Power Control Assessment in Induction Heating Systems with Voltage Source Inverter and Resonant L-LC Load

Transcription

1 Annls of the nversty of Crov, Electrcl Engneerng seres, No. 38, 04; ISSN Power Control Assessment n Inucton Hetng Systems wth Voltge Source Inverter n esonnt L-LC Lo Mhel Popescu, Alexnru Btolenu, n Alexnr Ptrcu Fculty of Electrcl Engneerng nversty of Crov Crov, omn mpopescu@em.ucv.ro, lex.tolenu@em.ucv.ro, ptrscu@em.ucv.ro Astrct The ttenton n ths pper s recte to the power control n n nucton hetng system for semless ppes consstng of sngle-phse voltge source nverter wth L-LC resonnt lo supple y three-phse full controlle rge rectfer. The mxml power trnsfer from the nverter output to the work pece s ensure y the proper esgn of the mtchng nuctor. The power control s cheve through the nverter output current y mkng use of Proportonl-Integrtor-Dervtve controller esgne ccorng to the Moulus Optmum crteron n essler vrnt. An expermentl pltform se on SPACE DS03 control or s use for the prctcl mplementton of the control system. It works together wth Mtl/Smulnk envronment n the conceve grphcl user nterfce llows nterctng wth the experment. The expermentl setup of the nucton hetng system s presente n the ssessment of the control system performnce uner fferent tests s performe. Depenng on the prescre vlue of the nverter output current n the mpose opertng frequency, fferent stutons my occur. The possltes of mnshng the swtchng losses through zero-current swtchng n of ncresng the power when the opertng frequency s over the resonnce vlue re lso ponte out. All the results llustrte the proper operton n goo performnce of the control system. I. INTODCTION Clerly, the most common power genertor opte n the nustrl pplctons of the energy-effcent process of nucton hetng (IH) s the nrect c c sttc converter wth ether full-rge current source nverter (CSI) or full-rge voltge source nverter (VSI) []-[]. Due to the vntges of VSIs, such s etter converter utlzton, smple lmtng the swtchng overvoltge n smplest chevement of zero-current swtchng, they re preferre n the moern nucton hetng systems [], [4]- [7], [], [], [4]. Compre to the trtonl resonnt lo of VSI consstng of the seres crcut of hetng col n compenston cpctor, the newer topology clle seresprllel L-LC lo les to smller current through the trnsformer seconry n n ncrese short-crcut mmunty [4], [5], [7], [9], [], [3]. In ths structure, mtchng nuctor s e t the VSI output, n seres wth the prllel resonnt tnk (the hetng col n prllel wth the compenston cpctor). Thus, y optng the prllel resonnce, the current t the nverter output s n ctve current n the current through the nucton col s lmost snusol. eferrng to the opertng frequency of the voltge source nverter, t s relte to the resonnce frequency of the resonnt lo n must e contnuously pte to the lo contons. Mostly, phse-locke loop (PLL) ntegrte crcut evces re use to trck the resonnt frequency throughout the system operton [], [5]. As regrs the control of the power trnsferre to the lo, there re two possltes. The former nvolves the use of full-controlle lne-commutte rectfer [4], [5], [6], wheres the ltter requres chrgng the resonnt nverter to ensure the power control n ton to the pproprte opertng frequency [6], [], [], [7]-[9]. The nucton hetng system tken nto conserton n ths pper conssts of resonnt L-LC lo fe y sngle-phse full-rge VSI v three-phse fullcontrolle rge rectfer (Fg. ). The pper s orgnze s follows. Secton II summrzes the opte confgurton of the nucton hetng system. The next secton s ntene to synthesze the power control crcut y mkng use of trnsfer functons-se pproch. In Secton IV, the expermentl setup n results of some tests re presente to vlte the opte techncl soluton. Fnlly, the mn conclusons of the reserch re gven. II. THE SYSTEM OF INDCTION HEATIN In ths pper, the hetng process of the semless ppes s tken nto conserton. The hete pece moves through the nuctor t preset spee n the requre output power epens on the grent of temperture. As shown n Fg., the prllel resonnt lo conssts of the equvlent crcut of the nucton col n hete pece (nuctnce L n resstnce ) n prllel wth the compenston cpctor C. By mens of the mtchng nuctor (nuctnce L n resstnce ), the power trnsfer from the nverter output to the nucton col s mxmze [9]. The IBTs-se sngle-phse fullrge VSI proves squre wve voltge to the lo crcut n the swtchng frequency must trcks the resonnt frequency. 70

