A Novel Concept for Transformer Volt Second Balancing of a VIENNA Rectifier III Based on Direct Magnetizing Current Measurement

Transcription

1 A Novel Concep for ransformer Vol Second Balancing of a VIENNA Recifier III Based on Direc Magneizing Curren Measuremen Franz Sögerer Johann W. Kolar Uwe Drofenik echnical Universiy Vienna Dep. of Elecrical Drives and Machines Power Elecronics Group Gusshaussrasse 7/37 A-4 Vienna, AUSRIA / Europe el Fax, fsoegerer@ieam.uwien.ac.a ABSRAC For a VIENNA Recifier III differen urn-on and urn-off delay imes of he power ransisors and differen on-sae volages of he valves would cause an unbalance of he posiive and negaive vol seconds applied o he high frequency ransformer wihin a pulse period and/or resul in ransformer sauraion wihou addiional measures. his paper proposes a novel concep for acively ensuring a symmeric magneizaion wih swiching frequency of he ransformer magneic core of a VIENNA Recifier III based on direc measuremen of he magneizing curren. he magneizing curren is deermined by subracion of he ransformer primary and he secondary currens being weighed according o he ransformer urns raio. he subracion is realized by magneic compensaion employing a hrough-hole DC curren ransducer. A deviaion from a symmeric magneizaion wihin a pulse period is deeced and used by a conroller for closed-loop balancing of he vol seconds applied o he ransformer primary in order o eliminae an exising asymmery. he conroller is designed based on sampled daa sysem heory. he heoreical consideraions and he conroller dimensioning are verified by experimenal resuls gained from a 8.5kW prooype of he VIENNA Recifier III. inpu filer capacior volage cause a deviaion of he acual volage applied o he ransformer primary side from he ideal volage shape which is assumed for he calculaion of he relaive on-imes of he power ransisors in order o guaranee a ransformer vol seconds balance. A consideraion of he parasiic effecs in he course of he calculaion of he ransisor on imes is no possible due o he dependence of he componens on he sysem load sae, juncion emperaure ec. herefore, he ransformer primary volage conains besides pulse-frequency componens also low-frequency harmonics ha may cause sauraion of he ransformer magneic core. A symmerizaion of he magneizaion by passive means, i.e., by he inserion of ohmic resisors and/or by an arificial increase of parasiic resisances of he wiring is no possible and/or sufficien for high power and highly efficien sysems []. Keywords: VIENNA Recifier, ransformer Vol Second Balancing, ransformer Magneizing Curren. Inroducion In [] a novel single-sage hree-phase PWM recifier sysem wih sinusoidal inpu currens and high-frequency isolaed and conrolled oupu volage has been inroduced (cf. Fig.). As shown in Fig. segmens of he AC-side line-o-line volage are applied o he ransformer primary winding. he secondary side volage is recified and filered by a low-pass filer L O,C O. For suppressing swiching frequency harmonics of he recifier inpu curren i U,i which is formed by pulse-widh modulaed segmens of he ransformed oupu curren an inpu filer has o be employed. his resuls in a sinusoidal ime-behavior of he curren drawn from mains. he magneizaion of he ransformer ideally is symmeric and wih pulse frequency, i.e. no low-frequency componens are presen under he assumpion of ideal componens. However, in pracice he power semiconducor on-sae volages, ohmic losses, finie ransisor urn-off imes, delayimes of he ransisor gae drive circuis and he ripple of he u, / P u U,R u U,S u U,S uu,r Fig.: Power circui of he VIENNA Recifier III and local ime-behavior of he ransformer primary volage u, ( P denoes a pulse period), he balance of he posiive and negaive vol seconds applied o he ransformer primary wihin a pulse half period is poined ou by doed areas. P

