Warsaw Unversty of Technology Faclty of Electrcal Engneerng Insttte of Control and Indstral Electroncs Ph.D. Thess M. Sc. Marsz Cchowlas! Thess spervsor Prof. Dr Sc. Maran P. Kamerkowsk Warsaw, Poland 4 - -
The work presented n ths thess was carred ot drng my Ph.D. stdes at the Insttte of Control and Indstral Electroncs at the Warsaw Unversty of Technology. Some parts of the work were realzed n cooperaton wth Unversty of Aalborg, Denmark (Internatonal Danfoss Professor Programme Prof. Frede Blaabjerg), Frst of all, I wold lke to thank Prof. Maran P. Kamerkowsk for contnos spport, help and frendly atmosphere. Hs precos advce and nmeros dscssons enhanced my knowledge and scentfc nspraton. I am gratefl to Prof. Stansław Próg from the AGH Unversty of Scence and Technology, Cracow and Prof. Włodzmerz Koczara from the Warsaw Unversty of Technology for ther nterest n ths work and holdng the post of referee. Frthermore, I thank my colleages from the Intellgent Control Grop n Power Electroncs for ther spport and frendly atmosphere. Specally, to Dr. D.L. Sobczk and Dr. M. Malnowsk for hs spport for my edcaton. Fnally, I wold lke to thank my whole famly, partclarly my wfe Knga and son Kba for thers love and patence. - -
Table of Contents. Introdcton 7. Front-end Rectfers for Adjstable Speed AC Drves 4. Introdcton 4. Adjstable Speed AC Drves 4.3 Drve System Confgratons 5.4 Dode rectfers 6.5 Harmonc Lmtatons 4.6 Conclsons 7 3. Basc Theory of PWM Rectfer 8 3. Operaton of the PWM Rectfer 8 3. Mathematcal descrpton of PWM Rectfer 33 3.3 Block dagram of PWM rectfer 35 3.4 Operatng lmts 37 4. Introdcton to Actve Flterng 39 4. Basc confgraton 4 4. Control of Shnt Actve Flters 4 4.3 Types of Harmonc Sorces 4 4.4 Analyss of Shnt Actve Flter (SAF) Operaton wth Dfferent Harmonc Sorces 44 4.5 Conclsons 47 5. PWM Rectfer wth Actve Flterng Fncton 49 5.. Introdcton 49 5.. Control Methods of PWM Rectfer 5 6. Dmensonng of Power Converters 64 6. PWM Rectfer ratng 65 6.. Shnt Actve Power Flter (SAF) Ratng 68 6.3. PWM Rectfer wth Actve Flterng Fncton Ratng 7 6.4 Desgn of Passve Components 73-3 -
6.5 Conclsons 78 7. Smlaton and Expermental Reslts 79 7. Voltage Orented Control (VOC) 8 7. Vrtal Flx Based Drect Power Control (VF-DPC SVM) 86 7.3 Smmary and Comparson of Compensatng Reslts 9 7.4 Rectfyng and Regeneratve Mode of PWM Rectfer Operaton 9 7.5 Typcal Grd Voltage Dstorton 95 7.6 Inflence of Passve Components, DC-lnk Voltage and Converter Power Varatons 7.7 Dscsson on Dgtal Sgnal Processor Implementaton 7.8 Conclsons 4 8. Smmary and Closng Remarks 7 Appendx 9 A. Harmoncs 43 A. Basc Harmonc Dstorton n Power System 8 A.3 Instantaneos decomposton of powers A.4 Smlatons and Expermental envronments 5 A.5 Revew and desgn of Crrent and Power Controllers References 47-4 -
Symbols α - phase angle of reference vector λ - power factor ϕ - phase angle of crrent ω - anglar freqency ψ - phase angle ε - control phase angle cosϕ - fndamental power factor f freqency (t), nstantaneos crrent k P, k I proportonal control part, ntegral control part t nstantaneos tme v(t), v - nstantaneos voltage Ψ S vrtal lne flx vector Ψ Sα vrtal lne flx vector components n the statonary α, β coordnates Ψ Sβ vrtal lne flx vector components n the statonary α, β coordnates Ψ Sd vrtal lne flx vector components n the synchronos d, q coordnates Ψ Sq vrtal lne flx vector components n the synchronos d, q coordnates S lne voltage vector Sα lne voltage vector components n the statonary α, β coordnates Sβ lne voltage vector components n the statonary α, β coordnates Sd lne voltage vector components n the synchronos d, q coordnates Sq lne voltage vector components n the synchronos d, q coordnates S lne crrent vector Sα lne crrent vector components n the statonary α, β coordnates Sβ lne crrent vector components n the statonary α, β coordnates Sd lne crrent vector components n the synchronos d, q coordnates Sq lne crrent vector components n the synchronos d, q coordnates Lst of symbols - 5 -
C converter voltage vector Cα converter voltage vector components n the statonary α, β coordnates Cβ converter voltage vector components n the statonary α, β coordnates Cd converter voltage vector components n the synchronos d, q coordnates Cq converter voltage vector components n the synchronos d, q coordnates C converter crrent vector Cα converter crrent vector components n the statonary α, β coordnates Cβ converter crrent vector components n the statonary α, β coordnates Cd converter crrent vector components n the synchronos d, q coordnates Cq converter crrent vector components n the synchronos d, q coordnates L nonlnear load crrent vector Lα nonlnear load crrent vector components n the statonary α, β coordnates Lβ nonlnear load crrent vector components n the statonary α, β coordnates Ld nonlnear load crrent vector components n the synchronos d, q coordnates Lq nonlnear load crrent vector components n the synchronos d, q coordnates dc DC lnk voltage dc DC lnk crrent L dc - DC lnk ndctor S a, S b, S c swtchng state of the converter C capactance I root mean sqare vale of crrent L ndctance R resstance S apparent power T tme perod P actve power Q reactve power Z - mpedance p,q- nstantaneos actve and reactve power p ref, q ref - reference vales of nstantaneos actve and reactve powers p A, q A - nonlnear load nstantaneos actve and reactve powers p A, q A - alternated vales of nstantaneos actve and reactve power - 6 -
Sbscrpts..a,..b,..c - phases of three-phase system..d,..q - drect and qadratre component.., -, - postve, negatve and zero seqence component..α,..β,.. alpha, beta components and zero seqence component..h harmonc order of crrent and voltage, harmonc component..n harmonc order..max - maxmm..mn - mnmm..ll - lne to lne..load - load..ref - reference..m - ampltde..rms - root mean sqare vale Abbrevatons APF Actve Power Flter AFF Actve Flterng Fncton ANN Artfcal Neral Network ASD Adjstable Speed Drves DPC Drect Power Control DSP Dgtal Sgnal Processor HPF Hgh Pass Flter LPF Low Pass Flter EMI Electro-Magnetc Interference IGBT Inslated Gate Bpolar Transstor PCC Pont Of Common Coplng PFC Power Factor Correcton PI Proportonal Integral (Controller) PLL Phase Locked Loop PWM Plse-Wdth Modlaton REC Rectfer SVM Space Vector Modlaton THD Total Harmonc Dstorton - 7 -
