Swiss Rectifier Output Voltage Control with Inner Loop Power Flow Programming (PFP)

Transcription

1 3 IEEE Proceengs of the 4th IEEE Workshop on ontrol an Moelng for Power Electroncs (OMPE 3), Salt ake ty, USA, Jne 3-6, 3 Swss Rectfer Otpt Voltage ontrol wth Inner oop Power Flow Programmng (PFP) P. ortés, F. Vanc, J. W. Kolar Ths materal s pblshe n orer to prove access to research reslts of the Power Electronc Systems aboratory / D-ITET / ETH Zrch. Internal or personal se of ths materal s permtte. However, permsson to reprnt/repblsh ths materal for avertsng or promotonal prposes or for creatng new collectve works for resale or restrbton mst be obtane from the copyrght holer. By choosng to vew ths ocment, yo agree to all provsons of the copyrght laws protectng t.

2 Swss Rectfer Otpt Voltage ontrol wth Inner oop Power Flow Programmng (PFP) P. ortes, M. F. Vanc an J. W. Kolar Power Electronc Systems aboratory ETH Zrch Physkstrasse 3, 89 Zrch, Swtzerlan Emal: Abstract A novel control scheme s propose for a threephase bck-type SWISS rectfer. Ths control s base on an nner loop power flow programmng that proves a well ampe behavor of the otpt flter an ecople npt flter an converter ynamcs. A D/D eqvalent crct of the SWISS rectfer s se for the analyss an evalaton of fferent control concepts for the swtchng stage of the converter. By sng fferent feeforwar loops for the calclaton of the ty cycles the behavor of the converter can be mofe to st a esre characterstc. In ths way, the converter can be programme for constant voltage transfer rato, constant otpt voltage, constant power transfer or other npt/otpt relatons. A comparatve evalaton of fferent nner loop control schemes s presente. The control schemes are compare analytcally sng small-sgnal lnear moels. The comparson consers the ynamc behavor as well as the ecoplng of the npt an otpt varables. Smlaton reslts sng the D/D eqvalent crct moel an the actal three-phase SWISS rectfer are presente. Accorng to the reslts, the PFP control acheves an mprove behavor of the converter n terms of ampng of the resonances an ecoplng of the npt an otpt varables, compare to the other control schemes. I. INTRODUTION Three-phase bck-type PF rectfers prove a we range of otpt voltages, compare to a boost-type voltage sorce rectfer, whle snsoal crrents are mantane at the npt. In aton, t s possble to lmt the otpt crrent n case of a short crct n the loa. These characterstcs make the bck-type rectfers stable for applcatons lke electrc vehcle battery chargers, power spples or front-en for electrc rves [] [3]. Among the fferent converter topologes that have been propose n the lteratre, only the sx-swtch bck-type rectfer an the SWISS rectfer are of nstral nterest []. Several control schemes has been propose for threephase bck-type rectfers. Most of them conser the sxswtch converter or a smlar three-swtch converter. The swtchng stage of the converter s molate sng hysteress comparators [4], plse-wth molaton [5] or space vector molaton [6], whle a cascae control strctre s sally consere for the otpt voltage control. An oter control loop reglates the otpt voltage an proves the reference for the nner control loop. There are two man optons for the nner loop: control of the c crrent [6] or control of the ac crrents [4]. These two schemes have been compare an evalate n [7]. A fferent approach ses the concepts of moel prectve control (MP) for a combne control an molaton of the rectfer for very low swtchng operaton n [8] an for smltaneos control of the npt an otpt n [9]. In ths paper, fferent control concepts for a 5 kw SWISS rectfer shown n Fg. are evalate. The control schemes are base on the analyss of the npt/otpt relatons n the power converter an the nteracton between the converter an the npt flter. A Power Flow Programmng (PFP) control scheme s propose for the nner loop. Ths control strategy proves a well ampe behavor of the otpt flter an ecople npt flter an converter ynamcs. An oter control loop s se for the otpt voltage. A D/D eqvalent crct of the SWISS rectfer s presente n Secton II. Ths moel allows a smpler evalaton an comparson of the control concepts explane n Secton III. The ynamc behavor of the converter wth the fferent schemes s analyze n Secton IV. omparatve smlaton reslts are shown n Secton V. The extenson of the PFP concepts s scsse n Secton VI. onclsons are presente n Secton VII. II. MODE OF THE SWISS RETIFIER The SWISS rectfer s a PF rectfer topology compose of a three-phase oe brge wth a thr harmonc njecton crct, combne wth a c-c bck converter (cf. Fg. ). A etale escrpton an evalaton of ths topology s presente n []. In ths converter, the local average vales of the crrents n the swtches T p an T n are molate n orer to be proportonal to the phase voltages that efne the otpt voltage of the oe brge. The N,A A N,B B N, µh F F,A F,B F, F, F µf 3µH ot R 47µF 3Ω Fg. Three-phase snsoal npt crrent bck-type SWISS rectfer. p n Tp Tn /3/$3. 3 IEEE

