A Study of Shunt Active Power Filters Applied to Three-Phase Four-Wire Systems

Transcription

1 European Assoaton or the Development o Renewable Energes Envronment and Power Qualty (EA4EPQ) Internatonal Conerene on Renewable Energes and Power Qualty (ICREPQ ) Santago de Compostela (Span) 8th to 3th Marh A Study o Shunt Atve Power Flters Appled to Three-Phase Four-Wre Systems E. J. Aord L. B. G. Campanhol S. A. O. Slva C. B. Nasmento and A. Goeel Department o Eletral Engneerng Federal Tehnologal Unversty o Paraná - UTFPR Av. Alberto Carazza 64 CEP 863- Cornélo Proópo (Brazl) Phone: (43) 3-4 Fax: (43) 3-4 e-mal: edson.aord@pr.edu.br leo_ampanhol@hotmal.om augus@utpr.edu.br laudnor@utpr.edu.br agoeel@utpr.edu.br Abstrat. Ths work presents a study o shunt atve power lters (APFs) whh are mplemented by means o both ourlegs and three ull-brdge voltage soure nverter (VSI) topologes. These topologes are appled n three-phase our-wre systems or reatve power ompenton and harmon urrent suppresson generated by nonlnear loads. The ompenton reerene urrents used n both APFs are extrated rom the synhronous reerene rame (SRF) based ontrollers. A mathematal analyss o the our-legs and the three ull-brdge topologes are presented n order to obtan the model n state spae and the transer untons o eah system allowng to set the proportonal-ntegral (PI) gans used n the urrent ontrollers. Smulaton results are presented n order to evaluate the perormane o the APFs approahes. Key words Harmon Suppresson Reatve Power Compenton Power Qualty Shunt Atve Power Flters. appled n sngle-phase and three-phase three-wre and our-wre systems. APFs are used to njet n the lne ompenton urrents n order to anel harmons and/or reatve omponents o the load urrents. For three-phase our-wre systems dependng on the ontrol strateges adopted the APF an ontrol eah phase ndependently. Thus t s posle to ompente all the harmon and reatve urrent omponents. In ths ase the ompenton o the unbalaned load s not taken nto aount [7]. Ths paper presents a study o two APF topologes whh are appled to three-phase our-wre systems suh as the our-legs (F-L) [3-6] and three ull-brdge (3F-B) [3 7-9] as shown n Fg. and Fg. respetvely. Both are used or harmon urrent suppresson reatve power ompenton and/or load unbalane ompenton.. Introduton Nowadays harmon polluton has rsen sgnantly n the power supply system due to the nreasng use o nonlnear loads suh as swthng power supples nverters sngle-phase and three-phase reters among others beng these used n ndustral ommeral and resdental applatons. These loads have ontrbuted or the generaton o a great ontent o reatve and harmons whh are responle by the hangng o the snusodal utlty voltage haratersts as well the urrents draned rom the power system ontrbutng to power qualty (PQ) degradaton. Besdes PQ problems arse when nonlnear sngle-phase loads are onneted to three-phase our-wre systems. Even these loads are peretly balaned harmon urrents rulate through the neutral ondutor whh wll always our due to the exstene o zero sequene omponents. The ampltudes o these urrents may exeed those o the ndvdual phase urrent whh an ause damage to the neutral ondutor and to the transormers where the loads are onneted [-3]. An alternatve method to solve or mnmze these problems s the use o shunt atve power lters (APFs) Fg.. Four-Legs (F-L) APF topology. Fg.. Three Full-Brdge (3F-B) APF topology. 9 RE&PQJ Vol. No. Aprl