UPF VF VF-DPC VSI Unty Power Factor Vrtal Flx Vrtal Flx Based Drect Power Control Voltage Sorce Inverter Basc Defntons Harmonc Dstorton HD = X n X % X RMS vale of frst harmonc of voltage or crrent X n RMS vale of n harmonc of voltage or crrent Total Harmonc Dstorton THD Power Factor = X n n > % X X RMS vale of frst harmonc of voltage or crrent X n RMS vale of n harmonc of voltage or crrent I PF = cosϕ I Partal Weghted Harmonc Dstorton PWHD = h= 4 I hi h % Harmonc Constant HC = h= I h I h % Remark: Please note that lteratre s nmbered sng [x,y] nomenclatre, where x denotes a topc and y nmber of paper - 8 -
. Introdcton Modern electrc devces are sally fed by dode or thyrstors front-ends. Sch eqpment generates hgher harmoncs nto a grd. Nowdays those problems are gong more and more seros. Grds dstrbances may reslt n malfncton or damage of electrcal devces. Therefore, crrently many methods for elmnaton of harmonc pollton n the power system are developed and nvestgated. Restrctons on crrent and voltage harmoncs mantaned n many contres throgh IEEE 59-99 n the USA and IEC 6-3-/IEC 6-3-4 n Erope standards, are assocated wth the poplar dea of clean power. Harmonc redcton technqes can be dvded as shown n Fg.., where two man grops can be seen: - devces for cancellaton of exstng harmoncs, - grd frendly devces, whch do not generate (or generate lmted nmber) harmoncs. Fg.. Most poplar crrent harmonc redcton technqes n three-phase networks - 9 -
The classcal method of crrent harmonc redcton ses passve LC flters (Fg..) [7,.5,.7]. They are sally constrcted as capactors and ndctors seres or parallel-connected to the grd. Each harmonc (5 th, 7 th, th, 3 th ) reqres ts own passve flter (see Fg..). Ths means that flters can not be desgned n a general way bt mst be desgned accordng to each applcaton. Sch a solton has advantages of smplcty and low cost. However, among dsadvantages are: A passve flters are desgned for a partclar applcaton (sze and placement of the flters elements, rsk of resonance problems), hgh power losses as a reslt of hgh fndamental crrent, passve flters are heavy and blky. 5 th 7 th th 3 th Fg... LC passve flters The smpler way to harmonc redcton of dode rectfer crrents are addtonal seres ndctors sed n the npt or otpt of rectfer (typcal per nt vale s -5%) (see Chapter ). Other technqe, based on mxng sngle and three-phase (Fg..3a) non-lnear loads [7.7,.], gves a redced THD becase the 5 th and 7 th harmonc crrent of a sngle-phase dode rectfer often are n conter-phase wth the 5 th and 7 th harmonc crrent of a three-phase dode rectfer. Smlated npt crrent waveform s presented n Fg..3 b. - -
Fg..3. Mxed sngle and three-phase nonlnear loads and typcal lne crrent waveforms The mltplse rectfer [3] gves another possblty to decrease crrent harmoncs content. Althogh t s easy to mplement, t possess several dsadvantages sch as: blky and heavy transformer, hgher voltage drop, and hgher harmonc crrents at non-symmetrcal load or lne voltage condtons. 6-plse rectfer -plse rectfer 4-plse rectfer Y Y Y Y Y Y Y Y Fg..4. Basc schemes and typcal lne crrent waveforms of mltplse rectfers A modern alternatve to the passve flter s applcaton of the Shnt Actve Flters (SAF) [5, 7, 8], whch, thanks to sed closed feedback loops, gves better dynamcs and control of harmonc as well as fndamental crrents. Actve flters are generally dvded nto two - -
grops: the actve shnt flter (crrent flterng) (Fg..5) and the actve seres flter (voltage flterng). S S L Non-lnear load C APF L Fg..5. Three-phase shnt actve flter together wth non-lnear load The three-phase (two-level) shnt SAF conssts of voltage sorce brdge converter. Ths topology s dentcal to the PWM nverter. SAF represents a controlled crrent sorce C whch added to the load crrent L yelds snsodal lne crrent S and provde: harmonc compensaton (mch effectves than passve flters). compensaton of fndamental reactve components of load crrent, load symetrzaton (from grd pont of vew), Parallely to excellent performance, SAF possess few dsadvantages as: complex control strategy, swtchng losses and EMC problems. Therefore, nclson of a small LC or LCL passve flter between the grd and the SAF s necessary. S Load Fg..6 PWM Rectfer The other possble redcton technqe of crrent harmonc s applcaton of PWM Rectfer (Fg..6). Two types of PWM converters, wth a voltage sorce otpt [4] (Fg..7a) and a crrent sorce otpt (Fg..7b) can be sed. Frst of them called a boost rectfer (ncreases the voltage) operates at fxed DC voltage polarty, and the second, called a bck rectfer (redces the voltage) operates wth fxed DC crrent flow. - -
a) b) load load L dc La a U C La a b b Lb Lc c 3xL U dc Lb Lc c 3xL U dc Fg..7 Basc topology of PWM rectfer a) boost wth voltage otpt, b) bck wth crrent otpt 3xC Among the man featres of PWM rectfers are: b-drectonal power flow, nearly snsodal npt crrent, reglaton of npt power factor to nty, low harmonc dstorton of lne crrent (THD below 5%), adjstment and stablzaton of DC-lnk voltage (or crrent), redced capactor (or ndctor) sze de to the contnes crrent. Frthermore, t can be properly operated nder lne voltage dstorton and notchng, and lne voltage freqency varatons. Ths thess s devoted to nvestgaton of two dfferent control strateges for boost type of three-phase brdge PWM rectfers. A well-known method based on crrent vector orentaton wth respect to the lne voltage vector (Voltage Orented Control - VOC) s compared wth control strategy based on nstantaneos drect actve and reactve power control based on vrtal flx estmaton called Vrtal Flx based Drect Power Control (VF-DPC). Addtonally, n both control strateges an Actve Flterng Fncton s appled. Therefore, the followng thess can be formlated: Applcaton of Actve Flterng Fncton to PWM Rectfer control strategy provdes more effcent tlzaton of power electroncs eqpment and leads to netralzaton of harmoncs generated by other nonlnear loads. Ths, t mproves the lne crrent and voltage at the pont of common coplng (PCC). - 3 -