2 Insering an air-gap in he ransformer core would resul in an increase of he maximum olerable magneizing curren [3], which would reduce he resisance values required for a passive symmerizaion. However, a magneizing curren being oo high in magniude resuls in a significan low-frequency harmonic disorion of he mains curren and in an increase of he conducion losses of he power semiconducors. Alernaively, as proposed in [3] (cf. pp. 3-3), [4] a blocking capacior could be conneced in series wih he ransformer primary for blocking any low-frequency componens of he ransformer primary volage. he volage which hen acually is applied o he ransformer primary winding does only conain componens wih swiching frequency. However, as has become clear by a closer experimenal analysis of his concep, a resonance beween he main inducance of he ransformer and he blocking capacior migh occur. As described in [4], [5] also hall-sensors or small inducors could be employed for a direc measuremen of he ransformer magneic flux. However, aiming for low manufacuring effor in he case a hand he applicaion of such conceps is no feasible. In his paper a novel concep for guaraneeing a symmeric magneizaion of he high-frequency ransformer of he VIENNA Recifier III is presened [6]. here, he magneizing curren is deermined by subracing he ransformer secondary curren and he ransformer primary curren being weighed according o he ransformer urns raio. he subracion which is performed by muual magneic compensaion, i.e. by a DC curren ransducer, resuls in a signal which is used as inpu of a closed loop magneizing curren conrol which guaranees a symmeric ransformer magneizaion by properly changing he local average value of he ransformer primary volage. he following discussion is based on he magneizing curren i m = i m N /N referred o he primary side. 3 Conrol of he Magneizing Curren Before analyzing he srucure of he magneizing curren conroller in deail a shor descripion of he conrol of he VIENNA Recifier III is given. Because of he complexiy of he sysem and/or he high compuaional effor for calculaing he swiching imes of he power ransisors he conrol of he sysem is performed by a digial signal processor (ADSP 6). During each pulse half period ( / P = 6μs ) he DSP akes samples of he inpu volages and he oupu volage of he converer and compues he urn-on imes of he power ransisors S i (i=,,3,,-) under consideraion of a pulse-frequency symmeric magneizaion of he ransformer and a sinusoidal guidance of he recifier inpu currens. Since he measuremen of he inpu values and he compuaion of he urn-on imes akes abou μs he calculaed swiching imes are available a he end of he acual pulse half period and, herefore, are applied wihin he nex pulse half period. he calculaed duraion of he on-imes of he swiches are ransformed ino gae-signals of he power ransisors [] by hree PWM oupu sages (implemened by a PLD, ALERA EPM 78) and a logic circui (realized by an EPROM). magneizing curren sensor u, i, N N i, u, n = N N n = magneizing curren Direc Measuremen of he ransformer Magneizing Curren As described above he magneizing curren is measured by subracion of he weighed ransformer primary and secondary currens. he subracion is performed direcly by using a hrough-hole DC curren ransducer. here, he urns raio has o be chosen according o he ransformer urns-raio (in he case a hand 6:). For high-power sysems he increase of he oal componen coss due o he sensing of he magneizing curren is marginal in comparison o he gained increase of sysem performance and reliabiliy. he concep also allows o keep he safey margin considered in he ransformer core dimensioning low and herefore helps o reduce he ransformer realizaion effor. u, i, i, i =, N N ideal ransformer N N i, i m =i, -i, i, u, In Fig. he configuraion for measuring of he magneizing curren using a hrough-hole DC curren ransformer is shown in connecion wih he ransformer equivalen circui. Figure depics he ime-behavior of ransformer primary curren, he ransformer secondary curren and he resuling magneizing curren. Remark: In case of a non-ineger urns ransformer raio N /N he primary curren can be measured by an AC-curren sensor wih a urns raio i /i =N /N. he oupu curren of he AC-curren sensor and he secondary curren i, are hen compensaed by n =n = for he magneizing curren sensor. i, i m Fig.: (c) Direc measuremen of he magneizing curren of a ransformer by using a DC curren ransducer, n =N /N, n = (shown for n =, n =), equivalen circui and magneizing curren sensor, ime behavior of primary curren, secondary curren and (c). magneizing curren i m (referred o he secondary side).