2 The algorthms used to extrat the three-phase ompenton reerene urrents are based on the SRF []. Whle the F-L topology uses the three-phase SRFbased algorthm the 3F-B uses the sngle-phase one. Mathematal analyses o the two topologes are developed n order to present the method used to obtan the state spae equaton and the transer untons that represent the phyl systems. Smulaton results are presented to evaluate the perormane o the APFs studed whh are modulated usng the spae vetor modulaton (SVM) [ ].. SRF-Based algorthms In ths work SRF-based algorthms are used to extrat the three-phase ompenton reerene urrents ( a b ) used by the APFs. The F-L topology shown n Fg. uses the tradtonal SRF-based algorthm ( dq -axes). Despte the proportonal-ntegral (PI) ontrollers o the system have been desgned to operate n the synhronous rotatng reerene rame the SVM s perormed n the statonary reerene rame ( αβ -axes) [ ]. On the other hand the 3F-B shown n Fg. utlzes the SRF-based algorthm adapted or sngle-phase systems. Thus the ontrol o ths struture an be desgned to operate ndependently n eah phase o the three-phase system. A. SRF-Based Algorthm Appled to F-L Topology The three-phase SRF-based algorthm used n the F-L topology or harmon suppresson reatve and load unbalane ompenton s shown n Fgure 3. Fg. 3. Blok dagram o the SRF-based algorthm. In ths method the load urrents ( La Lb L ) are measured and transormed rom a three-phase statonary reerene rame (ab) nto two-phase statonary reerene rame ( αβ ) as gven by (). α β Thus the urrent quanttes o the αβ -axes an be transormed nto two-phase synhronous reerene rame ( dq -axes) usng () where os θ and sn θ are the synhronous unt vetors obtaned rom any phase-loked loop (PLL) system. d osθ q snθ snθ osθ α β La Lb L () () Now the dq urrents are omposed by d and a parts. The d part represents the undamental load urrents (atve and reatve) and the a part represents the harmon omponents that an be extrated usng a hgh pass lter (HPF) as mplemented n Fg. 3. The d-axs urrent d represents the sum o the undamental atve urrent ( d d ) and a parel o the load harmon urrent ( d h ). By lterng d the urrent d d (Fg. 3) s obtaned whh represents the undamental atve load urrents n the synhronous rame. Thus the a omponent d h s obtaned by subtratng the d d omponent o the total urrent n d-axs ( d ) whh allow to aheve the harmon parel o the load urrent. In the synhronous rame the q-axs urrent ( q ) represents the sum o the undamental reatve load urrents and part o the load harmon urrents. It an be totally used to alulate the reerene ompenton urrents. The nverse transormaton rom the two-phase synhronous reerene rame dq nto two-phase statonary rame αβ s obtaned by (3). α osθ snθ dh (3) β snθ osθ q The nverse transormaton rom statonary rame αβ nto three-phase statonary rame ab s shown by (4) n whh the ompenton reerenes urrents are obtaned. a α b [ Tab ] β (4) 3 [ T ab ] () 3 3 B. SRF-Based Algorthm Appled to 3F-B Topology The SRF-based algorthm used n the 3F-B topology s shown n Fgure 4. The rst strategy adopted to ontrol the 3F-B topology s to treat eah phase ndependently as a ttous threephase system. Thus only load harmon suppresson and reatve power ompenton are arred out and the load unbalaned urrent ompenton s not taken nto aount. Fg. 4. Blok dagram o the sngle-phase SRF-based algorthm. Thereby measurng the three-phase load urrents ( La Lb L ) t s posle to obtan three ttous RE&PQJ Vol. No. Aprl

