1616 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003

Efficiency Analysis of a High-TemperatureSuperconducting Induction Heater

Niklas Magnusson and Magne Runde

Abstract—In an induction heater for heating of aluminum bil-lets, the main reason for using high-temperature superconducting(HTS) tapes instead of conventional copper conductors is to reducethe large power losses in the induction coil. In this work we presenthow to calculate the different loss contributions of an inductionheater based on HTS tapes. Calculations of these losses are used inthe design of an HTS induction heater with a rated power of about10 kW operating at liquid nitrogen temperature. The calculationspredict an optimal current that yields the highest efficiency of theinduction heater.

Index Terms—AC losses, induction heating, HTS coil.

I. INTRODUCTION

L ONG-LENGTH, robust, high-temperature supercon-ducting (HTS) tapes with high current densities are

available today on the market [1]. These tapes are primarilydesigned for DC use. An important step to be taken by the tapemanufacturers to make the HTS tapes reach a broad market inAC power applications is to reduce the AC losses. Meanwhileattention should be paid to how to utilize the HTS tapes andhow to construct applications based on them.

In most conventional power applications, such as power ca-bles, transformers or reactors, the current density is 1–4 A/mmin the copper or aluminum conductors. This current density re-sults in losses of 20–80 mW/Am. For an HTS tape operating at77 K to reduce the power losses when replacing a conventionalconductor, it needs to have losses lower than 1.5–6 mW/Amtaking a cooling penalty factor of 12 into account (the numberof watts needed in a cooling machine to remove one watt gen-erated at 77 K).

An induction heater can be seen as a special case of a trans-former, where the induction coil constitutes the primary windingand the workpiece to be heated is a short-circuited one-turn sec-ondary winding. When industrially employing Hz induc-tion heating to large billets of nonmagnetic, high-conductivitymaterials such as aluminum, the copper conductors in the induc-tion coil carry current densities of the order 20 A/mm. For anHTS tape, when replacing conventional conductors to reduce thelosses in such an induction heater, it needs to have losses lowerthan 30 mW/Am in average. This number is by a factor of 5–20

Manuscript received August 5, 2002. This work was supported in part througha European Community Marie Curie Fellowship.

N. Magnusson is with SINTEF Energy Research, NO-7465 Trondheim,Norway (e-mail: niklas.magnusson@sintef.no).

M. Runde is with SINTEF Energy Research, NO-7465 Trondheim, Norway,and also with the Department of Electrical Power Engineering, NorwegianUniversity of Science and Technology, NO-7491 Trondheim, Norway (e-mail:magne.runde@sintef.no).

Digital Object Identifier 10.1109/TASC.2003.812807

Fig. 1. Schematic overview of the upper half of the induction heater. Theheater is symmetric around the dashed-dotted line. The aluminum workpiecehas a diameter of 80 mm and a length of 215 mm, whereas the inner diameterof the HTS coil is 130 mm and the length is 257 mm.

greater than for most other power applications where the use ofHTS tapes is considered.

In this work we describe how to calculate the different losscomponents and show calculated results for a 10 kW HTS in-duction heater. The results are compared to values of the lossesobtained from initial measurements on a recently constructedinduction heater of this size.

II. I NDUCTION HEATER DESIGN

The design of the induction heater is described in detail in [2].Here a brief review of the design is given following Fig. 1. Thealuminum workpiece to be heated is placed in the center andis enclosed by high-temperature thermal insulation. The HTScoil is built up of 24 double pancake coils, each wound withtwo tapes in parallel. In addition, the double pancake coils areconnected two by two in parallel yielding a total of four paralleltapes. At the coil ends flux-diverters are inserted in the formof transformer sheets to straighten the magnetic field and henceto reduce the radial magnetic field, which otherwise results inunacceptably high losses. The HTS coil is immersed in liquidnitrogen inside a fiberglass reinforced epoxy cryostat.

