Estimating Temperature Rise of Transformers Orenchak G. 2004)
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Power E l ec t roni c s T ec hnol ogy J ul y 2004 w w w. pow erel ec t roni c s.c om 14 Estimating Estimating Estimating Estimating Estimating T T T T T emper emper emper emper emper atur atur atur atur ature Rise e Rise e Rise e Rise e Rise o f o f o f of o f T T T T T r r ransf ansf ansf ansf ansf o r or o r or ormer me r mer me r mers s s B y ca lcul ati ng core loss esand winding los s es ,trans former t emperat ure rise ma y be predict ed. T hrough appropri a t e core ma terial se lection,core loss es may be minimi z ed a t t he e xpected op era t ing temperature. B B B B By G y G y G y G y G eo r eo r eo r eo r eo rge G. ge G. ge G. ge G. ge G. Or O r O r O r O renchak, enchak, enchak, enchak, en ch ak , G eneral Manager, T S CF erri t e International, Wadsworth, Ill. T ransformers for power applications often are limited in size by an accept- able temperature rise. An acceptable temperature rise of a transformer is usually dependent on limitation s of the materials used in t he tr ansformer, s af ety age ncy regulations or h igh-temp eratu re reliabili ty iss ues as sociated with o ther component parts close to the transformer. The tempera- ture rise of a transformer is due to the power loss dissi- pated by the transformer in the form of heat. The power loss of a transformer consists of core loss and of winding coil losses, and can be predicted accurately. Core Losses Core losses significantly contribute to the temperature rise of a t ransf ormer. Hysteresis loss , eddy curr ent loss and residual loss all contribute to the total core loss. At high flux densities and relatively low frequencies, hysteresis losses are usually dominant. Hysteresis loss is the amount the magnetization of the ferrite material lags the magnetizing force because of molecular frictio n. Th e loss of energy ca used by hysteres is loss i s propor tion al to th e area of the static or low-fre quency B-H loop. At high frequencies, eddy current losses usually domin ate. E ddy curren t losses result from a varying indu c- tion that produces electromotive forces, which cause a current to circulate within a magnetic material. These eddy currents result in energy loss. Understand- ing the behavior of the combined total core loss as func- tions of fl ux density and o f freque ncy is mos t im port ant. Fig Fig Fig Fig Fig. 1 1 shows the relationship of core loss v ersus frequency for power-grade fe rr ite mat erials. Fig Fig Fig Fig Fig. 2 2 2 2 2 shows the relation - ship of core loss versus flux density for power-grade ferrite materials. Manufacturers typically combine and ex pand t he info rmation on Fig Fig Fig Fig Figs. s. s. s. s. 1 1 1 and 2 2 2 2 2 by publishin g c ore loss as a functio n o f flux density at various frequen cies and on logarithm ic sc ales , as shown in Fig Fig Fig Fig Fig. 3. 3. 3. 3. 3. Notice both core loss versus frequency and core loss ve rsus flux density relationsh ips are e xpon ent ial. S ymmet ri- cal sine wave, square wave and unidirectional square wave voltage excitations all result in approximately the same core loss, providing the frequency and total flux density excursion remain the same. Manufacturers t ypically publish core loss, as measured, us- ing symmetr ical si nu soidal voltag e excitation. For the excitation types men- tioned, core loss can be obtained in a straig htforwa rd mann er from manufacturers’ published graphs or calculated from core loss for- TSF-50ALL Flat Line 0 50 100 150 200 250 300 2550 75 100 125150 175 200 225 250 275 Frequency (kHz) C o r e l o s s ( m W / c c ) TSF-50ALL Flat Line 0 100 200 300 400 500 600 700 800 900 1000 500 1000 1500 2000 2500 3000 Flux density (gauss) C o r e l o s s ( m W / c c ) F ig. 1. Core loss versus frequency at 1000 gauss. F i g.2. C ore los s ve rsus flux density at 100 kHz .
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By calculating core losses and winding losses, transformer temperature
rise may be predicted. Through appropriate core material selection, corelosses may be minimized at the expected operating temperature.
