Thermal Power Density Barriers of Converter Systems

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1 Thermal Power Density Barriers of Converter Systems Uwe DOFENIK and Johann W. KOLA Power Eletroni Systems Laboratory (PES ETH Zurih ETH-Zentrum / ETL H CH-89 Zurih Switzerland Phone: Fax: drofenik@lem.ee.ethz.h Abstrat With the desire to integrate power onverters into larger systems high power density beame a very important issue. In this paper we disuss the thermal limits of the power density of onverter systems. It is shown that these limits are partly given by today s tehnology and partly given by physis. Employing the given equations one an quikly estimate the maximum possible power density of a onverter design. Considering the limitations disussed in the paper will be helpful in setting up roadmaps related to future trends in onverter power density. Introdution We define power density of a onverter system as onverter output power divided through onverter volume. With the general trend to integrate power onverters into larger and omplex systems there is a strong pressure on researh and development to inrease the power density. The power density is limited by the seleted topology the indutive omponents the apaitive omponents and the ooling system (see [] for a detailed disussion. In setion we disuss the general limits of fored onvetion ooling whih is often muh more effetive than natural onvetion. Employing a heat sink plus fan the ooling system power density is limited by the fan s power onsumption in some appliations by the noise of the fan and by the thermal ondutivity of the heat sink material. Optimizing the heat sink geometry for a given fan harateristi minimizes the ooling system volume for a given thermal resistane. In order to be able to generally ompare different ooling system tehnologies (like different power levels operating temperature levels natural or fored onvetion water ooling heat pipes we employ the Cooling System Performane Index (CSPI [] whih an also be understood as a volumetri thermal ondutivity [] defined as CSPI G ( HS W W S a K K liter = = HS K CS S a W CS ( [ ] [ ] Vol liter Vol liter In setion we investigate how the limits found in setion influene the power density of the whole onverter system. Simple equations to estimate the power density of ube-shaped onverter systems are given. The disussion performed in setion will make lear that in ase of pure natural onvetion small systems will always show higher power densities than large systems. But assembling one large onverter from many small sub-onverters does not help to inrease the total power density beause additional outer surfae will be needed for ooling all internal sub-onverters. Generally the absolute dimensions have a strong impat on the power density. ( In setion we shown that besides optimization of the CSPI a further and often signifiant inrease of the onverter power density an be ahieved by inreasing the temperature levels of power semiondutors and/or heat sink surfae.. Cooling System Optimization In order to optimize a heat sink employing fored onvetion one has to take into aount the thermal resistane of the heat sink material the thermal resistane due to onvetion and the temperature inrease of the air flowing through the heat sink hannels. The following optimization is based on the heat sink design of Fig.. d (a s P V n = 5 b b/n t Δp F [N/m ] Δp F (b Δp CHANNEL k. Δp F V F [m /s] operating point V F Fig.: (a Geometry of the heat sink with thermal losses P V [W]. overing the area A _= b L with L as heat sink length in air flow diretion. (b Fan harateristi showing fan pressure dependent on the air flow V F. Generally the fin geometry defines hannels whih provide a pressure drop Δp CHANNEL for the air flow. The air flow driven by a fan behaves aording to the fan harateristi as shown in Fig.(b. The resulting operating point defines the air flow that based on the fin geometry is laminar or turbulent. Based on flow and air properties the onvetive heat transfer from the fin surfae into the air in the hannels an be alulated. All