3 statonary reerene rame n αβ -axes ( α a β ). a The aqured load urrent s treated as the α -oordnate o the ttous αβ -axes or nstane α a La. Subsequently α has a π radan phase delay a produng the ttous β -oordnate ( β ). a Thereore three ttous two-phase systems represented by (6) are obtaned n the αβ -axes and the transormaton rom the statonary three-phase rame ab nto statonary system αβ s not neesry. Thus only the transormaton rom αβ -axes nto dq-axes s taken nto aount as gven by (). αa βa L ( ωt) a ( ωt π ) La Fnally the ompenton reerene urrents ( a are obtaned dretly rom dq-axes as gven by (7). a h a [ ] b os snθ b (6) ) d θ a a (7) qa The seond strategy adopted to ontrol the 3F-B topology s shown n Fg. whh the ompenton o the load unbalaned urrents s taken nto aount. In ths ase the nput urrents wll be ontrolled to beome s a snusodal and balaned. To mplement ths strategy the outputs o the LPF shown n Fg. 4 whh represents the atve urrent o eah phase treated ndependently are used as the nput urrent quanttes o the SRF algorthm shown n Fg.. Thus the nput snusodal and balaned reerene urrents s a an be obtaned. Now the ompenton reerene urrents are obtaned subtratng a s o a L a as gven by (8). a L (8) s a a Fg.. Blok dagram o the unbalaned load ompentng. 3. Shunt APFs appled to our-wre systems The desrpton o the two APFs studed n ths paper and ther respetve mathemat modelng are presented n ths seton. A. Four-Legs topology The F-L topology (Fg. ) s mplemented usng our-leg ull-brdge VSI onverter [3-6] Thus one o the our-leg s used to ontrol the neutral urrent. The ontrol o F-L topology mplemented s based on SRF ontroller. Thereby the mathematal modelng s presented n order to obtan the state spae system and the transer untons n the dq rame. To perorm the modelng all the ouplng ndutanes and ther resstanes are assumed to be dental suh as L a L b L L n L and R La R Lb R L R Ln R L. Thus rom Fg. the nverter output voltages an be expressed by: d dn u anpwm R L. L v L R L. n (9) d dn u bnpwm R L. L v L R L. n () ds dn u npwm R L. s L vs L R L. n () where uanpwm ua u ubnpwm ub un and u npwm u u. n n As ts dervatve orm s gven by: s sn d d ds dsn () Addng (9) () and () and usng some algebra manpulatons the ollowng state equatons an be ound: d [( 3u anpwm ubnpwm unpwm ) ( 4vR 3v v vs )] L (3) 4L [( u 3u u ) ( 4v v 3v v )] d anpwm bnpwm npwm R L s (4) 4L [( u u 3u ) ( 4v v v 3v )] ds anpwm bnpwm npwm RL s 4L () The state-spae system s dened as: x& t A.x t B.u t F.w t (6) d d T d s x& ( t) ; [ ] T [ u u u ] T anpwm bnpwm npwm x ; u ; [ v v v ] T s w. Thus usng (3) (4) () and (6) s posle to obtan the matres that represent the state-spae model o the F-L topology nto the statonary rame ab as ollows: 3 RL A L B 3 4L 3 (7) 3 F 3 4L 3 In order to represent (6) nto the statonary rame αβ the transormaton matrx gven by () s used. Thus (6) an be rewrtten as: T ab.x& αβ ( t) A.T ab.xαβ ( t ) (8) B.T.u t F.T.w t ab αβ ab αβ Multplyng both sdes o (8) by [ ] obtaned as ollows: s & s T ab x αβ RE&PQJ Vol. No. Aprl

4 x& t A.x t B.u t F.w t (9) αβ αβ αβ αβ αβ αβ αβ 4 RL A αβ L B αβ 4 4L () 4 F αβ 4 4L To represent (9) nto dq -axes the transormaton matrx gven by () s used. T dq os ωt snωt snωt osωt Thus (9) an be rewrtten as: dq dq αβο dq dq T.x ( t ) A.T.x ( t ) B.T.u ( t ) F.T.w ( t ) αβ dq dq αβ dq dq () () Isolatng the terms n () and through some manpulatons x& dq s obtaned as ollows: x & (t ) A.x (t ) B.u (t ) F.w (t ) (3) dq dq dq dq dq dq dq RL ω L R L Adq ω L R L (4) L 4 4 B dq 4 4L F dq 4 4L The blok dagram o the phyl system n dq -axes s shown n Fg. 6 where D d D q and D are the duty yles n the synhronous reerene rame whh are obtaned rom the SVM and V d s d-bus voltage. Fg. 7. Model o the deoupled system n dq oordnates. Thus n the synhronous dq -rame negletng the ross-ouplng the transer untons o the system G ps( d q) and G ps are gven by (). G ps( d q )( s ) ( R s.l ) L G ( s ) 4( R s.l ) ps L () The blok dagram o the urrent ontroller s shown