In order to prove the above thess, the athor sed an analytcal and smlaton based approach, as well as expermental verfcaton on the laboratory setp wth a 5kVA IGBT converter. In the analytcal approach mathematcal descrpton based on space vector are appled. The followng smplfcatons were assmed when formlated smlaton models: power transstors were consdered as deal swtches, however, the voltage drop has been taken nto accont, power dodes were dealzed, models of passve components nclded ndctance wth resstance and capactance wth resstance. The thess deals wth analyss and comparatve stdy of dfferent control strateges for PWM Rectfers havng Actve Flterng Fncton (AFF). At legatng a general nformaton regardng dode rectfers, to well nderstand and recognton of harmoncs problems generated by them are presented and dscssed. Two dfferent control schemes for PWM Rectfers and three dfferent methods for elmnaton of crrent harmoncs are presented. Addtonally, nformaton concernng desgn of crrent and power controllers, selecton of passve components and power converter ratng calclaton are consdered. The PhD thess conssts of 8 chapters The frst Chapter Introdcton gves short overvew of harmonc redcton technqes and formlates man goals of the thess. The second one Front-end Rectfers for Adjstable Speed Drves deals wth reqrements for dode rectfer, whch are most common sed n nverter fed adjstable speed drves. Several models of dode rectfers wth dfferent AC and DC sde flters are presented, as well as nformaton abot crrent harmoncs generated by sch a rectfers. Addtonally, reqrements for passve elements of dode rectfers are presented. Fnally, nternatonal norms devoted to harmoncs pollton n the grd are nclded. The thrd chapter ttled Basc Theory of PWM Rectfer conssts of theoretcal nformaton, mathematcal models, basc reqrements and lmtatons for PWM rectfers. The forth chapter Introdcton to Actve Flterng descrbes basc prncples of parallel actve power flters, prncples of shnt actve flters for crrent and voltage harmoncs sorces. The ffth chapter PWM Rectfer wth Actve Flterng Fncton presents and nvestgates, an nterestng opportnty for PWM rectfer flterng fncton. It s a reslt of conjncton a PWM rectfer and Actve Power Flter. Both of them has the same power crct, as well as a control strateges are very smlar, therefore sch eqpment can be nterestng alternatve for expensve actve flterng nts. Two dfferent control strateges are descrbed: VOC (Voltage Orented Control) wth two dfferent methods of compensaton - 4 -
hgher crrent harmoncs and VF-DPC (Vrtal Flx based Drect Power Control). Very mportant chapter sxth Dmensonng of Power Converters deals wth dmensonng of power converter, takng nto accont a parameters lke: demanded actve power of DC load, npt flter ndctance, reactve and harmoncs power ntended to compensaton. Addtonally, reqrements for passve elements of power converters are presented. The chapter sevenths enttled Smlaton and Expermental Reslts presents smlaton models developed n thess and selected waveforms whch show operaton of nvestgated control algorthms. Also, comparatve stdy of Voltage Orented Control (VOC) verss Drect Power Control (DPC) s presented. The last chapter eght Smmary and Closng Conclsons gves general overvew and fnal conclsons on dscssed topc. Several nformaton, devoted to harmonc dstorton n power system, nstantaneos decomposton of powers accordng to dfferent athors lke: Peng, Akag, etc. are presented n Appendx A.. Addtonally, general nformaton concernng smlaton models, sed smlaton packages (SABER, MATLAB/SIMULINK, PLECS) and laboratory setp are gven n Appendx A.4. Also, Appendx A.5 presents desgn algorthms for crrent (for VOC) and power (for VF-DPC), PI type reglators. An Artfcal Neral Network based, resonant crrent controllers as well as delta modlaton and hystereses controllers are presented. In the athor s opnon the followng parts of the thess represent hs orgnal contrbtons: elaboraton of Vrtal Flx based Drect Power Control for PWM rectfers wth Actve Flterng Fncton control strategy (Chapter 5), elaboraton of methodology for converter power rato calclatons dependng on applcaton PWM Rectfer, Actve Power Flter, PWM Rectfer wth Actve Flterng Fncton (Chapter 6), development of two smlaton algorthms n Matlab/Smlnk and SABER wth control algorthm n C langage for nvestgaton of proposed soltons (Appendx A.4), mplementaton and nvestgaton of varos closed-loop control strateges for PWM rectfers: Vrtal Flx Based Drect Power Control (VF -DPC), Voltage Orented Control (VOC), as well as open loop and closed loop control strateges for PWM Rectfer wth Actve Flterng Fncton, practcal verfcaton on the expermental setp based on a mxed RISC/DSP (PowerPC 64/TMS3F4) dgtal controller. - 5 -
. Front-end Rectfers for Adjstable Speed AC Drves. Introdcton Voltage sorce nverters (VSI) fed adjstable speed drves (ASD) are freqently sed n ndstry, especally n energy savng applcatons. In the conventonal solton the nverter s fed by a dode or thyrstor rectfer [7.8] wth a large DC lnk capactor. Sch a rectfer takes a hgh dstorted AC-grd crrent. Freqent se of sch rectfers as ASD front-ends has reslted n seros tlty problems lke crrent and voltage harmoncs, reactve power, voltage notches, etc. Voltage harmoncs de to crrent harmoncs becomes the man problem for tlty. A sal way to redce hgh crrent harmoncs s applcaton of a DC or AC-sde ndctors. Compared to DC-sded smoothng ndctor, an AC-sde ndctor creates an electrcal dstance between grd and a drve. However, the AC-ndctor s a sorce of addtonal losses, has a meanngfl dmenson and determnes an addtonal cost. Fg.. shows scheme of tlty nterface for converter-fed drves [7.]. These soltons do not provde recommended IEEE 59 harmonc standards, whch reqre voltage dstorton lmtaton at tlty-cstomer pont of common coplng (PCC). IEEE 59 s a jstfcaton for sng of power qalty compensators. V S Motor PCC AC sde flter Dode rectfer DC sde flter Inverter Fg.. Converter-Fed adjstable drves tlty nterface typcal scheme. Adjstable Speed AC Drves The ASDs npt crrent characterstcs depend on: drve type, ts load, and the characterstcs of the spplyng system [7.4, 7.5]. The npt crrents harmonc dstorton can vary over a wde range. However, for prposes of analyss t s possble to dentfy two basc waveform types as bellow []. - 6 -