2 these relations an be desribed employing analytial and empirial equations ([] [4] whih allows a systemati optimization of the fin geometry for a given fan. Following the proedure desribed in [4] the total thermal resistane of the heat sink (from heat sink surfae to ambient air at the fan inlet is power onsumption of the fan P FAN max employing (8. The ooling system volume Vol CS in (9 is defined as volume of heat sink plus volume of fan. 4 λ HS = 8 W/mK 8 ( HS * th S a = th FIN + onv + ( with ondutive heat flow through the fins * F FIN λhs L ΔpF s V L onvetive heat flow from fin surfae into air ( CSPI (P FAN =W CSPI Cu = 6 CSPI Al = λ HS = W/mK N OPT = [mm] 6 4 N [rpm] Δp s s (4 4 4 F onv. + VF L ΔpF L and a ontribution due to the temperature rise of the air heating up along the hannel from inlet to outlet (5 V F CSPI (P FAN =5W 4 CSPI Cu = CSPI Al = 7 λ HS = 8 W/mK λ HS = W/mK N OPT = N [rpm] Generally maximum air flow rate V F pressure drop Δp F and power onsumption of the fan P FAN are dependent on the fan s rotating speed N [rmp] and diameter D [m] as desribed generally in [5] as V F m s = knd (6 Δ p F N m = kn D (7 P W = k N D (8 FAN [ ] 5 Investigating a large number of ommerially available fans with wide variations of their geometries [6] we alulated the parameters of (6 - (8 to be within the ranges k = [ ] k = [ ] and k = [ ]. For omparison of different heat sink designs onerning power density we employ the Cooling System Performane Index (CSPI ([] [] as defined in ( whih an be expressed independently from a speifi fan by employing (6 - (8. This results in CSPI = Vol = ( HS S a CS ( + A λ A + A s HS A4 A A max / A AA k P FAN max / max / k FAN k FAN + s P s P ( ( Here we use the abbreviations A = - k /k A = 5-4 k -.5 A = 6.5 k.5 /k and A 4 = k -. In (9 the fan speed N has been substituted by the maximum aeptable (9 4 8 [mm] Fig.: Optimizing a ooling system employing (9 for heat sink materials aluminium and opper. For a typial 5kW-onverter with 95% effiieny we assume the needed area for the power semiondutors to be A =m. The maximum aeptable power onsumption of the fan is (a P FAN =W and (b P FAN =5W. If the hannel width s in (9 is set to values maximizing the CSPI theoretially optimized urves an be plotted as given in Fig.. If the maximum aeptable power onsumption of the fan is set to W (Fig.(a and employing a fan diameter =4mm (equal to fin length as shown in Fig.(a a theoretial maximum CSPI Al_ = an be ahieved for an aluminum heat sink (W/Km and a maximum CSPI Cu_ =6 for opper (8W/Km. The required fan speed would be N OPT_ = 5rpm for both materials. In ase of =mm the CSPI-values would be around but the required fan speed would be 6rpm signifiantly inreasing noise and reliability problems. In ase the maximum aeptable power onsumption of the fan is inreased to 5W as shown in Fig.(b the CSPI for =4mm an be inreased to 7 and/or. Experimental prototypes of optimized heat sinks for typial 5kW-onverters are shown in Fig.. These heat sinks have been designed aording to the theoretial optimum given in Fig.(a. Based on measured th -values we reeived CSPI Al =7.5 and CSPI Cu =.6. Both CSPI-

values are % below the theoretial optimum beause of manufaturing onstraints that do not allow to fully exploit the theoretial optimum [7] and the fan employed has a speed of N=55rpm [6]. (a (b Fig.

(b opper n= s=.mm t=.5mm b==4mm d=mm L=8mm S_a =.K/W.

Vol SYS onverter effiieny η SYS maximum aeptable temperature differene between power semiondutor juntion and ambient and thermal resistane th defining the heat flow from the semiondutors to ambient.

3 values are % below the theoretial optimum beause of manufaturing onstraints that do not allow to fully exploit the theoretial optimum [7] and the fan employed has a speed of N=55rpm [6]. (a (b Fig.: Optimized heat sinks with fan SanAe 4x4x8mm/5dB [6] and with A =m (a aluminum n=6 s=.5mm t=.mm b==4mm d=mm L=8mm S_a =.6K/W; (b opper n= s=.mm t=.5mm b==4mm d=mm L=8mm S_a =.K/W.. Thermal Limits of the Converter Power Density Generally the power density of a onverter is defined as POUT SYS ηsys th = = ( VolSYS ηsys VolSYS with onverter output power P OUTSYS onverter volume Vol SYS onverter effiieny η SYS maximum aeptable temperature differene between power semiondutor juntion and ambient and thermal resistane th defining the heat flow from the semiondutors to ambient. For the following general disussion we assume the thermal resistane between semiondutors and heat sink surfae to be small ompared to the thermal resistane assoiated with onvetion at the heat sink surfae. number n FIN = a /(s+t is defined by fin thikness t and hannel width s. Beause the effetive ooling surfae is proportional to the volume it is onvenient to use the previously defined CSPI in the following alulations. The thermal resistane of natural onvetion at the surfae of a ube-shaped (base length a onverter is ( α = n a ( n C f with heat transfer oeffiient α [W/m K] and number of ooled surfaes n Cf. For fored onvetion realised by a ooling system integrated in the onverter the aording thermal resistane is ( f = kcs a CSPI ( whih an be diretly derived from ( with k CS _=_Vol CS _/_Vol SYS desribing the volume share of the ooling system. The thermal resistane in ( is th = th = n th f ( resulting in a general expression for the onverter power density of a ube-shaped onverter system as d = n a + CSPIk ( α W S a SYS m C f CS ηsys (4 with maximum aeptable sink - ambient temperature differene S-a. To alulate the heat transfer oeffiient for natural onvetion we have to make some assumptions about the heat emitting plate. In ( (4 all six ube sides are emitting heat. In the following we will assume that just the horizontal top-plate ontributes to natural onvetion. Employing (.8 in [8] the ayleigh number for a heated horizontal square-shaped plate is generally given as a = β ( T T g L ν Pr (5 TOP a We set g=9.8 T a = C and harateristi length L= A/U=.5 a β = /(7+=.4e-. Assuming a plate temperature T=6 C we an setν(6 C= e-5 and Pr(6 C=.7. This results in a Nusselt number Nu =.54 a = /4 m TOP6 C TOP6 C =.54 (.66 a = 4 a 7 /4 /4 (6 Fig.4: (a Surfae area of the ube employing natural onvetion is proportional to the square of the length A onv ~ a. (b Internal surfae area onsisting of fins is proportional to the third order of the length A onv ~ a. a / (s+t ~ a. As shown in Fig.4(a the natural onvetion at the outer surfae of a ube-shaped onverter is proportional to the square of its base length. If fored onvetion is employed by realizing a part of the onverter volume as heat sink plus fan the effetive ooling surfae and therefore heat transfer to ambient via fored onvetion is proportional to the third order of the length (Fig.4(b. Here the fin With the definition of the Nusselt number Num = α L / λai (7 and the thermal air ondutivity λ AI (6 C = e- we reeive for the heat transfer oeffiient of the horizontal top-plate of the ube-shaped volume α = a (8 /4 TOP6 C 5 In ase of vertial walls the Nusselt number is aording to (.8 in [8]