At the current level of 190 A , the maximum magnetic fieldis 250 mT (axially) at the inside of the coil. The frequencyis 50 Hz. The heat-flow from the coil to the nitrogen bath gen-erates a temperature difference of a few degrees and hence the

1051-8223/03$17.00 © 2003 IEEE

MAGNUSSON AND RUNDE: EFFICIENCY ANALYSIS OF A HIGH-TEMPERATURE SUPERCONDUCTING INDUCTION HEATER 1617

operating temperature of the coil becomes about 80 K when ex-posed to the current rating.

III. L OSSCALCULATION

A. HTS Coil Losses

In the HTS coil, losses in the form of hysteresis and offlux-flow occur. Both the hysteresis and the flux-flow contri-butions depend on the current in the tape,, and the magnitudeas well as the orientation of the magnetic field,. To simplifycalculations, the losses due to the magnetic field componentoriented parallel to the surface of the HTS tape,, and thelosses due to the field component oriented perpendicular tothe surface of the tape, , are treated separately. Althoughthis separation may be physically incorrect, it has only a smallinfluence on the results. In the major part (in the middle) ofthe coil the parallel field determines the losses, whereas at thecoil ends the perpendicular field dominates the losses. Onlyin a small region of the coil the losses due to parallel andperpendicular fields are of comparable magnitude.

The AC losses are modeled semi-empirically using hysteresismodels based on the critical state [3] and flux-flow models em-ploying power law dependent DC- characteristics. The fit-ting parameters of the models were obtained from measure-ments on a tape similar to the one used in the HTS coil. Themodels are briefly reviewed below. The losses in the HTS tapeare given in watts per meter, and the total losses of the coil canbe obtained by integrating the tape losses over the length of thetape constituting the coil.

Hysteresis losses due to combinations of parallel magneticfields and transport currents are modeled using slab geometry.The loss equations for currents below the critical current be-come [4] shown in (1), where is the frequency, a fitting pa-rameter introduced in [5], the tape cross-section area, thepenetration field fitted to experimental data,and . The critical current, , is assumed to be inde-pendent of (set to the self-field critical current), and therefore

is valid for the currents of interest in the coil.Hysteresis losses due to combinations of perpendicular mag-

netic fields and transport currents are modeled using strip ge-ometry. The loss equation for zero current becomes [6],

(2)

where is a fitting parameter introduced in [7], the widthof the tape, a characteristic magnetic field fitted to experi-

mental data and . The current dependencywas accounted for by an empirical relation valid in the currentrange to ( in self-field) for the specific tape,

(3)

Flux-flow losses are modeled using the DC- characteris-tics for both parallel and perpendicular magnetic fields:

(4)

where is the period time, the current, and andare the parallel and the perpendicular electric fields which aregiven by power law dependencies,

(5)

where is 1 V/cm determined by the chosen standard criticalcurrent criterion. and the exponents and are fitted toexperimental data obtained from DC- measurements.

B. Other Losses

Iron losses appear in the flux diverters. These losses are cal-culated using a standard iron loss equation of the form,

(6)

where , and are given by material data. The first termincludes the hysteresis losses, the second term the eddy currentlosses and the third term the excess losses.

Current leads are used between the HTS coil at liquid ni-trogen temperature and the current source at room tempera-ture. The current leads are designed following the guidelinesin [8], where the minimum losses are calculated to about 22mW/A in an un-cooled current lead. The losses in the cur-rent leads consist of heat generated by the current in the leadsand of heat in-leak through the leads to the nitrogen bath. Anoptimum length-to-area ratio of the current leads is chosen tominimize the total losses. At the design current, 190 A, thisratio is 20 000 m/m resulting in losses in each current lead ofapproximately 9 W. For currents below 190 A the resistivelosses decrease , while the heat in-leak increases. At zerocurrent W. Similarly, for currents greater than 190A the resistive losses increases , and a part of the ad-

,

(1)

1618 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003

ditional power dissipated is conducted to the room temperatureend of the lead.

Heat from the aluminum workpiece is radiated/conductedinto the surrounding, high-temperature thermal insulation. Bysimulating the thermal process using finite element analysis,the heat losses were estimated to 200 W on average whenheating the workpiece to 500C. As these losses appear atroom temperature, they do not need to be multiplied by thecooling penalty factor.

