thermal investigation of permanent-magnet synchronous...

4404 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 8, AUGUST 2014

Thermal Investigation of Permanent-MagnetSynchronous Motor for Aerospace Applications

Themistoklis D. Kefalas, Member, IEEE, and Antonios G. Kladas, Senior Member, IEEE

Abstract—This paper concerns the thermal investigation ofa surface-mounted permanent-magnet synchronous motor de-signed for high-temperature aerospace actuation applications. Afinite-element package was developed, enabling accurate 3-D tran-sient thermal analysis by considering complex and unsymmetri-cal actuator housing configurations. Its validity was verified bymeasurements carried out at different duty cycles and operatingconditions.

Index Terms—Actuators, aerospace engineering, aerospace in-dustry, computer-aided analysis, electric machines, finite-element(FE) methods, numerical analysis, permanent-magnet machines,thermal analysis, time-domain analysis.

NOMENCLATURE

A Sum of the m areas comprising the outer surface ofthe PMSM (in square meters).

hi ith convection coefficient (in watts per square meterper kelvin).

m Number of areas comprising the outer surface of thePMSM.

q Heat transfer rate (in watts).q′′i ith heat flux transfer per unit area (in watts per square

meter).sij Stiffness matrix element, i for row and j for column.T si ith mean surface temperature (in kelvin).AEA All-electric aircraft.PMSM Permanent-magnet synchronous motor.

I. INTRODUCTION

NOWADAYS, the application of political, environmental,and economical trends to air transport lead to the all-

electric aircraft (AEA) [1]–[3]. The unavoidable eliminationof high-pressure hydraulic lines is going to produce a de-manding thermodynamic environment for electric actuators due

Manuscript received January 30, 2013; revised April 26, 2013 and July 18,2013; accepted July 27, 2013. Date of publication August 15, 2013; date ofcurrent version February 7, 2014. The research leading to these results hasreceived funding from the European Union Seventh Framework Programme(FP7/2007-2013) under Grant Agreement AAT.2008.4.2.4-234119 CREAMwithin the TEIP Consortium Member.

The authors are with the School of Electrical and Computer Engineering,National Technical University of Athens, GR-15780 Athens, Greece (e-mail:[email protected]; [email protected]).

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

Digital Object Identifier 10.1109/TIE.2013.2278521

to the resulting localized heating effects and reduced thermaldissipation.

This paper describes the thermal analysis of a surface-mounted permanent-magnet synchronous motor (PMSM) de-signed for high ambient temperatures, inadequate convectiveheat transfer, and short overload conditions encountered in anaerospace actuation application.

Conventional electric-machine thermal analysis includeslumped-parameter networks [4]–[12] and the computationalfluid dynamics (CFD) analysis [13]–[15]. Other approachesappearing in the technical literature are the finite-element (FE)method used in conjunction with lumped-parameter models for2-D [16]–[19] and 3-D [20], [21] steady-state thermal analyses.

The aerospace application under consideration involves ahighly integrated actuator using a housing of complex andunsymmetrical geometric characteristics. The solution of theparticular thermal problem requires detailed transient 3-D anal-ysis where the temperature gradient cannot be ignored. Nev-ertheless, in this case, the convective heat transfer mechanismof the PMSM is insignificant and the CFD analysis is not nec-essary to be adopted. The FE method advantage over the CFDanalysis is the reduced computational cost. Furthermore, the FEmethod enables temperature gradient evaluation and complexgeometry representation and parameterization in contrast withthe lumped-parameter network analysis [22].

II. BRIEF DESCRIPTION OF THE PMSM

A Rosenbrock-based optimization algorithm [23] wasadopted in order to determine the optimum design configurationof a PMSM working at high ambient temperature (200 ◦C) andshort overload conditions. The design and operational charac-teristics of the optimum PMSM are shown in Table I.

For the specific PMSM, a nonoverlapping all-teeth-woundfractional-slot concentrated-winding configuration and high-temperature samarium cobalt (SmCo) permanent magnets wereused [23]. Fig. 1 shows an assembled prototype PMSM on thetest rig.