4 / 6 9 /6 8 / 7 NumWALL = a ( + (.49 Pr (9 or espeially for T=6 C / NumWALL 6 C = ( a ( resulting in a heat transfer oeffiient / α WALL6 C = ( + 7. a (. a Assuming natural onvetion only at the horizontal top plate of the ube-shaped onverter (4 an be ombined with (8 giving ( TOP6 C W S a 5/4 d SYS ( 5a CSPI kcs m = + ηsys ( whih is plotted in Fig.5. As shown there in ase of dominating fored onvetion the onverter power density d f is in approximation independent from the absolute onverter size while in ase of pure natural onvetion d n dereases inverse proportional with the base length. One an also see that in ase of pure natural onvetion small systems will always show higher power densities than large systems. Assembling one large power onverter from many small sub-onverters does not hange this fundamental relationship between absolute size and power density beause additional outer surfae and/or hannel volume will be needed for ooling all internal sub-onverters.... d n [kw/dm ] d f [kw/dm ] (CSPI= P OUTf [kw] (CSPI= P OUTn [kw]... a [m] Fig.5: Converter power density and output power dependent on absolute size of a ube-shaped onverter for dominating fored onvetion (index f solid line and pure natural onvetion at the top plate (index n dashed line. Parameters are η SYS =.95 S-a =5 C CSPI= k CS =.5. shown in Fig.6 a ube represents the worst shape in terms of maximum power density if all six surfaes are ooled equally (solid line. More realistially for typial onverter systems we assume only one single side to be ooled by natural onvetion whih results in the ratio ( / = k (4 shown as dashed line in Fig.6. In this ase there is no loal minimum. The more plate-like the shape is the higher the theoretially possible power density will be. Therefore onverters of very small output power employing natural onvetion and being of flat shape will typially show very high power density. d SYS / d SYS.67.5 k=.5.4 : k=.5 k = h / a 5 k=5 Fig.6: Simple thermal model of onverter systems of different shape but with equal volume employing pure natural ooling at their surfae. (Solid Line: All surfaes are equally ooled (n CS = 6. (Slashed Line: Only one surfae (square-shaped base length a is ooled (n CS =.. Influene of Power Semiondutor Temperature Levels The power density of a ooling system an be written as POUT SYS ηsys dcs = = CSPI. (5 VolCS ηsys Therefore besides optimization of the CSPI a further inrease of the power density an be ahieved by inreasing the maximum aeptable juntion temperature. Espeially when employing SiC whih allows juntion temperatures well above 5 C this effet an be exploited []. If at a given temperature T ambient = 45 C the maximum juntion temperature an be raised from 5 C to 75 C by replaing Si-semiondutors with SiC the power density d CS will rise by a fator.65. For two shapes representing naturally ooled onverters with equal effiieny equal maximum temperature and equal volume the ration of power densities follows as / = ( + k ( k ( under the assumption that all six surfaes are equally ooled by natural onvetion. In ( one shape is a ube and the deviation of the seond shape (base length a height h from the ube is haraterized by k = h/a. As P VD T JT TJ-S P VT T S P VSYS TJD DJ-S (HS S-a T ambient Fig.7: Stationary thermal model of a power transistor (losses P VT and a diode (losses P VD mounted onto the heat sink with temperature T S. The heat sink employing onvetion is fully represented by S_a (HS.