3 n F,eq n F,eq ot R Fg. D/D eqvalent crct of the SWISS rectfer. brectonal swtches operate at twce the mans freqency an prove a path to fee the fference between the postve an negatve crrents, p an n, back to the phase voltage wth lower absolte vale. A 5 kw system wth a swtchng freqency of 36 khz s consere n ths paper. In orer to smplfy the analyss of the system ynamcs an esgn of the fferent control concepts, a D/D eqvalent crct of the SWISS rectfer can be obtane, aaptng to the bck topology the transformaton prncple propose n [] for a boost rectfer. In ths eqvalent crct, the SWISS rectfer s moelle as a bck converter (cf. Fg. ), an the npt flter parameters are scale to match the ynamcs of the three-phase system ( F,eq = 3 F, F,eq = 3 F an n = 3 ûn ). The relaton between the average vales of the npt an otpt voltages an crrents s efne by the ty cycle of the swtchng evce, ū = ū () =. () By sng fferent relatons an feeforwar loops n the calclaton of the ty cycle, the npt/otpt relatons n the power converter can be mofe to ft a specfc reqrement or a esre behavor. Ths ea has been se n [] for provng a resstve behavor at the converter npt. In aton to the resstve behavor, several other optons are possble sch as constant crrent, constant voltage or constant power transfer [], whch can be programme for the npt or for the otpt of the swtchng stage of the converter. In ths paper, fferent feeforwar optons are ste for applcaton to the SWISS rectfer: constant npt crrent, constant otpt voltage, constant power transfer an constant npt resstance. III. ONTRO SHEMES The control scheme for the SWISS rectfer consers an oter control loop for the otpt voltage ot an an nner loop wth fferent feeforwar optons. As a reference, the constant voltage transfer rato scheme wth no feeforwar loops s also presente. A. onstant voltage transfer rato A smple scheme way to calclate the ty cycle conssts of scalng the reference voltage by a constant vale, the nomnal npt voltage n,.e. = n, as shown n Fg. 3(a). In ths way, a constant rato between the converter otpt voltage an the npt flter capactor voltage, an between the npt an otpt crrents, an, s establshe. These relatons lea to nteracton between the npt an otpt flters, as t s epcte n the lnearze moel shown n Fg. 3(b). B. onstant npt crrent A metho to ecople the npt crrent from varatons of the otpt crrent s mplemente by nclng a feeforwar loop of the otpt crrent, as shown n Fg. 4(a). By calclatng the ty cycle sng the actal vale of the otpt crrent, =, the resltng npt crrent s eqal to ts reference, =. As shown n Fg. 4(b), the lnearze moel presents no nflence of the otpt flter ynamcs n the behavor of the npt crrent. However, there s a coplng from the npt voltage to the otpt flter, an the feeforwar loop ntroces a negatve feeback n the otpt flter ynamcs that mproves the ampng of the otpt flter resonance.. onstant otpt voltage A metho to ecople the otpt voltage from varatons of the npt voltage s mplemente by nclng a feeforwar loop of the npt capactor voltage, as shown n Fg. 5(a). By calclatng the ty cycle sng the actal vale of the npt voltage, = ū, the resltng otpt voltage s eqal to ts reference, ū =. As shown n Fg. 5(b), the lnearze moel presents no nflence of the npt flter ynamcs n the behavor of the otpt flter. However, there s a coplng from the otpt flter to the npt flter. In aton, the stablty of the npt flter s affecte by the ntrocton of a postve feeback that nees to be compensate by the nclson of a passve ampng of the npt flter. D. onstant power flow programmng Ths control metho s base on the power balance between the npt an otpt of the swtchng stage of the converter, an enomnate as Power Flow Programmng (PFP) control. Gven an otpt power reference P, prove by the otpt voltage controller, the reqre npt crrent reference s calclate as = P ū, (3) then, by sng the relaton of npt an otpt crrents gven by (), the reqre ty cycle s expresse as = = P ū. (4) Ths metho reslts n the nclson of feeforwar loops of the npt capactor voltage ū an the otpt nctor crrent [], as shown n Fg. 6(a). The PFP control proves a ecople operaton of the npt flter an the otpt flter, whch s reflecte n the lnearze moel of the system shown n Fg. 6(b). As observe n the moel, a