III. 3-D FE CODE DESCRIPTION

A. Description of Numerical Techniques

1) FE System Assembly: For the storage of the FE matrices,a modified Morse technique was used that enables quick searchof an element of the stiffness matrix. The specific FE system as-sembly scheme consists in the production of two appropriately

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KEFALAS AND KLADAS: THERMAL INVESTIGATION OF PMSM FOR AEROSPACE APPLICATIONS 4405

TABLE IDESIGN PARAMETERS OF OPTIMIZED PMSM

Fig. 1. Assembled prototype PMSM on the test rig.

sorted vectors that store the row and column of the diagonal andnonzero elements sij of the sparse stiffness matrix.

2) FE Solver: The improvement of the solution time ofthe 3-D FE transient analysis was accomplished by using thesystem assembly procedure integrating the modified Morsetechnique in combination with the conjugate gradient methodwith Van der Vorst preconditioning.

The heat conduction solver accuracy has been validated bycomparing its results to analytical solutions existing in the caseof thermal conduction in a cylindrical rod of finite length [24].

3) Mesh Size Reduction: A significant reduction of theFE mesh size and the corresponding computational cost wasachieved by replacing the winding turns, the air–varnish–epoxycomposite of the stator slots, and the iron-laminated statorby homogeneous regions with appropriately defined materialattributes. In all cases, the thermal properties of the specific re-gions were evaluated experimentally and by taking into accountempirical factors. In particular, the homogenization techniqueimplemented for winding-part discretization reduction in thethermal analysis is detailed in [22]. This technique is usedfrequently in electromagnetic analysis [25]–[27] and has beenadopted for thermal analysis [28], [29].

4) Mesh Parameterization: During the optimization pro-cess, the geometry design parameters of the FE model constantlychange. In this case, the mesh parameterization technique isemployed in order to avoid repeatedly using the mesh gener-ation and FE system assembly procedures.

5) Time-Step Generator: The computational cost of thetransient thermal analysis was reduced by using a time-stepgenerator procedure that improved the resolution at the firststeps and minimized the required number of steps of the tran-sient analysis.

B. Electromagnetic and Thermal Phenomena Weak Coupling

The 3-D thermal FE analysis is weakly coupled with amultiple-slice 2-D FE code already presented [23] for theevaluation of the thermal sources. In fact, the important dif-ference of time constants between thermal and electromagneticphenomena has been exploited in order to ensure updating ofboth copper conductivity and permanent-magnet magnetizationvariation with temperature as proposed in [30].

This is achieved by implementing an appropriate steady-state 2-D FE electromagnetic analysis for several PMSM crosssections at every time step of the transient 3-D FE thermalsimulation. Moreover, the temperature variation of the thermalconductivity has been equally taken into account.

C. Particular Boundary Conditions Development

Due to the high integration of the actuator, the housing of thePMSM has a complex and unsymmetrical geometry with no2-D or 3-D symmetry. In order to emulate this housing, a novelnumerical method is developed. The proposed method consistsin the application of properly defined boundary conditions atthe outer surface of the PMSM in contact with the housing. Thesurface is partitioned into m areas, each representing a differentcomponent of the actual housing e.g., a fin or the area betweentwo fins. At each area, a different boundary condition is appliedso that (1) is satisfied, where q′′i is the heat flux transfer perunit area of the ith area, hi is the convection coefficient of theith area, and T si is the mean surface temperature of the ith area.The first term of (1) must satisfy (2), where q is the heat transferrate, i.e., the sum of the PMSM heat sources, and A is the sumof the m areas

m∑

i=1

q′′i =m∑

i=1

hi · T si (1)

m∑

i=1

q′′i =q

A. (2)

In particular, for the airgap thermal transfer, approximateconvection coefficients proposed in [31] have been imple-mented, providing sufficient accuracy for the studied PMSM,as will be shown in Section VI.

D. Code Structure

A FE package has been assembled for the 3-D FE transientand steady-state analyses of actuators. It consists of seven codesthat integrate the aforementioned techniques, and it is structured


Fig. 2. Structure of the developed FE package.

as shown in Fig. 2. The control code calls and passes variablesto the remaining six codes as follows:

1) The FE preprocessor procedure is called, which producesthe geometry and attributes of the 3-D FE model. Thespecific procedure parameterizes almost all of the geom-etry and operating variables of the actuator.

