IEEE ISIE 2006, July 9-12, 2006, Montreal, Quebec, Canada

Power Converter Thermal Modeling Based on

Experimental Parameter IdentificationD.V. Malyna, J.L. Duarte, M.A.M. Hendrix, F.B.M. van Horck

Technical University of Eindhoven, The Netherlandsd.v.malyna@ tue.nl

Abstract-In this paper a modeling technique that describes thethermal behavior of a power converter is presented. Theprediction is obtained by means of a simulation program,developed by the authors. A linear thermal model of the converteris extracted from measurements on the converter prototype. Inthe simulation process the thermal and electrical behavior arecoupled and solved by an iterative approach. The approach wasvalidated by measurements on the test prototype.

I. INTRODUCTION

Analysis of the combined thermal and electrical behavior ofpower converters is an essential tool for power converterdesign. Converters are designed with restrictive specificationsand must provide an effective solution. For instance, it isdesirable that the total component cost is low and the convertersize is small. In most cases heat dissipation acts as a limitingfactor.A converter is usually designed considering an approximate

thermal model. A test prototype is measured and the thermalbehavior is studied. If the design constraints are not satisfied, adesigner tunes parameters of the converter to improve thetemperature distribution. In many cases it is quite difficult tosee the correlation between distributed heat sources andelectrical losses in different parts of the circuit.A systematic design flow considering thermal issues is

presented in this paper. A converter is designed considering anapproximate thermal model and a test prototype is built. Athermal model of the prototype is experimentally found. Then acombined electrical and thermal simulation is performed tocalculate electrical losses and temperatures. Thesetemperatures are used to correct the parameters of thethermally dependent components, e.g. transistors, diodes andcopper of the windings [2]. The simulation continues as long asvariations of the temperature caused by change of thecomponent values are not negligible.

In this paper the parameters of the proposed linear thermalmodel are identified experimentally. The resulting thermalmodel is supplied to the simulator M_SIM [3], and the loadvariation behavior is given as an example. The results of thesimulations are compared with the measurements and show agood match.

II. MODELING METHOD

The design procedure shown in Fig. 1 starts with the circuitdiagram and some initial guesses for the values of temperaturedependent parameters (i.e. winding resistances, MOSFETRDS on' etc.) An accelerated simulation is performed to

achieve the operating point of the electrical circuit. Theelectrical losses P for each component are used by the thermalsimulator. The thermal simulator calculates the componenttemperatures fromAT=RO .P, (1)whereP is a vector of electrical losses,R. is a thermal resistance matrix,

and corrects the component values according to temperature-based rules, which will be discussed in Section III.When the temperature change from cycle to cycle remains

within specified boundaries the iteration process is terminated:AT1 - AT (2)

ATwhereATj, AT are vectors of the temperature change of the j -th

and j -1 -th iteration for all referred components,£ is the relative tolerance for the temperature variation.

Fig. 1. Flowchart of the combined electrical and thermal simulation

1-4244-0497-5/06/$20.00 C 2006 IEEE 2620

III. ELECTRICAL SIMULATION

In this case a switched circuit is described as a piece-wiselinear system. The circuit equations are solved by thesimulation program M_SIM (Matlab Simulator), developed bythe authors [3]. The simulator uses an method to accelerateachieving the steady-state of the converter.The structure of a power electronic converter circuit changes

periodically. Switches in the circuit are opening and closingduring operation. Thus, the converter is described by M sets ofmatrices {A,B,u} , which depend on each configuration of the

switches asx=Am x+Bmu,m=l ...M, (3)wherex - state vector,A, B - space matrices,u - independent source vector,For each stage m within M, the solution of (3) for a given

fixed time step h is found bex= eAh 1 .(eA h -I).Bmur. (4)A graphical interpretation of (4) is shown in Fig. 2a. In

steady-state the value of the state-space vector at the beginningof the previous interval is equal to the value of the vector at thebeginning of the next interval.

For thermal design these steady-state values are of interest.Transients decay very slowly (see Fig. 2b), resulting inconsiderable simulation overhead. However, it is possible toaccelerate simulations by removing the transients [3]. Theapproach is shown in Fig. 2b by bold solid lines.When the steady state is achieved, the state vector value at

the beginning of the period is equal to the state vector value atthe end of the period, as summarized by

f(T,xO) -x0 = 0 (5)

The simulation is terminated when the energy flow in thereactive components remains within the specified precision

E' 1 -FE LI-2 C. U2< C where E= mean mean (6)EJ ' 2 2

whereEJ, EJ-1 are the energies of j -th and j-i -th iterations,L, C are the values of inductors and capacitors,I m Umean are the mean values of the inductor currents and

capacitor voltages.The simulator M_SIM reads a netlist file produced by the

"Schematics" editor from the Cadence® PSPICE package anddetermines the state-space matrices necessary to simulate aconverter in the accelerated way as described above.Library cells, used by the program, are summarized in

TABLE I. Additionally, the simulator calculates all theinstantaneous, the RMS and the mean values of the state spacevector {us (T) u RMS umean }. Electrical losses in all resistive

branches, diodes, and transistors, including switching losses,are calculated as well, being collected in a vectorP=[P P2 ..].Pn ]

Application of the simulator to a set of test convertersshowed a significant improvement in the simulation speed: 3-20 times, depending on the converter type and its parameters[3].