4 n F,eq n F,eq * ot Un U * R s ot R Otpt stage Inpt flter n s * ot I F,eq s n F,eqs - n (a) D/D eqvalent crct an control (b) nearze moel (wthot the PI otpt voltage controller) Fg. 3 Eqvalent crct of the SWISS rectfer wth a constant voltage transfer rato control scheme. * n F,eq n F,eq U I D ot * R Otpt stage Inpt flter s U I s ot R D * ot F,eq s F,eqs n - n (a) D/D eqvalent crct an control (b) nearze moel (wthot the PI otpt voltage controller) Fg. 4 Eqvalent crct of the SWISS rectfer wth a constant npt crrent control scheme. * n F,eq n F,eq ot ot U * ot I F,eq s - U* U (a) D/D eqvalent crct an control s R R Otpt stage Inpt flter * s F,eqs n n (b) nearze moel (wthot the PI otpt voltage controller) Fg. 5 Eqvalent crct of the SWISS rectfer wth a constant otpt voltage control scheme. n F,eq P* ot I s P* I R s R Otpt stage Inpt flter * P* (a) D/D eqvalent crct an control - n F,eq * ot U P* U F,eq s F,eqs n n (b) nearze moel (wthot the PI otpt voltage controller) Fg. 6 Eqvalent crct of the SWISS rectfer wth a constant nterface power flow control scheme. ot

5 n F,eq n F,eq ot R Otpt stage Inpt flter G* U I U G* I U G* I s ot s R * G * - * ot U F,eq s n F,eq s * G n (a) D/D eqvalent crct an control (b) nearze moel (wthot the PI otpt voltage controller) Fg. 7 Eqvalent crct of the SWISS rectfer wth a constant nterface resstance control scheme. postve feeback n the npt flter s ntroce, as n the case of the prevos scheme. Regarng the otpt stage, a negatve feeback of the nctor crrent s ntroce, provng a ampng of the otpt flter that mproves the ynamc behavor of the otpt voltage. 5A * 5A E. onstant npt resstance In orer to prove a resstve behavor at the npt of the swtchng stage of the power converter, the eas presente n [] can be apple. Gven a reference conctance G = /R, the reqre npt crrent reference can be calclate as = G ū, (5) an the reqre ty cycle s expresse as = = G ū. (6) The resltng control scheme s shown n Fg. 7(a). Ths scheme ntroces negatve feeback n the npt an otpt flter, mprovng the ampng n both converter ses. However, there s coplng from the npt to the otpt flter, as shown n the lnearze moel n Fg. 7(b). A smmary of the npt/otpt relatons for the swtchng stage of the bck-type converter for the fferent feeforwar control schemes s shown n Table I. These relatons can be also epcte as a crrent/voltage crve for each control scheme, as shown n Fg. 8. The constant npt crrent behavor s shown n Fg. 8(a) where the npt crrent s nepenent of the voltage. A constant otpt voltage characterstc s shown n Fg. 8(b). For a constant power transfer scheme, the npt an otpt ses are operatng at fferent ponts of the same constant power crve, as shown n Fg. 8(c). A lnear crrent/voltage relaton s mpose wth the constant npt resstance scheme, as shown n Fg. 8(). IV. DYNAMI BEHAVIOR OF THE ONTRO SHEMES onserng the lnearze small-sgnal moels of each control scheme, an eqvalent crct of the swtchng stage of the converter can be erve. As shown n Fg. 9(a), the (a) onstant npt crrent 5A P * r o r 6V 6V (c) onstant power transfer * 6V (b) onstant otpt voltage 5A r 6V () onstant npt resstance Fg. 8 rrent/voltage relatons n the swtchng stage of the converter for the fferent control schemes. small-sgnal eqvalent crct for the constant npt crrent scheme presents an eal crrent snk at the npt an an eal voltage sorce wth a postve nner resstance r o at the otpt. The nner resstance r o proves ampng for the otpt flter resonance. The eqvalent crct for the constant otpt voltage s shown n Fg. 9(b), where the npt se behaves as an eal crrent snk wth a negatve parallel nner resstance r an the otpt se as an eal voltage sorce. The negatve nner resstance s also present n the npt se when the constant power transfer scheme s se, as shown n Fg. 9(c). Wth ths scheme, the otpt se presents a postve seres nner resstance r o. In a constant npt resstance scheme, postve nner resstances are present at the npt an otpt ses, as shown n Fg. 9(), provng ampng for the npt an otpt flter.