TYPE : Dscontnos mode - Hgh Dstorton Crrent Waveform. Ths s a representaton of all ASDs that have voltage sorce nverters wthot an addtonal ndctor for crrent smoothng (Fg..3a). The total harmonc crrent dstorton can be over 8%. Actally, t can be hgher for small drves bt waveform of Fg..3b s a good representaton for larger drves or grops of smaller drves. TYPE : Contnos mode - Low Dstorton Crrent Waveform. Ths mode represents behavor of DC drves, large AC drves wth crrent sorce nverters, and smaller AC drves wth voltage sorce nverters and added ndctor for crrent smoothng (Fg..4a). The typcal waveform of Fg..4b has a THD level of 3%, whch s obtaned for an AC drve wth a 5% ndctor. The sgnfcant harmonc redcton s obtaned for ASDs jst by addng an ndctor at the rectfer npt. Fg..5 llstrates the effect of AC-sde ndctance sze on npt crrent dstorton. It s possble to nclde ths ndctance n the DC lnk of the drve, provdng the same harmonc crrent redcton beneft..3 Drve system confgratons "#$#%&'( A DC-sde ndctor can be added to a three-phase rectfer (Fg..) for harmonc redcton. Wth the dc ndctor of a sffcent amont, the npt crrent becomes a sqare waveform. By addng an nfnte dc ndctor, a perfect sqare waveform can be obtaned. However, a perfect sqare waveform wll have dffcltes to meet the ndvdal lmts for hgher order harmoncs. V S Motor Fg... Dode rectfer wth DC sde capactor and ndctor. Inpt crrent THD=6%-3% - 7 -
"#$#"&''( Another solton s to add a seres AC-sde ndctor or passve flter to remove ndvdal harmoncs. Fg..3 shows the crct arrangement wth a LC flter n front of the rectfer together wth a DC-sde ndctor. Generally, sch a LC flter can be tned to the 5 th or 7 th harmonc becase they are most mportant. Once the 5 th harmonc s cancelled, rest of harmoncs can also be redced sgnfcantly n the same way. V S Motor Fg..3. Dode rectfer wth DC sde capactor and ndctor flter and AC sde ndctor. Inpt crrent THD=3%-4% Fg..4 compares harmonc contents for dfferent DC-sde ndctors. The three-phase dode rectfer generates abot 7-percent 5th harmonc. After addng % and 5% DC-sde ndctor, the 5th harmonc content s redced to 35% and 5%, respectvely. Therefore, an ndvdal harmonc flter n addton to the DC-sde ndctor s necessary to meet IEC -3-4 standards. 8 6 T h r e e p h a s e r e c t f e r % D C n d c t o r 5 % D C n d c t o r I E C - 3-4 S t a n d a r d HD [%] 4 5 7 9 3 5 7 9 H a r m o n c n m b e r Fg..4. Comparson between dfferent three-phase blt-n passve compensaton reslts and IEEE standard - 8 -
.4 Dode rectfers "#)#%#* &'( The dealzed model of three-phase dode rectfer wth nfnte DC-sde ndctor s presented n Fg..5a. a) b) L DC A B C L o a d A /6π 5/6π π Fg..5 Ideal three phase rectfer wth nfnte DC-sde ndctor L dc and no grd mpedance (a), Voltages and crrents of dealzed three phase rectfer (b). The dealzed rectfers crrent assmed to be smooth on the DC-sde (nfnte L DC ) and, for neglected commtaton effects (L S =), occrs an deal sqare. As shown o Fg..5b the crrent changes nstantaneosly from zero to a fnte vale. Every phase s condctng only drng /3 of the perod. The npt dode rectfer crrent can be descrbed n followng form: 5 π < ωt < π 6 5 I π < ωt < π 6 6 sa ( t) = π < ωt < π 6 6 5 I π < ωt < π 6 6 5 π < ωt < π 6 The dealzed npt crrent can be also expressed by Forer seres as: (.) 3 4I sa ( t) = (snωt sn 5ωt sn 7ωt snω t sn3 ωt...) (.) π 5 7 3 There s no trple harmoncs, becase consdered three-phase system operates wthot netral wre. The dealzed three-phase dode rectfer has THD=3.%. Eqatons (.6a) and (.6b) - 9 -
can be sed to determne the order and magntde of the harmonc crrents drawn by a sxplse dode rectfer: h = 6 k ± k =,, 3. (.3a) I h = / h (.3b) I Ths, the hgher harmonc orders are: 5 th, 7 th, th, 3 th etc., wth a 5 Hz fndamental freqency, that corresponds to 5, 35, 55 and 65 Hz, respectvely. The per nt magntde of the harmoncs of the fndamental s the recprocal of the harmonc order: % for the 5 th, 4,3% for the 7 th, etc. Eqs. (.)-(.) are calclated from the Forer seres for deal sqare wave crrent (crtcal assmpton for nfnte ndctance on the npt of the converter). Eqaton (.) s farly good descrpton of the harmonc orders generally encontered. The magntde of actal harmonc crrents often dffers from the relatonshp descrbed n (.). The shape of the AC crrent depends on the npt ndctance of converter. The rpple crrent s proportonal to /L tmes the ntegral of the DC rpple voltage and nverse proportonal to L DC ndctance. rpple = U DCdt L (.4) "#)#"* &'( A dode rectfer wth DC-sde smoothng capactor s common sed front-end rectfer n ndstry. Its constrcton s very cheap and compact, however from the grd pont of vew t has the worst behavor. a) b) L o a d Fg.. 6. Three-phase rectfer wth smoothng DC sde capactor a) crct, b) typcal waveforms - -
The dealzed model of three-phase dode rectfer wth DC-sde capactor s presented n Fg..6a. Typcal npt crrent waveform presents Fg..6b, and as shown t contans hgh nmber of hgher harmoncs and the THD s over 8%. "#)#$* '( &' &'( The dealzed model of three-phase dode rectfer wth AC-sde ndctor and DC-sde capactor s presented n Fg..7a [.5,.6,.8]. Typcal npt crrent waveforms are presented n Fg..7b and.7c wth % and 5% AC-sde ndctor, respectvely. It can be seen that, an npt crrent of Fg..7c conssts less hgher harmoncs and has lower THD compared wth crrent of Fg..7b. Fg..7. Dode rectfer wth AC-sde ndctors (a) and typcal for % and 5% ndctor (b). - -
8 Inpt crrent THD [%] 7 6 5 4 3 3 4 5 Choke ndctance [%] Fg..8. Effect of npt ndctance on ASDs npt crrent dstorton Fg..8 presents effect of npt ndctor on npt crrent THD. The npt crrent THD decrease wth ncreasng vale of npt ndctance. Therefore, sch a solton partally solves a harmonc problem. However, applcaton of npt ndctance generates some addtonal problems. One of them s the phase shft between fndamental harmoncs of grdvoltage and npt crrent, whch s very mportant parameter determnng the reactve power level. Fg..9 shows that t strongly depends and ncreases n case of ncreasng npt ndctance or load power. Phase shft between frst harmoncs of lne voltage and npt crrent [deg] - -5 - -5 4 8 6 npt ndctance [m H ] DC [A] Fg..9. Phase shft between frst harmoncs of grd voltage and npt crrent verss AC-sde ndctance or load power. - -
Fg.. presents smlated waveforms for dode rectfer wth AC-sde ndctance and DCsde capactance for two dfferent load condtons. The decreasng ampltde and phase shft s present n case of ncreasng load condtons. That gves an addtonal reactve power taken by the converter. Fg... Typcal npt crrent waveforms for two dfferent DC-sde crrents: Idc=3A (ble), Idc=5A (green) Appled npt ndctance vale has an addtonal effect on a dode rectfer operaton [9]. Adopton of t, besdes of decreasng of harmonc dstorton and ncreasng of reactve power determne of decreasng of t parameter. Fg... parameter of dode rectfer npt crrent verss npt ndctance vale t a) L L =mh, b) L L =mh - 3 -
