DSpace at VNU: Parameter Identification Method for a Three-Phase Induction Heating System

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL 51, NO 6, NOVEMBER/DECEMBER 2015 4853 Parameter Identification Method for a Three-Phase Induction Heating System Bao Anh Nguyen, Quoc Dung Phan, Duy Minh Nguyen, Kien Long Nguyen, Olivier Durrieu, and Pascal Maussion, Member, IEEE Abstract—This paper describes a new method for the online parameter estimation of an induction heating system Simulations and experiments are presented in order to measure its impedance matrix for more exact control in closed loop In previous papers, various parameter identification methods including offline methods were introduced and compared for current inverters It has been demonstrated that parameter identification is necessary to achieve good control of the inductor currents A “pseudoenergy” method for a simple and fast implementation is compared to a classical “V /I with phase shift” method They are experienced on a reduced-power three-phase coupled resonant system supplied with voltage inverters with satisfying results Index Terms—Identification, induction heating, modeling, multiphase, parameter tuning I I NTRODUCTION N OWADAYS, induction heating systems are widely used in industry because they provide safety, cleanness, better performance, and higher efficiency when compared to the classical heating systems, convection heating systems, and radiation heating systems because the heat could be generated deep inside the material They are usually used in metal industry for many applications such as heating, welding, melting, drying, and merging [1], [2] With the development of power electronics and microprocessors, higher temperature, more precise temperature profile, and power could be achieved The structure of a classical induction heating system consists of power converters, microcontrollers, and resonant circuits The power converter configurations can be half-bridge, full-bridge, single switch, or multilevel con- Manuscript received July 1, 2014; revised March 20, 2015; accepted June 9, 2015 Date of publication July 8, 2015; date of current version November 18, 2015 Paper 2014-METC-0502.R1, presented at the 2014 IEEE Industry Applications Society Annual Meeting, Vancouver, BC, Canada, October 5–9, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLI CATIONS by the Metals Industry Committee of the IEEE Industry Applications Society B A Nguyen and Q D Phan are with the Power Delivery Department, Faculty of Electrical and Electronics Engineering, Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam (e-mail: ngbaoanh85@gmail.com; pqdung@hcmut.edu.vn; phan_quoc_dung@yahoo.com) D M Nguyen, K L Nguyen, O Durrieu, and P Maussion are with the LAboratoire PLAsma et Conversion d’Energie (LAPLACE), INPT, UPS, ENSEEIHT, Université de Toulouse, 31071 Toulouse, France (e-mail: minh.nguyen.duy@Laplace.univ-tlse.fr; kienlong.nguyen@alumni.enseeiht.fr; olivier.durrieu@Laplace.univ-tlse.fr; pascal.maussion@Laplace.univ-tlse.fr) Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org Digital Object Identifier 10.1109/TIA.2015.2453259 verter [3] Numerous applications can be found for domestic appliances in [1], [3], and [4] for many years The resonant circuit consists of resistors, inductors, and capacitors It is well known in induction heating that the inductor is one of the most important parts of a resonant converter because it has to face high power, high frequency, and high temperature The inductance of the inductor sets the inverter operating point and safe operating area, and it is affected by the operating frequency and temperature Therefore, monitoring this parameter is very important to get the best performance and remains an issue Previous papers [5] put in evidence that a precise control of the inductor currents in multiphase systems was necessary to reach the reference temperature or power density profile in work piece Multiphase systems are good candidates to increase the heating power in industry applications As a consequence, as the equivalent inductor depends on the load, system parameters are required for optimal controller tuning As the load properties can vary (type of metal, thickness, form, temperature, width, etc.), inverter loads will change a lot, and online parameter identification becomes an issue Some algorithms have been developed to monitor the impedance, and they depend on the settings of estimation methods and may not always converge [6] A “pseudoenergy” method has been proposed [7], but harmonics cause some errors in the calculation All of these algorithms can be qualified as “offline,” i.e., the parameters are calculated when the system does not operate Another algorithm is “3-D numerical modeling” which uses