principle of a mult-load single converter system

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 2, MARCH 2000 223

Principle of a Multi-Load/Single Converter Systemfor Low Power Induction Heating

Francois Forest, Eric Labouré, Francois Costa, Member, IEEE, and Jean Yves. Gaspard

Abstract—The induction heating appliances used for cookinggenerally include two or four inductors and in the most commonsolution, a converter is connected to each inductor. The main aimof this paper is to suggest a way of building a multi-load/single con-verter system, based on the use of a series-resonant ZVS inverter,supplying several resonant loads. The principle can be probablyextended to different applications (dc-to-dc converters, high powerinduction heating applications) but our study has been restrictedto a low power induction heating context. In order to make thisstudy, suitable models for the loaded inductors had to be found.Therefore, in the first part of this document, a number of differentelectical inductor models, from the basic - equivalent circuit toa representation taking into account eddy currents effects, are pre-sented. The second part describes the multi-load operating prin-ciple with respecting ZVS conditions, by the analysis of an - in-ductor model. Finally, the third part completes this work with sim-ulations, including a more realistic model of the inductors and theassociated experimental validation. These emphasize the interestof this original system that is currently being evaluated for an in-dustrial application.

Index Terms—Induction heating, inductor modeling, multiloadsystem, ZVS series-resonant inverter.

I. INTRODUCTION

OVER the last ten years, extensive development of induc-tion heating for cooking has led to a number of different

converters designs, of which the most commonly used are theZVS series-resonant inverter and the single ended resonant con-verters operating in ZCS or ZVS mode (see Fig. 4). The currentproblem is no longer designing new topologies for a single con-verter dedicated to one inductor, but to improve and optimiseinduction hotplates made up of several inductors on which thepower must be separately regulated. This requires a global studyof the inductors as well as on the power supply. In this area, thispaper presents a multi-load/single converter concept, to simplifythe electronic part, with the parallel advantage of a common op-erating frequency, very significant in such applications. Beforetackling the main topic, some loaded-inductors models will firstbe presented that will be required in the final validation.

II. L OW POWER INDUCTION HEATING

A. Inductor Modeling

To design converters in such applications efficiently, it is nec-essary to have models which describe a plane inductor loaded

Manuscript received June 2, 1998; revised September 17, 1999. Recom-mended by Associate Editor, L. Xu.

The authors are with ENS de Cachan/Lesir, Cachan Cedex 94235, France(e-mail: [email protected]).

Publisher Item Identifier S 0885-8993(00)02338-3.

Fig. 1. Simplified inductor models.

(a) (b)

Fig. 2. Improved inductor models.

Fig. 3. Experimental results and model comparison.

by a pan correctly. Electromagnetic modeling is a three-dimen-sional problem, complicated by the varying pan characteristicsvarieties (geometry, material) and variable operating frequency.This part must be treated by the inductor designer. Our aim hereis to build electrical models based on inductor identification and

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224 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 2, MARCH 2000

Fig. 4. Converter topologies.

Fig. 5. Principle of the multi-load/single converter system.

which can be used in the final sizing of a converter by simula-tion.

In a first simplified approach, a loaded inductor can be de-scribed by a series or parallel- circuit [Fig. 1(a) and (b)]where is associated to the total power (losses and power load)provided to the inductor, and is associated to the inductive ef-fect of the inductor winding coupled to the pan. The first draw-back of the equivalent circuit is that is must be used as a singlefrequency model. Satisfactory results concerning the power es-timation cannot be expected by using it in time-varying simu-lation including a converter. However, it simplifies the analysisand is used for the first sizing of the particular resonant con-verter studied below.

A more suitable equivalent circuit is given in Fig. 2(a). Theloaded inductor can be considered as an inductive device whose

magnetic core is the pan. So,and are the series resistorand the leakage inductance of the winding, andand , theparallel parameters corresponding to the flux and to the mag-netic losses in the pan. Nevertheless, this improved model doesnot take into account the eddy currents losses which are fre-quency dependent. Thus, a final circuit is shown in Fig. 2(b).The substitution for by the parameters is a solu-tion from conductor modeling including eddy currents effects[1], [8] (other - stages could be added to improve the modelbut at the cost of added complexity).

To validate the last model form described above, an industrialinductor loaded by different typical pans (12 or 22 cm diameters,stainless steel, cast iron, etc.) has been tested. The equivalentserie resistor (the real part of the impedance) and induc-tance (the imaginary part of the impedance) have been


FORESTet al.: PRINCIPLE OF A MULTI-LOAD/SINGLE CONVERTER SYSTEM 225

Fig. 6. Electrical waveforms in a series-resonant load.

