Phase Locked Loop based Pulse Density Modulation Scheme for the Power Control of Induction Heating Applications

Transcription

1 Jounal of Powe Eleconics, Vol. 5, No., pp. 6577, Januay JPE 57 hp://dx.doi.og/0.63/jpe IN(Pin): / IN(Online): Phase Locked Loop based Pulse Densiy Modulaion cheme fo he Powe Conol of Inducion Heaing Applicaions Booma Nagaajan and Rama Reddy ahi * * Depamen of Elecical and Eleconics Engineeing, Jeusalem College of Engineeing, Chennai, India Absac Resonan convees ae well suied fo inducion heaing (IH) applicaions due o hei advanages such as efficiency and powe densiy. The conol sysems of hese appliances should povide smooh and wide powe conol wih fewe losses. In his pape, a simple phase locked loop (PLL) based vaiable duy cycle (VDC) pulse densiy modulaion (PDM) powe conol scheme fo use in classd invees fo IH loads is poposed. This VDC PDM conol mehod povides a wide powe conol ange. This conol scheme also achieves sable and efficien ZeoVolagewiching (ZV) opeaion ove a wide load ange. Analysis and modeling of an IH load is done o pefom a ime domain simulaion. The design and oupu powe analysis of a classd invee ae done fo boh he convenional pulse widh modulaion (PWM) and he poposed PLL based VDC PDM mehods. The conol pinciples of he poposed mehod ae descibed in deail. The validiy of he poposed conol scheme is veified hough MATLAB simulaions. The PLL loop mainains opeaion close o he esonan fuency iespecive of vaiaions in he load paamees. The poposed conol scheme povides a linea oupu powe vaiaion o simplify he conol logic. A pooype of he classd invee sysem is implemened o validae he simulaion esuls. Key wods: ClassD invee, Inducion heaing, Phase locked loop, Pulse densiy modulaion, Zeo volage swiching I. INTRODUCTION IH sysems ae used in many indusial, domesic and medical applicaions due o hei high pefomance. IH echnology akes advanage of conacless enegy ansfe o he wok piece o obain fase heaing, impoved safey, and highe efficiency han convenional heaing mehods. The coe componen of an IH sysem is he powe supply. An IH powe supply sysem is usually composed of a ecifie sage and a esonan invee. eies esonan invees (RIs) ae widely used as a high fuency souce [], []. In RIs, he esonan ank cicui is fomed by a wok coil and a capacio. A RI fed wih a volage souce epesens a simple and coseffecive soluion [3][5]. Howeve, he oupu powe of such an invee is conolled by adjusing he DC inpu volage. A conolled ecifie wih a DClink capacio has Manuscip eceived May, 04; acceped Aug. 6, 04 Recommended fo publicaion by Associae Edio Yan Xing. CoespondingAuho:booma_nagaajan@yahoo.com Tel: ,Fax: , Jeusalem College of Eng. * Dep. of Elecical and Eleconics Eng., Jeusalem College of Eng., India been convenionally used o povide a vaiable DC volage so ha he oupu powe of he invee ges adjused. Howeve, he size and cos of his convenional aangemen is lage [5][8]. To ovecome hese poblems, he powe conol of an invee, fed by an unconolled ecifie using fuency modulaion, phaseshif vaiaion and asymmeical volage cancellaion conol is discussed in many sudies o egulae he oupu powe. An impoan goal of powe conol is o achieve an efficien and useful poduc. Invees wih he above modulaion schemes esul in inceased swiching losses because i is impossible fo he swiching devices o be always uned on and off a zeo cuen o zeo volage insans. Geneally, IH applicaions use a fuency modulaion scheme o conol he oupu powe. Vaiable fuency conol is a basic mehod which is used fo vaiable load condiions. Vaiable fuency conol is used fo half bidge and full bidge RIs [9]. Howeve, pulse fuency modulaion conol causes many poblems since he swiching fuency has o be vaied ove a wide ange o accommodae he wos combinaions of loads. The 05 KIPE

2 66 Jounal of Powe Eleconics, Vol. 5, No., Januay 05 efficiency of an invee deceases significanly wih an incease in he swiching fuency o lowe he oupu powe. The majo disadvanage of his mehod is he lage fuency ange uiemen fo a wide ange of oupu powe conol. Fo a fuency below esonance, he file componens ae bulky because hey mus be designed fo he low fuency ange. Fo opeaion above esonan fuency, fas swiching devices ae uied o mainain conol in he highe fuency ange. In addiion, he sof swiching ange of a fuency modulaed high fuency invee is elaively naow. The conol of a RI wih a consan swiching fuency wih a vaiable pulse widh is one of he ways o avoid he poblems of vaiable fuency conol [0], []. Theefoe, classd invee opologies using PWM conol, phaseshif conol and asymmeical volage conol have been poposed. In fixed fuency opeaion, he invee is opeaed a a consan fuency and conol of he oupu powe wihou vaiaions in he fuency. Howeve, hese conol uiemens and opeaing chaaceisics incease he complexiy of he design due o he fixed fuency swiching uiemen which limis hei pefomance. Phase shifed PWM conol was used fo full bidge invees o adjus he oupu powe [][4]. In a IH powe supply sysem using a phaseshif PWM conol, zeo volage swiching (ZV) opeaion is no possible unde ligh load condiions. This conol saegy canno be used fo half bidge invees. Asymmeical volage conol saegy is also used fo he conol of oupu powe. I gives impoved efficiency due o is consan swiching fuency and ZV opeaion [5].This mehod esuls in high un on losses unde low load condiions due o he NONZV opeaion of he swiches. A