3 Sample P P 3 P ransformer. According o he measured magneizaion of he ransformer he disribuion of he on-imes of hese wo redundan inpu curren space vecors is defined. he value of he magneizing curren a he end of a pulse half period can be derived by wo mehods which are inroduced in he following. P P 3 P 3.. Sampling of he Magneizing Curren (Mehod ) Fig. 3: Sampling ime insans, ransformer primary volage u,, resuling magneizing curren i m and ime behavior of he filered magneizing curren f. 3. Conrol Srucure P P 3 P For he conrol of he magneizaion of he ransformer he value of he magneizing curren a he end of each pulse half period i m ( k ) ( k = k / P, k=,,3..) is needed because in case of symmeric magneizaion of he ransformer he magneizing curren equals zero a hese ime insans independen of he degree of modulaion or dynamic changes (see Fig. 3). In case of asymmeric magneizaion of he ransformer he values of i m ( k ) are no equal o zero and follow he inegraed DC componen of he applied ransformer volage. (heoreically, he sampling of he magneizing curren a differen ime insans is possible oo, alhough he acual degree of modulaion has o be considered in ha case.) he sampling of he magneizing curren a he end of each pulse half period shows he advanage of no swiching acions occurring a hese imes. his significanly reduces he influence of disurbances on he measured values of he magneizing curren. he value of he magneizing curren a he end of each pulse half period is sampled and used for calculaing he swiching paern of he nex pulse half period. he inpu curren shape of he VIENNA Recifier III is no influenced by his scheme because of he exisence of wo redundan recifier inpu curren space vecors wih opposie magneizaion effec on he i = m,ref - f D Δu K(z) GH he simples way for measuring he magneizaion of he ransformer is sampling of he oupu signal of he magneizing curren sensor a each pulse half period ( k = k / P, k=,,3..). he cu-off frequency of he magneizing curren sensor causes a delay of he measured signal compared o he acual magneizing curren resuling in an error of he sampling value. For i m ( k ) = a sampling value ( k ) occurs (Fig. 3). Furhermore, he fas change of he poenial of he primary and secondary ransformer windings and he capaciive coupling and/or he high frequency behavior of he magneizing curren sensor [7] resul in spurious signals disoring he measured value. herefore, sampling of he signal could be falsified. o reduce he spurious signals he oupu signal of he magneizing curren sensor has o be filered by a low-pass filer giving he signal f. his low-pass filer causes a furher delay of he measured signal and, herefore, an increased error of he sampling scheme. he ime-behavior of he magneizing curren shows opposie slope for wo subsequen sampling ime insans. herefore, he average value of wo subsequen samples (f ( k- ) f ( k )) is zero. he DSP herefore uses he average value of he las wo samples (f ( k- ), f ( k )) for correcion of he low-frequency componen of he ransformer primary volage. If no averaging of he sample values is performed a variaion of he conroller oupu signal occurs for subsequen pulse half periods. Fig. 4 shows he block diagram of he magneizing curren conrol. For he sake of simpliciy he leakage inducance of he ransformer and he ohmic resisances are negleced. he ransformer is defined by is main inducance L H. Here, he symbol x means he local averaging of he value x during one sampling period = P /. u, sl H s s Fig. 4: Filer Sensor Block diagram of he conrol of he ransformer magneizing curren based on he sampling of he magneizing curren (mehod ). he averaging of he las wo sample values is performed by a dead ime D == P / and addiion wih he nondelayed value. he ransfer funcion K(z) = ½ K /z considers he facor ½ for averaging of he las wo sample values, he proporional gain consan K of he magneizing curren conroller, and he dead ime defined by he signal processing ime of he DSP. he conrolled sysem consiss of only he ransformer main inducance L H (inegraor /sl H ) neglecing he leakage inducance of he ransformer and he ohmic resisances for he sake of simpliciy. Furhermore, a P-elemen represening he ransfer funcion of he magneizing curren sensor and a P-elemen represening he filering of he sensor signal are considered.

