of the heatsink is determined by means of astep-response test. Applying a third-order fit to the experimen-tal data allows to extract the Cauer-equivalent R and C valuesof Table V. Case-ambient thermal model inputs are the sum ofall power module losses

∑Ploss and the ambient temperature

Tamb. In addition, the model offers the possibility to includea PT100 heatsink temperature sensor, if available. By usinga predict-update algorithm (Kalman filter) with adequatelytuned process and measurement noise covariance matrices,temperature estimation accuracy can be improved compared toan entirely model-based approach. Fig. 17 shows a record ofthe losses and temperatures of IGBT-FWDI pair 1 as calculatedby the model during operation of the drive.



9

TABLE VCAUER-TYPE FIN-AMBIENT RC-NETWORK PARAMETERS

C1 C2 C3 R1 R2 R3

[J/K] [J/K] [J/K] [K/W] [K/W] [K/W]760 3707 59738 0.0257 0.0448 0.0132

Fig. 17. Loss and thermal model output for IGBT-FWDi pair 1. Recordedduring experiment at 67 Nm, 1000 RPM, Ts = 1/10000 s, Udc = 550 Vand Tfin = 50 C.

IV. ACTIVE THERMAL MANAGEMENT

Temperature (cycling) of inverter and motor componentsis the limiting factor defining the maximum attainable peaktorque and power density. Derating the drivetrain with aconservative current limit will mitigate thermal stress butalso degrade performance, often unnecessarily, due to thelack of actual thermal-state feedback. The active thermalmanagement loop shown in Fig. 2 monitors temperatures andcontrols losses through adaptation of switching frequency andcurrent amplitude limits. As a result, power module junctionsand stator windings are protected from excessive temperature(cycling). In contrast to a derating approach, output torqueis only restricted when the predefined thermal limits areeffectively approached. In addition, closed-loop thermal con-trol exploits the available thermal capacity, benefiting short-time peak torque and overload capability. Fig. 18 gives ablock diagram of the active thermal management strategy.Because individual junction temperatures can differ signifi-cantly, especially during standstill or low speed high torqueoperation, the maximum instantaneous value of all six IGBTsor FWDIs is considered. To prevent the remaining temperatureripple from propagating into the current limit, an asymmetricfilter tracking the the peak temperature values is applied,providing a relatively smooth signal to the controller. Whenthis value approaches the predefined maximum allowablejunction temperature Tj,lim, appropriate action is required.First, switching frequency fswitch = 1/Ts is reduced fromthe nominal value of 10 kHz in discrete steps by means of a

+- ++IGBT

+- ++FWDI

+- ++Winding

Fig. 18. Block diagram of the junction and stator winding temperaturelimiting strategy. Losses are actively controlled by adapting the switchingfrequency and current limit according to the available temperature margin.

four-level hysteresis controller. This reduces switching lossesaccording to (26) and (27), without affecting output torque.As a side effect, slower switching increases phase currentripple, yielding additional harmonic loss in the motor and arise of audible noise. In order to limit these parasitic effectsand maintain acceptable current control loop performance,minimum allowable switching frequency is set at 4 kHz.

A second control action sets adaptive constraints to thecurrent amplitude, according to the respective FWDI, IGBTand stator winding temperature margins. Following the generalcontrol law (30), the maximum allowable power loss P ∗

loss canbe calculated for each semiconductor device and the statorwinding. The first term indicates the additional power loss,necessary to reach the temperature limit Tlim within a timeτcl with C the equivalent thermal capacitance. The secondterm P loss,ss indicates the component’s power loss, requiredto maintain temperature at a constant level. As dissipatedpower equals injected power in steady-state, P loss,ss canbe estimated as the low-pass filtered average loss of theconsidered component.

P ∗loss =

C

τcl(Tlim − Tmeas) + P loss,ss (30)

This control law is implemented for the IGBT and FWDIjunctions as shown in Fig. 18. From the junction-case tran-sient thermal impedance curve (Fig. 16), a third-order Foster-type RC-network was extracted (Table III). The second RCelement accounts for the largest temperature step (44.8% oftotal thermal resistance) with a small time constant. Becauseonly fast temperature changes are to be controlled by theproportional action (first term) of (30), thermal capacitancevalues Ci (0.222 J/K) and Cf (0.132 J/K) were set accordingto this dominant RC element with the assumption of a nearlyconstant heat sink temperature. The closed-loop time constantτcl,j was set at 0.05 s which provides a good balance betweenfast response (high transient peak torque) and control systemstability. To put this value in perspective, the largest open-loop junction-case time constant is equal to 0.442 s. A similarapproach for setting the stator winding temperature control



10

parameters was followed, with the stator winding thermalcapacitance Cw = 2367 J/K and time constant τcl,w = 10 s.