disconinuous mode powe conol scheme fo loss minimizaion is also discussed in he lieaues [5][8]. In he above papes, a powe conol scheme of IH loads wih he ZV opeaing condiion in he whole load ange is no discussed. This pape discusses a simple PLL based VDC PDM powe conol scheme of he vaiable powe ZV classd invees fo IH applicaions. The aim of his sudy is o conol he powe ove a wide load ange unde he ZV condiion o impove he oupu powe of IH sysems. In his pape, he powe supply fo inducion heaing (IH) sysems based on a classd RI is descibed. The oupu powe of he invee is conolled using a VDC based PDM. When he invee is opeaed a a swiching fuency highe han is esonan fuency; i can mainain ZV opeaion in he whole load ange [9][]. The effecive paamees fo he uivalen esisance and inducance of an IH load vay houghou he heaing cycle [], [3]. Thus, i becomes necessay o change he opeaing fuency of he invee in ode o mainain he esonance condiion accoding o load vaiaions. The pesened conol cicui employs a fuency acking sysem o monio load vaiaions. The conol cicui also employs a PDM pulse geneaion logic cicui which povides modulaed gae signals o he gae dive cicuiy a he acked load esonan fuency. Unde PDM, he swiching losses ae fixed and he oal oupu powe of he invee ges inceased. In he poposed scheme, he invee opeaion a esonance is mainained such ha he losses ae a a minimum. This impoves he efficiency of he IH sysem ove a wide ange of powe. The poposed modulaion echnique wih a fuency acking sysem can achieve a linea oupu powe vaiaion which simplifies he conol algoihm. II. YTEM DECRIPTION A block diagam of an IH powe supply sysem is shown in Fig.. The classd invee akes enegy fom he 50Hz AC inpu souce hough an unconolled ecifie. The DC volage is conveed ino a highfuency AC volage by using he classd invee. Then, he invee supplies a highfuency cuen o he inducion coil. To ack he esonan fuency of he load, a phase locked loop (PLL) is used. A he acked load fuency, PDM gae pulses ae geneaed and applied o he swiches. A. Chaaceisics and Modeling of an IH Load An IH load consiss of a wokcoil and a wokpiece. In IH sysems, mos of he wokpieces have a cylindical shape. They ae heaed by being placed inside he wok coil wih one o moe uns. In IH applicaions, a magneic field is induced in he wok coil. This causes eddy cuens in he wok piece. These eddy cuens give ise o a heaing effec. Mos of he hea in he wokpiece is geneaed by eddy cuens. Basically, an IH load is a ansfome epesenaion of he elecomagneic inducion acion beween he wok coil (pimay) and he load (seconday) as shown in Fig.. The ansfome paamees ae difficul o measue. Theefoe, i is bee o epesen he IH load using a simplified model. The IH load can be modeled by means of a seies combinaion of is uivalen esisance R and inducance L as shown in Fig.. These paamees depend on seveal vaiables, including he shape of he heaing coil, he disance beween he wokpiece and he IH coil, he empeaue, he elecical conduciviy and magneic pemeabiliy, and he fuency. In he ansfome uivalen of an IH load, L is he self inducance of he wok coil. L is he inducance in he seconday side of he IH load, M is he muual inducance of he ansfome, and R is he esisance of he IH load. The uivalen values of he IH sysem R and L change wih he geomey, load maeials, empeaue, and exciaion fuency. A change in he paamees makes he oupu powe conol hade. Fo his eason, a complee analysis of he uivalen paamees R and L of he IH sysem is

3 Phase Locked Loop based Pulse Densiy Modulaion cheme fo 67 Fig.. Block diagam of IH powe supply sysem. Fig.. Tansfome uivalen cicui of IH load. Equivalen seies RL cicui of IH load. povided hee. The volage uaions of he ansfome model of he IH load ae given below: whee, ω = V = jω L I + jmω I () L L L L ( R jωl ) IL 0 = jω MI + + () πf f s is he swiching fuency, and ω is he angula swiching fuency. I L and V L ae he cuen and volage in he wok coil, especively. The load cuen I L can be obained fom () which is given as: jωmil IL = (3) R + jω L Equaions () and (3) give he following expession: ( L L M ) é ω ù M R LR + ωl V L = + jω ê ú (4) R + ωl êë R + ωl úû The eal and imaginay pas of he above uaion ae epesened as R and L as given in he following uaions (5) and (6): L R R L ω M = (5) R + ω M ωl ω L = L (6) R + The geneal ime consan of he load (τ) is defined as: L = (7) R Equaion (7) can be esimaed using uaions (5) and (6) as: since: M L L = (8) R ( R + ω L ) R = (9) R ω The muual coupling coefficien (K) fo a coupled cicui is geneally defined as: M K = L L (0) olving (6) and (0) yields he following expession: ( L L ) ( L L ) R + ω K = () ω L In uaion (), K is expessed wih R, L and L. B. Analysis of a ClassD Invee Fig. 3 shows he configuaion of he classd invee sysem fo an IH load. The classd invee consiss of wo swiches and and wo esonan capacios wih a capaciance of C / and an IH load. When he invee is fed wih he DC inpu volage and ae alenaely used o allow a highfuency AC cuen o he IH coil. Fig. 3 shows he uivalen cicui model of he classd invee. The swiches of he classd invee ae opeaed a above he esonan fuency in ode o achieve ZV duing un off [4], [5]. Convenionally, classd invee swiches ae opeaed wih pulse widh modulaed gae pulses. In his pape powe conol using PDM is discussed. The PDM invee epeas un and sop in accodance wih a conol suence o adjus is oupu volage.