2) A first-order tetrahedral mesh generator is used in order toconstruct the FE mesh. The quality and size of the meshare determined by the control program.

3) The control code calls the FE system assembly procedurethat integrates the modified Morse technique. This proce-dure uses as input the Cartesian coordinates of the nodesand the list of the tetrahedra.

4) The input files for the 3-D FE thermal transient solverare the files produced by the mesh generator and thesystem assembly codes. The specific solver produces anoutput file containing the temperature distribution of theFE model for every time step of the transient analysis.Furthermore, during the particular stage, the storage ofthe stiffness matrix is carried out and boundary conditionsand material attributes are assigned to the FE model.

5) The control program calls the postprocessor procedurethat modifies to an appropriate format the output files ofthe FE solver.

6) Finally, the postprocessor Gmsh is called, which producesgraphic representations of the geometry, mesh, and tem-perature distribution of the FE model.

Fig. 3. Detail of the 3-D FE mesh of the PMSM consisting of 2 · 106 nodesand 1.2 · 107 elements.

Fig. 4. Cross section of the 3-D FE mesh of the PMSM.

The control program, preprocessor, FE system assembly, FEsolver, and postprocessor codes were written by the authors,whereas for the mesh generation and the FE graphics represen-tation, the open-access codes TetGen, TetView, and Gmsh wereadopted [32], [33].

IV. FE RESULTS

A. Computational Cost of the 3-D FE Transient Analysis

A sensitivity analysis was carried out for mesh sizes rang-ing from 4 · 105 to 1.2 · 107 elements in order to determinethe optimum FE mesh size. The sensitivity analysis showedthat a mesh size of 1.5 · 106 was the optimum compromisebetween computational effort and analysis accuracy. The re-spective computational effort and relative error for a ten-step FEtransient thermal analysis were 1523 s and 2.3%, respectively,using a typical desktop PC. A detail of the densest FE meshtested is shown in Fig. 3. A cross section of the 3-D FE meshdepicting the regions comprising the model is shown in Fig. 4.

B. Results of Thermal Transient Analysis

Using the FE package of Section III, the authors performed3-D FE thermal transient analyses of the PMSM for differentduty cycles and load conditions.

The temperature distributions of the PMSM running undermaximum load conditions over 140 min is shown in Figs. 5


Fig. 5. PMSM temperature distribution at 2.54 s. (a) Winding. (b) Stator core.(c) Stator. (d) Rotor.

and 6. The specific results were obtained by a ten-step transientanalysis where the time step ranges from 0.18 s for the first stepto 5626 s for the tenth step.

More specifically, Fig. 5 shows the temperature distributionof the windings, the stator core, the stator, and the rotor at the

Fig. 6. PMSM temperature distribution. (a) 26.1 s. (b) 82.7 s. (c) 825 s.

third time step of the analysis. Fig. 6 shows the temperaturedistribution for three steps of the transient analysis.

Fig. 7 shows a comparison of the local maximumand minimum temperature distributions versus time of thePMSM.


Fig. 7. Local maximum and minimum temperature variations over 140 min.

Fig. 8. (a) Experimental setup. (b) DAQ system and measurement instruments.

V. EXPERIMENTAL SETUP

The experimental setup used for evaluating the thermal per-formance of the PMSM is shown in Fig. 8. It consists of thefollowing components:

1) prototype PMSM;2) separately excited direct current machine (22 kW);

Fig. 9. Prototype PMSM inside the thermal chamber.

3) data acquisition (DAQ) system;4) digital and analog instruments;5) torque gauge;6) variable electrical loads;7) air-forced cooling apparatus.

The voltage across the PMSM stator terminals was capturedusing active differential voltage probes. The specific voltageprobes measure floating potentials by converting the high inputvoltage (≤ 1400 V peak) into a low voltage (≤ 5 V). The 3-dBfrequency of the voltage probe is 18 MHz, the rejection rate oncommon mode at 50 Hz is 90 dB, and the attenuation factor isequal to 205 [27], [34].