TABLE IM SIM LIBRARY CELLS

Passive Switches Sources

DRon Eon C:R D n Es,

L Ron

,C;z y X Roff

C

X1 22XN~ XNxo2 xo

11

X. X.S

x

01

I1

3 j+1

2

Steady-state

1 v

Acceleration x° f(xo,T)| -~8>J algorithm

O Al B, u1 T Al B, u1 2T t t1 A B U2

1 A2 B2 U22 ~~~~~~~~~~~2

a) b)Fig. 2. Conventional and accelerated simulations: a) numerical integration of a state-space vector b) steady-state determination

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x

The temperature dependencies of the electrical parameters are:

a) Copper resistanceRT =R0 .(1+a.AT), (7)

where RO is resistance at 27'C and a is a thermal coefficient.

AT is the temperature increase above To=270C.b) Diodes

(ATRon =Ron o En+)Eo =Eon o-0.002 AT, (8)

298where Ron-o and Eon 0 are forward resistance and forward

voltage drop of the diode at 27°C respectively.

c) MOSFETs

RT-DS=RO_DS {(25+/AT) F-i + 54 } where

F = 1.024 VDS0 1124 (9)

RO DS is the drain-source resistance at 270C,VDS is the nominal datasheet drain-source voltage of theMOSFET.

IV. DERIVATION OF THE THERMAL MODEL

The difficulty of estimating convection coefficients inpractice makes published methods only limitedly useful [2]. Ithas therefore been decided to apply the approach suggested inFig. 3.

Heat-dissipative components {l,2,3,...,nl are located on the

PCB and electrical dissipation (power {PI...PIJ) is injected into

them. Thus, the components are heated up and at the same timethe resulting temperature of each component {IT . ..7 I is

measured and registered.A linear thermal model is proposed asP = GO IAT, where

GI G12 . Glj ... GlnG21 G22 ..G2j ...G2n

G - : : *. : , (10)-Gil Gi2 Gij Gin

Gnl Gn2 ..Gnj . Gnn

if i j thenG = 1 1 else G.jRi j=l Rij. Rij.

The model consists of a set of thermal resistances R. from

the nodes to the ambient, and internode resistances R1>. The

equivalent thermal circuit diagram is presented in Fig. 4.Losses are represented by the current sources {fP ...I.4, and

temperatures {T, ...T. 4 are represented by node f1, 2,3,...,n}voltages. The ambient temperature is represented as a DCsource, 7Tb -

Tamb

TambTamb

PiFig.3 Experimental method for deriving the thermal model

The losses {fP...PI} are measured, and at the same time

temperatures {T ...T } are registered. The experimentalmeasurements are performed several times with differentvalues of {PI...PI} to collect the necessary amount of data for

identification of the matrix Go in (10). The inverse of Gogives the matrix of thermal resistances RO.

Rln

V.CASE STUDY.

R2nR13 wice at 0k

R3n

1 R12 2 R23 3 n

Tl T2 T3 Tn

The equat cR R22 o t R33 ( Fign

( ) Tamb

Fig.4 Linear thermal model

V. CASE STUDY

A commercial power supply was chosen as a test prototype(see Fig. 5a). It contains several converters, but only the LLC(see Fig. 5b) was used. For simplicity only the 24V output wasloaded with a maximum current of 2.5A; the converterswitches at 100kHz.The equivalent circuit diagram of the converter (see Fig.6),

as implemented in the simulation program M_SIM, containsthree mutually coupled inductors. The values of the inductorswere measured [1]. Losses in the windings are determined bythermally dependent DC resistances U1,U2,U3 and thermallyindependent AC resistances R1,R2,R3. The resistor R5represents core losses.