5 Inreasing the hip size of a power semiondutor will not only redue the ondution losses in ase of a MOSFET but another effet valid for all semiondutors is the redution of the thermal resistane from juntion to sink beause J-S is inverse proportional to the hip size. Vol CS [dm ].5.5 T J = 5 C J-S 5 C T J = 75 C J-S 75 C J-S [K/W] Fig.8: Graphial representation of (6 assuming the thermal equivalent iruit shown in Fig.7 with the parameters η SYS =.95 T a =45 C CSPI= P OUTSYS =5KW. Assuming equal losses P VT = P VD =.5_P VSYS of diode and transistor in Fig.7 furthermore setting J-S = TJ_S = DJ-S the ooling system volume beomes TJ T ambient CS ( J S = J S CSPI POUT SYS η Vol ( SYS (6 with T J as the maximum aeptable value for the juntion temperatures T JT and T JD. This fundamental dependeny of Vol CS on J-S is shown in Fig.8 graphially for two different juntion temperatures. As long as J-S is not too small ompared to S-a (HS the ooling system volume an be signifiantly redued by reduing the thermal resistane of the semiondutors. This an be simply ahieved by employing a ertain number of power semiondutors in parallel. If the thermal resistane of the semiondutors reahes a ritial value J-S it beomes impossible to operate the system within the given thermal parameters. Fig.8 also shows that inreasing the juntion temperatures is very effetive in reduing the volume and therefore in inreasing the power density. The hoie of the thermal resistane values (HS S-a and J-S will define the heat sink temperature T S. Based on (5 the ooling system volume an be written in dependeny of the heat sink temperature as POUT SYS ( η SYS VolCS ( TS = ( TS Tambient CSPI (7 whih is shown in Fig.9 for two different values of the system output power. The loser the heat sink temperature is to the ambient the larger heat sink volume is needed to keep the onverter system within its thermal boundaries. With the heat sink temperature lose to the maximum aeptable juntion temperature the volume an be minimized. As already disussed before this an be ahieved by minimizing J-S (Fig.8. Vol CS [dm ].5.5 T a =45 C P OUTSYS = kw P OUTSYS = 5kW T J <75 C T S [ C] Fig.9: Graphial representation of (7 with the parameters η SYS =.95 T a =45 C CSPI=. Literature [] Kolar J. W. Drofenik U. Biela J. Heldwein M. L. Ertl H. Friedli T. ound S. D. "PWM Converter Power Density Barriers" Proeedings of the 4th Power Conversion Conferene (PCC'7 Nagoya Japan April - 5 CD-OM ISBN: X (7 [] U. Drofenik G. Laimer J. W. Kolar Theoretial Converter Power Density Limits for Fored Convetion Cooling in Proeedings of the International PCIM Europe 5 Conferene Nuremberg Germany June 7-9 pp (5 [] M. F. Holahan "Fins Fans and Form: Volumetri Limits to Air- Side Heatsink Performane" IEEE Trans. on Components and Pakaging Tehnologies vol. 8 Issue June 5 pp [4] U. Drofenik J. W. Kolar Analyzing the Theoretial Limits of Fored Air-Cooling by Employing Advaned Composite Materials with Thermal Condutivities > 4W/mK in Proeedings of the 4th International Conferene on Integrated Power Systems (CIPS'6 Naples Italy June 7-9 (6 [5] S. L. Dixon "Fluid Mehanis and Thermodynamis of Turbomahinery" ISBN Butterworth-Heinemann 4th edition (998 [6] Sanyo Denki Co. Ltd. Webatalog Cooling Fan and CPU-Cooler DC-Fan datasheets published at etail.php?master_id=78 (February 7 [7] U. Drofenik J. W. Kolar "Sub-Optimum Design of a Fored Air Cooled Heat Sink for Simple Manufaturing" in Proeedings of the 4th Power Conversion Conferene (PCC 7 Nagoya Japan April - 5 (7 [8] H. D. Baehr and K. Stephan Wärme- und Stoffübertragung (in German ISBN X rd edition Springer-Verlag (998.

Part G-4: Sample Exams

Part G-4: Sample Exams 1 Cairo University M.S.: Eletronis Cooling Faulty of Engineering Final Exam (Sample 1) Mehanial Power Engineering Dept. Time allowed 2 Hours Solve as muh as you an. 1. A heat sink