Warsaw University of Technology. Faculty of Electrical Engineering

Transcription

1 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 - -

2 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. - -

3 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 Block dagram of PWM rectfer Operatng lmts Introdcton to Actve Flterng Basc confgraton 4 4. Control of Shnt Actve Flters Types of Harmonc Sorces Analyss of Shnt Actve Flter (SAF) Operaton wth Dfferent Harmonc Sorces Conclsons PWM Rectfer wth Actve Flterng Fncton Introdcton Control Methods of PWM Rectfer 5 6. Dmensonng of Power Converters PWM Rectfer ratng Shnt Actve Power Flter (SAF) Ratng PWM Rectfer wth Actve Flterng Fncton Ratng Desgn of Passve Components

4 6.5 Conclsons Smlaton and Expermental Reslts Voltage Orented Control (VOC) 8 7. Vrtal Flx Based Drect Power Control (VF-DPC SVM) Smmary and Comparson of Compensatng Reslts Rectfyng and Regeneratve Mode of PWM Rectfer Operaton Typcal Grd Voltage Dstorton 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

5 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 -

6 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 -

7 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 -

8 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 -

9 . 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 n the USA and IEC 6-3-/IEC 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 -

10 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. - -

11 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 - -

12 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. - -

13 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)

14 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 -

15 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

16 . 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 []

17 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 -

18 "#$#"&''( 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 S t a n d a r d HD [%] 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 -

19 .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 I π < ωt < π 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 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 -

20 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 - -

21 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). - -

22 8 Inpt crrent THD [%] 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] 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. - -

23 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 -

24 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 [%] 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

25 Dode rectfer wth DC-sde capactance and ndctance 43 a) b) Lne crrent THD [%] Grd crrent THD [%] DC-lnk capactance [F] 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, DC-lnk capactance [F] 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 -

26 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] 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

27 .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 kV 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 < < < < > I SC - maxmm short crct crrent at the PCC - 7 -

28 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 <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 >

29 .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

30 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

31 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 -

32 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 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 -

33 Fg 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

34 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

35 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

36 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 ±/

37 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 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 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

38 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 α Fg 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 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

39 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:

40 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 -

41 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 ,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 -

42 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 -

43 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 a) Closed loop SAF, b) qvalent crct for closed loop control of SAF

44 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 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 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

45 Fg 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 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

46 Fg 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 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

47 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

48 )#)#" Z S S L Z L S C G L Fg 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

49 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

50 5. PWM Rectfer wth Actve Flterng Fncton 5. Introdcton Shnt Actve Power Flters (SAF) [5.8 5.] and PWM rectfers [4] are two typcal examples from several soltons, whch are sed for harmoncs elmnaton. Both of them have bascally the same power crct confgraton and can operate based on the same control prncple. SAF are able to compensate not only crrent harmoncs, bt also a reactve power and load nbalance. Desgn and control have been nvestgated n many papers [5., 5., and 5.3] where se ness of SAF was proved. PWM Rectfers [4] as non-polltng eqpment wth snsodal npt crrents are gong to be more poplar becase of several advantages lke: -B-drectonal power flow, -Closed loop based stablzaton of otpt DC voltage, -Low harmonc dstorton of lne crrents, -Reglaton of npt power factor to nty. Ths chapter explores another task of PWM rectfer - actve flterng fncton, whch adds a) V S L S S L L L Motor C L C U DC Motor DSP b) V S L S S L L L Motor C L C Motor DSP Fg. 5.. Control strategy a) open loop wth 4 crrent sensors and b) closed loop wth crrent sensors - 5 -