As shown n Fg.. an npt ndctance vale has a great nflence on t parameter of dode rectfer grd crrent. A large vale of npt ndctance decrease sgnfcantly of t parameter. Addtonal npt ndctance s the smplest method to redce grd crrent harmoncs generated by dode rectfers feded adjstable speed drves (ASD) converters. Smmarzng, the npt ndctor has followng mpact on dode rectfer operaton: Sgnfcantly redce a grd crrent THD, Decrease a t parameter, Increase reactve power vale taken by the converter, A sorce of addtonal voltage drop. "#)#) Dode rectfer wth DC-sde capactance 8 6 Grd crrent THD [%] 4 8 4 6 8 DC-lnk capactance [F] Fg... Grd crrent THD verss DC-lnk capactance Fg.. shows the grd crrent THD verss DC-lnk capactance. A large vale of capactance provde more smooth shape of DC-lnk voltage, however a grd crrent wll have hgher ampltde. That sgnfcantly ncrease a grd crrent THD. - 4 -
Dode rectfer wth DC-sde capactance and ndctance 43 a) b) 4 38 36 Lne crrent THD [%] 4 4 39 38 Grd crrent THD [%] 34 3 37 3 4 6 8 DC-lnk capactance [F] 3 4 5 DC-lnk ndctance [mh] Fg..3. a) Grd crrent THD verss DC-lnk capactance, b) Grd crrent THD verss DC-lnk ndctance In ths staton a DC-lnk ndctance provde a contnos mode of dode rectfer operaton. Therefore, both a large vale of a DC-lnk capactance and ndctance provde decreasng of npt crrent THD. However, there are the maxmal vales for capactance and ndctance (5F and 3mH, respectvely), above whch ncreasng of those parameters s not proftable, becase the grd crrent THD do not decrease enogh. Dode rectfer wth AC-sde ndctance and DC-sde capactance a) b) 34, 33,5 8 Grd crrent THD [%] 33, 3,5 3, Grd crrent THD [%] 6 4 3,5 4 6 8 DC-lnk capactance [F] 5 5 5 AC-sde ndctance [mh] Fg..4. a) Grd crrent THD verss DC-lnk capactance, b) Grd crrent THD verss AC-sde ndctance Here, for a grd crrent smoothng the AC-sde ndctor s appled. Smlar, lke n prevos staton both a large vale of a AC-sde ndctance and DC-lnk capactance provde decreasng of npt crrent THD. Moreover, there are also the maxmal vales for capactance - 5 -
and ndctance (5F and 5mH respectvely), above whch ncreasng of those parameters s not proftable, from a grd crrent THD pont of vew. Compared to a PWM Rectfer, a dode rectfer needs mch bgger vales of passve elements to obtan stable DC voltage and acceptable npt crrent THD vale [.3]. However, even wth bg vale of npt ndctors, a dode rectfer s not able to complete nternatonal norms from the grd crrent THD pont of vew. C = P ot π 54 f U U grd LL DC (.5) C [F].5..9.6.3 4 6 8 P [kw] Fg..5. DC-sde capactor vale verss the otpt power Fg..5 presents a DC-sde capactor vale verss the otpt power for chosen and stable vale of DC-lnk voltage and gven peak rpple DC-lnk voltage reqrements. A dode rectfer to have the peak rpple voltage on the same level lke a PWM Rectfer needs larger DC-lnk capactor sze. Ths can be a reslt, that a dode rectfer operates wth a grd freqency f grd, whle a PWM Rectfer operates wth a swtchng freqency f s whch s mch faster than the grd freqency. A voltage sorce PWM nverter wth dode front-end rectfer s one of the most freqently power confgraton sed n varable speed AC drves. Ths solton has followng advantages: smple, robst and low cost. However, t allows only ndrectonal power flow. Therefore, regeneratve mode s not possble and energy mst be dsspated on power resstor controlled by chopper connected across the DC lnk. The other mportant dsadvantages are: low power factor and hgh level of harmoncs present n an npt crrent. - 6 -
.5 Harmonc Lmtatons Severe crrent or voltage harmoncs may damage or malfncton varos electronc eqpment sppled from the grd. However, a level of grd dstorton where those problems can occr s not precsely defned. The man reason of harmoncs n power system s electronc eqpment manly a dode rectfers, mostly spread power electronc AC/DC converters. The reason of dode rectfer poplarty s very smple, t s cheap, robst, effcent, relable and has a small sze. However, a dode rectfer has one bg dsadvantage sgnfcantly dstorted npt crrent. Therefore, problems related to harmoncs prodced n the grd by dode rectfers, cased necessty of defne and arrange reqrements for nonlnear electronc eqpment. Internatonal norm precsely defne maxmal harmonc content n a grd voltage as well as n the crrent taken by electronc eqpment. Norms dvde electronc devces dependng on maxmm permssble crrent and force an applcaton of eqpment lke passve and actve flters or PWM Rectfers. "##%*,,,%-(%--" %--" Ths standard sets lmts for harmonc voltage and crrents at the Pont of Common Coplng (PCC), therefore the focs s only on the power system. It places responsblty on large commercal and ndstral consmers. Voltage Dstorton Lmts Bs Voltage at PCC Indvdal voltage dstorton [%]* Total voltage dstorton [%] below 69kV 3. 5. 69kV to 38kV.5.5 Above 38kV..5 * maxmm for ndvdal harmonc Crrent Dstorton Lmts Maxmm odd harmonc crrent dstorton n percent of I L for general dstrbton systems (.V 69kV) I SC /I L < <n<7 7<n<3 3<n<35 35<n TDD < 4...5.6.3 5. <5 7. 3.5.5..5 8. 5<. 4.5 4..5.7. <. 5.5 5... 5. > 5. 7. 6..5.4. I SC - maxmm short crct crrent at the PCC - 7 -
I L - fndamental of the average (over months) maxmm monthly demand load crrent at PCC TDD total demand dstorton, harmonc crrent dstorton n % of maxmm demand load crrent (5 or 3 mnte demand) "##"*,'.%///($("*,'%/// "*,'%///($(" " The Eropean standard IEC 6 defnes the crrent dstorton lmts for eqpment connected to the pblc spply system. The objectve s to lmt the voltage dstorton and s addressed to small cstomer eqpment. Emphass on pblc, low-voltage and hosehold. IEC -3- Lmts for Class D Eqpment Harmonc order Maxmm permssble harmonc crrent per watt Maxmm permssble harmonc crrent N ma/w A 3 3.4.3 5.9.4 7..77 9.5.4.35.33 3<n<39 (odd har. only) 3.85/n Refer to class A "##$*,'.%///($()*,'%/// )*,'%///($() ) Ths standard s addressed for larger cstomers (sngle and three-phase harmonc lmts). It gves a consderaton of the short crct rato R SCC. IEC -3-4 lmts for three-phase eqpment Mnmal R SCC Upper lmts for harmonc dstorton factors Lmts for ndvdal harmonc n % of I THD PWHD I 5 I 7 I I 3 66 7 9 6 8 9 5 8 75 5 33 4 8 5 35 39 3 8 3 8 35 48 46 4 5 5 45 58 5 5 35 5 >6 7 57 6 4 5 8-8 -