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+400V

- f X TrDl 24V@2A

T2 ~~~~~~~~~C,C=33OpFi.i-J - = =|=C2D2 C, C4 8.2nF

* II11 11_w Tw~~~~~~~~~~~~~~~~~~~4 ' PI! C, c=1200,uFTr: n=10

L, = ImH

a) b)Fig. 5 LLC converter: a) photograph b) schematic diagram

IT1I ID3 t%U_+i3 l C4The test setup for extraction of the thermal model is shown

T Ul R2 Ml ...............R3 U2 in Fig. 8a. The converter board is painted black to keep theT |D1l 1 |same emissivity coefficients for all surfaces. The temperature

|T22 D4 R5 | Q M2 l Ri measurements were performed by an IR camera using the test%% A t =T g T setup of Fig. 8b.

~~~~C2X M3 DCD2

R4 U3 | lodes D1,D2

Fig. 6 LLC schematics in M_SIM| ~~~~~Core l

The sources of heat dissipation (MOSFETs Tl,T2, diodesDl,D2 and transformer Tr) are shown in Fig. 5a by arrows. Winding of theThe winding and core losses of the transformer are taken intoaccount.The transformer was unsoldered from the PCB and modified

as in Fig. 7. The airgap was removed and two extra windings,excitation and high-ohmic dissipation, were wound over the Transistors T1,T2main windings. High-frequency AC current was applied to the PCBoftheconverter

excitation winding, thus emulating core losses. DC current was DC DCapplied to the dissipation winding to emulate conduction

a)

losses. High-ohmic wire is wound in such a way, that the EMF,which is generated by the excitation winding, is cancelled (seeFig. 7).

Excitation winding

High-ohmic winding

DCm

~~~ACf25kHz

Fig. 7 Generation of the losses in the winding and the core b)

Fig. 8 The test setup for extraction of the thermal modela) structure of the setup b) photograph of the setup

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VI. IDENTIFICATION AND VERIFICATION OF THE THERMALMODEL

The least squares fitting method can be easily applied to (13) todetermine the coefficients GII, G12... G44.The thermal model was verified by providing the power

verc'tor P from TART ,F TT The. rf-<iultincQ tht-rmnl ri.<Jrtnnre.The electrical losses were determined at the set point (see was ound to be

TABLE II), around which the losses were varied to collect the matrix was found to bedata. Specific loss values, P, and temperature increase 14.322 1.467 1.132 1.308AT=T -T (11) R = 1.467 9.444 2.951 3.410 . (14)measured abR = G-1are specified in the appropriate columns of TABLE II. 1.132 2.951 13.323 9.980In this case the thermal model (10) is L 1.308 3.410 9.980 11.531

PT G1 G12 G13 G14 ATTPD G12 G22 G23 G24 ATD

PW G13 G23 G33 G34 ATWPCr G14 G24 G34 G34 ATjr ,

(12)

The relative deviationsP. -P9P = , i = I....8,

set

JT = predicted -measured/measured

(15)

(16)

are calculated and summarized in TABLE III. Five pointsWhen considering N sets of measurements, from TABLE II were used for identification of the model.P1) P2) ... p N)l and fATfl) AT2 ) AT fN) it is Afterwards the model was checked at three verification points.IlI I II The modeling error is 10% maximum, and about 5% average.possible to rewrite (12) as

p(l)T

P1)D

p(l)w

P1)Crp(2)T

p(N)_ Cr-

ATT(') ATD') AT AT)A 0 0 0 0 0 0

o ATT') 0 0 ATD') AT AT)ATC1) 0 0 0

o ° ATT'1) 0 0 ATDJ' 0 AT A)ATJ1) 0

o o 0 \ATTE' 0 0 ATD' 0 ATw ATC1T2 T2 2 2)AT ATD ATw2)ACr 0 0 0 0 0 0

0 0 0 ATT( 0 0 ATD 0 ATw ATr

(13)

TABLE IIRESULTS OF THE MEASUREMENTS

Transistors Diodes Winding Core |

PT (W) A TT (OC) PD (W) AT (°C) Pw (W) ATw (0C) | Cr (W) AATc (0C)0.919 - 1.982 - 1.047 - 1.385 - Set point

1 0.936 19.7 1.645 25.6 1.022 35 1.330 34.12 0.788 20.3 2.210 29.5 0.921 32 1.180 31.7 Model3 0.821 17.1 2.306 29.8 1.113 33.3 1.153 32.8 identification4 0.934 18.1 1.877 26.5 0.796 32.6 1.548 33.4 points5 0.887 18.8 2.120 28.1 1.300 34.3 1.150 33.36 0.97 20.0 1.958 26.3 1.061 33.2 1.510 32.5 Model7 1.019 20.8 2.048 27.2 1.109 33.7 1.400 33.1 verification8 0.920 20.0 2.051 27.0 1.120 32.0 1.150 32.7 points

