IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 2, MARCH 2000
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Principle of a Multi-Load/Single Converter System for Low Power Induction Heating Francois Forest, Eric Labouré, Francois Costa, Member, IEEE, and Jean Yves. Gaspard
Abstract—The induction heating appliances used for cooking generally include two or four inductors and in the most common solution, a converter is connected to each inductor. The main aim of this paper is to suggest a way of building a multi-load/single converter system, based on the use of a series-resonant ZVS inverter, supplying several resonant loads. The principle can be probably extended to different applications (dc-to-dc converters, high power induction heating applications) but our study has been restricted to a low power induction heating context. In order to make this study, suitable models for the loaded inductors had to be found. Therefore, in the first part of this document, a number of different electical inductor models, from the basic - equivalent circuit to a representation taking into account eddy currents effects, are presented. The second part describes the multi-load operating principle with respecting ZVS conditions, by the analysis of an - inductor model. Finally, the third part completes this work with simulations, including a more realistic model of the inductors and the associated experimental validation. These emphasize the interest of this original system that is currently being evaluated for an industrial application.
Fig. 1. Simplified inductor models.
(a)
(b)
Fig. 2. Improved inductor models.
Index Terms—Induction heating, inductor modeling, multiload system, ZVS series-resonant inverter.
I. INTRODUCTION
O
VER the last ten years, extensive development of induction heating for cooking has led to a number of different converters designs, of which the most commonly used are the ZVS series-resonant inverter and the single ended resonant converters operating in ZCS or ZVS mode (see Fig. 4). The current problem is no longer designing new topologies for a single converter dedicated to one inductor, but to improve and optimise induction hotplates made up of several inductors on which the power must be separately regulated. This requires a global study of the inductors as well as on the power supply. In this area, this paper presents a multi-load/single converter concept, to simplify the electronic part, with the parallel advantage of a common operating frequency, very significant in such applications. Before tackling the main topic, some loaded-inductors models will first be presented that will be required in the final validation. II. LOW POWER INDUCTION HEATING A. Inductor Modeling To design converters in such applications efficiently, it is necessary to have models which describe a plane inductor loaded Manuscript received June 2, 1998; revised September 17, 1999. Recommended by Associate Editor, L. Xu. The authors are with ENS de Cachan/Lesir, Cachan Cedex 94235, France (e-mail: forest@lesir.ens-cachan.fr). Publisher Item Identifier S 0885-8993(00)02338-3.
Fig. 3.
Experimental results and model comparison.
by a pan correctly. Electromagnetic modeling is a three-dimensional problem, complicated by the varying pan characteristics varieties (geometry, material) and variable operating frequency. This part must be treated by the inductor designer. Our aim here is to build electrical models based on inductor identification and
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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 simulation. In a first simplified approach, a loaded inductor can be described 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 effect of the inductor winding coupled to the pan. The first drawback of the equivalent circuit is that is must be used as a single frequency model. Satisfactory results concerning the power estimation cannot be expected by using it in time-varying simulation including a converter. However, it simplifies the analysis and is used for the first sizing of the particular resonant converter studied below. A more suitable equivalent circuit is given in Fig. 2(a). The loaded inductor can be considered as an inductive device whose
magnetic core is the pan. So, and are the series resistor and , the and the leakage inductance of the winding, and parallel parameters corresponding to the flux and to the magnetic losses in the pan. Nevertheless, this improved model does not take into account the eddy currents losses which are frequency dependent. Thus, a final circuit is shown in Fig. 2(b). by the parameters is a soluThe substitution for tion from conductor modeling including eddy currents effects [1], [8] (other - stages could be added to improve the model but at the cost of added complexity). To validate the last model form described above, an industrial inductor loaded by different typical pans (12 or 22 cm diameters, stainless steel, cast iron, etc.) has been tested. The equivalent (the real part of the impedance) and inducserie resistor (the imaginary part of the impedance) have been tance
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FOREST et al.: PRINCIPLE OF A MULTI-LOAD/SINGLE CONVERTER SYSTEM
Fig. 6.
225
Electrical waveforms in a series-resonant load.