51 advantages of SAF and PWM Rectfers. So, the PWM rectfer spples ts load and at the same tme compensates AC grd crrent. Ths concept was at frst ntrodced n works [ and 4]. The open loop control strategy llstrated n Fg. 5.a reqres addtonal control fnctons and measrement of nonlnear load crrent ( L ). In contrast the closed loop control strategy presented n Fg. 5.b s based on PWM Rectfer operaton and do not reqre addtonal crrent sensors or any modfcatons n control algorthm. The dfference reslts from locaton of lne crrent sensors. Compared to open loop control strategy, where crrent harmonc content and power factor mprovement can be controlled ndependently, sch a system performs both of these fnctons smltaneosly. 5. Control Methods of PWM Rectfer The dynamc and statc performance of PWM Rectfer depends strongly on adopted control methods. Therefore, n the next secton some basc control strateges sed for PWM Rectfers wll be presented. #"#%#74 '74' Voltage Orented Control (VOC) s based on coordnate transformatons between statonary αβ and synchronos rotatng dq reference system. It garantees fast transent response and hgh performance n steady state. Becase of VOC ses an nternal crrent control loops fnal performance of the system strongly depends on appled crrent control technqes [.] mentoned n Appendx. The conventonal VOC system (Fg. 5.3) ses synchronos crrent control n rotatng reference coordnates, as shown n Fg. 5.. A meanngfl featre for ths type of crrent controller s sgnal processng n two coordnate systems. The frst s statonary α-β and the second s synchronosly rotatng d-q coordnate system. Three phase measred vales are converted to eqvalent two-phase system α-β and then are transformed to rotatng coordnate system n a block α-β/d-q: kd cosγ US snγ USkα k = q snγ US cosγ k (5.a) US β Thanks to the above transformaton the control vales are DC sgnals. An nverse transformaton d-q/α-β s sed on the otpt of control system and t gves a reslt on rectfer reference sgnals n statonary coordnate: kα cosγ US snγ USkd k = β snγ US cosγ k (5.b) US q - 5 -

52 The angle of the voltage vector US s defned as: ( ) ( ) sn γ = / (5.a) US Sβ Sα Sβ ( ) ( ) cos γ = / (5.b) US Sα Sα S β In voltage orented d-q coordnates, the AC lne crrent vector C s splt nto two rectanglar components C = [ Cd, Cq ] (Fg. 5.). The component Cd determnates actve power, where Cq decdes abot reactve power flow. Ths the actve and the reactve power can be controlled ndependently va actve and reactve components of lne crrent vector C. The UPF condton s met when the lne crrent vector, C, s algned wth the lne voltage vector, S. By placng the d-axs of the rotatng coordnates on the lne voltage vector S a smplfed dynamc model can be obtaned. q-axs Cq Cβ β axs Sβ ϕ S Cd γ US =ωt Cα S = Sd Sα ω d-axs (rotatng) α axs (fxed) Fg. 5.. Vector dagram of VOC. Coordnate transformaton of lne crrent, lne voltage and rectfer npt voltage from statonary α β coordnates to rotatng d-q coordnates The grd voltage eqatons n the d-q synchronos reference frame are as follows: dcd Sd = R Cd L Cd ω L Cq (5.3) dt dcq Sq = R Cq L Cq ω L Cd (5.4) dt Accordng to Fg. 5.3, the q-axs crrent s set to zero n all condton for nty power factor control whle the reference crrent Cd s set by the DC-lnk voltage controller and adjst the actve power flow between the grd and the DC-lnk. For R eqatons (5.3), (5.4) can be redced to: dcd Sd = L Cd ω L Cq (5.5) dt - 5 -

53 dcq = L Cq ω L Cd (5.6) dt Wth the q-axs crrent reglated to zero, the followng eqatons (5.5 and 5.6) becomes d = (5.7) dt C Sd L Cd Cq ω L Cd = (5.8) As crrent controller, the PI-type can s sed. However, the PI crrent controller has no satsfactory performance, becase of the copled system descrbed by Eqs. (5.5), (5.6). Therefore, for hgh performance applcaton wth accracy crrent trackng at dynamc state the decopled controller shold be appled. The otpt sgnals from PI controllers after dq/ transformaton (Eq. (5.b)) are delvered to a Space Vector Modlator (SVM) whch generates swtchng sgnals for power transstors. dc_ref dc d_ref PI PI - q_ref = dc ca cb cc abc dq d - - q - - d_err q_err PI PI d q dq αβ sα sβ PWM γ l γ l Fg Basec block of VOC scheme #"#" 5... VOC wth actve flterng fncton: total harmonc compensaton method As an actve flter, PWM rectfer s able to compensate hgher harmoncs n a grd crrent taken by the whole load. In order to compensate hgher harmoncs addtonal control block (AFF) has to be added to standard VOC strategy (Fg. 5.4). A PWM Rectfer part of control s the same lke descrbed n prevos chapter. The dstorted crrents la, lb, lc are delvered to the abc/dq transformaton, where a fndamental (5 Hz) harmonc becomes a DC qantty and other harmoncs are non-dc vales. Next those sgnals are delvered to the Hgh Pass Flter (HPF), whch provdes the hgher harmoncs sgnals extracton. Then hgher harmoncs compensatng sgnals d_fr, q_fr are added wth an opposte