.6 Conclsons Internatonal standards mpose voltage and crrent harmonc lmts. Many soltons has been desgned to deal wth these standards. The smplest compensaton method s to se an AC-sde ndctor or an AC-sde LC flters. However, when sng these passve compensaton methods some problems can occr: - Rectfer npt voltage dstorton and otpt DC lnk voltage redcton by AC-sde ndcton. - Rectfer npt crrent agmentaton by parallel connected flters. The actve compensaton s therefore preferred n case of performance bass, bt ts cost and complexty s a man problem. - 9 -
3. Basc Theory of PWM Rectfer As shown n Chapter, dode rectfers are most freqently appled converters n AC/DC power converson. However, becase of sgnfcantly dstorted npt crrent, whch s not acceptable n respect to nternatonal standards, dode rectfers shold be replaced be other, not polltng and lne power frendly eqpment. Therefore, converters whch present a low nteracton on the grd are gong more nterested. The three phase VSC (Voltage Sorce Converter) appled as a grd nterface stage called Boost actve rectfer, can take near snsodal npt crrent wth a near nty power factor bt also t can work n both rectfyng and regeneratve modes. From the relablty and effcency pont of vew a PWM Rectfers are very promse soltons [, 4, 6., and 6.4]. The PWM Rectfer, by many s consdered as most obvos alternatve to conventonal dode rectfer. Ths chapter ntrodces and presents bascs of operaton of PWM Rectfer and operaton lmtatons. Also, mathematcal models n dfferent reference frames are presented. The basc reqrements of a PWM Rectfer can be defned as follows: b-drectonal power flow, low harmonc dstorton of lne crrent, reglaton of npt power factor to nty, adjstment and stablzaton of DC-lnk voltage, redced DC flter capactor sze. 3. Operaton of the PWM Rectfer Fg. 3.b shows a sngle-phase representaton of the PWM boost Rectfer crct presented n Fg. 3.a. The L and R represent the lne ndctor. S s the lne voltage and C s the brdge converter voltage controllable from the DC-sde. Magntde of C depends on the modlaton ndex of the VSC and DC voltage level. - 3 -
a) b) jωlc RC L C R S c Fg. 3.. Smplfed representaton of three-phase PWM rectfer for b-drectonal power flow a) Man crct b) sngle-phase representaton of the rectfer crct (a) q ε C S jl C d (b) C q ε S R C C jl C d C R C Fg. 3.. Phasor dagram for the PWM rectfer a) rectfcaton at nty power factor b) nverson at nty power factor Indctors L connected a npt of PWM converter wth a grd are ntegral part of the rectfer crct. It brngs crrent sorce character of npt crct and provde boost featre of converter. The lne crrent C s controlled by the voltage drop across the ndctance L nterconnectng two voltage sorces (grd and PWM converter). It means that the ndctance voltage I eqals the dfference between the lne voltages S and the converter voltage C. When a phase angle ε and ampltde of converter voltage C s controlled, ndrectly phase and ampltde of lne crrent s controlled. In ths way average vale and sgn of DC crrent s controlled and s proportonal to actve power flowng throgh converter. The reactve power can be controlled ndependently wth shft of fndamental harmonc crrent C n - 3 -
respect to voltage S. Fg. 3. presents general phasor dagram for both rectfcaton and regeneraton modes when nty power factor s reqred. The fgre shows that the voltage vector C s hgher drng regeneraton (p to 3%) then rectfer mode [6.6]. Ths, PWM Rectfer has two operaton modes: Rectfyng mode, Regeneratng mode. Natrally, n a real system the power losses are present becase of: Power transstors swtchng losses, AC-sde ndctor losses, Heatng losses and others. P losses V S Load Rectfyng mode P grd = P load P losses Regeneratng mode P grd = P load - P losses Fg. 3.3. Power flow n actve PWM rectfer A three-phase symmetrc system represented n a natral coordnate system by phase qanttes lke for example voltages (Fg. 3.4), can be replaced by one resltant space vector. k = k A( t) akb ( t) a kc ( t) 3 (3.) Where: ka( t), kb ( t), kc ( t) - denote arbtrary phase qanttes n a system of natral coordnates (A, B, C) satsfyng the condton k ( t) k ( t) k ( t) =, a, a - Complex nt vectors, - Normalzaton factor 3 A B C - 3 -
Fg. 3.4. Confgraton of space vector Man crct of brdge converter (Fg. 3.a) conssts of three legs wth IGBT transstor or, n case of hgh power, GTO thyrstors. The brdge converter voltage can be represented wth eght possble swtchng states (sx-actve and two-zero) descrbed by eqaton 3.. Fg. 3.5a presents converter strctres for eght dfferent swtchng states. k= U k= U S a = S b = A B C S c = U D C S a = S b = A B C S c = U D C - - k= U 3 k= 3 U 4 S a = S b = A B C S c = U D C S a = S b = A B C S c = U D C - - k= 4 U 5 k= 5 U 6 S a = S b = A B C S c = U D C S a = S b = A B C S c = U D C - - U U 7 S a = S b = A B C S c = U D C S a = S b = A B C S c = U D C - - Fg. 3.5a Possble swtchng states (S a, S b, S c ) of PWM brdge converter - 33 -
k 3 j( k ) π / 3 U DCe k =...6 = k =,7 (3.) As mentoned n Fg. 3.5a eght possble states of the converter can be presented n vector representaton (Fg. 3.5b). Therefore, demanded command vector, wll be constrcted sng the nearest accessble vectors [.,.]. Fg. 3.5b Representaton of npt voltage as a space vector Fg. 3.5b presents of npt voltage as a space vector as was mentoned n Fg. 3.5a. Only one swtch n the leg of converter (Fg. 3.a) can be trn on n one tme, f two of them wll be trn on, the short crct of DC-lnk wll happen. To protect the converter, a delay tme (dead tme) n transstor swtchng sgnals mst be appled [.3]. The dead tme effect prodces a nonlnear dstorton of the average voltage trajectory. Therefore, for the proper operaton a compensaton of dead tme s reqred. - 34 -
3. Mathematcal descrpton of PWM Rectfer U DC U DC U DC U DC U DC U DC U DC U DC U DC U DC U 3 DC U 3 DC Fg. 3.6 Representaton of converter otpt voltages: a) eqvalent scheme of the converter, b) otpt voltages $#$#% Three phase grd voltage and the fndamental lne crrent are descrbed as: = E snωt (3.3a) AN m π BN = Em sn( ωt ) 3 (3.3b) π CN = Em sn( ωt ) 3 (3.3c) = I sn( ωt ϕ) (3.4a) AN m π BN = Im sn( ωt ϕ) 3 (3.4b) π CN = Im sn( ωt ϕ) 3 (3.4c) where E m (I m ) and ω are ampltde of the phase voltage (crrent) and anglar freqency, respectvely. Wth assmpton - 35 -
AN BN CN (3.5) we can transform eqatons (3.3) to a statonary α-β system and the npt voltage n α-β frame are expressed by: 3 S α = Em sn( ωt) (3.6) 3 Sβ = Em cos( ωt) (3.7) Smlarly, the npt voltages n the synchronos d-q coordnates are expressed by: 3 Sd E m Sα Sβ = = (3.8) Sq $#$#"* Lne to lne npt voltages of PWM rectfer can be descrbed as: = ( S S ) (3.9a) AB A B DC = ( S S ) (3.9b) BC B C DC = ( S S ) (3.9c) CA C A DC and phase voltages are eqal: AN = fa DC (3.a) BN = fb DC (3.b) CN = fc DC (3.c) where: f f f a b c S A ( SB SC ) = (3.a) 3 SB ( S A SC ) = (3.b) 3 SC ( S A SB) = (3.c) 3 The f a, f b, f c are assme, ±/3 and ±/3. - 36 -