n Fg. 8 where the PI ontroller s used. Thereby the losed loop transer untons ( d q) ( s) / ( d ) ( s) and ( s) ( s) / are obtaned respetvely as ollows: ( d q ) s Kp( d q ) s K( d q ) s L.s ( R Kp )s K ( d q ) L ( d q ) ( d q ) s Kp s K L s 4L.s ( 4R Kp )s K q (6) (7) The detals o the Current Reerene Generaton and Control blok represented n Fg. 8a are shown n Fg. 8b. Fg. 8. Blok Dagram o the F-L urrent ontroller; Current Reerene Generaton and Control detals. C. Three Full-Brdge topology Fg. 6. Phyl system model o the F-L n dq oordnates. The ross-ouplng between the dret and quadrature axes an be elmnated usng the deoupled model shown n Fg. 7 where the shaded blok s the deouplng term. The 3F-B topology shown n Fg. s mplemented usng three sngle-phase ull-brdge VSI onverters [3 7-9]. The man haraterst o ths topology s the ndependent ontrol o the three phases. Another mportant aspet to be onsdered s that the d-bus s redued by a ator o 3 when t s ompared wth the F-L topology. Thereby ths topology ould be an nterestng hoe or hgh power applatons [7]. As an be seen n Fg. the number o swthng deves s nreased when ompared wth the F-L topology (Fg. ). Besdes three sngle-phase RE&PQJ Vol. No. Aprl

5 solaton transormers are requred due to the sharng o the me d-bus voltage. The ontrol o 3F-B topology s mplemented nto the three-phase statonary ab-rame beng also presented the mathematal modelng where the transormers are assumed to be deals and the transormaton ratos o them are equal to one. Thus through Fg. the output voltage o eah nverter an be wrtten as: d ua R napwm L. L v (8) d ub R nbpwm L. L v (9) ds u R npwm L. s L vs (3) Isolatng ds ( a ) / (3) (3) and (33) are obtaned. ( R L. ua v ) d (3) napwm L ( R L. ub v ) d (3) nbpwm L ( R L. s u vs ) ds (33) npwm L From (3) (3) (33) and (6) the matres that represent the state-spae models n the ab-rame are gven by (34). RL A B L L (34) F L From (34) the ab transer untons o the phyl system ( G ps( a ) ) are obtaned as: G ps( a )( s ) ( R L.s ) L (3) The blok dagram o the sngle-phase urrent ontroller s shown n Fg. 9 where the losed loop transer untons ( s) ( ) / ( a ) ( s) are gven by (36). a b ( a ) ( s) ( a ) s Kp( a ) s K( a ) L.s ( R Kp )s K L ( a ) ( a ) (36) loads as shown n Fg.. The parameters o APFs and PI ontroller gans are shown n Table I. Fgure shows the three-phase unompented loads urrents ( La Lb L ). Fgure and Fg. 3 show the ompented soure urrents ( urrent ( sn ) and the d-bus voltage ( V d s ) the neutral ) or the F-L and 3F-B topologes respetvely. As an be noted the APFs are perormng harmon urrent suppresson reatve power ompenton and load unbalaned ompenton. Fg.. Three-phase our-wre system eedng nonlnear loads. - Table I - Parameters o the shunt APFs. Parameters F-L 3F-B d-bus voltage (V d ) 4V 3V d-bus apator (C d ) 3mF 3mF Indutor (L ) mh mh Indutor (L n ) mh -- PI ontroller parameters Proportonal gan Kp (dq) 3.4 Kp 3.4 (urrent loop) Integral gan (urrent loop) Proportonal gan (d-voltage loop) Integral gan (d-voltage loop) Kp 6 K (dq) 7 K 683 K 7 Kp v.3 Kp v. K v K v Tme [s] - Fg.. Three-phase load urrents: La Lb and L Tme [s] Fg. 9. Blok dagram o the 3F-B urrent ontroller (per phase). 4. Smulaton Results To very the behavor o the two topologes they were smulated wth the omputatonal tool MATLAB/Smulnk n whh the three-phase onverters operate at khz swthng requeny. The smulatons were perormed onsderng a three-phase our-wre system eedng three unbalaned nonlnear V o l t a g e [ V ] Tme [s] Tme [s] () Fg.. F-L topology: and s sn ; () V d. 3 RE&PQJ Vol. No. Aprl