In a next step, the three power loss constraints need to betranslated in current amplitude limits. For the stator winding,this is quite straightforward given the copper loss equation (3).For the IGBT and FWDI, an inverse average loss model wasderived with inputs the actual DC-link voltage Udc, switchingperiod Ts, angle between phase voltage and current ϕ andmodulation index amplitude δ. Finally, the most stringentcurrent limit is selected and saturated between zero and theabsolute maximum motor/inverter current |I|max. The result-ing current amplitude limit |I|lim is transmitted to the PMSMcurrent vector control algorithm explained in loop (Section II).This block calculates the best possible dq-current setpointswithin the actual current (and voltage) constraint.

As a side note, the following remark should be made. Inthis paper, the junction and motor temperature estimation andthermal management strategy are elaborated for the air-cooledinverter and motor of Fig. 3. In contrast, actual traction drivesare (in most cases) equipped with a dedicated water-glycolbased cooling system with coolant temperature regulation.This may support drives to keep steady-state component tem-peratures below critical values, but the thermal time constant istoo large to timely detect and react to sudden junction temper-ature rise. Therefore, the proposed active thermal managementstrategy is a valuable addition. With a specific liquid-cooledjunction/motor temperature observer and dynamic switchingfrequency and current limit adaptation, the controller is ableto react to fast temperature changes. In a slower control loop,a water-glycol based cooling system will guarantee a stablebase temperature for effective heat dissipation.

V. EXPERIMENTAL RESULTS

In this section, extensive experimental results are providedto assess the performance and behaviour of the control strategyunder different (dynamic) load conditions.

A. Locked-rotor Maximum Torque Test

Traction drives frequently operate at low speed, high torque.This implies low-frequency power cycling, with a large in-crease of junction temperature amplitude and cycle. Particularcaution is necessary at standstill operation, when DC currentsput quasi-continuous stress on a limited number of switchingdevices. Therefore, besides rated current, minimum allowablefrequency at full load and maximum permissible standstill cur-rent are also critical parameters, specified in inverter datasheets(Table VI). In order to protect the inverter with a fixed currentcontrol limit, it must account for worst-case load, i.e. stand-still operation, at maximum heatsink temperature. However,this implies a sub-maximal utilization of the drive’s thermalcapacity in non-worst-case operating points. With the proposedactive thermal management strategy, (short-time) standstilltorque capability can be improved significantly because it takesthe actual thermal state into account. This is illustrated with alocked-rotor maximum torque test.

In a first experiment shown in Fig. 19(a), the fixed phasecurrent limit is set to 22 A (|I|lim = 26.94 A) according