6 TABE I Inpt/otpt voltage an crrent relatons for fferent control schemes. ontrol scheme Voltage rrent onstant voltage rato onstant npt crrent ū = n ū ū = ū = n = onstant otpt voltage ū = = ū onstant power transfer ū = P onstant npt resstance ū = G ū = P ū = G ū r (a) onstant npt crrent r (b) onstant otpt voltage Imagnary Axs (secons - ) Imagnary Axs (secons - ) (a) Real Axs (secons - ) x 4 4 x 4 4 x 4 (c) Real Axs (secons - ) x 4 Imagnary Axs (secons - ) Imagnary Axs (secons - ) 4 x 4 (b) Real Axs (secons - ) x 4 4 x 4 () Real Axs (secons - ) x 4 r Fg. Poles an zeros of the converter for the fferent control schemes. r (c) onstant power transfer () onstant npt resstance Fg. 9 Small-sgnal eqvalent crct of the swtchng stage for the fferent control schemes. The effect of the fferent control schemes n the placement of the converter poles an zeros s shown n Fg.. For a constant npt crrent control, the otpt flter poles are locate n the real axs, as shown n Fg. (a), e to the ampng prove by the nner resstance r o, whle the poles of the npt flter reman nampe. In a constant otpt voltage scheme, the poles of the otpt flter are not ampe an the poles of the npt flter move to the rght half-plane e to the negatve nner resstance r at the npt se, as shown n Fg. (b). A smlar behavor of the npt flter poles can be observe when a constant power transfer scheme s se. However, the otpt flter poles are locate n the real axs, as shown n Fg. (c). For a constant npt resstance scheme, both eqvalent nner resstances, r an r o are postve an the poles of the npt an otpt flter are locate n the left half-plane, as shown n Fg. (). V. RESUTS Smlaton reslts for the D/D moel wth the fferent control schemes are performe for open loop operaton,.e. the otpt voltage controller s omtte. A step change from 4 V to 45 V s apple n the vale of the reference for the converter otpt voltage. Reslts for the constant voltage rato scheme [cf. Fg. 5(a)] are shown n Fg. (a). The oscllatons n the otpt voltage, e to the otpt flter resonance, are ampe only by the loa,

7 Inpt/otpt voltages [V] ot Tme [ms] Inpt/otpt voltages [V] ot Tme [ms] Inpt/otpt crrents [A] 5 5 n Tme [ms] Inpt/otpt crrents [A] 5 5 n Tme [ms] (a) Reslts sng the eqvalent D/D crct. (a) Reslts for nomnal power (eqvalent crct) Inpt/otpt voltages [V] Inpt/otpt crrents [A] Tme [ms] F,B F, Tme [ms] ot F,A F,B F, F,A (b) Reslts for the three-phase bck-type SWISS rectfer. Fg. Smlaton reslts for the constant otpt voltage control scheme (PFP, cf. Fg. 5). A step change n the converter otpt reference s apple. The otpt voltage controller s omtte for these reslts. an the oscllatons n the otpt crrent are transferre to the npt crrents e to the coplng of the npt an otpt ynamcs. The same behavor s observe when the constant otpt voltage scheme s mplemente for the SWISS rectfer, as shown n Fg. (b). Reslts sng the constant power transfer control scheme [PFP, cf. Fg. 6(a)] for a step change n the reference power P for two fferent operatng ponts are shown n Fg. (a) an Fg. (b). A well ampe response of the otpt voltage s observe an the oscllatons of the npt voltage are not transferre to the otpt voltage, emonstratng the ecople operaton