54 sgn to the standard VOC reference sgnals Cd, Cq and n the same provde hgher harmoncs compensaton. = r d _ err Cd _ ref Cd d _ f = r q _ err Cq _ ref Cq q _ f (4.9) dc_ref dc Cd_ref PI PI - Cq_ref = dc ca cb cc abc dq γ l Cd - - Cq - - d_err q_err PI PI d q dq γ l ab s a sb PWM la lb abc dl HPF d_ fr lc dq ql HPF q_ fr γ l AFF Fg Block dagram of VOC scheme wth Actve Flterng Fncton (AFF) block based on total harmonc compensaton The compensatng sgnals are hgh freqency components, added to the DC vales reference sgnal prodce non-dc reference sgnals passed to a PI controllers. These gve non deal condtons for PI controllers operaton and prodce an addtonal phase shft between reference and actal crrent

55 5... VOC wth actve flterng fncton: selectve harmonc compensaton method dc_ref dc Cd_ref PI PI - Cq_ref = dc ca cb cc abc dq Cd - - Cq - - d_err q_err PI PI d q dq αβ sα sβ PWM γ l d_fr q_fr γ l γ l αβ dq la lb abc dl_5h LPF d_5h dq dq d_7h LPF dl_7h abc la lb lc dq ql_5h LPF q_5h αβ αβ q_7h LPF ql_7h dq lc -5* γ l 5 harm -5* γ l 7* γ l 7 harm 7* γ l harm 3 harm Fg Block dagram of VOC wth Actve Flterng Fncton (AFF) scheme based on selectve harmonc compensaton In scheme of Fg. 5.5 actve flterng fncton operates ndependently on few dfferent man crrent harmoncs, lke 5 th, 7 th, th and 3 th n harmonc synchronos coordnates [5.5, 5.5, 5.7]. Moreover, nonlnear load crrents la, lb, lc are transformed to dq frame sng stably angle γ l for each harmonc ntended to compensaton. Then the dstorted crrents la, lb, lc are delvered to the Low Pass Flter (LPF), whch provdes the hgher harmoncs sgnals extracton. Next after back transformaton dq/αβ these sgnals dfr and qfr are added wth an opposte sgn to the standard VOC reference sgnals Cd and Cq gvng fnal commands d_err, q_err delvered to PI crrent controllers. The same procedre s sed for all specfed harmoncs

56 #"#$ dc_ref dc PI PI d_ref - q_ref = dc sa sb sc abc dq d - - q - - d_err q_err PI PI d q dq abc sα sβ PWM γ l γ l Fg VOC closed loop control strategy Closed loop control strategy of Fg. 5.6 operates lke conventonal VOC wth the only change on crrent sensor locaton nstead PWM rectfer npt crrents La, Lb, Lc, the sorce crrents Sa, Sb, Sc are measred and controlled. The nonlnear load crrent L s not measred (see Fg. 5.b). It s natrally created by the converter as a reslt of ac-lne crrent sensor locaton at pont of common coplng (PCC), where the system controls the crrent to be snsodal and may be determned by consderng the smmaton of crrents at the PCC: C = S L The sorce crrents Sa, Sb, Sc are measred and taken nto control strategy. #"#)7 89& & '7(&'67 &'67 Basc prncples of vrtal flx based actve and reactve power estmaton s presented below. It s economcally motvated to replace the AC-lne voltage sensors [3.] wth a vrtal flx (VF) estmator [4, 6., ]. The prncple of VF s based on assmpton that the voltages mposed by the lne power n combnaton wth the AC sde ndctors can be consdered as qanttes related to a vrtal AC motor (see Fg. 5.7). Where R and L represent the stator resstance and leakage ndctance of the vrtal motor. Lne to lne voltages: U Sab, U Sbc, U Sca can be consdered as ndced by a vrtal flx. Hence the ntegraton of the voltages leads to determnaton of a vrtal flx vector Ψ S, n statonary α-β coordnates presents Eq