a numerical method to identify the permeability, but it is not used to calculate the impedance matrix [8] The performance will be increased if the impedance is monitored online while the system is still working Different online methods have already been developed, but they are limited to one-phase systems, and the impedance matrix is rather complex [9], [10] Particle swarm optimization is used in [11] to achieve parameter identification of a system load in domestic induction heating, in which equivalent single series resistance–inductance highly depends on temperature, pot material, etc However, PSO is known to be time-consuming Parameter identification could be based on an analytical statespace model of an electrical equivalent circuit and multimodel reset observers for domestic induction cookers in [12] A large amount of unknown pots (150 indeed) has been tested This observer needs parameter settings, the hybrid observer behaves as a proportional-integral observer, but the integral term is reset according to a specific reset map Parameter extraction of the electrical equivalent model of a coupled double concentric coil for induction heating purposes is provided with Fourier 0093-9994 © 2015 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information 4854 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL 51, NO 6, NOVEMBER/DECEMBER 2015 TABLE I PARAMETERS OF THE I MPEDANCE M ATRIX coil 2, and coil 3, respectively This leads to the induced voltages V21 and V31 across inductor and inductor 3, which allow calculating Z21 , Z31 (R21 , L21 , R31 , L31 ) The other terms, Z22 , Z12 , Z32 and Z33 , Z13 , Z23 are identified by the same process on phase and phase Lii = transform in [13] but with high sampling rate Integration requires several periods to improve the evaluation accuracy of the parameters of the × matrix Moreover, the “pseudoenergy” method [7] and another one based on the calculation of some [Iinv , V ]/I terms have also already been proposed for multiphase current inverters [14] in an offline implementation (Table I) This paper deals with their online adaptation in a classical single-board computer dedicated to control, with low sampling rate, without specific measurement equipment and at a reduced computational cost The final objective is to apply the pseudoenergy method to a multiphase induction heating system, with voltage inverters in order to identify its impedance matrix and to properly set the current controllers The whole system and concept is first checked with simulation results and verified with experimental results on a reduced-power system The test bench is limited to the electrical part (no thermal part in here), composed of a reduced-power three-phase coupled resonant system supplied with voltage inverters II T HREE - PHASE I NDUCTION H EATING S YSYEM A previous paper [5] focused on a three-phase induction heating system composed of three concentric inductor coils which are arranged face to face in a transverse flux and a disk plate, i.e., the load to be heated It has been shown on this device that parameter estimation was necessary and possible In the present work, a reduced-element system is proposed to emulate the electrical part of a three-phase induction system with voltage control and with a resonant circuit in a serial association The test bench is composed of six voltage inverters with a common dc source, but only the first three inverters are used here for simplicity reasons and validation of the concept The three inverters supply a three-phase coupled load as showed in Fig Each phase includes a full-bridge converter, a resistor, a capacitor, and a serial inductor situated on a common core, as it can be seen in Fig A mathematic model of this structure of coils is built in MATLAB in order to study its theoretic impedance matrix, which is also a basis to compare with other methods This model also allows us to calculate the impedance matrix with different numbers of turns of each inductor or air gaps between the coils The process includes two stages: calculating reluctances by the equivalent magnetic circuit presented in Fig and calculating the impedance matrix by the V /I method with phase shift According to (1)–(6), when phase is supplied by a sinusoidal voltage VS , inductor current I1 is calculated from VS and Z11 The equivalent magnetic circuit will help in calculating the fluxes φ1 , φ21 , and φ31 which flow through inductor coil 1, Ni2 Rei Z ii = Rii + jωLii (1) (2) Ii = VS Z ii (3) φi = I i Ni Rei (4) V ij = Ni ωφij i Z ij = V ij Ij (5) (6) where Lii Ni Rei φi self-inductance of inductor i; number of turns of inductor i; equivalent reluctance of case i; flux through coil I As showed in Fig 4, the power electronic part is composed of six independent voltage