Thermal leakage through the cryostat walls adds only mar-ginally to the total losses if the cryostat is properly vacuum in-sulated with multiple layers of superinsulation inserted in thevacuum space.

IV. POWER DISSIPATION IN THEALUMINUM WORKPIECE

The power dissipated in the aluminum workpiece dependson the magnetic field generated by the HTS coil (proportionalto the current in the coil), the resistivity of the workpiece (in-creases with temperature) and the geometries of the coil and theworkpiece. From finite element calculations, the average powerdissipation in the aluminum workpiece heated from room tem-perature to 500C was found to be given by

[W] (7)

At the rated current the heating power becomes 5.1 kW.

V. RESULTS

The tape used in both the experiments and in the calculationsis a standard multi-filamentary Bi-2223/Ag HTS tape acquiredfrom American Superconductor Corporation. The tape dimen-sions were 4.1 mm 0.3 mm including an 0.05 mm stainlesssteel reinforcement on each side.

A. Measured Values

Initial testing of the induction heater revealed uneven currentsharing between the parallel pancake coils. For parallel HTScoils with low resistance the current distribution becomes to alarge extent determined by the inductances of the coils. In fact,for two fully coupled parallel coils with zero resistance, all cur-rent flows in the coil with the lowest self-inductance.

In the HTS induction heater an uneven current sharing tookplace in three pairs of double pancake coils. From testing atroom temperature and higher frequencies it was found that atleast three quarters of the current was carried by one and onlyone quarter by the other of two parallel pancake coils. Usingthis current distribution in the three pairs with uneven currentsharing, the losses were calculated for the entire inductionheater. In Fig. 2 these losses are compared to values obtained bymeasuring the liquid nitrogen boil-off during testing. The levelof losses is considerably higher than what would have beenexpected for a coil with a homogeneous current distribution.The main reason for this increase is the large perpendicularmagnetic field component appearing in pancake coil pairs withuneven current sharing.

Fig. 2. Measured (rings) and calculated (line) power losses dissipated in thenitrogen bath for the induction heater with uneven current sharing power in theworkpiece.

Fig. 3. Power in the workpiece and losses in the induction heater separatedinto different loss components. Note that for losses appearing at liquid nitrogentemperature a cooling penalty factor of 12 has been considered. The iron losseshave been omitted since they are negligible compared to the other contributions.

B. Modeled Performance

The problem with uneven current sharing between pancakecoils can be solved by connecting all double pancake coils inseries. The results of this section assume that a homogeneouscurrent distribution between four HTS tapes is obtained. By con-necting the pancake coils in series, only two tapes will carrythe current and consequently the total current of the coil will behalved, whereas the number of turns will be doubled.

Fig. 3 shows the modeled losses of the induction heater aswell as the power in the workpiece. In the current range of100–200 A, hysteresis dominates the losses. At the currentrating, the parallel and perpendicular magnetic field lossesare of the same order of magnitude. At higher currents theflux-flow losses increase rapidly as the current becomes larger

MAGNUSSON AND RUNDE: EFFICIENCY ANALYSIS OF A HIGH-TEMPERATURE SUPERCONDUCTING INDUCTION HEATER 1619

Fig. 4. Efficiency of the induction heater as a function of current. WorkpieceandE is the total energy losses during heating of a billet. The efficiencyof the considered induction heater is shown as a function of current in Fig. 4.The highest value of the efficiency is 59% at a current of 190 A.

than the magnetic field dependent critical current in parts of thecoil. At low currents, the heat in-leak through the current leadsand the heat transferred from the workpiece are the dominatingfactors.

The efficiency, , of the heating process is determined by,

(8)

The frequency is 50 Hz. where is the energy associatedwith the temperature increase in the However, the curve is ratherflat and in the current region 100–200 A, the efficiency variesbetween 52 and 59% only.

VI. DISCUSSION

The losses in the HTS tape at the current rating are 11mW/Am, which is about one third of the losses in the conductorof a full-scale conventional induction heater. Furthermore, theoverall efficiency, 59%, is comparable with the highest valuesseen in industrial induction heaters for aluminum.