of the converter. In orer to verfy the propose control scheme, the constant power transfer control strategy s mplemente for the SWISS rectfer. Smlaton reslt for a step change n the reference power P s shown n Fg. (c).the otpt voltage presents a well ampe behavor an a ecople response of the npt flter s observe. A goo match n the Inpt/otpt voltages [V] Inpt/otpt voltages [V] Inpt/otpt crrents [A] Inpt/otpt crrents [A] ot Tme [ms] 5 n Tme [ms] (b) Reslts for half nomnal power (eqvalent crct) Tme [ms] F,A F,B F, Tme [ms] ot F,A F,B F, (c) Smlaton reslt for the SWISS rectfer at nomnal power Fg. Smlaton reslts sng the constant power transfer control scheme (cf. Fg. 6). The otpt voltage PI controller s omtte. ynamc behavor of the three-phase system wth respect to the D/D moel s observe. In orer to evalate the ecoplng of the npt an otpt flter ynamcs, smlaton reslts for a step change

8 Inpt/otpt voltages [V] Tme [ms] Inpt/otpt crrents [A] n Tme [ms] (a) Reslts for a step change n the loa resstance from 3 Ω to 36 Ω. ot 5A (a) 6V 5A 6V Fg. 4 Nonlnear crrent/voltage relatons n the swtchng stage of the converter. n F,eq n F,eq (b) ot R Inpt/otpt voltages [V] Tme [ms] Inpt/otpt crrents [A] 5 n Tme [ms] (b) Reslts for a % step change n the spply voltage n. Fg. 3 Smlaton reslts for the constant power transfer control scheme (cf. Fg. 6). Evalaton of the ecoplng between the npt an otpt flter ynamcs. The otpt voltage controller s omtte for these reslts. ot * (a) Freqency shapng of the power transfer relatons. n F,eq n F,eq k * P * - * ot ot R G * (b) Inpt mpeance programmng. - * ot Fg. 5 Dynamc coplng n the swtchng stage of the converter. n the loa resstance are shown n Fg. 3(a) for a constant power transfer control scheme. As the reference power P s kept constant, the otpt voltage ot ncreases an the otpt nctor crrent ecreases when the loa resstance s ncrease. There s no notceable effect of the loa step n the npt crrent an voltage. For a step change n the spply voltage n, the capactor voltage an the npt crrent n change an strong oscllatons are present rng the transent, as shown n Fg. 3(b). The otpt voltage ot an crrent are present no notceable change, emonstratng the goo ecoplng acheve wth the constant power transfer scheme. VI. FURTHER EXTENSIONS OF PFP A. Dfferent programme behavors In aton to the prevosly presente control schemes, the PFP schemes can be extene n several ways. The crrent/voltage relatons n the swtchng stage can e efne as nonlnear relatons, as shown n Fg. 4. Frthermore, the coplngs n the swtchng stage can be efne also n the freqency oman by ntrocng flterng n the feeforwar loops, as shown n Fg. 5(a). Another opton consers the extenson of the constant npt resstance to a npt mpeance programmng, by efnng resstve, capactve an nctve components n the calclaton of the reference crrent, as shown n Fg. 5(b). B. Applcaton to boost-type converters The same concept of PFP control schemes can be apple to boost-type systems lke the D/D converter shown n Fg. 6. By sng feeforwar loops of the npt crrent n an/or the otpt voltage ot, the followng nner loop PFP schemes can be consere: onstant npt voltage, where the ty cycle s calclate as = / ot.