invertors with six separate control signals This inverter consists of six independent full-bridge converters (special integrated circuit) with dead-time and thermal shutdown implemented inside The outputs of the inverter legs can be connected in parallel or series Six protection systems are used against overcurrent or short-circuit protection The technical parameters of this reduced power test bench are expressed as max dc voltage: 48 V, wide range of switching frequency: up to 100 kHz, and max current: A A capacitor bank has been calculated in order to compensate the reactive power on the three phases This leads to C = [3.74, 3.37, 3.75 μF] The switch control signals can be generated either from a pulse generator or from MATLAB/Simulink with a digital control board Moreover, these control signals are isolated from the power stage for safety reasons For example, inverter voltage n◦ and current are presented in Fig 5, for example, while the other currents can be seen in Fig In Fig 3, the load consists of three inductors organized in series configuration and a ferrite core as work piece coupled A matrix model of the system is given in (7), where sinusoidal currents I1 , I2 , and I3 feed the three coils through the three inverters The so-called “impedance matrix” Z in (8), (9), and (10) carries all of the information on the state of the load via its parameters ⎡ ⎤ ⎡ V1 R1 + jL1 ω ⎣V2 ⎦ = ⎣ jM21 ω jM31 ω V3 jM12 ω R2 + jL2 ω jM32 ω ⎤⎡ ⎤ I1 jM13 ω jM23 ω ⎦⎣I2 ⎦ R3 + jL3 ω I3 (7) NGUYEN et al.: PARAMETER IDENTIFICATION METHOD FOR A THREE-PHASE INDUCTION HEATING SYSTEM 4855 Fig System PSIM model with voltage inverters, serial capacitors, coupled-inductors, and sensors Fig Six-phase voltage inverter Fig Three coupled coils Ri , Li Mij self-resistance and inductance for inductor I; mutual inductance between phases i and j ⎡ Z11 Z = ⎣Z21 Z31 Z12 Z22 Z32 Zl,l = Ri + jωLi Zl,k = jωMi,j ⎤ Z13 Z23 ⎦ Z33 (8) (9) (10) III I DENTIFICATION BY V /I M ETHOD WITH P HASE S HIFT Fig Three coupled coils and their equivalent magnetic circuits In this method, all of the three capacitors have been removed for the load to be supplied directly by a sine wave from a frequency generator Consequently, only resistors, selfinductors, and coupling terms are identified In the first experiment, phase is supplied with a sinusoidal voltage, while phase and phase are opened The necessary values to be measured are V1rms , V2rms , V3rms , I1rms , and phase shifts 4856 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL 51, NO 6, NOVEMBER/DECEMBER 2015 Fig Inverter output voltage and current Fig Voltage V (CH1), induced voltages V (CH2), V (CH3), and current I1 (CH4) Fig Inductor currents in phases 1, 2, and between V1 /I1 , V2 /I1 , V3 /I1 in Fig Then, the impedance parameters Z11 , Z21 , Z31 are calculated by Z ij = Vi = Rij + jXij = Rij + jωLij Ij (11) Similarly, measurements on phase and phase will give Z12 , Z22 , Z32 and Z13 , Z23 , Z33 It is easy to understand that this method does not lead to accurate results Indeed, I measurements that could be noisy will lead to division by a false term and false impedance values, while phase measurements via zero crossing are often difficult to achieve, particularly in an online automatic mode IV O FFLINE I DENTIFICATION BY P SEUDOENERGY M ETHOD In the pseudoenergy method, the capacitors are not removed in order to stay in the resonant mode The identification process is composed of three successive steps during which the three phases are supplied independently and successively This method was first described in [7] in an offline mode owing to a specific and complex apparatus (Rogowski coils and Le Croy oscilloscope) It will be first implemented in the offline mode Fig Phase and voltages and currents during the identification step on phase with modulated angle on inverter and phases and open circuited CH1: V 1, CH2: I1, CH3: V 2, and CH4: I2 in a real-time single-board controller, with a reduced sample frequency and 12-b AD converters Then, the online mode will be presented in Section V In the first step, phase is supplied by the square voltage generated by the corresponding inverter, while phase and phase are opened (their inverter control signals are not activated) Identification of the terms of the first column of matrix Z is achieved Then, the second step consists in supplying phase j, while I2 and I3 are null in order to measure the parameters of column in the Z matrix Finally, step is the same for phase At resonant frequency, a sinusoidal current appears in phase i The measured values to calculate Rii , Rij , Rik , Xii , Xij , and Xik , i.e., the terms in the first column of (8), are the voltages across the RL parts of phases i, j, and k which are Vi , Vj , Vk , respectively, and current in phase