B. Converter Topologies for Low Power Induction Heating
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-resonant inverter. The adjustment of the resonant capacitor means that it is possible to work at different resonant frequencies within the 10 kHz–200 kHz range, with a quasi-sinusoidal inductor current (amplitude controlled by the inverter DC link voltage adjustment). Then, from the resonant frequency and resonant cavalue can be deduced. The power pacitor values, the relative inductor measurement (using a high bandwidth power analyzer) value. Finally, the parameters of the progives the associated posed model [Fig. 2(b)], giving the results which are nearest to the experimental ones, are found using an identification algorithm. The graphs in Fig. 3 show an example (stainless steel pan) of the good agreement which can be obtained between the measurements and the model. This approach has been successfully applied to all the pans that have been tested. is very Two models can then be used. The first one suitable for first harmonic studies. The second one (six parameters) is a wide band frequency model and can therefore be used for temporal studies, but it requires simulation tools. It should be not available anymore if magnetic saturation effects appear in the pan material, but, for classical inductors and pans, this can only be produced by a current injection level in the inductor above the nominal conditions.
For low power induction heating, the main topologies that have been considered in publications [4]–[6], [9], [10] are shown in Fig. 4. The most commonly used is the series-resonant inverter [Fig. 4(a)], operating in ZVS mode, particulary convenient with a 230 V or 400 V mains supply and a 2.5 kW–6 kW power range. For the family of single ended converters, the search for available solutions leads to the ZVS and ZCS converter topologies in Fig. 4(b) and (c). These converters can work in half wave or full wave mode (note that these definitions are relative to the switch voltage for ZVS and switch current for ZCS). They induce a large oversizing of the switches that usually limits their applications to 100 V–120 V power mains (1 kW–2 kW power range). Since this study covers 230 V mains power context, and because the principle described requires particular converter characteristics, we shall turn our attention, in what follows, to the series-resonant inverter. III. PROPOSED MULTI-LOAD/SINGLE CONVERTER SYSTEM As already stated, an induction hotplate can include two or four 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 solution is heavy in terms of components number. Parallely, it can induce acoustic harms because of the asynchronous switching frequencies of the different inverters, creating low-frequency interferences which are amplified by the pans. In the second method, a single inverter supplies several inductors, successively connected to this inverter by electromechanical switches. It is an interesting and low-cost solution but the power distribution between the different inductors must be performed using very low-frequency switching, so it is not completely satisfactory. The aim of our proposal is to retain the single inverter design but to remove the low-frequency electromechanical switching. Some authors have proposed other solutions [7] but which are not well-suited to the low power and low-cost applications.
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Fig. 8.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 2, MARCH 2000
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 inverter supply, by a square wave voltage, series-resonant loads, made of inductors associated with resonant capacitors. The qualitative shape of the power in each resonant load versus the switching frequency is given Fig. 5. The value and the resonant frequencies must be chosen to obtain the required power on each source. At the present time, the most obvious solution to achieve this end is to set the frequency so that it controls the power of one of the loads (“master-load” with a constant capacitor value) and to introduce steps on the other resonant capacitors (“slave-loads”), adjustable by
electromechanical switches. These are only activated to change the 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 for any number of resonant loads, a realistic and interesting solution is to apply it in a two-load configuration. In this particular case, the most natural control mode is to keep the switching frequency between the two resonant frequencies. An essential consideration is then the switching mode of the inverter. In such applications, the ZVS mode is the most suitable both in terms of
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FOREST et al.: PRINCIPLE OF A MULTI-LOAD/SINGLE CONVERTER SYSTEM
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voltage (from high-level to low-level), under steady-state conditions. A positive value of this switched current indicates a ZVS mode. During the first half-period, the normalized expresand capacitor voltage are sions for inductor current
(1)
(2) with Damping factor Fig. 9. Study schemes.
Normalized frequencies
Normalized currents Normalized voltages Normalized power
From (1) and (2), and with gives
Fig. 10.