2 Annls of the nversty of Crov, Electrcl Engneerng seres, No. 38, 04; ISSN Control r Three-phse power trnsformer Fullcontrolle rge rectfer u L C u IBTs sngle-phse full-rge VSI u L u c C L Equvlent IH lo Prllel resonnt lo As the resonnt frequency epens, on the one hn, on the hete ppe, the opte nuctor n compenston cpctnce, n, on the other hn, on the ynmc vrton of ther prmeters, n uto-ptve frequency control loop s requre. In ton, to fcltte the swtchng process of nverter s IBTs through zerocurrent swtchng, the prescre frequency shoul slghtly excee the resonnce vlue. In the opte structure of the control system, the nverter output current s regulte through three-phse full-controlle rectfer, n orer to hnle the power trnsmtte to the lo. III. SYNTHESIS OF THE POWE CONTOL SYSTEM The control loop of the nverter output current s synthesze strtng from the lock grm n Fg.. The followng trnsfer functons re llustrte: C (s) - trnsfer functon of the current controller; (s) - trnsfer functon of the three-phse full-rge controlle rectfer; DC (s) - trnsfer functon of the DC-lnk crcut; VSI (s) - trnsfer functon of the sngle-phse rge VSI; OT (s) - trnsfer functon of the equvlent output lo; T - trnsfer functon of the current trnsucer. A. The trnsfer Functons n the Forwr Pth The three-phse full-controlle rectfer s consere s frst orer element n the ssocte trnsfer functon s [0]: s c s s Fg.. Block grm of the opte nucton hetng system. st, () where the proportonl tme constnt ( ) epens on the rms lne-to-lne voltge n the trnsformer seconry ( s ),.e. 3, () s n the ntegrl tme constnt (T μ ) s gven y the verge e-tme of the frng crcut n epens of the supply frequency. The trnsfer functon of the DC-lnk crcut s expresse strtng from the followng fferentl equton t the rectfer output uner no lo conton: u L u, (3) t where the occurrng qunttes re llustrte n Fg., except, whch s the DC-lnk resstnce. Tkng nto ccount tht u t, (4) C the Lplce trnsform of (3) les to: ( s ) L Thus, DC C s ( s ) C s ( s ) ( s ). (5) s s s C s L C s. (6) After ntroucng the electrc (T e ) n electromgnetc (T em ) tme constnts of the DC-lnk crcut,.e. expresson (6) ecomes: Te C em L DC T, (7). (8) T s T T s s e The trnsfer functon of the sngle-phse squre wve ( rns) voltge source nverter s expresse se on the rms funmentl component of the output voltge [], em e + - E(s) Current controller C (s) c (s ) (s DC-lnk (s) (s) ectfer (s) Voltge source Mtchng (s Equvlent I (s) I ) crcut nverter nuctor ) IH lo + + (s) DC (s) VSI (s) Compensto n cpctor I c (s) Current trnsucer OT (s) T Fg.. Trnsfer functons-se lock grm of the nucton hetng system. 7