4 68 Jounal of Powe Eleconics, Vol. 5, No., Januay 05 Fig. 3. Cicui configuaion of classd invee. Equivalen cicui of classd invee. Fo simulaion sudy, an IH load is consideed wih an uivalen cicui of a seies combinaion of esisance R and inducance L. This seies banch wih R and L in combinaion wih C foms he esonan cicui. The oupu powe analysis of he esonan cicui unde he convenional PWM mehod fo he classd invee can be descibed by he following paamees. The angula esonan fuency (ω ) of he seies esonan cicui is given by: ω = () L C whee C is he capaciance of he esonan capacio. The nomalized angula swiching fuency (ω ) is expessed as: ωs ω n = (3) ω The chaaceisic impedance (Z o ) of he IH load is: 0 = ωl C ωc L Z = = (4) The qualiy faco (Q L ) of he IH coil is given by: ωl Z0 Q L = = = (5) R ω R C R The uivalen impedance (Z ) of he esonan ank cicui is given by he following uaions: æ ö Z ç = R + j ωsl (6) è ωsc ø æ ö Z = R + QLç ωn (7) è ωn ø The oupu volage of he classd invee conneced o he IH load is V o : V = V d fo 0 < ω π (8) 0 fo π <ω π The fundamenal componen (V o ) of he oupu volage can be found fom he Fouie analysis: V = V inω fo 0 < ω π (9) 0 m s s Whee, he peak value of he oupu load volage (V m ) is: Vd Vm = 0.637V d (0) p The load cuen (I o ) hough he esonan ank cicui is descibed by he following uaion: I = I in(ω ) () 0 m s f The phase angle (Ø) of he load cuen is: æ ö Ø = an Q L ç ω n () è ω n ø Whee, he peak value of he oupu load cuen (I m ) is: I m = V Z m = p.r V Cosf d æ + QLç ωn è ω n ö ø (3) The convenional oupu powe (P o ) of he classd invee is given in he following uaions: P o R Vd = Im = (4) æ ö π R ( + QL ) çωn ω è n ø d V Cos f = π R Veff Cos f = (5) R In he convenional PWM mehod he oupu powe is vaied by vaying duy cycle of he powe swiches. A desied oupu powe (P desied ) can be obained by vaiaion of he PWM conol duy aio (D PWM ). P = P D (6) desied o PWM The D PWM is given by he following uaion: TON DPWM = T (7) Whee T ON is he un on ime of he swich and T is he oal ime peiod. In he PWM conol he sof swiching ange is vey naow since T ON is vaied o conol he oupu powe. C. Design Pocedue of he Cicui Consains The design of he classd invee and he IH load paamees ae descibed in his secion. Fo he oupu powe P o, he uivalen esisance of he IH load is given by he following uaion: Veff R = Cos θ P (8) By he definiion of he qualiy faco of he esonan cicui given in uaion (5), he uivalen inducance L of he heaing coil wih Q L of.8 is given by: o

5 Phase Locked Loop based Pulse Densiy Modulaion cheme fo 69 L QLR = (9) w Finally, he calculaion of he value of he esonan capacio can be done as pe uaion (), by he definiion of he esonan fuency. C = (30) w L To educe he swiching losses duing he un off condiion, a lossless snubbe capacio (C s ) is used wih he swich. Typically, he classd opeaion mode implies ha C s is much lowe han C [5][8]. As a esul, he swiching wavefoms in he invee have a diec impac on all of he invee losses. Duing he chage inevals, he oupu cuen can be consideed consan, due o he small snubbe capacios used in he classd invee. D. Powe Consumpion in he MOFET wiches of he ClassD Invee Powe losses in he powe eleconic swiches include he conducion and swiching losses. The swiching losses can also be classified ino unon and unoff losses. The classd invee uses wo MOFETs wih ani paallel diodes. The conducion and swiching losses fo he MOFET and diode ae analyzed below. The oal powe loss in he MOFET (P M ) is deemined using he following uaion: M CM P = P + P (3) WM P CM is he conducion loss in he MOFET, and P WM is he swiching loss in he MOFET. P CM is given by: CM DONI Dms P = R (3) R D is he ON sae esisance of he swich, ON is he on/off sae of he swich, and I Dms is he ms value of he cuen hough he MOFET. The P WM in he MOFET is: VI d off f s PWM = 6 (33) V s is he on sae volage of he swich, I d is he insananeous value of he swich cuen a he ime of swiching, off is he un off ime of he swich, and f s is he swiching fuency. The oal powe loss (P D ) in he ani paallel diode is: P = P + P (34) D CD WD P CD is he conducion loss in he diode, and P WD is he swiching losses in he diode. P CD is defined as: P = V I (35) CD DO F V is he ON sae volage acoss he diode, and I F is aveage value of he fowad cuen hough he diode. P WD in he diode is given by: WD DI fms P = R (36) whee R D is he