, this
Load power versus switching frequency.
inverter efficiency and the stresses applied to the semiconductor devices concerned. For a standard system using an inverter supplying a single series-resonant load, it is well known that the ZCS and ZVS mode are obtained for a switching frequency respectively below and above the resonant frequency [2], [3], [5]. In our particular two-resonance solution, it is very important to determine the ZVS operating zones, in order to evaluate the viability of a large power range control. To show the tendency, an analytical study using the simplified - model of the loaded inductors is proposed. The electrical waveforms for a series-resonant load , supplied by a square wave inverter, below and above the resonant frequency, are shown in Fig. 6. and the capacFirst of all, we look at the inductor current at the negative switching of the inverter itor voltage value
Finally, the normalized values of
and
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are given by
(3)
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Fig. 11.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 2, MARCH 2000
Total switched current versus switching frequency.
where (4)
These expressions can be used to determine the total switched current provided by the inverter operating on two resonant loads, characterized by damping factors and their resonant frequencies
We can also calculate the normalized load power
(5)
As above, the ZVS mode is obtained for . An example of temporal current waveforms, in such an operating mode, is given in Fig. 7. In a more general approach, Fig. 8 shows a parametric rep) of the total resentation (the parameter being the ratio for the switched current and of the power in each load ( for the load 2), versus the switching frequency. The load 1, is the reference of the normalized freresonant frequency . The damping factor values have been quency and , extremums of the typical values set to
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FOREST et al.: PRINCIPLE OF A MULTI-LOAD/SINGLE CONVERTER SYSTEM
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elaborate model (requiring the use of numerical simulation), and then checked experimentally. This is the aim of the next part. IV. SIMULATIONS AND EXPERIMENTAL TEST RESULTS
Fig. 12.
Example of simulated and experimental waveforms.
measured on the loaded inductor corresponding to the particular application. leads to the This particular choice most unfavourable case, in terms of the size of the ZVS operating zone. Nevertheless, the resulting power range, with respect to ZVS mode, is very satisfactory, if we specify the following three points, according to the particular application: is the 1) a master load is defined for which the power highest chosen by the system user and associated with the , constant value capacitor , that defines 2) the maximum value of the total power the sizing of the inverter, can be provided to this master load if the other inductor is not used, 3) the sum of the power values in the two loads must be . limited to the maximum power value (for ) is in fact , So, the maximum value of can be and if the operating point where obtained, all the required power range is covered. The curves in the Fig. 8 show that this operating point is more or less reached and approximately equal to 1.5 and 1.2. with ratio This theoretical analysis based on an elementary model of the inductor shows the viability of the two-load/single inverter system. However, to take into account the real behaviour of a loaded inductor, these results must be confirmed with a more
In this final part, the improved inductor model described in Section II [Fig. 2(b)] will be employed. An initial sizing of a two-loads system based on the previous results has been realized using data extracted from our preliminary inductor study. The relative schemes are given in Fig. 9. Obviously, the parameters of the inductor models must be chosen according to the characteristics of the pan being considered. is approximatively 20 kHz. In The resonant frequency fact, as this inductor model includes six parameters, a resonant frequency cannot easily be defined, so the parametric study will . be conducted as a function of the ratio With the two identical industrial inductors, many different load configurations have been tested (about twenty with the twenty corresponding models). Some of the results are presented below, related to identical and standard pans loading the two inductors. In Fig. 10, the representation of the measured power in each stage, versus the switching frequency, shows a good agreement between the experimental results and the . simulation, except for the highest value of the capacitor The most important result is that the tendency which is brought out 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 the theoretical ones calculated. This indicates a ZVS operating zone, for a real loaded inductor, larger than it was previously estimated. All the tested configurations lead to the same conclusion. An example of simulated and experimental current kHz, waveforms, for the same operating point ( µF, µF) is given in Fig. 12. V. CONCLUSION In this paper, a multi-load/single converter design, dedicated to induction heating, in cooking applications, has been discussed and validated. The possibility of setting the power of two inductors with a single inverter, maintaining in parallel ZVS mode, has been demonstrated by an analytical study of the model of the inductor, two resonant-loads circuit using a then through the simulation on a complete model and the final experimental tests. This leads to a major simplification of the electronic part of multi-inductor hotplates with a single frequency control. A twoinductor industrial appliance is currently under evaluation. An extension of this study, concerning a four-inductor hotplate, is now to be considered. REFERENCES [1] C.-S. Yen, Z. Fazarinc, and R. L. Wheeler, “Time-domain skin-effect model 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 resonant converter,” in Proc. IEEE Power Electron. Specialists Conf. Rec., 1982, pp. 85–100. [3] Y. Cheron, H. Foch, and J. Salesses, “Study of a resonant converter using power transistors in a 25 kW X-rays tube power supply,” in Proc. IEEE Power Electron. Specialists Conf. Rec., 1985, pp. 295–306.