3 Annls of the nversty of Crov, Electrcl Engneerng seres, No. 38, 04; ISSN (9) It results tht VSI contns only the proportonl component VSI, s s VSI s VSI. (0) In orer to express the trnsfer functon of the equvlent output crcut (mtchng nuctor n resonnt crcut), n terms of rto of Lplce trnsforms of nverter output current n nverter output voltge, the rchhoff's lws n the Lplce omn re pple. Thus, the followng equtons re otne: ( s ) ( s ) I ( s ) s L I ( s ) ; () I ( s ) I ( s ) I ( s ) ; () s L I ( s ) c ( s ) ; (3) ( s ) I c( s ). (4) s C They llow expressng I (s) n (s) s functon of (s): I ( s ) s C s L I ( s ) ; (5) s L ( s ) I( s ). (6) s C s L After replcng (6) nto (), the equvlent output crcut trnsfer functon s otne n the followng form: OT s I s s s L s C s L s L s C s L C Assumng tht s L. s L (7) s L s L, (8) s C s L C when the frequency excees the resonnce vlue n fter ntroucng the electromgnetc tme constnt of the mtchng nuctor ( Tem L ), the fnl expresson of OT (s) s otne: OT s L s T em. (9) s B. Desgn of Current Controller The prmeters of the nverter current controller re synthesze n ccornce wth the Moulus Optmum crteron n essler vrnt [6], []. Frst, the trnsfer functon of the fxe prt s expresse: F s s s s s st Te s TemTe s T s. em DC VSI OT (0) As t cn e seen n (0), F (s) contns two omnnt tme constnts (T e n T em ) tht cn e remove y choosng PID-type current controller. The trnsfer functon of the opte PID current controller s wrtten s: C s pt s TT s, () T s where p s the proportonl constnt n T n T re the ntegrl n ervtve tme constnts, respectvely. Then, the ttenton s recte to oth open-loop n close-loop unty feeck trnsfer functons ( (s) n (s)): s C s F s T ; () s s s. (3) Bse on (0) n (), the fnl form of (s),.e. T s st st st pt s TT s st T s T T s em e em e em, (4) llows removng the omnnt tme constnts of the DClnk crcut through the followng contons: T T ; (5) e TT T Tem. (6) Te p Next, tkng nto ccount (5), (6) n (4), the followng form of (3) s otne: s T st p st st em. (7) Accorng to Moulus Optmum crteron, t s foun tht only the coeffcent of n the enomntor of expresson of the squre of (s) moulus contns fference []: 7

4 Annls of the nversty of Crov, Electrcl Engneerng seres, No. 38, 04; ISSN T T em T T T. (8) T Thus, conton of cncellng gves the expresson of ntegrl constnt, T 4 T T T em. (9) Then, contons (5) n (6) prove the followng expressons for the proportonl n ervtve tme constnts: p 4 T T e T T em ; (30) TeTem T. (3) 4 T T Tem The otne expressons (from (9) to (3)) for the prmeters of the PID controller show tht they o not epen on the lo prmeters. IV. POWE CONTOL SYSTEM PEFOMANCE ASSESSMENT The ssessment of the control system performnce ws crre out y usng n expermentl setup se on the electrcl scheme shown n Fg. 3. As shown, on the power supply se, there re the threephse contctors ( 0, n ) llowng the generl connecton n the chrgng of the DC-lnk cpctor through the lmtng resstors. The nrect c c power converter conssts of: - three-phse full-controlle rge rectfer wth thyrstors (600 A, 800 V); - sngle-phse voltge source nverter wth IBTs (00 A, 700 V); -. DC-lnk crcut compose of flterng col (L ) of 0. mh/500a n flterng cpctor (C ) of 000μF/00V). At the nverter output, there s mtchng col of 5 turns, whch s me of copper tue - Ø 4 mm n hs four ntermete sockets of fve turns ech (Fg. 4). Its nner meter s 70 mm n the length s 8 cm. In orer to mxmze the ctve power trnsmtte to the lo, the optml numer of 0 turns of the mtchng col [9] ws chosen for ll experments. The cpctnce of compenston cpctor s 64F (=3000 V, I=.6 ka, f=0 khz). The workng pece to e hete s Cron steel ppe % whose outer meter s 68 cm, n wll thckness s 3mm. In ths concrete stuton, the controller s prmeters re: T = s; T = s; p = The control n mngement of the expermentl moel were performe on SPACE DS03-se pltform. The control or s equppe wth PowerPC 750X processor runnng t CP clock of Hz for fst flotng-pont clculton. The conceve grphcl user nterfce llows nterctng wth the experment, nclung the mposton of the coeffcent of forcng the cpctve component ( c ) n orer to ncrese the swtchng frequency over the resonnce frequency. In ths mnner, the IBTs zerocurrent swtchng cn e cheve. ) ) ) Fg. 3. Pctures of the expermentl setup: ) nverter; ) nuctor; c) mtchng col; ) coolng equpment. c) L V V 3 0 L T Th Th 3 Th 5 TI L / TI S T T T 3 A A T C T L / C L A V 4 V Th 4 Th 6 Th Fg. 4. The electrcl scheme of the nucton hetng system for expermentl setup. 73