TABLE VIINVERTER RATINGS

Rated power 17 kVARated current 24 A

Tripping current 43 AMax. standstill current (10 kHz) 22 A

Min. frequency at full load 3 HzMax. heatsink temperature 90 C

to the prescribed maximal standstill current at a switchingfrequency of 10 kHz. This corresponds to a standstill torqueof approximately 66 Nm. Heatsink temperature is assumedconstant at 50 C, to exclude its influence on junction temper-atures from the comparison. Note that this is well below themaximum allowable heatsink temperature of 90 C (Table VI).The PMSM rotor is locked in a position corresponding tomaximal current amplitude in phase b. According to thenegative sign of ib, FWDI 2 and IGBT 5 conduct currentand show the largest temperature increase. Due to the lowmodulation index at standstill operation (low voltage) andthe larger thermal resistance of the FWDI compared to theIGBT, the diode reaches the highest steady-state temperatureof 74 C. Also notice the shape of the step-response, withthe largest time constant around 0.5 s corresponding to thejunction-case transient thermal impedance curve in Fig. 16 andTable III. Furthermore, non-conducting IGBTs 2-4-6 (index i)and FWDIs 1-3-5 (index f) only show a slight temperatureincrease due to the common case-heatsink resistance. In asecond experiment (Fig. 19(b)), active thermal management isenabled (without adaptive switching frequency) with a junctiontemperature limit Tj,lim set to 74 C (max. steady-statetemperature of the previous test). The junction temperaturecontroller was tuned according to (Section IV) with a closed-loop time constant of 0.05 s. Due to the dynamic currentlimit, the available thermal capacity is exploited resultingin a transient peak torque of over 150 Nm. This value islimited by an absolute current limit |I|max of 52.66 A (43 Aphase current). FWDI 2 reaches Tj,lim with a slight overshoot.In steady-state, temperatures and torque output are equal tothe previous fixed current-limit test. In traction applications,the additional transient peak starting torque (for equal peaktemperature) is a major benefit because it allows the drivetrainto overcome high static loads and friction. Once the vehicleis in motion, dynamic friction will be lower and the drivechanges from DC to AC operation. The latter is less stressfulbecause power losses are divided over more switching devices.In the third test (Fig. 19(c)), switching frequency adaptationis enabled as well. When Tj,lim is approached, switchingfrequency is reduced in steps from 10 to 4 kHz. Consequently,switching losses are reduced which can be seen as notches inthe junction temperature profiles. Transient peak torque is notincreased further because the absolute current limit |I|max isreached. Steady-state torque however, is increased from 66 to110 Nm for equal junction temperature increase with respectto the heatsink.



11

(a) Fixed current limit: inverter maximum stand-still phase current 22 A (datasheet rating).

(b) Active thermal management (dynamic currentlimit) with Tj,lim = 74C.

(c) Active thermal management (dynamic currentlimit and fswitch) with Tj,lim = 74C.

Fig. 19. Maximum standstill torque test (locked-rotor).

B. Maximum Acceleration Test

This series of tests compares the maximum attainable ac-celeration (0 to 1500 RPM), with and without the proposedactive thermal management strategy. The speed-controlled DC-drive emulates a realistic vehicle load characteristic [42] (largeinertia), according to the following differential equation:

Tel = Jdω

dt+ sign(ω) · C + sign(ω) ·Dω2 (31)

with Tel the PMSM torque, ω the angular motor frequency,J = 6.5 kg.m2 the emulated inertia, C = 5 Nm the Coulomb-friction and D = 1.4e−3 Nm/(rad/s)2 the drag coefficient.Fig. 20(a) shows the first experiment, in which a fixed currentlimit is applied, equal to the maximum allowable standstillcurrent of 22 A (|I|lim = 26.94 A). It takes the drivetrain 22 sto reach the speed setpoint of 1500 RPM. Due to the currentlimit, torque is restricted at 66 Nm. After approximately16 s, the voltage limit |U |lim imposed by the 550 V DC-link is reached. Hence, additional field-weakening current idis injected to prevent overmodulation. However, this reducesthe maximum deliverable torque. The heatsink temperatureis assumed constant at 50 C. Notice that at low speed,temperature cycles and peak values are considerably largerthan at high speed for equal torque generation. Compared tostandstill operation (Fig. 19(a)), peak junction temperaturesare approximately 10 C lower. Furthermore, the temperatureprofiles show the shift of losses from the FWDIs to theIGBTs at increasing motor voltage due to the increasing

duty cycles. Active thermal management is enabled (withoutadaptive switching frequency) in Fig. 19(b), with an arbitraryjunction temperature limit Tj,lim of 70 C. With these settings,it takes the drivetrain approximately 11 s to reach 1500 RPM.With a short 140 Nm torque peak at standstill, the motor startsaccelerating. As speed increases, more losses are allowed forequal FWDI peak junction temperatures. Hence, |I|lim canbe increased resulting in a rise of output torque from 90 to120 Nm, until the IGBT peak junction temperatures becomethe limiting factor. This acceleration torque remains constantuntil 8 s, when |U |lim requires additional negative d-currentfor field-weakening. Fig. 20(c) shows an identical experiment,but now with adaptive switching frequency. From the junctiontemperature profiles it can be seen that Tj,lim is only reached atthe start of the acceleration. The switching frequency reductionquickly reduces losses, allowing a larger |I|lim and hence alsooutput torque. The torque reaches a peak value of 140 Nm,which is restricted by the prescribed absolute current limit|I|max = 52.66 A (43 A phase current). Hence, the 1500 RPMspeed setpoint is attained after 5 seconds.