9 n F,eq n ot R t can be easly extene to other confgratons sch as boost-type rectfers, nverters, an A/D/A converters wth an wthot energy storage. REFERENES Fg. 6 Boost-type D/D converter. onstant otpt crrent, where the ty cycle s calclate as = / n. onstant power transfer, where the ty cycle s calclate as = P /( ot n ). onstant otpt resstance, where the ty cycle s calclate as = G ot / n. VII. ONUSIONS Ths paper presents a new concept for the control of the bck-type SWISS rectfer. The control scheme consers an oter control loop for the otpt voltage an an nner feeforwar loop for controllng the swtchng stage of the converter. Several feeforwar optons for the nner loop are analyze an compare n terms of ynamcs an coplng of the npt an otpt ses. The propose PFP control scheme wth constant power transfer proves ecoplng of the npt an otpt flter ynamcs an ampng of the otpt flter resonance. For the evalaton of the fferent control schemes a D/D eqvalent crct s se to moel the SWISS rectfer ynamc behavor. Ths moel allows a smpler analyss an assessment of the performance wth the fferent schemes. In aton to the basc schemes, the extenson of the PFP concept s presente. The possble extensons ncle the se of nonlnear crrent/voltage relatons, freqency shapng of the power transfer relatons an the possblty of programmng any type of mpeance at the npt of the swtchng stage of the converter. The propose control scheme s stable for three-phase bck-type A/D converters an D/D converters, bt [] J. Kolar an T. Frel, The essence of three-phase PF rectfer systems - Part I, IEEE Transactons on Power Electroncs, vol. 8, no., pp , 3. [] T. Soero, T. Frel, an J. Kolar, Swss rectfer - A novel threephase bck-type PF topology for electrc vehcle battery chargng, n Proceengs of the 7th Annal IEEE Apple Power Electroncs onference an Exposton (APE),, pp [3] T. Nssbamer, G. Gong, M. Helwen, an J. Kolar, ontrolorente moelng an robst control of a three-phase bckboost PWM rectfer (VRX-4), n Proceengs of the 4th IEEE Instry Applcatons Socety Annal Meetng, vol., 5, pp [4] N. Zargar an G. Joos, A crrent-controlle crrent sorce type nty power factor PWM rectfer, n IEEE Instry Applcatons Socety Annal Meetng, vol., Oct. 993, pp [5] T. Nssbamer an J. Kolar, Avance molaton scheme for three-phase three-swtch bck-type PWM rectfer preventng mans crrent storton orgnatng from slng npt flter capactor voltage ntersectons, n Proceengs of the IEEE 34th Annal Power Electroncs Specalst onference (PES 3), vol. 3, Jne 3, pp [6] G. Marqes, A PWM rectfer control system wth D crrent control base on the space vector molaton an A stablsaton, n Proceengs of the 7th Internatonal onference on Power Electroncs an Varable Spee Drves (onf. Pbl. No. 456), Sept. 998, pp [7] T. Nssbamer an J. Kolar, omparatve evalaton of control technqes for a three-phase three-swtch bck-type A-to-D PWM converter system, n Proceengs of the Norc Workshop on Power an Instral Electroncs (NORPIE ), Ag.. [8] P. orrea, J. Rorgez, I. zama, an D. Anler, A prectve control scheme for crrent-sorce rectfers, IEEE Transactons on Instral Electroncs, vol. 56, no. 5, pp , May 9. [9] P. ortes, J. Kolar, an J. Rorgez, omparatve evalaton of prectve control schemes for three-phase bck-type PF rectfers, n Proceengs of the 7th Internatonal Power Electroncs an Moton ontrol onference (IPEM), vol.,, pp [] H. Mao, D. Boroyevch, an F. ee, Novel rece-orer smallsgnal moel of a three-phase PWM rectfer an ts applcaton n control esgn an system analyss, IEEE Transactons on Power Electroncs, vol. 3, no. 3, pp. 5 5, 998. [] S. Snger, Realzaton of loss-free resstve elements, IEEE Transactons on rcts an Systems, vol. 37, no., pp. 54 6, 99. [] R. Kng, Feeforwar control laws for the bck converter, n Proceengs of the IEEE 4th Workshop on ompters n Power Electroncs, 994, pp