5 Annls of the nversty of Crov, Electrcl Engneerng seres, No. 38, 04; ISSN Moreover, ncresng frequency s wy of ncresng the power trnsmtte to the lo when the rectfer cplty s reche. After the system ntlzton process (chrgng the DC-lnk cpctor), the control system of the nverter output current s strte y settng the esre vlue n vlton of the controller output. The control system response n the wveforms of the mn qunttes re prove through the grphcl user nterfce. In the frst set of tests, the prescre vlue of the nverter output current s 300 A (Fg. 5). As shown n Fg. 5, when the opertng frequency s equl to the resonnt frequency (5488 Hz), even f the mxml vlue the DC-lnk voltge (53 V) s mpose y the control loop, t s nsuffcent to cheve the prescre current. The nverter output current t resonnce s low n ts rms vlue s of out 43 A (Fg. 5 n 5). However, y forcng the cpctve component of the current t the nverter output ( c =.38), the prescre current s cheve wthout ny over-current (Fg. 5c). The nverter nput voltge fe y rectfer s mxml n the power requre y the resonnt lo s prove y the vlue of the opertng frequency (598 Hz), over the resonnce vlue. The wveforms of voltge n current t the nverter output (Fg. 5) ncte hgh swtchng losses, s the zero-current swtchng s not cheve. It ws foun tht the IBTs soft swtchng t zero-current correspons to c =.3 (Fg. 5f), whch mens swtchng frequency of 565 Hz. Ovously, the set current of 300 A cn not e otne n ths cse (Fg. 5e). The responses of the current controller n Fg. 6, Fg. 7 n Fg. 8 show tht the mnml vlue of the coeffcent c tht ensures the chevement the prescre current ecreses s the prescre current ecreses. It must e note tht, n ll these cses, the mxml level of the rectfer output voltge ws reche. As t cn e seen n Fg. 8 compre to Fg. 6 n Fg. 7, the set current s otne uner zero-current swtchng conton. When the esre vlue of the nverter output current s equl to or ellow 78 A, the current control loop s le to prove the requre current wth mnml swtchng losses (zero-current swtchng) y proper rectfer output voltge whch s lower thn 53 V. For nstnce, when the prescre current s 30 A, t cn e otne t zerocurrent swtchng ( c =.3) for n nverter nput voltge of 96 V (Fg. 9). As epcte n Fg. 0, the current flowng through nuctor s lmost snusol n n opposton to the slghtly storte current through the compenstng cpctor. As expecte, the nverter output current s sgnfcntly lower thn oth nuctor n cpctor currents., I (A) = 300 A; c = () u (V), (A) = 300 A; c = () = 300 A; c =.38 = 300 A; c =.38, I (A) (c) u (V), (A) () = 300 A; c =.3 = 300 A; c =.3, I (A) (e) u (V), (A) (f) Fg. 5. esponse of the current controller ((), (c), (e)) n wveforms of voltge n current ((), (), (f)) t the nverter output for prescre current of 300A n fferent vlues of c. 74

6 Annls of the nversty of Crov, Electrcl Engneerng seres, No. 38, 04; ISSN = 00 A; c =.3 = 00 A; c =.3, I (A) () u (V), (A) () Fg. 6. esponse of the current controller () n wveforms of voltge n current t the nverter output () for prescre current of 00A n c =.3. = 00 A; c =.7 = 00 A; c =.7 I, I (A) () u (V), (A) () Fg. 7. esponse of the current controller () n wveforms of voltge n current t the nverter output () for prescre current of 00A n c =.7. = 78 A; c =.3 = 78 A; c =.3, I (A) () u (V), (A) () Fg. 8. esponse of the current controller () n wveforms of voltge n current t the nverter output () for prescre current of 78A n c =.3. = 30 A; c =.3 = 30 A; c =.3 I, I (A) () u (V), (A) () Fg. 9. esponse of the current controller () n wveforms of voltge n current t the nverter output () for prescre current of 30A n c =.3. 75