Current probes based on the Hall Effect were used forcapturing the phase currents. The specific probes provide agalvanic isolation between the primary circuit (high power) andthe secondary circuit (electronic circuit) and very good linearity(< 0.2%). The current measurement range is ±36 A peak, andthe 1-dB frequency of the probe is 150 kHz.

The output of the probes was connected to a noise-rejectingshielded BNC I/O connector block (BNC-2110) via passiveprobes (TP6060). A noise-rejecting shielded cable (SHC68-68-EP) connects the DAQ device directly to the BNC-2110connector block.

The DAQ device used was National Instruments (NI) 6143. Itis based on a dedicated analog-to-digital converter (ADC) perchannel architecture. NI 6143 has eight differential channels,an ADC resolution of 16 bit, a maximum sampling rate of250 kSamples/s per channel analog input, and a ±5 V analoginput signal range. The analysis of the captured data was carriedout by using LabVIEW software. Three virtual instruments(VIs) were created with the use of LabVIEW. The purpose ofthe first VI was the real-time measurement of the voltage andphase current waveforms, fast Fourier transform, peak, rms, andtotal harmonic distortion (THD) values. The second VI wasused for capturing the voltage and phase current waveforms forthe maximum sampling rate of the DAQ device. The third VIwas used for manipulating the acquired voltage and current data[27], [34].

The ambient temperature of the PMSM was controlled by anenvironmental chamber equipped with a PID controller (Fig. 9).For that purpose, two metal plates attached to the housing of thePMSM were used and a thermal insulation material was placed


Fig. 10. Thermocouple arrangement for temperature measurements.

Fig. 11. First and second sets of simulated and measured temperaturevariations.

between the PMSM housing and the plates in order to minimizeheat dissipation.

Fig. 10 shows the arrangement of five type-k thermocouplesused for temperature measurements. Three thermocouples wereattached to the housing of the PMSM: One was attached tothe center of a stator tooth, and one was placed on one of thewinding ends. When the rotor was stationary, a sixth type-kthermocouple was used to measure the shaft temperature [4].

VI. COMPARISON OF SIMULATED AND

EXPERIMENTAL RESULTS

Seven experiments were carried out for different duty cycles,operating conditions, and load conditions using the experimen-tal setup of Section V. The first set of measurements was carriedout for a rotating speed of 750 r/min, phase currents of 4.92 A,and line-to-neutral voltage of 49 V. The ambient temperaturewas 25◦C, and the measurements were carried out for 120 minusing a constant ohmic load.

The second set of measurements was carried out for the sameambient temperature at 1000 r/min, phase currents of 6.45 A,and line-to-neutral voltage of 65 V for 120 min. In the particularset, an increased load was used in order to raise the steady-state temperature of the PMSM. Fig. 11 shows a comparisonof simulated versus measured temperature variations at the

Fig. 12. Third and fourth sets of simulated and measured temperaturevariations.

winding end, the housing center, and the housing end of thefirst and second sets of measurements.

In order to evaluate the thermal impact on the PMSM of rapidload conditions, two more sets of measurements were carriedout, each of them consisting of two subcycles. A constantohmic load was used, ensuring an increased loading of thePMSM for a limited time period at the first subcycle. Then,the load was removed and the air-forced cooling apparatus wasused in order to decrease rapidly the PMSM temperature. Thethird set of measurements was carried out at 1200 r/min, withphase currents of 9.5 A, and torque of 14.2 N ·m for 60 min.A centrifugal fan producing 98 m3/h was used for coolingdown the PMSM. For the fourth set of measurements, increasedload and air volume flow rates (400 m3/h) were used. It wascarried out at 1200 r/min, with phase currents of 13.7 A, line-to-neutral voltage of 79 V, and torque of 21.8 N ·m for 60 min.Fig. 12 shows the comparison of simulated versus measuredtemperature variation at three locations of the PMSM of thethird and fourth sets of measurements.

For the fifth set of measurements, a mixed cycle was em-ployed using variable loads and high air-forced cooling condi-tions. The first subcycle was obtained for constant loads thatresulted in a winding-end temperature rise of 10 ◦C/min. Thesecond subcycle was obtained by regulating the loads over60 min in order to maintain the winding-end temperatureconstant. Finally, the third subcycle was obtained by using theair-forced cooling apparatus in order to achieve a winding-end temperature decrease of 10 ◦C/min. Fig. 13 shows therespective comparison of simulated versus measured temper-ature distributions at three locations of the PMSM for twoconsecutive duty cycles.