ON sae esisance of he swich, and I fms is he ms value of he fowad cuen hough he diode. The oal losses in he invee module include he MOFET and Fig. 4. Theoiical wavefoms of gae pulses. Fig. 5. Theoiical wavefoms of oupu volage and cuen wih PDM conol. diode losses. E. Analysis of he PDM Conol Algoihm Powe conol is an impoan goal o be achieved in an IH load o mainain a uied empeaue. The powe inpu o he woking coil of an IH load has o be conolled o conol he heaing of he wok piece. Convenionally, his is achieved by he conol of he classd invee using he PWM echnique. In he convenional PWM based powe conol, he oupu powe is conolled hough D PWM. In he PWM scheme, D PWM is he conol vaiable fo coninuous powe egulaion. A vaiaion of D PWM causes a violaion in he sof swiching opeaion which leads o highe swiching losses and educed oupu powe. A pulse modulaion echnique called VDC PDM wih fuency acking using a PLL fo powe conol is poposed in his pape. The pinciple of he PDM is o conol he swiching of he invee by he pulse densiy conol mehod, in which he oupu powe conol is done hough conolling he aio of he coninuous pulseon signal and he coninuous pulseoff signal. The main advanage of PDM is is linea dependency on he onime of he oupu powe. The basic idea of he poposed PDM conol is ha, by assuming a conol cycle of ime (T PDM ), he invee ansmis powe o he load in T A ime and i sops woking in he emaining (T PDM T A ) ime. Thus he oupu powe is elaed o he impulse densiy. In his way he oupu powe can be changed by changing he pulse densiy. The PDM based gae signals fo swiches and ae shown in Fig.4. When compaed wih convenional PWM conol opeaion, he PDM opeaion educes he swiching losses because he MOFET is always uned on and off unde zeo volage duing esonan opeaion.

6 70 Jounal of Powe Eleconics, Vol. 5, No., Januay 05 Fig. 6. Block diagam of conol scheme fo classd invee. Fig.7. D PDM conol signal and gae pulses o and. The oupu volage and cuen wavefoms of he classd invee wih he PDM conol ae descibed in Fig.5 wih he assumpion ha he qualiy faco of he esonan cicui is finie. Hee, he T PDM of he PDM paen is long enough o make he ampliude of he esonan cuen flucuae. The envelope of he esonan cuen shows ha he fisode esponse hough he seies esonan cicui is of a secondode sysem. A powe analysis of he classd invee wih he PDM conol is given below. The envelope of he esonan cuen (i E ) is given by: i i E E ( ) = I ç e + I e ( 0 T ) m æ ç è ö A (37) ø ( ) = i ( T ) e ( T T ) A A TPDM PDM e I = I (38) m e I m is he maximum cuen in fullpowe opeaion, and I is he iniial value of he envelope i E. If Q L is infinie, he ampliude of he esonan cuen is in popoion o he pulse densiy. æ ö lim i E = I m ç (39) è TPDM ø In he PDM, he aveage oupu powe (P) is obained by muliplying V d and i E as, follows: P = Vd I p Vdi p = ò0 E TPDM M T A + T e PDM ( ) d (40) æ e ö + V ç dim e T p T PDM ç PDM e è ø If he oal ime T PDM of he PDM opeaion is much smalle han he ime consan (τ), he ampliude of he esonan cuen is in popoion o he pulse densiy. As a esul, no flucuaion occus in he ampliude of he esonan cuen. Thus, he oupu powe is in popoion o he squae of he pulse densiy, as given by: lim æ ö P = Vd I m ç p T (4) PDM è ø When T PDM >>τ, he oupu powe is in popoion o he pulse densiy because he esonan cuen becomes a disconinuous wavefom. æ ö lim P = Vd I m ç p (4) è TPDM ø The effecive IH load powe is adjused by conolling he aio beween he on and off peiods. The PDM duy cycle (D PDM ) is given by he following uaion: D PDM = (43) T PDM A desied oupu powe can be obained by a vaiaion of D PDM. The em D PDM is also called a modulaion index o

7 Phase Locked Loop based Pulse Densiy Modulaion cheme fo 7 (c) (d) (e) (f) Fig. 8. D PDM conol signal fo 00% D PDM. Oupu volage wih 00% D PDM. (c) Zoomed view of he oupu volage wih 00% D PDM. (d) Oupu cuen wih 00% D PDM. (e) Zoomed view of he oupu cuen wih 00% D PDM. (f) Oupu powe wih 00% D PDM. pulse densiy, and is value deemines he oupu powe. In his pape D PDM is consideed as a conol vaiable. The desied powe (P desied ) fo diffeen load condiions can be obained as follows: P = P D (44) desied d o PDM V Cos f = DPDM (45) p R In his pape, he maximum oupu powe of he high fuency invee is obained fo a modulaion index value ual o one. III. CONTROL CHEME I is necessay o opeae an invee close o he esonan fuency o