7 Annls of the nversty of Crov, Electrcl Engneerng seres, No. 38, 04; ISSN = 30 A; c =.3 = 30 A; c =.3, c, (A) c () u (V), (A) u () Fg. 0. Wveforms of the qunttes t the nverter output for prescre current of 30A n c =.3. The grphcl epenence n Fg. llustrtes the mnml vlues of the forcng coeffcent c for whch fferent prescre currents cn e otne. As shown, wthout forcng the cpctve component of the lo current ( c =), menng the opertng t resonnt frequency, mxml current of 43 A rms cn e ensure y the rectfer control. As prevously stte, y optng c =.3, the zerocurrent swtchng s otne. In ths cse, the nverter cn prove mxml current of 78 A. As the esre current ncreses, the requre vlue of c ncreses n the resulte opertng frequency ncreses..4 c (A) Fg.. Coeffcent c versus the mxml nverter output current V. CONCLSIONS In the nucton hetng system for semless ppes wth voltge source nverter n resonnt L-LC lo, the opte control of the power trnsferre to the lo s se on the regulton of the nverter output current. A PID controller llowng the control of the nverter nput voltge n the posslty of ncresng the opertng frequency over the resonnt vlue re oth tken nto conserton. It s foune tht, for the resultng frequency prove y the control loop (etermne y lo n coeffcent of forcng the cpctve component of the current), two stutons my occur,.e.:. The mxml DC-lnk voltge s nsuffcent to cheve the prescre current;. The DC-lnk voltge vlue llows chevng the prescre current. For oth stutons, t s shown tht the current control loop opertes properly. The operton t zero-current swtchng s otne y ncresng the control frequency over the resonnce vlue s result of ncresng the cpctve component of the nverter current. Strtng from the fnng tht there re stutons n whch the prescre current cn not e otne even uner the mxml rectfe voltge n tht n ncrese of the nverter output current s possle y ncresng the control frequency, soluton to ncrese the flexlty of the control system cn e entfe. Ths soluton wll e the suject of future nvestgtons n cn e mterlze y ntroucng loop for clcultng the coeffcent of forcng the cpctve current, se on the current error. ACNOWLEDMENT Ths work s the result of reserch ctvty wthn rnt 35/..0, POSCCE-A-O EFEENCES [] F.P. Dwson n P. Jn, A comprson of lo commutte nverter systems for nucton hetng n meltng pplctons, IEEE Trns. Power Electron., vol. 6. no. 3, pp , July 99. [] A. Nmmln, J. Shokrollh Moghn, n J. Mlmonfre, A current-fe prllel resonnt push-pull nverter wth new csce col flux control for nucton hetng pplctons, Journl of Power Electroncs, vol., no. 5, pp , Sept. 0. [3] V. unev, D. Loveless, n. Cook, Hnook of Inucton Hetng, Mrcel Dekker, 003, ch. 8. [4] S. Deckerhoff, M. J. yn, n. W. De Doncker, Desgn of n IBT-se LCL resonnt nverter for hgh-frequency nucton hetng, n Proc. 34th Inustry Applctons Conference, vol. 3, oct. 3-7, 999, pp [5] J.M. Esp, E.J. Dee, E. Nvrro, E. Snchs, n A. Ferreres Fetures n esgn of the voltge-fe L-LC resonnt nverter for nucton hetng, n Proc. Power Electroncs Speclsts Conference, 999, pp [6] J.M. Burío, L.A. Brrgán, F. Montere, D. Nvrro, n J. Acero, Asymmetrcl voltge-cncellton control for full-rge seres resonnt nverters, IEEE Trns. Power Electron., vol. 9, no., pp , Mr [7] J. M. Esp Huert, E. J. Dee rc Sntmr,. rc l, n J. Cstello Moreno, Desgn of the L-LC resonnt nverter for nucton hetng se on ts equvlent SI, IEEE Trns. In. Electron., vol. 54, no. 6, pp , Dec

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