3.3 Block dagram of PWM rectfer $#)#% ( The voltage eqatons for balanced three-phase system wthot the netral connecton (Fg. 3.) can be wrtten as: S = I C (3.) dc S = RC L C (3.3) dt Sa Ca Ca Ca d Sb R Cb L Cb = Cb dt Sc Cc Cc Cc and addtonally for crrents d dt dc C SaCa SbCb ScCc dc (3.4) = (3.5) A block dagram of PWM rectfer correspondng to Eqs(3.3-4) s shown n Fg. 3.7. Sa - S R sl Ca dc sc - dc S a a f a - Sb S b - S b R sl f b Cb - 3 Sc S c - Sc R sl Cc f c - Fg. 3.7. Block dagram of voltage sorce PWM rectfer n natral three-phase coordnates $#)#" (3 3 Eq.3.3 after coordnate transformaton wll receve followng form: dcd Sd = RCd L ωlcq Cd (3.6a) dt - 37 -
dcq Sq = RCq L ωlcd Cq dt (3.6b) ddc C = ( Cd Sd CqSq ) dc dt (3.7) where: S d = S cos ωt S snωt ; = S cosωt S snωt α β S q β Sα = (Sa Sb Sc ) ; S β = ( S b S c ) 6 A block dagram of PWM Rectfer n synchronos rotatng d-q model [6.5] s presented n Fg. 3.8. α Fg. 3.8. Block dagram of voltage sorce PWM rectfer n synchronos d-q coordnates R can be practcally neglected becase voltage drop on resstance s mch lower than voltage drop on ndctance, what gves smplfcaton of Eq. 3.3. dc S = L C (3.8) dt Sa Ca Ca d Sb L Cb = Cb dt (3.9) Sc Cc Cc Sα d Cα C α L = Sβ dt (3.) Cβ Cβ Therefore, Eq. 3.6a and b receve followng shape: dcd Sd = L ωlcq Cd (3.a) dt - 38 -
dcq Sq = L ωlcd Cq (3.b) dt The actve and reactve power sppled from the grd s gven by { * } p = = = (3.) Re S C Sα Cα Sβ Cβ Sa Ca Sb Cb Sc Cc * { S } Sβ Cα Sα Cβ ( Sc Ca Sa Cb Sb Cc ) q = Im = = (3.3) 3 It gves n the synchronos d-q coordnates: 3 p = ( SqCq SdCd ) = EmIm (3.4) q = ( ) (3.5) Sq Cd Sd Cq For a nty power factor operaton, followng condtons can be obtaned: Cq =, Sq =, Sd 3 = Em, Cd 3 = Im, q = (3.6) 3.4 Operatng lmts For proper operaton of PWM rectfer a mnmm DC-lnk voltage s reqred [4, 6, 6.3]. Generally t can be determned by the peak vale of lne-to-lne grd voltage. Defnng the natral DC-lnk voltage vale, as possble to obtan n case of not operatng transstors, ther freewheelng dodes becomes a standard three-phase dode brdge. Therefore, the boost natre of the actve rectfer leads to: U 3 =, 45 (3.7) DC mn S ( rms) S ( rms) If ths condton s not flflled, the fll control of the npt crrent s not possble. Moreover, to keep the swtchng losses down, a DC-lnk voltage shold be as low as possble. Typcally, the reference vale for the controlled DC-lnk voltage shold be chosen abot % above the natral DC-lnk voltage. If nty power factor s s reqred for PWM Rectfer operaton, t can be obtaned n case of: C = S I (3.8) The voltage drop across the ndctor ( I ) depends on reactance of the ndctor at the npt freqency and on the npt crrent. The magntde of the swtchng voltage vectors depends on the DC-lnk voltage level. Ths means that the maxmm AC voltage ( S ) a PWM Rectfer can generate n the lnear PWM regon. Assmng the grd sde resstance eqal to zero and neglectng the converter losses the actve power can be calclated as follows: - 39 -
U DC PC = 3S C = 3S (3.9) ωl Ths means that hgh vale of a DC-lnk voltage and small vale of the npt ndctor, determne a hgh power ratng of the rectfer. The actve power can be also defned sng DClnk voltage and load crrent as follows: C 3( S C C ) DC DC P = R = U I (3.3) Therefore, the npt crrent becomes: C S S 4PC = R R 3R f the followng relaton s satsfed: (3.3) P C S 3 (3.3) 4R At steady state operatng condtons the capactor crrent s zero. Ths the converter otpt power s: P = U (3.33) C DC C and the maxmm load crrent that can be delvered s obtaned: C,max S 3 = (3.34) 4RU DC - 4 -
4. Introdcton to Actve Flterng 4. Basc Confgraton The Shnt Actve Flters (SAF) can be dvded nto two grops [5., 5.3, 5.4]: a shnt and seres type of APF. The frst one grop serve for crrent and the second one for voltage compensaton. Shnt Actve Flters (SAF) [5.] are most often sed for compensatng crrent dstorton prodced by nonlnear loads, lke dode or thyrstors rectfers fed adjstable speed drves. General scheme and typcal waveforms are shown n Fg. 4.a and b respectvely. a) b) 5 Lne crrent 5 dode rectfer crrent actve flter crrent crrent -5 - -5,8,85,9,95,3 tm e Fg. 4.. a) Basc confgraton of Shnt Actve Flter (SAF) b)typcal waveforms for npt crrent of a dode rectfer compensaton The SAF crrent njecton has a large nflence on the grd crrent and only a small on the nonlnear load (dode rectfer) crrent [5.9]. The grd voltage can be modfed by SAF, partclarly when t s mch dstorted and as a reslt, t modfes the load crrent. The SAF effect on the load crrent s small bt may lead to nstable operaton n some cases f the desgner has not taken ts dynamcs nto accont. If ths small nflence s neglected and the - 4 -
load s consdered as a crrent sorce, there s no nteracton between the AF and the load crrents. 4. Control of SAF Two man ways to cancel the grd crrent harmoncs dependng on whch crrent s measred can be mantaned. These two ways have a dfferent control strctre and lead to dfferent propertes. )#"#%4 Ths method s based on load crrent measrement and then the harmonc content s extracted from the load crrent (Fg. 4.). In ths way, the SAF njects the compensatng crrent nto the grd, wthot nformaton abot the grd crrent [5.7]. All errors n the system, lke parameter ncertantes, measrement errors or control errors, wll appear n the grd crrent as nfltered harmoncs. The most mportant advantage of open loop method s system stablty, bt t s connected wth extended control algorthm and enlarged nmber of crrent sensors. a) S L S S L L L M otor C L C U DC DSP b) z S S C S C G L Fg. 4.. a) Open loop Shnt Actve Flter (SAF), b) Eqvalent crct for open loop control of SAF C = G L (4.) - 4 -
C G S = G (4.) ( ) S = L G (4.3) Fll compensaton can be acheved f: G G s the eqvalent transfer fncton of the SAF, ncldng detecton crct and delay of the control. In general, G has a fncton of notchng for the fndamental component G = and f G h = for harmoncs. )#"#"' Another way to generate the reference crrent s to measre the grd crrent. In ths way, n addton to the nner load crrent control loop, there s an oter grd crrent loop n the control. Ths method does not allow harmonc correcton wthot phase balancng and reactve power compensaton. The control algorthm s less complcated then n open loop method and reqres mnmal nmber of crrent sensors. a) S L S S L L L Motor C L C DSP b) z S S C S G C L Fg. 4.3. a) Closed loop SAF, b) qvalent crct for closed loop control of SAF - 43 -