achieve a educion in he swiching losses. An IH load is modeled by means of a seies combinaion of is uivalen esisance R and inducance L. These paamees depend on seveal vaiables, including he shape of he heaing coil, he disance beween he wokpiece and he IH coil, he empeaue, he elecical conduciviy, he magneic pemeabiliy, and he fuency. When he load paamees change, hee is a change in he esonan condiion. I becomes necessay o vay he invee swiching fuency duing opeaion due o changes in he paamees which depend on he esonan fuency of he load cicui. Theefoe, he conol cicui should employ a fuency acking sysem o ack he esonan fuency of he newly changed paamees. A uned fuency acking sysem using a phase locked loop (PLL) is used o accomplish he above pefomance. When a wok piece of a diffeen meal is inseed ino he IH coil, is geomey, conduciviy and pemeabiliy cause he inducance of he heaing coil o change. Consideing he fac ha he esonan capaciance is fixed, he ank cicui is diven o is new esonan fuency by acking he swiching fuency of he invee. The PLL cicui can ack he esonan fuency due o is fas dynamic esponse. Fig. 6 shows a block diagam of he PLL based conol cicui developed fo he PDM invee. The poposed conol cicui and is deailed opeaion ae explained hee. Thee ae hee pas ha make up he conol cicui.. A PLL cicui is used fo he phase lock conol beween Io and V o. A PLL is a device which causes one signal o ack anohe signal. This keeps he oupu signal synchonized wih a efeence inpu signal in ems of fuency and phase. I mainains a swiching fuency close o he esonance fuency in ode o achieve he ZV condiion. I consiss of a phase deeco (PD), a lowpass file (LPF), and a volageconolled oscillao (VCO). The zeo cossing of he oupu cuen signal was compaed wih he zeo cossing of he oupu volage signal in ode o deec he diffeence in he phase using he exclusiveor gae, which is used as he PD. The oupu signal fom he exclusiveor gae was fileed by an RC low pass file which is basically a PI compensao o ge he aveage value of he volage. The aveage volage confims he phase diffeence beween he volage and he cuen a load. The oupu of he PI compensao is he aveage value of he eo volage which changes he VCOs oupu fuency of oscillaion in ode o mainain he phase angle when he paamees of he IH load ae vaied. When he fuency of I o and V o ae unual, he PD gives an oupu signal which indicaes he fuency diffeence, and when locked i indicaes a phase diffeence. The oupu signal of he PD is used o shif he VCO owad he lock befoe capue, and hen i holds he fuency in he lock condiion. Unde he

8 7 Jounal of Powe Eleconics, Vol. 5, No., Januay 05 (c) (d) Fig. 9. Conol signal fo 50% D PDM. Oupu volage wih 50% D PDM. (c) Oupu cuen wih 50% D PDM. (d) Oupu powe wih 50% D PDM. (c) (d) (e) (f) Fig. 0. Conol signal fo 0% D PDM. Oupu volage wih 0% D PDM. (c) Zoomed view of oupu volage wih 0% D PDM. (d) Oupu cuen wih 0% D PDM. (e) Zoomed view of oupu cuen wih 0% D PDM. (f) Aveage oupu powe wih 0% D PDM.. locked condiion he I o and V o signals have he same fuency. The VCO oupu signal is diecly fed back o he logical cicui o poduce PDM pulses. 3. A PDM pulse geneaing cicui fo oupu powe conol is he second pa of he conol cicui. The diffeence beween he efeence oupu powe (P ef ) and he acual oupu powe (P o ) geneaes an eo signal which is pocessed hough he PI conolle and a compaao o obain a PDM conol signal ha conols he D PDM of he PDM cicui. Based on he conol signal D PDM, he PDM gae signals fo swiches and ae geneaed. When he D PDM conol signal is high, high fuency swiching signals ae applied o he swiches. On he ohe hand, when D PDM is low, he gae signals ae no applied o he swiches as shown in Fig. 7. The low fuency D PDM conol signal and he high fuency signal simulaneously undego zeo cossing a he onoff ime of he swiches. This shows he synchonizaion beween he wo fuency signals. The PDM cicui, in combinaion wih he PLL cicui, achieves ZV opeaion. A sa up he D PDM is se o uniy. Unde ha condiion, he VCO which defines he woking fuency of he invee geneaes a fuency above he esonan fuency of he load. Afe his, he conol volage of he VCO ges changed unil he woking fuency of he invee is close o he esonan fuency of he new load. The PDM modulaion is pefomed coninuously by he feedback loop. As he ZV condiion is guaaneed by he VCO loop, he PDM modulao adjuss he oupu powe.