i, named Ii The currents in phases j and k must be equal to zero in order to cancel the coupling terms in phase i and in (7) Assuming that the voltages and currents are sinusoidal, the following equations can be written Starting from the same principle as in the classical method, the rms values of the currents (12) and NGUYEN et al.: PARAMETER IDENTIFICATION METHOD FOR A THREE-PHASE INDUCTION HEATING SYSTEM 4857 Fig Block diagram of the identification process on phase the voltages are first determined, and cos(ϕ) is calculated by (13), with n as the number of integration periods nT Irms = cos(ϕ) = n·T i2 dt (12) vi · ij Vi · Ij (13) nT vi ij = n·T Rij = Xij = vi · ij dt = Pij Pij Ij2 (15) − P2 Sij ij Ij2 Sij = Vi · Ij Qi = (14) Si2 − Pi2 (16) Fig 10 Phase and voltages and currents during the identification step on phase with reduced current in inverter CH1: V 1, CH2: I1; CH3: V 2, and CH4: I2 (17) (18) Of course, accuracy of cos(ϕ) and the other terms will be increased with the number of integration periods The pseu- dopower average is given by (14) The coupling terms involving i and j quantities with i = j are called “pseudopower” because they are the product of currents and voltages that not necessarily coexist in the same circuit They represent power in terms of unity but may have no physical meaning The mutual 4858 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL 51, NO 6, NOVEMBER/DECEMBER 2015 TABLE II I MPEDANCE M EASUREMENTS A CCORDING TO D IFFERENT M ETHODS ( IN O HMS ) resistance is obtained by dividing the “pseudoactive power” by the square of the corresponding rms inductor current as described in (15) The calculation of the capacitance or reactance (16) requires the calculation of “pseudoapparent power” (17) which is calculated as the product of the supplied rms current and the voltage induced In fact, as it can be easily seen in Fig 8, voltages are not sinusoidal Consequently, all of the measured values have to be low-pass filtered through first-order digital filters at the fundamental frequency (1500 Hz) As depicted in Fig 8, where phase and are open circuited, the current in phase is perfectly sinusoidal, while the other currents in phase and are equal to zero The parameter identification runs properly Fig gives the block diagram which is implemented on the DSP board to measure R11 , R21 , R31 , X11 , X21 , and X31 parameters during the first identification step, when phase is supplied and currents should be null in the other phases The importance of this last point will be discussed later It will be shown that the system must operate at reduced power just to ensure that the currents in phase or will not exist due to the back EMF which is generated by the coupling effects between phases and or phases and In that case, currents will circulate through the reverse diodes of the bridges When the control signals of inverter are off, even if the phase voltage is maximum as in Fig 10, the induced voltage on phase is not higher than the supply voltage Thus, there is no current flowing through the inverter diodes, and this leads to good identification results, such as listed in Table II Finally, it is worth noticing that these rather good identification results are obtained with a reduced sample period, i.e., only 12 times the fundamental frequency This consideration will help in reducing the computational burden, and it is positive for real-time implementation of this identification method Moreover, capacitors may vary with temperature or may differ from the supplier values given in the data sheet This method will also provide estimation of C, the capacitor bank as listed in Table III Voltages across them could be obtained through (19), assuming as previously stated that voltages across the RL parts are measured with dedicated sensors and filters TABLE III M EASUREMENTS OF C APACITORS BY THE P SEUDOENERGY M ETHOD Fig 11 Command signal of the identification process (CH1), phase voltage V (CH4), and phase current I2 (CH2) TABLE IV I NFLUENCE OF Toff OF THE I DENTIFICATION R ESULTS Once each inverter voltage can be deduced from the dc bus voltage and the duty cycles, and not directly measured, capacitors NGUYEN et al.: PARAMETER IDENTIFICATION METHOD FOR A THREE-PHASE INDUCTION HEATING SYSTEM 4859 TABLE V I MPEDANCE M EASUREMENTS AT D IFFERENT O PERATING P OINTS ( IN O HMS ) W ITH THE O NLINE P SEUDOENERGY M ETHOD derive from (20) Of course, these voltages across Ci are far from sinus and also need low-pass filtering VCi = Vinvi − VRLi (19) [Ii ] [Vci ] (20) Ci ω = V O NLINE I DENTIFICATION BY P SEUDOENERGY M ETHOD Fast identification of the system parameters becomes an objective of dramatic importance in the very particular case of rolling plates Their characteristics such as