4 i = m,ref D Rese Δu K(z) GH u, sl H - s s Fig. 5: Sensor Block diagram of he ransformer magneizing curren conroller for inegraion of he magneizing curren in secions (mehod ). he averaging is performed via a reseable inegraor. Because he inegrain has o be performed symmerically around he ime insans k = k / P, k=,,3... a delay of D = ½ =¼ P of he measured magneizing curren is necessary. he conroller K(z)= K /z comprises he proporional gain consan K of he conroller and he dead ime according o he signal processing ime of he DSP. 3.. Inegraion of he Magneizing Curren in Secions (Mehod ) For improved inerference suppression concerning he magneizing curren a he sampling ime insans averaging by inegraion in secions [8] can be applied. As shown in Fig. 6, wo reseable inegraors (A, B) wih according sample-hold elemens (C, D) are used. he wo inegraors are conrolled in a way ha always one inegraor inegraes he measured magneizing curren symmerically around he zero line (forming he average value during ha ime period, herefore), while he oupu value of he oher inegraor is sored in he sample-hold elemen, o be acivaed aferwards. A delay of he measured signal according o he ime consan of he measuremen ½ = ¼ P is necessary because he inegraion of he measured magneizing curren has o be done symmerically o he sampling ime insans. As shown in Fig. 7 he inegraion of he measured magneizing curren covers wo calculaion ime inervals of he DSP. In case of load variaions and/or changes of he degree of modulaion his can resul in a local error of he calculaed magneizaion of he ransformer. his is a basic drawback of mehod. he wo inegraors ac alernaely so ha he oupu value of one inegraor is always sored and available for furher calculaions while he oher inegraor forms he average value. In P P 3 P Hold A S/H C P P 3 P In A/B B D S/H Hold P P 3 P Fig.7: ime behavior of he inegraion of he magneizing curren in secions (mehod ) for a sep change of he degree of modulaion. 3. Conroller design In In Hold Hold 3.. Sampling of he Magneizing Curren (Mehod ) he z-ransformaion of he conrol circui shown in Fig. 4 gives he following ransfer funcion of he open loop: K z B z z FO ( z) =. A C D () z LH z z e z e A/B Fig.6: Circui for inegraion of he magneizing curren in secions and conrol signals wih A = ( ), B =, C =, D = ()

5 Figure 8 shows he roo-locus diagram (for L H =3mH, =μs and =3μs) in he z-plane and he roo-locus diagram ransformed back ino he w-plane employing he usinapproximaion [9], [] showing curves of consan damping. he limi of sabiliy is reached for a proporional gain consan of K=43 V/A. As shown in Fig. 8 he conroller design can be based on a dominan pole pair. o achieve a minimum conrol error he amplificaion of he conroller should be as high as possible. Wih increasing amplificaion however also seling ime and overshoo will increase. As a compromise he damping of he dominan subsiue-p-elemen is chosen wih D=.5 which resuls (according o Fig. 8) in a proporional gain consan of K=56 V/A According o pracical invesigaions wihin one pulse period a maximum DC componen of he ransformer primary volage of V can occur. Figure 9 shows he disurbance ransfer funcion for a disurbance sep of u, = V and a conroller gain of K=56 V/A. he use of a simple proporional conroller resuls in a saionary conrol error of.8a. he seling ime is.45ms and he maximum conrol error is.a in his case. For a maximum value of he magneizing curren î m =.66A his is a relaive error of.6% and herefore accepable. 