Additionally, two sets of measurements were carried outfor different ambient temperatures using the thermal chamberdescribed in Section V. Each of them consists of two subcyclesof temperature rise and decrease. For the first subcycle, aconstant ohmic load was used, and for the second subcycle, air-forced cooling conditions were employed. The sixth set wascarried out at 1200 r/min for 120 min. An ambient temperatureof 25 ◦C was controlled by the thermal chamber. Figs. 14


Fig. 13. Fifth set of simulated and measured temperature variations.

Fig. 14. Comparison of simulated versus measured temperature variationsover 120 min (housing center, ambient 25 ◦C).

Fig. 15. Comparison of simulated versus measured temperature variationsover 120 min (winding end, ambient 25 ◦C).

and 15 show the comparisons of the simulated and measuredtemperature variations for two locations, the motor housingobtained by thermocouple 1 and the winding end obtained bythermocouple 5. Figs. 14 and 15 show that the winding end isthe critical temperature component of the PMSM. The seventh

Fig. 16. Comparison of simulated versus measured temperature variationsover 40 min (housing center, ambient 70 ◦C).

set of measurements was carried out at 1200 r/min at an ambienttemperature of 70 ◦C for 40 min. Fig. 16 shows the comparisonof simulated and measured temperature variations of the PMSMhousing. In all seven experimental sets, the simulated andmeasured temperature variations agree within 1% to 4% for allmeasured points.

VII. CONCLUSION

The 3-D FE transient thermal analysis presented in thispaper was developed as part of a project concerning a newactuator development ensuring aileron guidance and emergencyaerodynamic brake functions in aerospace applications.

The heat sources of the actuator are calculated by convenientmultislice 2-D FE electromagnetic analysis weakly coupledwith thermal analysis. Also, the proposed thermal analysisincludes an innovative technique enabling consideration of thecooling provided by the particular complex and unsymmetri-cal housing of the considered actuator. The aforementionedtechniques were integrated to a FE package presenting taskparallelism computing capabilities. By using the specific FEpackage, a ratio of 5.4, of real time to transient analysis time,per processor core was achieved.

REFERENCES

[1] W. Cao, B. C. Mecrow, G. J. Atkinson, J. W. Bennett, and D. J. Atkinson,“Overview of electric motor technologies used for more electric aircraft(MEA),” IEEE Trans. Ind. Electron., vol. 59, no. 9, pp. 3523–3531,Sep. 2012.

[2] X. Huang, A. Goodman, C. Gerada, Y. Fang, and Q. Lu, “Design of afive-phase brushless DC motor for a safety critical aerospace application,”IEEE Trans. Ind. Electron., vol. 59, no. 9, pp. 3532–3541, Sep. 2012.

[3] T. D. Kefalas and A. G. Kladas, “Finite element transient thermalanalysis of PMSM for aerospace applications,” in Proc. ICEM, 2012,pp. 2566–2572.

[4] D. G. Dorrell, “Combined thermal and electromagnetic analysis ofpermanent-magnet and induction machines to aid calculation,” IEEETrans. Ind. Electron., vol. 55, no. 10, pp. 3566–3574, Oct. 2008.

[5] J. Nerg, M. Rilla, and J. Pyrhönen, “Thermal analysis of radial-flux elec-trical machines with a high power density,” IEEE Trans. Ind. Electron.,vol. 55, no. 10, pp. 3543–3554, Oct. 2008.

[6] A. Di Gerlando, G. Foglia, and R. Perini, “Permanent magnet machinesfor modulated damping of seismic vibrations: Electrical and thermalmodeling,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3602–3610,Oct. 2008.


[7] N. Jaljal, J.-F. Trigeol, and P. Lagonotte, “Reduced thermal model of aninduction machine for real-time thermal monitoring,” IEEE Trans. Ind.Electron., vol. 55, no. 10, pp. 3535–3542, Oct. 2008.