9 Phase Locked Loop based Pulse Densiy Modulaion cheme fo 73 Fig.. wich volage (V s ) and swich cuen (i s ) a 00% D PDM wich volage (V s ) and swich cuen (i s ) a 0% D PDM. (c) (d) Fig.. Hadwae layou of he pooype. D PDM conol signal(00%) and high fuency PWM pulses (0.5v/div,0.0s/div). (c) Expeimenal oupu volage a 00% D PDM (0V/div,0.05µs/div). (d) Expeimenal oupu cuen a 00% D PDM (A/div,µs/div). IV. DICUION OF THE IMULATION AND EXPERIMENL REULT The validiy of he poposed scheme was veified by he simulaion and expeimenal esuls obained on a pooype of an IH sysem. Fo he simulaion a schemaic of a classd invee and he conol cicui have been implemened fo ime domain simulaion using MATLAB. ince he invee oupu powe depends on he pulse densiy of he gae signals, a sudy of he efficiency of he PDM invee fo diffeen values of D PDM mus be made. The design specificaions and cicui paamees used fo he classd invee fo an IH load using commecial MOFET and diode modules ae lised in Table I. The paamees ae designed accoding o he consideaions given in he pevious secions. In Table I i is shown ha he swiching fuency is geae han he esonan fuency o achieve he ZV condiion. A simulaion of a classd invee using he poposed scheme is pefomed wih a vaiaion of he load powe fom 0% o 00% by vaying D PDM fom 0% o 00%. A high swiching fuency (f s ) of 5 khz is chosen and a low fuency (f PDM ) of 5 Hz is chosen o BLE I PECIFICATION OF CLAD INVERTER AND IH LOAD YTEM Componens ymbol Values Powe P 00 W500W wiching f s 5 khz3khz fuency DClink capacio C f 00 e6 Resisance R 57 ohms Inducance L e30.05 e3h Resonan f 0 khz7khz Fuency PDM fuency f PDM 5 Hz Resonan Capacio C.59 e6f avoid acousic noise. The simulaion is caied ou fo diffeen values of D PDM. Fo veificaion of he aed oupu powe, he D PDM conol signal is geneaed a 00% of he duy cycle as shown in Fig. 8. The simulaed esul of he oupu volage unde a full load is shown in Fig. 8. A zoomed view of he oupu volage is given in Fig. 8(c). Unde he full load condiion,

10 74 Jounal of Powe Eleconics, Vol. 5, No., Januay 05 (c) (d) Fig. 3. Expeimenal esuls a 0% D PDM. D PDM conol signal and high fuency swiching signal (V/div, 0.0s/div) PDM gae signals o and (V/div, 50µs/div) (c) Oupu volage a 0% D PDM (40V/div,50µs/div) (d) Oupu cuen a 0% D PDM (A/div,5µs) he oupu cuen flows coninuously due o he 00% D PDM as shown in Fig. 8(d). A zoomed view of I o is given in Fig. 8(e). The oupu powe coesponding o he 00% D PDM is shown in Fig. 8(f). I can be obseved ha fo a modulaion index value ual o one, he maximum oupu powe of he invee is obained. Gae pulses ae geneaed wih a D PDM of 50% of he duy cycle. The coesponding conol signal is shown in Fig. 9. The simulaed esuls of V o and I o a a 50% D PDM ae shown in Figs. 9 and 9(c), especively. I can be obseved fom he wavefoms ha V o and I o ae disconinuous in naue. When D PDM is 50%, he aveage cuen ges lowe due o he disconinuous flow of I o. This causes a decemen in he aveage oupu powe as shown in Fig. 9(d). Thee ae no cuen spikes because he high fuency and low fuency PDM swiching signals ae synchonized a he on and off ime. The D PDM conol signal a 0% is shown in Fig. 0. The simulaed esuls of V o and a zoomed view of V o a a 0% D PDM ae shown in Figs. 0 and 0(c), especively. The coesponding oupu cuen I o and a zoomed view ae shown in Figs. 0(d) and 0(e), especively. Wih a 0% D PDM, he aveage oupu powe sill ges deceased due o he disconinuous flow of I o. ince he swiching fuency is mainained close o he esonan fuency of he load by he PLL, even wih he change in D PDM fom 0% o 00%, ZV of he swich can be achieved duing he un off condiion. This can be obseved fom Figs. and. In boh of he wavefoms, he ise in he swich cuen akes place duing he zeo sae of he swich volage. These wavefoms ensue he ZV un off opeaing condiion unde any powe level achieved wih vaiaions of he conol vaiable D PDM. Due o he ZV condiion, he swiching losses ae educed. This validaes he poposed PLL based VDC PDM conol saegy applied o a IH sysem. To validae he poposed scheme in a classd invee cicui, an expeimenal laboaoy seup was fabicaed. The classd invee is supplied using a full bidge diode ecifie. The ecifie was consuced using fou IN5408 diode swiches. The classd invee was consuced using wo powe swiches fo DCAC convesion. The powe swiches wee MOFETs (IRF840) which can wihsand a maximum volage