C = G S (4.4) C S G L = G L = G (4.5) (4.6) Fll compensaton can be acheved for G 4.3 Types of Harmonc Sorces The harmonc sorces are manly dvded nto two grops: crrent and voltage types, dependng on mpedance [5.4]. )#$#%5 '6 6 a) b) AC Sorce Z S Z S L d Harmonc sorce S AC Sorce L Harmonc Crrent Sorce Fg. 4.4. Typcal harmonc crrent sorce a) block scheme, b) eqvalent crct The common sorces of harmonc crrents are thyrstor converters (Fg. 4.5) where a sffcent dc ndctance L d forces a constant DC crrent. The grd voltage and rectfer crrent are presented n Fg. 4.5. Becase of crrent contents, ths behaves lke a crrent harmonc sorce. However, as a crrent sorce of harmoncs can be also shown a dode rectfer wth a smoothng capactor and addtonal AC or DC ndctors, appled for decreasng hgh order harmoncs content. - 44 -
Fg. 4.5. Voltage and crrent of thyrstor rectfer (commtaton effect s neglected) )#$#"5 76 a) AC Sorce Z S Harmonc sorce b) Z S L S AC Sorce L Harmonc Voltage Sorce Fg. 4.6. Typcal Harmonc Voltage Sorce A dode rectfer wth smoothng capactor (Fg. 4.6) becomes another common harmonc sorce. Fg. 4.7 present ts voltage and crrent waveforms. The rectfer crrent s hghly dstorted, ts harmonc are affected by the ac sde mpedance. Therefore ths behaves lke a voltage harmonc sorce. - 45 -
Fg. 4.7. Voltage and crrent of dode rectfer 4.4 Analyss of Shnt Actve Flter (SAF) Operaton wth Dfferent Harmonc Sorces A Shnt Actve Flter (SAF) s a PWM nverter placed n parallel wth a load (harmonc sorce) to nject a harmonc crrent wth the same ampltde as that of the load, bt opposte phase nto the ac system. A pre crrent sorce of harmonc represents z L, whereas a pre voltage sorce of harmonc represents zl. )#)#%6 5 '6 Z S S L S C G Z L LO Fg. 4.8. Basc prncple of shnt actve flter wth harmonc crrent sorce Fg. 4.8 presents basc prncple of SAF for harmonc crrent sorce, where the harmonc sorce s presented as a Norton s eqvalent crct. Z S s sorce mpedance, I LO s the eqvalent harmonc crrent sorce, Z L s the eqvalent mpedance on the load sde whch may nclde passve flters and power factor correcton capactors. All eqatons n the - 46 -
followng analyss are n per nt representaton. Followng eqaton from Fg.4.8 can be obtaned: C S L = G (4.7) L ZL S = LO ZL ZL ZS ZS G G ZL S = G LO ZL ZL Z G S ZS G G Focsng on harmoncs ZL Z G >> h S h (4.8) (4.9) (4.) whch s the reqred operatng condton for the SAF to cancel the load crrent harmonc. When t s satsfed, the Eqs. (4.7)-(4.9) can be wrtten as: C = (4.) Lh Sh Sh ( G) LOh ( G) (4.) Z L Sh Lh = LOh (4.3) ZL It s seen from the eqaton (4.) that sorce crrent becomes snsodal becase of G = for harmoncs when (4.) s satsfed. In the Eq. (4.) only G can be pre- h desgned and determned by the SAF, whle Z S and Z L are determned by the system. Becase of pre crrent harmonc sorce, represented by a thyrstor rectfer wth a large dc ndctance, we have ZL >> ZS. Eqatons (4.8) and (4.) can be redced respectvely: I I S LO = ( G) (4.4) G h << (4.5) So, the sorce mpedance Z S do not have an mpact for compensaton characterstcs of the SAF. Ths s an mportant advantage of SAF. However, for a parallel passve flter or power-factor mprovement capactors connected on ac sde of thyrstor rectfer, the load mpedance wll become very low for harmoncs. Therefore, the condton ZL >> ZS wll not satsfy any more. - 47 -
)#)#"6 5 76 Z S S L Z L S C G L Fg. 4.9. Basc prncple of shnt actve flter wth harmonc voltage sorce Fg. 4.9 shows the basc prncple of SAF wth harmonc voltage sorce, where the harmonc sorce s represented by Thevenn s eqvalent crct, a voltage sorce V L and mpedance Z L. From Fg.9 we can wrte followng eqatons: C S L = G (4.6) L S L = ZL ZS G S L S L = = G Z Z ( G) Z Z S G L S L (4.7) (4.8) Therefore, followng eqaton (represents reqred operatng condton for the SAF to cancel the load voltage harmonc) s satsfed Z S ZL >> p G h the grd crrent wll be snsodal. So, wth condton (4.9), eqatons (4.6)-(4.8) are: C = (4.) Lh = (4.) Sh Sh Lh Lh = (4.) ZL (4.9) Bt t s dffclt for SAF to satsfy eqaton (4.9), becase harmonc voltage sorce represents sally very low mpedance Z L for a dode rectfer wth a large smoothng capactor ZL as long no seres reactor placed on the ac sde of the rectfer. - 48 -
4.5 Conclsons A Shnt Actve Flters (SAF) have fast dynamc behavor, thanks to large energy storage are not senstve for load transents. However, njecton of hgh order harmoncs reqres large power ratng of appled VSI, typcally 5%-% related to load system. From the stablty pont of vew, are ndependent of system parameters and typcally not nflenced by the loads, except for capactve loads. Generally are appled for varable fndamental reactve power compensaton, sppresson of non-characterstc harmoncs and nbalanced systems. Relablty of the system s good for low voltage applcatons, however, over-ratng s reqred. SAF are proposed for low to medm power systems wth hghly dynamcs loads. General ftres of SAF are smmarzed n Table 4.. Table 4. Smmary of Shnt Actve Flter System confgraton Basc operaton prncple Adaptve loads Reqred operaton condtons Compensaton characterstcs Applcaton consderatons Operates as a crrent sorce Indctve or crrent-sorce loads or harmonc crrent sorce, e.g. phase-controlled thyrstor rectfers of ac drves Z L shold be hgh and the SAF shold meet G h << Excellent and ndependent of the sorce mpedance Z S, for crrent-sorce loads, bt depend on Z S when the load mpedance Z L s low Injected crrent flows nto the load sde and may case overcrrent to a capactve or voltage-sorce load A Shnt Actve Flters (SAF) has followng advantages: Controlled as a crrent sorce wth a smple control algorthm, Its operaton s not affected by spply voltage harmoncs, Can be nstalled as a black box, Can be nstalled as parallel nts to obtan hgher kva ratng, Has the same power crct and eqal control algorthm to PWM Rectfer. Therefore, has possblty of system ntegraton wth actve front-ends, Do not create dsplacement factor problems, Vable and cost-effectve for low and medm power applcatons, Is not stable for hgh peak harmonc crrent loads de to large power ratng reqrements. - 49 -