6 Tme [s] Tme [s] V o l t a g e [ V ] Tme [s] () Fg. 3. 3F-B topology: and s sn ; () V d. Table II shows the total harmon dstorton (THD) obtaned n the three-phase soure urrents ater the urrent ompenton or both topologes. Table II - Total Harmon Dstorton o the Soure Currents. THD% phase a phase b phase Wthout ompenton F-L ompenton F-B ompenton..9.7 As the 3F-B topology an ontrol eah phase ndependently by means o the SRF-based algorthm shown n Fg. 4 only harmon suppresson and reatve ompenton are perormed thus the unbalane load ompenton s not taken nto aount. For ths ondton Fg. 4 shows the ompented soure urrents ( s ( V d ) the neutral urrent ( sn ) and the d-bus voltage ). As an be noted the nput urrents are unbalaned although harmon ree. V o l t a g e [ V ] Tme [s] Tme [s] Tme [s] () Fg. 4. 3F-B topology: and s sn ; () V d.. Conluson Ths work presented a study o two shunt APF topologes suh as the F-L and the 3F-B. They were appled or harmon urrent suppresson reatve power ompenton and/or load unbalaned ompenton n three-phase our-wre systems. The SRF-based algorthms used to extrat the reerene urrents were presented. The F-L topology perormed nto αβ -axes was mplemented usng SVM. Through the modeled plant the PI ontrollers or F-L topology were set n synhronous rame allowng the elmnaton o the steady-state errors. Although the 3F-B APF uses addtonal swthes and solaton transormers when t s ompared wth F-L APF t requres lower d-bus voltage and s able to ontrol eah phase ndependently. Mathematal analyses o these two topologes were developed n order to obtan a lnear model that represents the phyl system allowng to set the gans o PI urrent ontrollers. The smulaton results were presented to evaluate the perormane o the shunt APFs approahes. Aknowledgement The authors grateully aknowledge the nanal support reeved rom CNPq proess n o 478/9-3 and rom Arauára Foundaton proess n o 6/ Reerenes [] T. M. Gruzs A survey o neutral urrents n three-phase omputer power systems IEEE Trans. on Industry Applatons vol. 6 no. 4 pp July/Aug. 99. [] P. Salmerón S. P. Ltrán R. S. Herrera and J. R. Vázquez A Pratal Comparatve Evaluaton o Derent Atve Harmon Flter n Pro. o ICREPQ paper 3. [3] B. Sngh K. A. Haddad and A. Chandra A Revew o Atve Flters or Power Qualty Improvement IEEE Trans. on Industral Eletrons vol. 46 no. pp Otober 999. [4] N. Mendalek Modelng and Control o Three-Phase Four-Leg Splt-Capator Shunt Atve Power Flter n Pro. o ACTEA pp [] R. Pregtzer J.G. Pnto L.F.C. Montero and J.L. Aonso Shunt Atve Power Flter wth Dynam Output Current Lmtaton n Pro. o ISIE pp [6] I. Z. Abdalla K. S. Rama Rao and N. Perumal Three-Phase Four- Leg Shunt Atve Power Flter to Compente Harmons and Reatve Power n Pro. o ISCI pp. -. [7] V. Khadkkar and A. Chandra An Independent Control Approah or Three-Phase Four-Wre Shunt Atve Flter Based on Three H- Brdge Topology under Unbalaned Load Condtons n Pro. o PESC pp [8] S. Sranthumrong H. Fujta and H. Akag Stablty Analyss o a Seres Atve Flter Integrated Wth a Double-Seres Dode Reter IEEE Trantons on Power Eletrons vol. 7 no. pp. 7-4 January. [9] C. L. Chen C. E. Ln and C. L. Huang An Atve Flter or Unbalaned Three-Phase System Usng Synhronous Deteton Method n Pro. o PESC vol. pp [] S. A. O. da Slva and R. A. Modesto A Comparatve Analyss o SRF-based Controllers Appled to Atve Power Lne Condtoners n Pro. o IECON pp [] A. Kouzou M. O. Mahmoud and M. S. Bouhert A New 3D- SVPWM Algorthm or Four-Leg Inverters n Pro. o IEMDC pp [] H. Pnhero F. Botterón C. Reh L. Shuh R.F. Camargo H.L. Hey H.A. Gründlng and J.R. Pnhero Spae Vetor Modulaton or Voltage-Soure Inverters: A Uned Approah n Pro. o IECON vol. pp RE&PQJ Vol. No. Aprl