and cuen of 500V and 8A, especively. An IH load was buil by using a coil having an oue diamee of 0mm and a hickness of 8mm. A wokpiece of 00*45mm has been chosen as he heaing load. The conol cicui fo he IH sysem is implemened wih he PDM conol saegy using a PIC6F877A mico conolle. The hadwae layou of he sysem is shown in Fig.. The VDC PDM scheme is validaed wih his hadwae seup fo a D PDM of 00% and 0%. Fo a 00% D PDM, high fuency pulses ae allowed o he swiches wihou modulaion as shown in Fig.. The expeimenal oupu volage and oupu cuen a a 00% D PDM ae shown in Figs. (c) and (d), especively, whee V o and I o coninuously delive he aed oupu powe. The D PDM conol signal a 0% and he high fuency signals ae shown in Fig 3. The swiching pulses fo swiches and ae shown in Fig 3. These pulses ae diven hough a gae dive cicui (IR0) o he swiches. Wih he same PDM conol signal, he expeimenal oupu volage is shown in Fig. 3(c). The expeimenal oupu

11 Phase Locked Loop based Pulse Densiy Modulaion cheme fo 75 (c) (d) (e) Fig. 4. Gae pulses o he swiches and he oupu volage (3kHz wih D PDM of 50%) (5V/div,50V/div,00µs/div). Oupu volage of he invee wih 3kHz fuency (40V/div,00µs/div). (c) Zoomed view of he oupu volage shown in (0V/div,0µs/div). (d) Tansien peiod fo he ise in oupu volage shown in (5V/div,µs/div). (e) Volage acoss he swich (V s ) and Cuen hough he swich (I s ) (0V/div,5A/div,0µs/div). (c) Fig. 5. Vaiaion of oupu powe fo diffeen values of D PDM. Vaiaion of invee module losses fo diffeen values of inpu powe. (c) Vaiaion of oupu powe fo diffeen values of inpu powe. cuen a a 0% D PDM is shown in Fig. 3(d). The opeaion of he invee cicui unde a 3 khz opeaing fuency wih a inceased load of 500W has been pefomed. The coesponding hadwae esuls of he gae pulses and he oupu volage ae shown in Figs. 4 and 4, especively. Fig. 4(c) shows he ansiion of he oupu fom he zeo powe peiod o he powe injecion peiod. The ansien peiod fo he ise in he oupu volage of he invee can be seen bee in Fig. 4(d). I akes 0ns o ge seled o he seady sae value. The volage acoss swich (V s ) and he cuen hough swich (I s ) duing he uning off condiion ae shown in Fig. 4(e). I can be obseved fom he wavefom ha he swiches undego he ZV condiion a he un off insan. Unde he fixed fuency opeaing condiion, he pesened VDC PDM conol ensues a wide powe vaiaion wih a vaiaion of he conol vaiable D PDM as shown in Fig. 5. Thee is a linea elaionship beween D PDM and he oupu powe. The vaiaion of he invee module losses fo diffeen values of he inpu powe is shown in Fig. 5. Wih a consan swiching fuency, he sof swiching condiion is mainained a diffeen values of he load powe. ince he ZV condiion is mainained in he poposed echnique, he invee losses ae educed when compaed o he PWM mehod. Fo diffeen inpu powes, he oupu powe of he convenional PWM and he poposed VDC PDM conol ae compaed in Fig. 5(c). I can be obseved ha he poposed conol scheme impoves he oupu powe moe han convenional one due o he educion in swiching losses. The claims of he poposed sudy compaed o he sudies discussed in ohe papes ae as follows:. The poposed

12 76 Jounal of Powe Eleconics, Vol. 5, No., Januay 05 sudy analyzes he PLL based VDC PDM conol fo he widely used half bidge invee cicui. This pape compaes he convenional PLL based PWM and he PDM conol logic wih espec o losses and oupu powe.. In he hadwae, he D PDM conol signal is geneaed by a PIC micoconolle. The ansien ime aken by he conol cicui o lock he esonan fuency a saup duaion is less due o he use of he micoconolle. When he locking ime is less, he swiching losses ae also less duing he saup duaion. The cos of he micoconolle is also less. 3. In he poposed sudy, he PDM conol cicui adjuss he oupu powe by vaying he PDM duy cycle insead of by vaying he PDM swiching fuency. i.e. The ime peiod of he low fuency signal (T PDM ) is no vaied. This avoids he poblems due o acousic noise. V. CONCLUION This pape pesened a PLL based VDC PDM powe conol scheme in a classd invee fo an IH load. The design and analysis of he invee fo IH applicaions ae pesened. The pinciple of he poposed conol scheme fo powe conol is also discussed in deail. The pefomance of he poposed conol scheme is veified hough simulaion esuls. Expeimenal veificaion of he VDC PDM scheme is also done wih a pooype module. Fom he simulaion and expeimenal esuls i can be concluded ha he conol scheme has he following advanages: a simple configuaion, a wide load powe conol ange, educed swiching losses and high efficiency when compaed o he convenional PWM scheme. The ZV opeaing condiion is guaaneed in he load ange of 0% o 00%. I has been obseved ha wih a D PDM below 0%, he load cuen is pulsaing and causes he NONZV condiion. REFERENCE [] J. Aceo, J. M. Bud ıo, L. A. Baag an, D. N. avao, R. Alonso, J. R. Gacia, F. Monede, P. Hen andez,. Lloene, and I. Gade, The domesic inducion heaing appliance: An oveview of ecen eseach, in Poc. Appl. Powe Elecon. Conf. Expo., pp , 008. [] A. Fujia, H. adakaa, I. Hioa, H. Omoi, and M. 