Fig. 7. Current waveforms for a two-load configuration.

determined with high level current in the inductor. To this end,the inductor, loaded by a pan, is supplied by a series-resonantinverter. The adjustment of the resonant capacitor means that itis possible to work at different resonant frequencies within the10 kHz–200 kHz range, with a quasi-sinusoidal inductor cur-rent (amplitude controlled by the inverter DC link voltage ad-justment). Then, from the resonant frequency and resonant ca-pacitor values, the relative value can be deduced. The powerinductor measurement (using a high bandwidth power analyzer)gives the associated value. Finally, the parameters of the pro-posed model [Fig. 2(b)], giving the results which are nearest tothe experimental ones, are found using an identification algo-rithm.

The graphs in Fig. 3 show an example (stainless steel pan) ofthe good agreement which can be obtained between the mea-surements and the model. This approach has been successfullyapplied to all the pans that have been tested.

Two models can then be used. The first one is verysuitable for first harmonic studies.

The second one (six parameters) is a wide band frequencymodel and can therefore be used for temporal studies, but it re-quires simulation tools. It should be not available anymore ifmagnetic saturation effects appear in the pan material, but, forclassical inductors and pans, this can only be produced by a cur-rent injection level in the inductor above the nominal conditions.

B. Converter Topologies for Low Power Induction Heating

For low power induction heating, the main topologies thathave been considered in publications [4]–[6], [9], [10] areshown in Fig. 4. The most commonly used is the series-reso-nant inverter [Fig. 4(a)], operating in ZVS mode, particularyconvenient with a 230 V or 400 V mains supply and a 2.5kW–6 kW power range.

For the family of single ended converters, the search for avail-able solutions leads to the ZVS and ZCS converter topologies inFig. 4(b) and (c). These converters can work in half wave or fullwave mode (note that these definitions are relative to the switchvoltage for ZVS and switch current for ZCS). They induce alarge oversizing of the switches that usually limits their applica-tions to 100 V–120 V power mains (1 kW–2 kW power range).Since this study covers 230 V mains power context, and becausethe principle described requires particular converter character-istics, we shall turn our attention, in what follows, to the se-ries-resonant inverter.

III. PROPOSEDMULTI-LOAD/SINGLE CONVERTERSYSTEM

As already stated, an induction hotplate can include two orfour inductors, in which the power must be separately adjusted.The current solutions do this in two different ways.

The first one associates an inverter to each inductor. This so-lution is heavy in terms of components number. Parallely, it caninduce acoustic harms because of the asynchronous switchingfrequencies of the different inverters, creating low-frequency in-terferences which are amplified by the pans.

In the second method, a single inverter supplies several induc-tors, successively connected to this inverter by electromechan-ical switches. It is an interesting and low-cost solution but thepower distribution between the different inductors must be per-formed using very low-frequency switching, so it is not com-pletely satisfactory.

The aim of our proposal is to retain the single inverter designbut to remove the low-frequency electromechanical switching.Some authors have proposed other solutions [7] but which arenot well-suited to the low power and low-cost applications.



Fig. 8. Total switched current and power in a two-load configuration.

A. Principle of the Multiloads/Single Converter Solution

The general principle is illustrated by the Fig. 5. A single in-verter supply, by a square wave voltage,series-resonant loads,made of inductors associated withresonant capacitors.

The qualitative shape of the power in each resonant loadversus the switching frequencyis given Fig. 5. The valueand the resonant frequencies must be chosen to obtain therequired power on each source. At the present time, the mostobvious solution to achieve this end is to set the frequencyso that it controls the power of one of the loads (“master-load”with a constant capacitor value) and to introduce steps onthe other resonant capacitors (“slave-loads”), adjustable by

electromechanical switches. These are only activated to changethe power division (no low-frequency switching).

B. Analysis with an R-L Model for a Two-Loads Application

If the principle described above is theoretically available forany number of resonant loads, a realistic and interesting solu-tion is to apply it in a two-load configuration. In this particularcase, the most natural control mode is to keep the switchingfrequency between the two resonant frequencies. An essentialconsideration is then the switching mode of the inverter. In suchapplications, the ZVS mode is the most suitable both in terms of



Fig. 9. Study schemes.

Fig. 10. Load power versus switching frequency.

inverter efficiency and the stresses applied to the semiconductordevices concerned.

For a standard system using an inverter supplying a singleseries-resonant load, it is well known that the ZCS and ZVSmode are obtained for a switching frequency respectively belowand above the resonant frequency [2], [3], [5]. In our partic-ular two-resonance solution, it is very important to determinethe ZVS operating zones, in order to evaluate the viability of alarge power range control. To show the tendency, an analyticalstudy using the simplified - model of the loaded inductorsis proposed. The electrical waveforms for a series-resonant load

, supplied by a square wave inverter, below and abovethe resonant frequency, are shown in Fig. 6.