Consider a typical full-scale 725 kW conventional inductionheater with 400 kW going into the workpiece and 325 kW oflosses. The workpiece in such a heater may have a length of 1.0m, a diameter of 0.20 m, and a maximum magnetic field of 640mT .

In the following, the efficiency of an HTS based inductionheater of this size will be estimated by up-scaling the calculatedresults from the 10 kW model.

By increasing the coil and billet length with a factor around 5,the effects of the radial magnetic field and the extra length of thecoil relative the workpiece are reduced. The power dissipated inthe workpiece increases by a factor 4.65, whereas the losses inthe coil only increase a factor of 3.2.

The increase in the diameter leads to better magnetic couplingbetween the coil and the workpiece. The circumference of thecurrent flow (and hence the power) in the workpiece increasesby a factor of 2.6 (considering the skin depth), whereas the av-

erage length of a coil turn (and the losses) only increases by afactor 1.9.

By increasing the magnetic field 2.56 times, the power in theworkpiece increases by a factor 6.55. The losses in the coil in-crease by a factor 10. This is due to the increased magnetic field(as a first approximation linearly at high fields) and to the largernumber of turns needed to generate the field (a factor of 2.56for the increased field strength and a factor of 1.5 for the re-duced current carrying capability due to the higher field). Also,the larger number of turns leads to a somewhat longer averageturn length.

When including the effects of all these factors, the losses in-crease by a factor of 61 when the power dissipated in the work-piece increases by a factor of 79 (from 5.1 to 403 kW).

The HTS tape used in the small-scale heater is not optimizedfor use in the relatively high AC magnetic fields of inductionheaters. By simply using a DC tape available on the market witha thinner region of superconducting filaments, the losses couldbe reduced by about 20% more. If a proper low AC loss tapebecame available, a loss reduction of another 50% could be an-ticipated.

These considerations lead to losses of about 85 kW (againtaking into account a cooling penalty factor of 12) to be com-pared to the 325 kW of the conventional induction heater.

VII. CONCLUSION

In the 10 kW HTS induction heater, hysteresis dominates thelosses, whereas the current rating is determined by the onset offlux-flow losses.

The efficiency of the small-scale HTS heater was calculatedto be 59%, which is comparable to state-of-the-art large-scaleconventional industrial heaters.

Using techniques available today, a full-scale HTS inductionheater has the potential to reduce the losses by 50% comparedto conventional heaters. With a low AC loss HTS tape one cananticipate the losses to be reduced by 75%.

REFERENCES

[1] J. Kellers, “Reliable commercial HTS wire for power applications,”Physica C, vol. 372–376, pp. 1040–1045, 2002.

[2] M. Runde and N. Magnusson, “Design, construction and test of a 10 kWsuperconducting induction heater,” presented at the Appl. Supercond.Conf., Houston, TX, USA, Aug. 4–9, 2002. presented.

[3] C. P. Bean, “Magnetization of high-field superconductors,”Rev. Mod.Phys., vol. 36, pp. 31–39, 1964.

[4] W. J. Carr, “AC losses from the combined action of transport current andapplied field,”IEEE Trans. Magn., vol. 15, pp. 240–243, 1979.

[5] N. Magnusson, “Semi-empirical model of the losses in HTS tapes car-rying AC currents in AC magnetic fields applied parallel to the tapeface,”Physica C, vol. 349, pp. 225–234, 2001.

[6] E. Brandt and M. Indenbom, “Type-II-superconductor strip withcurrent in a perpendicular magnetic field,”Phys. Rev. B, vol. 48, pp.12 893–12 906, 1993.

[7] A. Wolfbrandt, N. Magnussson, and S. Hörnfeldt, “AC losses in aBSCCO/Ag tape carrying AC transport currents in AC magnetic fieldsapplied in different orientations,”IEEE Trans. Appl. Supercond., vol.11, pp. 4123–4127, Dec. 2001.

[8] C. N. Rasmussen and C. Rasmussen, “Optimization of termination forhigh-temperature superconducting cable with a room temperature di-electric design,”IEEE Trans. Appl. Supercond., vol. 9, pp. 45–49, Mar.1999.