type, dimensions, temperature, etc., when placed under the induction generator, can suddenly change It is particularly true when the industrial process needs to heat two different types of work pieces one after another Assuming that a warning signal is sent during (or before) the change, the three identification steps can be launched successively, just during the duration of the change, i.e., time for the inductor crossing Under the assumption of a 1-m/s speed of the rolling piece and because each identification step is only few periods long, 100 periods, i.e., 66 ms, for example, the work piece displacement would be no more than 6.6 cm, just the dimension of the width of the soldering strip between the two work pieces! As a consequence, the resulting temperature disturbance will certainly be negligible As seen in Fig 11, when the gate signal at the beginning of the identification step switches phase and phase from on to off, the corresponding currents decrease down to zero In order to reduce the estimation error, the number of identification periods Toff must be high compared to the transients Moreover, identification must start after the transients A survey on this value is given in Table IV A convenient value is 100 times the system fundamental period which will lead to 7.2% error Because the system is supposed to work at different operating points and with some resonant frequency variations, additional experimental results are provided in Table V with satisfying results It has been shown in [15] that resonant controllers which have been successfully used in this type of application are robust enough to cope with misalignment and parameter estimation error Then, control of the inductor currents will be performed correctly VI C ONCLUSION This paper has described a new method for parameter estimation of a multiphase induction heating system Simulations and experiments were presented in order to measure its impedance matrix for more exact control in closed loop The “pseudoenergy” method is applied in comparison with the classical V /I method It achieves good results on a reducedpower three-phase resonant system with voltage inverters, even with a limited sample frequency Future work will deal with the online application of this method on a six-phase system and on a real full power induction heating system with transverse flux and concentric coils Moreover, heating magnetic steel with a nonlinear behavior and the corresponding parameter identification will also be an important issue in the future R EFERENCES [1] O Lucia, P Maussion, E J Dede, and J M Burdio, “Induction heating technology and its applications: Past developments, current technology, and future challenges,” IEEE Trans Ind Electron., vol 61, no 5, pp 2509–2520, May 2014 [2] I Yilmaz, M Ermis, and I Cadirci, “Medium-frequency induction melting furnace as a load on the power system,” IEEE Trans Ind Appl., vol 48, no 4, pp 1203–1214, Jul./Aug 2012 [3] I Millán, J M Burdío, J Acero, O Lucía, and D Palacios, “Resonant inverter topologies for three concentric planar windings applied to domestic induction heating,” Electron Lett., vol 46, no 17, pp 1225–1226, Aug 2010 [4] O Lucía, C Carretero, J M Burdío, J Acero, and F Almazan, “Multipleoutput resonant matrix converter for multiple induction heaters,” IEEE Trans Ind Appl., vol 48, no 4, pp 1387–1396, Jul./Aug 2012 [5] M Souley, M Caux, O Pateau, P Maussion, and Y Lefèvre, “Optimization of the settings of multiphase induction heating system,” IEEE Trans Ind Appl., vol 49, no 6, pp 2444–2450, Nov./Dec 2013 [6] X Zhe, C Xulong, H Bishi, K Yaguang, and X Anke, “Model identification of the continuous casting billet induction heating process for hot rolling,” in Proc 3rd Int Conf ISDEA, 2013, pp 942–945 [7] M Souley et al., “Methodology to characterize the impedance matrix of multi-coil induction heating device,” in Proc Electromagn Properties Mater Conf., Dresden, Germany, 2009, pp 201–204 [8] A Canova et al., “Identification of equivalent material properties for 3-D numerical modeling of induction heating of ferromagnetic workpieces,” IEEE Trans Magn., vol 45, no 3, pp 185–1854, 2009 [9] O Jimenez, O Lucia, I Urriza, L Barragan, and D Navarro, “Analysis and implementation of FPGA-based on-line parametric identification algorithms for resonant power converters,” IEEE Trans Ind Informat., vol 10, no 2, pp 1144–1153, May 2014 [10] O Lucia et al., “FPGA implementation of a gain-scheduled controller for transient optimization of resonant converters applied to induction heating,” in Proc IEEE APEC, 2013, pp 2520–2525 [11] A Dominguez et al., “Load identification of domestic induction heating based on particle swarm optimization,” in Proc 15th IEEE COMPEL, 2014, pp 1–6 4860 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL 51, NO 6, NOVEMBER/DECEMBER 2015 [12] D Paesa, C Franco, S Llorente, G Lopez-Nicolas, and C Sagues, “Adaptive simmering control for domestic induction cookers,” IEEE Trans Ind Appl., vol 47, no 5, pp 2257–2267, Sep./Oct 2011 [13] C Carretero, O Lucia, J Acero, and J M Burdio, “First harmonic equivalent impedance of coupled inductive loads for induction heating applications,” in Proc 38th IEEE IECON, 2012, pp 427–432 [14] K L Nguyen, S Caux, P Teixeira, O Pateau, and P Maussion, “Modeling and parameter identification of a multi-phase induction heating system,” in Proc Int Conf Electrimacs, Valencia, Spain, 2014 [15] K L Nguyen, O Pateau, S Caux, P Maussion, and J Egalon, “Robustness of a resonant controller for a multiphase induction heating system,” IEEE Trans Ind Appl., vol 51, no 1, pp 73–81, Jan./Feb 2015 Bao Anh Nguyen received the B.Tech degree in electrical and electronic engineering and the M.S degree in electrical engineering from Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam, in 2008 and 2011, respectively He is currently a Researcher with the Power Electronic Research Laboratory, Ho Chi Minh City University of Technology, where he is responsible for research and development of advanced control algorithms and power converters which are used in renewable-energy systems Quoc Dung Phan was born in Saigon, Vietnam, in 1967 He received the Dipl.-Eng degree in electromechanical engineering from Donetsk Polytechnic Institute, Donestk City, Ukraine, in 1991 and the Ph.D degree in engineering sciences from Kiev Polytechnic Institute, Kiev City, Ukraine, in 1995 He became an Associate Professor of electrical engineering with the Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam, in 2010 He is currently a Senior Lecturer with the Faculty of Electrical and Electronics Engineering, University of Technology He was a Visiting Professor at the LAboratoire PLAsma et Conversion d’Energie (LAPLACE), ENSEEIHT-INP, Toulouse, France, in 2013 and 2015 He is currently the Head of the Power Delivery Department and Power Electronics Research Laboratory, Ho Chi Minh City University of Technology His research interests include power electronics, electric machines, and their applications in industry and renewable energy Duy Minh Nguyen received the Engineer degree in electrical and electronics engineering from Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam, in 2014 He is currently working toward the Master’s degree in electrical and automation engineering at the University Paul Sabatier, Toulouse, France His research activities deal with identification method of multiphase induction heating systems and control and performance improvement of switched reluctance machines in concordance with power converters at the LAboratoire PLAsma et Conversion d’Energie (LAPLACE), Toulouse Kien Long Nguyen received the Master’s degree in automatic control and electrical engineering from ENSEEIHT-INP, Toulouse, France, in 2012 He then became a Research Engineer with the LAboratoire PLAsma et Conversion d’Energie (LAPLACE), Toulouse, and EDF R&D—Paris for automatic control of a three-phase induction heating system Olivier Durrieu received the Technician diploma in 1980 He is a Technician with the LAboratoire PLAsma et Conversion d’Energie (LAPLACE), Université de Toulouse, Toulouse, France He works as an electronic board designer and prototype maker for teaching and research Pascal Maussion (M’07) received the M.Sc and Ph.D degrees in electrical engineering from the Toulouse Institut National Polytechnique, Toulouse, France, in 1985 and 1990, respectively He is currently a Full Professor with the University of Toulouse, Toulouse, and a Researcher with the Centre National de la Recherche Scientifique Research Laboratory, LAboratoire PLAsma et Conversion d’Energie (LAPLACE), Toulouse He is currently the Head of the Control and Diagnosis Research Group, LAPLACE He teaches courses on control and diagnosis at the University of Toulouse His research activities deal with the control and diagnosis of electrical systems such as power converters, drives, and lighting, and with the design of experiments for optimization in control and diagnosis  ... This paper has described a new method for parameter estimation of a multiphase induction heating system Simulations and experiments were presented in order to measure its impedance matrix for more... I Urriza, L Barragan, and D Navarro, “Analysis and implementation of FPGA-based on-line parametric identification algorithms for resonant power converters,” IEEE Trans Ind Informat., vol 10,... Nguyen, S Caux, P Teixeira, O Pateau, and P Maussion, “Modeling and parameter identification of a multi-phase induction heating system, ” in Proc Int Conf Electrimacs, Valencia, Spain, 2014 [15]