First of all, we look at the inductor current and the capac-itor voltage value at the negative switching of the inverter

voltage (from high-level to low-level), under steady-state con-ditions. A positive value of this switched current indicates aZVS mode. During the first half-period, the normalized expres-sions for inductor current and capacitor voltage are

(1)

(2)

with

Damping factor

Normalized frequencies

Normalized currents

Normalized voltages

Normalized power

From (1) and (2), and with , thisgives

Finally, the normalized values of and are given by

(3)



Fig. 11. Total switched current versus switching frequency.

where

(4)

We can also calculate the normalized load power

(5)

These expressions can be used to determine the total switchedcurrent provided by the inverter operating on two resonant loads,characterized by damping factors and their resonant fre-quencies

As above, the ZVS mode is obtained for . An exampleof temporal current waveforms, in such an operating mode, isgiven in Fig. 7.

In a more general approach, Fig. 8 shows a parametric rep-resentation (the parameter being the ratio ) of the totalswitched current and of the power in each load ( for theload 1, for the load 2), versus the switching frequency. Theresonant frequency is the reference of the normalized fre-quency . The damping factor values have beenset to and , extremums of the typical values



Fig. 12. Example of simulated and experimental waveforms.

measured on the loaded inductor corresponding to the particularapplication.

This particular choice leads to themost unfavourable case, in terms of the size of the ZVS oper-ating zone. Nevertheless, the resulting power range, with respectto ZVS mode, is very satisfactory, if we specify the followingthree points, according to the particular application:

1) a master load is defined for which the power is thehighest chosen by the system user and associated with theconstant value capacitor ,

2) the maximum value of the total power , that definesthe sizing of the inverter, can be provided to this masterload if the other inductor is not used,

3) the sum of the power values in the two loads must belimited to the maximum power value .

So, the maximum value of (for ) is in fact ,and if the operating point where can beobtained, all the required power range is covered. The curves inthe Fig. 8 show that this operating point is more or less reachedwith ratio and approximately equal to 1.5 and 1.2.

This theoretical analysis based on an elementary model ofthe inductor shows the viability of the two-load/single invertersystem. However, to take into account the real behaviour of aloaded inductor, these results must be confirmed with a more

elaborate model (requiring the use of numerical simulation), andthen checked experimentally. This is the aim of the next part.

IV. SIMULATIONS AND EXPERIMENTAL TEST RESULTS

In this final part, the improved inductor model described inSection II [Fig. 2(b)] will be employed. An initial sizing of atwo-loads system based on the previous results has been real-ized using data extracted from our preliminary inductor study.The relative schemes are given in Fig. 9. Obviously, the param-eters of the inductor models must be chosen according to thecharacteristics of the pan being considered.

The resonant frequency is approximatively 20 kHz. Infact, as this inductor model includes six parameters, a resonantfrequency cannot easily be defined, so the parametric study willbe conducted as a function of the ratio .

With the two identical industrial inductors, many differentload configurations have been tested (about twenty with thetwenty corresponding models). Some of the results are pre-sented below, related to identical and standard pans loading thetwo inductors. In Fig. 10, the representation of the measuredpower in each stage, versus the switching frequency, showsa good agreement between the experimental results and thesimulation, except for the highest value of the capacitor.The most important result is that the tendency which is broughtout in the analytical study based on an elementary- model,is respected. It can be noted that the switched current values(Fig. 11) are always positive (ZVS mode) and higher than thetheoretical ones calculated. This indicates a ZVS operatingzone, for a real loaded inductor, larger than it was previouslyestimated. All the tested configurations lead to the sameconclusion. An example of simulated and experimental currentwaveforms, for the same operating point ( kHz,µF, µF) is given in Fig. 12.

V. CONCLUSION

In this paper, a multi-load/single converter design, dedicatedto induction heating, in cooking applications, has been dis-cussed and validated. The possibility of setting the power oftwo inductors with a single inverter, maintaining in parallelZVS mode, has been demonstrated by an analytical study of thetwo resonant-loads circuit using a model of the inductor,then through the simulation on a complete model and the finalexperimental tests.

This leads to a major simplification of the electronic part ofmulti-inductor hotplates with a single frequency control. A two-inductor industrial appliance is currently under evaluation.

An extension of this study, concerning a four-inductor hot-plate, is now to be considered.

REFERENCES

[1] C.-S. Yen, Z. Fazarinc, and R. L. Wheeler, “Time-domain skin-effectmodel for transient analysis of lossy transmission lines,”Proc. IEEE,vol. 70, no. 7, pp. 750–757, MONTH?? 1982.

[2] V. Vorperian and S. Cuk, “A complete analysis of the series resonantconverter,” inProc. IEEE Power Electron. Specialists Conf. Rec., 1982,pp. 85–100.