3.. Inegraion of he Magneizing Curren in Secions (Mehod ) Since he required dead ime D is equal o he half sampling ime he dead ime canno be described as polynomial funcion of z. he dead ime has o be implemened in form of a Padé-approximaion ( = D /). he z-ransformaion of he conrol circui of Fig.5 gives he following ransfer funcion of he open loop: z B z z z F ( z) = K. A C D E z LH z ( z ) z e z e O (3) x wih A =, B 3 =, C =, D =, E 3 = (4) Figure shows he roo-locus diagram (for L H =3mH, =μs and = D /=4μs) in he z-plane and he roo-locus diagram ransformed back ino he w-plane employing he usinapproximaion [9], [] showing curves of consan damping. he limi of sabiliy is reached for a proporional gain consan of K=7 V/A As in case of mehod he conroller design can be based on a dominan pole pair. As before, he damping is chosen wih D=.5 which resuls (according o Fig. ) in a proporional gain consan of K=48 V/A. Fig.8: x 4 Roo-locus diagram of he z-ransformaion and roo-locus diagram ransformed back ino he w-plane employing he usin-approximaion of he magneizing curren conroller for sampling of he magneizing curren (mehod ). he dashed line in indicaes consan damping D=.5. Figure shows he disurbance ransfer funcion for a disurbance sep of u, = V and a conroller gain of K=48 V/A. he use of a simple proporional conroller resuls in a saionary conrol error of.a. he seling ime is.44ms and he maximum conrol error is.4a in his case. For a maximum value of he magneizing curren î m =.66A his is an accepable relaive error of 4.5%..3.3 i m, m.5 i m, m Fig.9: Disurbance ransfer funcion of he magneizing curren conroller for sampling of he magneizing curren (mehod ) wih a conroller gain of K=56 V/A for a disurbing sep funcion of u, = V. x Fig.: Disurbance ransfer funcion of he magneizing curren conroller for inegraion of he magneizing curren in secions(mehod ) wih a conroller gain of K=48 V/A for a disurbing sep funcion of u, = V. x -3

6 .8 he experimenal resuls are in good agreemen wih he simulaed sep responses shown in Fig. 9 and Fig x A/div f.83a/div.69a/div Fig.: Roo-locus diagram of he z-ransformaion and roo-locus diagram ransformed back ino he w-plane employing he usin-approximaion of he magneizing curren conroller for inegraion of he magneizing curren in secions (mehod ). he dashed line in describes consan damping D=.5. 4 Experimenal Resuls x -4 he experimenal resuls are based on a laboraory prooype wih he following parameers: Inpu volage: U N = 4 V(line-o-line) Oupu volage: U O = 48 V Oupu power: P O = 8.5 kw Swiching frequency: f P = 3.5 khz ransformer main inducance: L H = 3 mh. he behavior of he sysem wih and wihou i m conroller is invesigaed and compared. herefore, he experimens are performed under reduced inpu volage U N =8V and reduced oupu power P O = kw. o measure he magneizing curren a hrough-hole DC curren ransformer CSNP66 from Honeywell has been used. Figure shows he magneizing curren measured by his curren ransformer and furher curren signals derived by low-pass filering and/or averaging. he phase shif caused by low-pass filering of he measured signal is obvious. his phase shif is compensaed by averaging done by he DSP (see Fig. 3). he sysem behavior for a sep change of he local average value of he ransformer primary volage of V is shown in Fig. 3. he average value of he magneizing curren is measured by inegraion in secions (as described in secion 3.. ). Fig.: Oupu signal of he magneizing curren ransducer, he low-pass-filered signal f and he locally averaged signal i,. m m In Fig. 4 he effec of he magneizing curren conroller is demonsraed. Wihou acive conrol he ime behavior of he magneizing curren shows a low frequency componen of high ampliude. Employing a magneizing curren conroller he magneizing curren can be held close o zero line. f.33a/div.7a/div Fig.3: Sep response of he magneizing curren for a sep change of he disurbance volage u, = V and conrol of he magneizing curren wih sampling of he magneizing curren (mehod ) and inegraion in secions (mehod ). f.33a/div.7a/div