BBBBBy Gy Gy Gy Gy Georeoreoreoreorge G.ge G.ge G.ge G.ge G.OrOrOrOrOrenchak,enchak,enchak,enchak,enchak, General Manager, TSCFerriteInternational, Wadsworth, Ill.
Transformers for power applicationsoften are limited in size by an accept-able temperature rise. An acceptabletemperature rise of a transformer isusually dependent on limitations of the
materials used in the transformer, safety agency regulationsor high-temperature reliability issues associated with othercomponent parts close to the transformer. The tempera-ture rise of a transformer is due to the power loss dissi-pated by the transformer in the form of heat. The powerloss of a transformer consists of core loss and of windingcoil losses, and can be predicted accurately.
Core LossesCore losses significantly contribute to the temperature
rise of a t ransformer. Hysteresis loss, eddy current loss andresidual loss all contribute to the total core loss. At highflux densities and relatively low frequencies, hysteresislosses are usually dominant.
Hysteresis loss is the amount the magnetization of the
ferrite material lags the magnetizing force because of molecular friction. The loss of energy caused by hysteresisloss is proportional to the area of the static or low-frequencyB-H loop. At high frequencies, eddy current losses usuallydominate. Eddy current losses result from a varying induc-tion that produces electromotive forces, which cause acurrent to circulate within a magnetic material.
These eddy currents result in energy loss. Understand-ing the behavior of the combined total core loss as func-tions of flux density and of frequency is most important.FigFigFigFigFig ..... 11111 shows the relationship of core loss versus frequencyfor power-grade ferrite materials. FigFigFigFigFig ..... 22222 shows the relation-ship of core loss versus flux density for power-gradeferrite materials. Manufacturers typically combine andexpand the information on FigFigFigFigFig s.s.s.s.s. 11111 and 22222 by publishing coreloss as a function of flux density at various frequencies andon logarithmic scales, as shown in FigFigFigFigFig ..... 3.3.3.3.3.
Notice both core loss versus frequency and core lossversus flux density relationships are exponential. Symmetri-cal sine wave, square wave and unidirectional square wave
voltage excitations all result inapproximately the same core loss,providing the frequency and totalflux density excursion remain thesame. Manufacturers t ypicallypublish core loss, as measured, us-ing symmetrical sinusoidal voltageexcitation.
For the excitation types men-tioned, core loss can be obtainedin a straightforward manner frommanufacturers’ published graphsor calculated from core loss for-
TSF-50ALL Flat Line
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Fig. 1. Core loss versus frequency at 1000 gauss. Fig. 2. Core loss versus flux density at 100 kHz.
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make materials that have minimumcore loss near the expected workingtemperature.
Numerous material grades opti-
mized for a specific ideal operatingtemperature now exist. The presentbrings additional discoveries that en-able ferrite manufacturers to developnew material grades that exhibit thesame low core loss over a wider oper-ating temperature range (50 mW/cm 3
at 100 kHz, 1000 gauss from roomtemperature to more than 100°C).
This new material grade will contr ib-ute to more energy-efficient productsbecause the core loss will be opt imizedover the entire operating tempera-
ture range. Products made fromthese materials will be safer becausethe chance of thermal runaway willbe less. These new material gradesalso will minimize required core in-ventories because one grade of mate-rial will be optimal for all power ap-plications, regardless of operatingtemperature.
Ferrite Material PropertiesAlthough material properties other
than core loss are unimportant in de-termining temperature rise or coresize of a transformer, other proper-ties are of interest if integrated mag-
netics (transformers and inductorswound on a common magnetic core)are being considered.
The magnitude and stability of TSF-50ALL Flat Line’s initial perme-ability over a wide operating tempera-ture may be advantageous for somelow flux-density signal applications.
Transformer applications requireenough permeability to providea good flux path so flux stays in theintended path and doesn’t stray out
of the core. Output power inductorapplications predominantly requirea gapped core. The gap depth sizebecomes a dominant factor while de-termining the component inductanceand the material permeability is rela-tively unimportant.
Transformer core size is often con-strained by the core loss of the core
TEMPERATURE RISE
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TSF-50ALL Flat LineTSF-5099TSF-7099 & TSF-boostTSF-7070TSF-8040TSF-5000
Fig. 5. Core loss versus temperature.