[3] Y. Cheron, H. Foch, and J. Salesses, “Study of a resonant converter usingpower transistors in a 25 kW X-rays tube power supply,” inProc. IEEEPower Electron. Specialists Conf. Rec., 1985, pp. 295–306.



[4] H. Omori, T. Twai, M. Nakaoka, and T. Maruhashi, “Circuits topologiesof self-controlled single-ended high frequency resonant inverters,” inProc. Euro. Power Electron. Conf. Rec., vol. 1, 1987, pp. 205–211.

[5] J. P. Ferrieux, J. P. Keradec, and Y. Baudon, “A high frequency series-resonant converter using COMFET transistor-application to inductionheating,” inProc. IEEE Ind. Appl. Soc. Conf. Rec., 1987, pp. 717–723.

[6] K. Isaki, I. Hirota, H. Yamashita, M. Kamli, H. Omori, and M.Nakaoka, “New constant-frequency variable powered quasi-resonanttopology using soft-switched type IGBTS for induction-heated cookingappliance,” inProc. Euro. Power Electron. Conf. Rec., vol. 2, 1995, pp.129–134.

[7] J. P. Ferrieux, M. C. Pera-Marion, J. P. Rognon, and J. Nuns, “Powercontrol of two induction loads supplied by a single generator: Two so-lutions,” in Proc. Euro. Power Electron. Conf. Rec., vol. 2, 1995, pp.379–384.

[8] E. Labouré, F. Costa, C. Gautier, and W. Melhem, “Accurate simulationof conducted interferences in isolated DC-to-DC converters regarding toEMI standards,” inProc. IEEE Power Electron. Specialists Conf. Rec.,vol. II, 1996, pp. 1973–1978.

[9] M. Kamli, S. Yamamoto, and M. Abe, “A 50 kHz–150 kHz half-bridgeinverter for induction heating applications,”IEEE Trans. Ind. Electron.,vol. 43, no. 1, pp. 163–172, 1996.

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Francois Forestwas born in Bethune, France, on Au-gust 2, 1956. He received the M.S. degree in electricalengineering from the Ecole Normale Supérieure deCachan, France, in 1982 and the Ph.D. degree fromthe University of Paris, Paris, France, in 1985.

Since 1989, he has been a Professor in theElectrical Engineering Department, Ecole NormaleSupérieure de Cachan, and leader of the ResearchPower Electronics Group, Laboratoire Electricité,Signaux et Robotique, ESA CNRS 8029. Hisresearch activities concern essentially soft-switching

converters study from low power dc-to-dc stages to high power PWM inverters,components modeling, and EMC applied to static converters.

Eric Labouré was born in Le Creusot, France, onNovember 22, 1966. He received the M.S. degree inelectrical engineering from INSA-Lyon, France, in1989 and the Ph.D. degree in electrical engineeringfrom the Ecole Normale Supérieure de Cachan,France, in 1995.

He is an Associate Professor in the Electrical En-gineering Department, Ecole Normale Supérieure deCachan, and he works in the Research Power Elec-tronics Group, Laboratoire d'Electricité, Signaux etRobotique, ESA CNRS 8029. His major fields of in-

terest are the understanding of EMC phenomena in power converters and theaccurate modeling of magnetic components in this domain.

François Costa (M’99) was born in Longueville,France, on December 14, 1958. He received theM.S. degree in electrical engineering from the EcoleNormale Supérieure de Cachan, France, in 1982 andthe Ph.D. degree in electrical engineering from theUniversity of Paris, Paris, France, in 1992.

Since 1989, he has been with the Research PowerElectronics Group, Laboratoire d'Electricité, Signauxet Robotique, ESA CNRS 8029. Since 1994, he hasbeen an Associate Professor with the Electrical En-gineering Department, Ecole Normale Supérieure de

Cachan. His research interests are high-frequency medium-power convertersfunctioning, EMI problems they generate, and HF instrumentation. His mainactivity is to analyze and to model parasitic phenomena in converters with theaim to control and to reduce them.

Jean Yves Gaspardwas born in Saint Jean de Mau-rienne, France, on November 9, 1964. He receivedthe Ph.D. Degree in electrical engineering from theEcole Centrale de Lyon, France, in 1993.

He is Advanced Research Manager with theBrandt Company, Paris, France. Prior to this, he wasactively involved in research in power electronicswith the Deutsche Thomson Brandt labs andin project management, especially on inductioncooking systems.

Dr. Gaspard is the Chair of the French Standard-ization Committee on Human Exposure to Electro Magnetic Fields and is aninternational expert in IEC Groups which works on assessment of human expo-sure to EMF in 0–9 kHz and 9 KHz–300 Hz frequency.


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principle of a mult-load single converter system