[8] Z. Gao, R. S. Colby, T. G. Habetler, and R. G. Harley, “A model reductionperspective on thermal models for induction machine overload relays,”IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3525–3534, Oct. 2008.

[9] C. Kral, A. Haumer, and T. Bäuml, “Thermal model and behavior of atotally-enclosed-water-cooled squirrel-cage induction machine for trac-tion applications,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3555–3565, Oct. 2008.

[10] G. Traxler-Samek, R. Zickermann, and A. Schwery, “Cooling airflow,losses, and temperatures in large air-cooled synchronous machines,” IEEETrans. Ind. Electron., vol. 57, no. 1, pp. 172–180, Jan. 2010.

[11] N. Bracikowski, M. Hecquet, P. Brochet, and S. V. Shirinskii, “Multi-physics modeling of a permanent magnet synchronous machine by usinglumped models,” IEEE Trans. Ind. Electron., vol. 59, no. 6, pp. 2426–2437, Jun. 2012.

[12] J. Le Besnerais, A. Fasquelle, M. Hecquet, J. Pellé, V. Lanfranchi,S. Harmand, P. Brochet, and A. Randria, “Multiphysics modeling:Electro-vibro-acoustics and heat transfer of PWM-fed induction ma-chines,” IEEE Trans. Ind. Electron., vol. 57, no. 4, pp. 1279–1287,Apr. 2010.

[13] F. Marignetti, V. D. Colli, and Y. Coia, “Design of axial flux PM syn-chronous machines through 3-D coupled electromagnetic thermal andfluid-dynamical finite-element analysis,” IEEE Trans. Ind. Electron.,vol. 55, no. 10, pp. 3591–3601, Oct. 2008.

[14] C. Micallef, S. J. Pickering, K. A. Simmons, and K. J. Bradley, “Improvedcooling in the end region of a strip-wound totally enclosed fan-cooledinduction electric machine,” IEEE Trans. Ind. Electron., vol. 55, no. 10,pp. 3517–3524, Oct. 2008.

[15] C. Jungreuthmayer, T. Bäuml, O. Winter, M. Ganchev, H. 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.

[16] L. Alberti and N. Bianchi, “A coupled thermal-electromagnetic analysisfor a rapid and accurate prediction of IM performance,” IEEE Trans. Ind.Electron., vol. 55, no. 10, pp. 3575–3582, Oct. 2008.

[17] A. Tenconi, F. Profumo, S. E. Bauer, and M. D. Hennen, “Temperaturesevaluation in an integrated motor drive for traction applications,” IEEETrans. Ind. Electron., vol. 55, no. 10, pp. 3619–3626, Oct. 2008.

[18] W. Li, J. Cao, and X. Zhang, “Electrothermal analysis of induction motorwith compound cage rotor used for PHEV,” IEEE Trans. Ind. Electron.,vol. 57, no. 2, pp. 660–668, Feb. 2010.

[19] T. A. Jankowski, F. C. Prenger, D. D. Hill, S. R. O’Bryan, K. K. Sheth,E. B. Brookbank, D. F. A. Hunt, and Y. A. Orrego, “Development andvalidation of a thermal model for electric induction motors,” IEEE Trans.Ind. Electron., vol. 57, no. 12, pp. 4043–4054, Dec. 2010.

[20] I.-C. Vese, F. Marignetti, and M. M. Radulescu, “Multiphysics approach tonumerical modeling of a permanent-magnet tubular linear motor,” IEEETrans. Ind. Electron., vol. 57, no. 1, pp. 320–326, Jan. 2010.

[21] S. Dwari and L. Parsa, “Design of Halbach-array-based permanent-magnet motors with high acceleration,” IEEE Trans. Ind. Electron.,vol. 58, no. 9, pp. 3768–3775, Sep. 2011.

[22] 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.

[23] E. M. Tsampouris, M. E. Beniakar, and A. G. Kladas, “Geometry opti-mization of PMSM comparing full and fractional pitch winding configu-rations for aerospace actuation applications,” IEEE Trans. Magn., vol. 48,no. 2, pp. 943–946, Feb. 2012.