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13 Phase Locked Loop based Pulse Densiy Modulaion cheme fo 77 heaing appliances, IEEE Tans. Powe Elecon, Vol. 6, No. 5, pp , May 0. [0] O. Luc ıa, J. M. Bud ıo, I. Mill an, J. Aceo, and D. Puyal, Loadadapive conol algoihm of halfbidge seies esonan invee fo domesic inducion heaing, IEEE Tans. Ind. Elecon., Vol. 56, No. 8, pp , Aug [] K. D. T. Ngo, Analysis of a seies esonan convee pulse widh modulaed o cuen conolled fo low swiching loss, IEEE Tans. Powe Elecon., Vol. 3, No., pp. 5563, Jan [] J. K. Byun, K. Choi, H.. Roh, and. Y. Hahn, Opimal design pocedue fo a pacical inducion heaing cooke, IEEE Tans. Magn., Vol. 36, No. 4, pp , Jul [3] O. Luc ıa, C. Caeeo, D. Palacios, D. Valeau, and J. M. Bud ıo, Configuable snubbe newok fo efficiency opimizaion of esonan convees applied o muliload inducion heaing, Elecon. Le., Vol. 47, No. 7, pp , Aug. 0. [4] G. C. Hsieh, and J. C. Hung, Phase lock loop echniquesa suvey, IEEE Tans. Indusial Elecon., Vol. 43, No. 6, pp , Dec.997. [5] H. Kaaca and. Kılın, Nonlinea modeling and analysis of esonan invee uning loops wih volagepump phasefuency deeco, IEEE Tans. Powe Elecon., Vol. 0, No. 5, pp. 0008, ep [6] O. Luc ıa, L. A. Baag an, J. M. Bud ıo, O. Jim enez, D. Navao, and I. Uiza, A vesaile powe eleconics esbench achiecue applied o domesic inducion heaing, IEEE Tans. Ind. Elecon., Vol. 58, No. 3, pp , Ma. 0. [7] H. anago, O. Luc ıa, A. Mediano, and J. M. Bud ıo, Modulaion scheme fo impoved opeaion of a RBIGBT based esonan invee applied o domesic inducion heaing, IEEE Tans. Ind. Elecon., Vol. 60, No. 5, pp , May 03. [8] H. anago, A. Mediano, and O. Luc ıa, High efficiency AC AC powe eleconic convee applied o domesic inducion heaing, IEEE Tans. Powe Elecon., Vol. 7, No. 8, pp , Aug. 0. Booma Nagaajan eceived he D.E.E.E. fom Thiagaaja Polyechnic, alem, Tamil Nadu, India, in 997, he B.. degee in Elecical Eleconics Engineeing fom Madas Univesiy, Chennai, India, in 000, and he Mase of Engineeing in Powe ysems Engineeing fom he College of Engineeing, Guindy, Anna Univesiy, Chennai, India, in 007. he is pesenly a Reseach chola in he Depamen of Elecical and Eleconics Engineeing, Jeusalem College of Engineeing, Cene fo Collaboaive Reseach, Chennai, India. he has 4 yeas of eaching expeience. he has published ove 5 echnical papes in naional and inenaional confeences poceedings and jounals. He cuen eseach ineess include esonan invees fo inducion heaing, inelligen conolles and powe qualiy. Rama Reddy ahi eceived his D.E.E.E. fom i Mullapudi Venkaaaya Memoial Polyechnic (MVM Polyechnic), Tanuku, Andha Padesh, India, and his Associae Membe of The Insiuion of Enginees India (A.M.I.E.) degee ceificae in Elecical Engineeing fom Insiuion of Enginees, India. He also eceived his Mase of Engineeing in Powe ysems and his Ph.D. degee in Powe Eleconics fom Anna Univesiy, Chennai, India. He is pesenly a Pofesso in he Depamen of Elecical and Eleconics Engineeing, Jeusalem College of Engineeing, Chennai, India. He has published ove 00 echnical papes in naional and inenaional confeences poceedings and jounals. He has secued an A.M.I.E. Insiuion Gold Medal fo obaining he highes maks. He has secued an AIMO Bes Pojec Awad, an ITE Naional Level Bes Teache Awad, and an IET CLN Diamond alue Awad. He has 5 yeas of eaching expeience. His cuen eseach ineess include esonan convees and FACT. He has eceived funds fo MODROB and Reseach and Developmen fom he All India Council of Technical Educaion (AICTE). He is a life membe of he Insiuion of Enginees (India), he Indian ociey fo Technical Educaion, he ysems ociey of India, he ociey of Powe Enginees, and he Insiuion of Eleconics and Telecommunicaion Enginees (India).