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[4] H. Omori, T. Twai, M. Nakaoka, and T. Maruhashi, “Circuits topologies of self-controlled single-ended high frequency resonant inverters,” in Proc. Euro. Power Electron. Conf. Rec., vol. 1, 1987, pp. 205–211. [5] J. P. Ferrieux, J. P. Keradec, and Y. Baudon, “A high frequency seriesresonant converter using COMFET transistor-application to induction heating,” in Proc. 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-resonant topology using soft-switched type IGBTS for induction-heated cooking appliance,” in Proc. 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, “Power control of two induction loads supplied by a single generator: Two solutions,” in Proc. Euro. Power Electron. Conf. Rec., vol. 2, 1995, pp. 379–384. [8] E. Labouré, F. Costa, C. Gautier, and W. Melhem, “Accurate simulation of conducted interferences in isolated DC-to-DC converters regarding to EMI standards,” in Proc. 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-bridge inverter for induction heating applications,” IEEE Trans. Ind. Electron., vol. 43, no. 1, pp. 163–172, 1996. [10] M. K. Kasimierczuk and D. Czarkowski, Resonant Power Converter. New York: Wiley, 1995.
Francois Forest was born in Bethune, France, on August 2, 1956. He received the M.S. degree in electrical engineering from the Ecole Normale Supérieure de Cachan, France, in 1982 and the Ph.D. degree from the University of Paris, Paris, France, in 1985. Since 1989, he has been a Professor in the Electrical Engineering Department, Ecole Normale Supérieure de Cachan, and leader of the Research Power Electronics Group, Laboratoire Electricité, Signaux et Robotique, ESA CNRS 8029. His research 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.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 2, MARCH 2000
Eric Labouré was born in Le Creusot, France, on November 22, 1966. He received the M.S. degree in electrical engineering from INSA-Lyon, France, in 1989 and the Ph.D. degree in electrical engineering from the Ecole Normale Supérieure de Cachan, France, in 1995. He is an Associate Professor in the Electrical Engineering Department, Ecole Normale Supérieure de Cachan, and he works in the Research Power Electronics Group, Laboratoire d'Electricité, Signaux et Robotique, ESA CNRS 8029. His major fields of interest are the understanding of EMC phenomena in power converters and the accurate modeling of magnetic components in this domain.
François Costa (M’99) was born in Longueville, France, on December 14, 1958. He received the M.S. degree in electrical engineering from the Ecole Normale Supérieure de Cachan, France, in 1982 and the Ph.D. degree in electrical engineering from the University of Paris, Paris, France, in 1992. Since 1989, he has been with the Research Power Electronics Group, Laboratoire d'Electricité, Signaux et Robotique, ESA CNRS 8029. Since 1994, he has been an Associate Professor with the Electrical Engineering Department, Ecole Normale Supérieure de Cachan. His research interests are high-frequency medium-power converters functioning, EMI problems they generate, and HF instrumentation. His main activity is to analyze and to model parasitic phenomena in converters with the aim to control and to reduce them.
Jean Yves Gaspard was born in Saint Jean de Maurienne, France, on November 9, 1964. He received the Ph.D. Degree in electrical engineering from the Ecole Centrale de Lyon, France, in 1993. He is Advanced Research Manager with the Brandt Company, Paris, France. Prior to this, he was actively involved in research in power electronics with the Deutsche Thomson Brandt labs and in project management, especially on induction cooking systems. Dr. Gaspard is the Chair of the French Standardization Committee on Human Exposure to Electro Magnetic Fields and is an international expert in IEC Groups which works on assessment of human exposure to EMF in 0–9 kHz and 9 KHz–300 Hz frequency.
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