7 Acknowledgmen Fig.4: ime behavior of he magneizing curren wihou (op) and wih (boom) magneizing curren conroller. 5 Conclusions wihou conrol mehod mehod.69a/div Wihou acive conrol of he magneizing curren here is he possibiliy of an unreliably high magneizing curren possibly resuling in a sauraion of he ransformer of he VIENNA Recifier III. If mehods are employed which allow higher magneizing curren and passive symmerizaion, he increased magneizing curren disors he ideal sinusoidal inpu curren shape. Measuring he magneizing curren employing a hrough-hole DC curren ransdformer resuls in a signal sufficien for acive symmerizaion of he magneizaion of he ransformer alhough he measuremen shows a relaively high noise level. I was shown ha a inegraing measuremen of he magneizing curren is no necessary and a simple sampling of he measured signal f is sufficien. Besides higher realizaion effor he inegraing measuremen of he magneizing curren informaion has he disadvanage of a emporary measuremen error in case of changes of he degree of modulaion. For sampling of he magneizing curren i has o be considered ha he sampling has o be performed wihin each pulse half period so ha he delay ime (resuling from he bandwidh limiaion of he magneizing curren sensor and he filering of he measured signal) of f compared o i m does no resul in an error when averaging he sampled signal values. he described mehod can also be employed wih DC-DC converer sysems. In his case a series capacior (generally resricing he dynamic behavior of he sysem) on he ransformer primary side can be omied and/or he magneizing curren can be kep low. he swiching losses are reduced and/or he efficiency improved. he higher coss of he magneizing curren ransdformer are neglecable for sysems of higher power. For employing he described mehod of magneizing curren conrol for a broader field of applicaions hrough-hole DC curren ransdformers wih large holes and relaively small insrumen range would be advanageous. he auhors are very much indebed o he Hochschuljubiläumssifung der Sad Wien for he generous suppor of he research of he Power Elecronics Group of he Dep. of El. Drives and Machines a he echnical Universiy of Vienna. REFERENCES [] Kolar, J.W, Drofenik, U., Erl, H., and Zach, F.C.:: VIENNA Recifier III A Novel hree-phase Single- Sage Buck-Derived Uniy Power Facor AC-o-DC Converer Sysem. Proceedings of he Nordic Workshop on Power and Indusrial Elecronics, Espoo, Finland, Aug. 6-7, pp. 9-8 (998). [] Wilson, D.: A New Pulsewidh Modulaion Mehod Inherenly Mainains Oupu ransformer Flux Balance. Proceedings of he 8 h Inernaional Solid-Sae Power Elecronics Conference, Dallas (X), April 7-3, pp. D- / D-/5 (98). [3] Mohan, N., Undeland,.M., and Robbins, W.P.: Power Elecronics Converers, Applicaions, and Design. nd Ediion, John Wiley & Sons, Inc. (995). [4] Klopper, S., and Ferreira, J.A.: A Sensor for Balancing Flux in Converers wih a High Frequency ransformer Link. Record of he 8 h IEEE Indusry Applicaions Sociey Annual Meeing, orono, Canada, Oc. -8, P. II, pp (993). [5] Pael, R.: Deecing Impending Core Sauraion in Swiched-Mode Power Converers. Proceedings of he 7 h Naional Solid-Sae Power Conversion Conference, pp. B-3/ B-3/ (98). [6] Kolar, J.W.: Verfahren und Vorrichungen zur Erfassung und Ausregelung eines Gleichaneiles des Magneisierungssromes von Hochfrequenz-Leisungsransformaoren in Sromricherschalungen. Ausrian Paen Applicaion A8/98, filed: Oc. 4, 998. [7] Pankau, J., Leggae, D., Schlegel, D., Kerkman, R., and Skibinski, G.: High Frequency Modelling of Curren Sensors. Proceedings of he 4 h IEEE Applied Power Elecronics Conference, Dallas, Vol., March 4-8, pp (999). [8] Chin,.H., Nakano, M., and Hirayama,.: Accurae Measuremen of Insananeous Values of Volage, Curren and Power for Power Elecronics Circuis. Proceedings of he 9 h IEEE Power Elecroncis Specialiss Conference, Fukuoka, Japan, May 7-, Vol., pp (998). [9] Duan, Y., Jin, H.: Digial Conroller Design for Swichmode Power Converers. Proceedings of he 4 h IEEE Applied Power Elecronics Conference, Dallas, March 4-8, Vol., pp (999). [] MALAB, he Mah Works, Inc.