[24] S. Whitaker, Fundamental Principles of Heat Transfer. New York, NY,USA: Pergamon, 1977.

[25] T. D. Kefalas, P. S. Georgilakis, A. G. Kladas, A. T. Souflaris, andD. G. Paparigas, “Multiple grade lamination wound core: A novel tech-nique for transformer iron loss minimization using simulated annealingwith restarts and an anisotropy model,” IEEE Trans. Magn., vol. 44, no. 6,pp. 1082–1085, Jun. 2008.

[26] T. D. Kefalas and A. G. Kladas, “Robust numerical analysis of woundcore distribution transformers,” in Proc. ICEM, 2008, pp. 1–6.

[27] T. D. Kefalas and A. G. Kladas, “Harmonic impact on distributiontransformer no-load loss,” IEEE Trans. Ind. Electron., vol. 57, no. 1,pp. 193–200, Jan. 2010.

[28] R. Wrobel, N. McNeill, and P. H. Mellor, “Performance analysis andthermal modeling of a high-energy-density prebiased inductor,” IEEETrans. Ind. Electron., vol. 57, no. 1, pp. 201–208, Jan. 2010.

[29] R. Wrobel and P. H. Mellor, “Thermal design of high-energy-density wound components,” IEEE Trans. Ind. Electron., vol. 58, no. 9,pp. 4096–4104, Sep. 2011.

[30] M. Beniakar, T. Kefalas, and A. Kladas, “Investigation of the impact ofthe operational temperature on the performance of a surface permanentmagnet motor,” J. Mater. Sci. Forum, vol. 670, pp. 259–264, 2011.

[31] G. I. Taylor, “Distribution of velocity and temperature between concentriccylinders,” Proc. R. Soc. Lond., vol. 151, no. 874, pp. 494–512, Oct. 1935.

[32] H. Si and K. Gärtner, “Meshing piecewise linear complexes by con-strained Delaunay tetrahedralizations,” in Proc. 14th Int. MeshingRoundtable, 2005, pp. 147–163.

[33] C. Geuzaine and J.-F. Remacle, “GMSH: A three-dimensional finite ele-ment mesh generator with built-in pre- and post-processing facilities,” Int.J. Numer. Methods Eng., vol. 79, no. 11, pp. 1309–1331, 2009.

[34] T. D. Kefalas and A. G. Kladas, “Analysis of transformers workingunder heavily saturated conditions in grid-connected renewable-energysystems,” IEEE Trans. Ind. Electron., vol. 59, no. 5, pp. 2342–2350,May 2012.

Themistoklis D. Kefalas (M’09) was born in Greecein 1977. He received the Electrical Engineering Ed-ucator degree from the School of Pedagogical andTechnological Education, Athens, Greece, in 1999and the Diploma and the Ph.D. degree in electricalengineering from the National Technical Universityof Athens, Athens, in 2005 and 2008, respectively.

Since 2010, he has been an Adjunct AssistantProfessor with the School of Pedagogical and Tech-nological Education. Since 2008, he has been anAdjunct Lecturer and Research Associate with the

School of Electrical and Computer Engineering, National Technical Universityof Athens. His research interests include electric machine and transformerdesign, modeling, and optimization.

Dr. Kefalas is a member of the Technical Chamber of Greece.

Antonios G. Kladas (S’80–A’99–M’02–SM’10)was born in Greece in 1959. He received the Diplomain electrical engineering from the Aristotle Univer-sity of Thessaloniki, Thessaloniki, Greece, in 1982and the D.E.A. and Ph.D. degrees from Pierre andMarie Curie University (Paris 6), Paris, France, in1983 and 1987, respectively.

He was an Associate Assistant with Pierre andMarie Curie University from 1984 to 1989. From1991 to 1996, he was with the Public Power Cor-poration of Greece, where he was engaged in the

System Studies Department. Since 1996, he has been with the School ofElectrical and Computer Engineering, National Technical University of Athens,Athens, Greece, where he is currently a Professor. His research interests includetransformer and electric machine modeling and design, and the analysis ofgenerating units by renewable energy sources and industrial drives.

Dr. Kladas is a member of the Technical Chamber of Greece.

thermal investigation of permanent-magnet synchronous...

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