C. Driving Cycle Test

To analyse the behaviour of the control strategy underrealistic vehicle loads, a driving cycle test was conducted. ThePMSM drive is speed-controlled with the objective of track-ing an aggressive, high speed and high acceleration drivingcycle n∗, while the DC-machine behaves as a dynamic load



12

(a) Fixed current limit: inverter maximum standstillphase current 22 A (datasheet rating).

(b) Active thermal management (dynamic currentlimit) with Tj,lim = 70C.

(c) Active thermal management (dynamic currentlimit and fswitch) with Tj,lim = 70C.

Fig. 20. Maximum acceleration test.

according to (31). A first test run without active thermal man-agement is shown in Fig. 21(a). The large current limit |I|limallows the drive to generate the necessary torque Tel to obtaina near-perfect tracking of the speed trajectory (n∗ ≈ nmeas).Due to the large emulated inertia, the torque and junctiontemperature profiles show large peaks during accelerationand regenerative braking with a rising trend due to the heatbuild-up in the heatsink (40 C ambient). At high speed,the aerodynamic drag torque component becomes significant.In addition, field-weakening operation generates additional

losses, causing a faster rise of junction and winding temper-atures around 300 s. A second test is shown in Fig. 21(b).Active thermal management is enabled with arbitrary junctionand stator winding temperature limits Tj,lim = 51C andTw,lim = 46C. During the first two start-stop cycles (0-130 s), speed and torque profiles are identical to Fig. 21(a).Junction temperatures however are significantly lower and arelimited at 51 C by means of switching frequency reduction,without affecting torque capability. However, as heat accumu-lates in the heatsink, junction temperature margins decrease.



13

Hence, the thermal management loop lowers the current limit(i.e. maximum deliverable torque). When accelerating fromstandstill for the third time (140 s), |I|lim is insufficient todeliver the required torque and nmeas starts to lag behindn∗. After 400 s, the PMSM winding temperature hits thespecified limit Tw,lim as well. Nevertheless, the drive keepson operating at maximum allowable temperatures, albeit withreduced performance.

VI. CONCLUSION

As most drivetrain failure mechanisms are related to tem-perature effects, it is key to prevent excessive thermal stresson switching devices and motor components. On the otherhand, performance should be maximized to meet the ever-increasing power density requirements. In view of this trade-off, this paper presented a control strategy for PMSM drives tooptimize torque and efficiency within voltage and temperatureconstraints. Based one real-time junction and motor temper-ature estimation, active thermal management is performedthrough switching frequency and current limit regulation. Incontrast to the conventional approach of setting a fixed currentcontrol limit, torque is only restricted when the temperatureboundaries are effectively reached. Hence, the control strategyfacilitates a better utilization of the drive. Future work shouldelaborate the trade-off between power density and lifetime inmore detail. From this analysis, optimal temperature limits forthe proposed control strategy can be derived.

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14

(a) Active thermal management disabled. (b) Active thermal management enabled (dynamic current limit and fswitch)with arbitrary limits Tj,lim = 51C and Tw,lim = 46C.

Fig. 21. Driving cycle test (speed trajectory tracking).

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15

Joris Lemmens (S’09) received the M.Sc. degreein electromechanical engineering from the LimburgCatholic University College (LCUC), Belgium, in2008. He is currently a Research Assistant at theESAT-ELECTA division of the University of Leuven(KU Leuven), Belgium, where he is working towardsthe Ph.D. degree since 2009. His research focuseson control algorithms for permanent magnet motordrives in traction applications.

Piet Vanassche (M’03) received the M.Sc. andPh.D. degrees in electrical engineering from theUniversity of Leuven (KU Leuven), Belgium, in1997 and 2003, respectively. He is COO and co-founder of Triphase NV, a KU Leuven spin-offcompany (founded in 2006) that offers solutions forrapid product development in power electronics. Asone of the lead control software designers, he is ac-tive in Triphase’s hybrid- and full-electric drivetrainprojects for commercial vehicles.

Johan Driesen (S’94–M’96–SM’12) received theM.Sc. and Ph.D. degrees from the University ofLeuven (KU Leuven), Belgium, in 1996 and 2000 re-spectively. Currently, he is a professor at KU Leuvenand teaches power electronics and drives. In 2000–2001 he was a visiting researcher in the ImperialCollege of Science, Technology and Medicine, Lon-don, U.K. In 2002, he was working at the Univer-sity of California, Berkeley. Currently, he conductsresearch on distributed generation, renewable energysystems, power electronics and drives.

optimal control of traction motor drives under electro-thermal constraints

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