TABLE IIIVERIFICATION OF THE THERMAL MODEL

Transistors Diodes Winding CoreN PT TT SPD STD SPw |6TW gpc Note

1 0.019 -0.050 -0.170 -0.043 -0.024 -0.056 -0.039 -0.0452 0.147 0.019 0.115 -0.005 -0.120 -0.001 -0.148 0.005 Model3 -0.142 0.049 0.163 0.015 0.063 0.023 -0.167 0.013 identification4 -0.106 -0.017 -0.053 0.003 -0.240 0.001 0.118 -0.002 points5 0.017 0.047 0.070 0.040 0.242 0.058 -0.169 0.0446 0.056 -0.003 -0.012 0.072 0.013 0.087 0.091 0.106 Model7 0.109 -0.005 0.033 0.062 0.059 0.067 0.011 0.073 verification8 0.001 -0.052 0.035 0.035 0.070 0.047 -0.169 -0.002 points

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La1 1 k

VII. SIMULATION AND MEASUREMENTS OF THE CONVERTER

Thermal and electrical behavior of the converter wassimulated with M_SIM. The converter load was variedaccording to TABLE IV. The losses P for each point andtemperature increase AT were calculated. Measurements forthe consecutive load points were performed by an IR cameraand listed in TABLE IV. The errors between measured andsimulated results

SYT = ATimulated -AT easured (17)sm ATmeasured

are calculated and listed in TABLE IV as well.A thermal snapshot of the converter is shown in Fig. 9.

The diodes of the output rectifier are the largest contributorsto the temperature rise.

Fig. 9 Thermal snapshot of the converter at Iload =2.5A, I.b =210C.

In TABLE IV the largest discrepancy betweenmeasurements and simulation is 24.3%. This is thought to becaused by the assumptions used for modeling the electricallosses and the limitation of a linear thermal model for thethermal behavior.

VIII. CONCLUSIONS

A combined electrical and thermal simulator was developedand tested with an experimentally identified thermal model.The simulation resulted in a good match with themeasurements. The combined modeling approach requires lowcomputational effort, being therefore suited to be included inconverter optimization software.

ACKNOWLEDGMENT

The authors would like to thank SenterNovem for theirfinancial support under project code IOP-EMVT 02207B andPhilips Power Solutions for the test samples and materials.

TABLE IVRESULTS OF THE SIMULATIONS AND MEASUREMENTS

Iload Simulation Measu- Error(A) Component rementV ________vP (W) AT (°C) AT (°C)

Transistors 0.713 15.55 15.4 0.010

1.50 Diodes 1.768 24.67 27.7 -0.109Windings 0.871 30.08 32.9 -0.086

Core 1.208 29.88 36.9 -0.190Transistors 0.768 17.02 15.7 0.084

1.75 Diodes 2.055 28.10 30.5 -0.079Windings 1.062 33.80 33.6 0.006

Core 1.222 33.00 36.6 -0.098Transistors 0.822 18.47 16.9 0.093

2.00 Diodes 2.337 31.48 33.4 -0.0572.00 Windings 1.265 37.59 35.0 0.074

Core 1.229 36.15 37.8 -0.044Transistors 0.890 20.12 17.0 0.184

2.25 Diodes 2.615 34.93 37.0 -0.056Windings 1.495 41.77 35.8 0.167

Core 1.237 39.57 38.2 0.036Transistors 0.941 21.58 18.5 0.166

2.50 Diodes 2.896 38.44 40.7 -0.055Windings 1.747 46.24 37.2 0.243

Core 1.244 43.18 40.2 0.074

REFERENCES

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1156 vol.2.[2] D.V. Malyna, E.C.W. de Jong, J.A. Ferreira, M.A.M. Hendrix, J.L.

Duarte, P. Bauer, A.J.A. Vandenput, "Combined Electrical andThermal Modeling in Power Supplies", 11-th European Conferenceon Power Electronics and Applications, September 2005.

[3] D.V. Malyna, J.L. Duarte, M.A.M. Hendrix, F.B.M. van Horck, "AComparison of Methods for Finding Steady-State Solution in PowerElectronic Circuits", Power Electronics and Motion ControlConference, 2004. IPEMC 2004. The 4th International Volume 3,14-16 Aug. 2004 Page(s):1700 - 1705 Vol.3.

[4] R.W. Erickson, D. Maksimovic, "Fundamentals of PowerElectronics", Kluwer Academic Publishers,2001.

[5] J.L. Duarte, M.A.M. Hendrix, "Computer-aided optimization ofswitching converters for low-power applications", EUT report 00-E-3 1, Eindhoven, Dec. 2000.

[6] J.W. Nilson "Electric Circuits", Addison-Wesley PublishingCompany, 1990.

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