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material. However, power inductorcore size is often constrained by thecore material’s saturation propertiesat operating temperatures.
Winding Coil Losses
Winding coil losses contribute toa transformer’s total loss. Copperlosses (I 2R losses) are easy to under-stand. Winding coil losses due to skineffect, proximity effect, effect of eddy
currents in the windings, effects fromfringing flux intersecting windingsnear the core gap, edge effects and ex-traneous conductor effects may be sig-nificant and should be considered. Forsimplicity, we’ll ignore these addi-
tional winding losses and consideronly I 2R copper losses.The resistance of each winding can
be calculated by mult iplying the meanlength turn of the winding by the cop-
per resistance for the appropriate wiresize and by the total turn count .RP or R S= MLT * R CU * NWhere:RP = primary coil resistance inRS = secondary coil resistance in
MLT = mean length turn in cmRCU = copper resistance in µ /cmN = turn count
The copper losses for each wind-ing are calculated with the followingformulaPCU = I 2 RWhere:PCU = copper loss in wattsI = current in ampsR = resistance in
Sum the primary and all the sec-
ondary winding losses to obtain thetotal winding losses, and then sum thetotal winding losses with the corelosses to obtain the total transformerlosses (P ).
Temperature RiseA transformer’s output power is
less than its input power. The differ-ence is the amount of power convertedinto heat by core loss and windinglosses. A combination of radiationand convection dissipate this heatfrom the exposed surfaces of the trans-former. Thus, the heat dissipation isdependent upon the total exposedsurface area of the core and the totalexposed surface area of the windings.
Temperature rise of a transformeris hard to predict with precision. Oneapproach is to lump the winding lossestogether with the core losses and as-sume that the thermal energy is dissi-pated uniformly throughout the sur-face area of the core and winding as-sembly at all ambient temperatures.This isn’t a bad assumption, becausethe majorit y of the trans-former’s sur-face area is ferrite core area rather thanwinding area, and the thermal conduc-tivity of ferrite (~40 mW/cm/ °C) ispoor at any temperature. With theseassumptions, the temperature rise of a transformer can be estimated by thefollowing formula:
T = (P /AT)0.833
Where:T = temperature rise in °C
TEMPERATURE RISE
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TEMPERATURE RISE
P = total transformer losses (power lost and dissipated asheat) in mW; A T = surface area of transformer in cm 2.
The exponent (0.833) used in the above formula to es-timate temperature rise has been derived from empiricaldata with the use of the following formula:x=ln(P @1st T/P @2nd T)/ln(1st T/2nd T)
FigFigFigFigFig ..... 66666 shows temperature rise versus power loss for sev-eral different size E core transformers.
The temperature rise of a transformer results in partfrom core loss and in part from winding coil losses. The
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Fig. 6. Temperature rise versus transformer power loss.
core losses and winding losses and temperature rise can beestimated with calculations by making a few assumptions.Because of the assumptions made, it may be necessary toprove the temperature rise empirically by measuring thetransformer using thermal couples. New ferrite materialsthat exhibit consistent core loss over a wide range of oper-
ating temperatures will simplify ferrite material selectionand prove valuable to the transformer industry. PETPETPETPETPETec hec hec hec hec h
References1. Snelling, E.C. “Soft Ferrites Proper ties and Applications,Second Edit ion,” Butterworth, 1988.2. McLyman, C. Wm. T. “Magnetic Core Selection for Trans- formers and Inductors,” Marcel Dekker Inc., 1982.3. McLyman, C. Wm. T. “Transformer and Inductor Design Handbook,” Marcel Dekker Inc., 1978.4. Jamerson, Clifford. “Targeting Switcher Magnetics Core Loss Calculat ions,” Power Electronics Technology, February
2002, Vol. 28, No. 2.5. Carsten, Bruce. “High Frequency Conductor Losses in Switchmode Magnetics,” PCIM, November 1986.6. “Soft Ferrites: A User’s Guide,” Magnetic Materials Producers Association, MMPA SFG-98, 1998.
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