57 Fg PWM Rectfer Wth the defntons Ψ S = S dt (5.9) where S Sα = = Sβ Ψ S S dt α α Ψ S = = Ψ S β S β dt C Cα = = Cβ S ab 3 3 (5.) Sbc (5.) 3 Ca 3 3 (5.) Cb 3 C α C = = Cβ CAM CBM (5.3) CCM Operaton of PWM rectfer s based on assmpton, that npt crrent c s controlled by the voltage drop across the ndctor L nterconnectng lne and converter voltage sorces. It means that the ndctance voltage I eqals the dfference between the lne voltage S and the converter voltage C S = C I (5.4)

58 and smlarly a vrtal flx eqaton can be presented as: ψ = ψ ψ (5.5) S C I q-axs I =jωl L C β axs S = Sq C Cα Sα Cq ϕ Cd Sβ Cβ Ψ S β γ ΨS =ωt Ψ S ω Ψ S α d-axs (rotatng) Ψ I Ψ C α axs (fxed) Fg Reference coordnates and vectors (for fndamental component): Ψ S vrtal lne flx vector, Ψ C vrtal flx vector of converter, Ψ I vrtal flx vector of ndctor, C converter voltage vector, S - lne voltage vector, I ndctance voltage vector, C npt crrent vector Based on the measred DC lnk voltage U dc and the dty cycles of SVM modlator S A, S B, S C the vrtal flx Ψ S components are calclated n statonary coordnates system as follows: Ψ α = U ( S ( S S ) dt L 3 S dc A B C Cα (5.6a) Ψ S β = U dc ( S B SC ) dt L (5.6b) C β The measred npt converter crrents ca, cb and the estmated vrtal flx components Ψ Sα,Ψ Sβ are sed for estmaton of the nstantaneos power. The voltage eqaton can be wrtten as d S = RC ( LC Ψ C ) (5.7a) dt In practce, R can be neglected, gvng d d d = Ψ = (5.7b) dt dt dt C C S L C L C Usng complex notaton, the nstantaneos power can be calclated as follows: p = Re( ) (5.8a) S C q = Im( ) (5.8b) S C where * denotes the conjgate lne crrent vector. The lne voltage can be expressed by the vrtal flx as

59 d d jωt dψs jωt jωt dψs jωt S = Ψ S = ( Ψ Se ) = e jωψ Se = e jω Ψ (5.9) S dt dt dt dt where Ψ S denotes the space vector and Ψ S ts ampltde. For the vrtal flx orented d-q coordnates (Fg. 5.), Ψ S =Ψ Sd, and the nstantaneos actve power can be calclated from (5.a) and (5.) as d Ψ = ω Ψ (5.) dt Sd p Cd Sd Cq For snsodal and balanced lne voltages, eqaton (5.) s redced to d Ψ Sd = (5.) dt p = ωψ (5.) Sd Cq whch means that only the crrent components orthogonal to the flx Ψ L vector, prodce the nstantaneos actve power. Smlarly, the nstantaneos reactve power can be calclated as: d Ψ = Ψ (5.3) dt Sd q Cq ω SdCd and wth (5.3) t s redced to: q = ωψ (5.4) Sd Cd As mentoned n [4] for snsodal and balanced lne voltage the dervatves of the flx ampltdes are zero. By smlaton and experment nvestgaton were proofed, that even for dstorted lne voltage the smplfed eqatons for the nstantaneos actve and reactve powers can be sed: p = ω ( Ψ Ψ ) (5.5a) Sα Cβ Sβ Cα q = ω ( Ψ Ψ ). (5.5b) Sα Cα Sβ Cβ The measred lne crrents Ca, Cb and the estmated vrtal flx components Ψ Sα,Ψ Sβ are delvered to the nstantaneos power estmator block

60 Fg VF-DPC control scheme A VF-DPC control strategy man scheme s presented n Fg The commanded (delvered from the oter PI DC voltage controller) actve power p ref and reactve power q ref (set to zero for nty power factor) vales are compared wth the estmated nstantaneos p and q vales, respectvely. The errors are delvered to PI controllers, where the varables are DC qanttes and steady state error were elmnated. The otpt sgnals from PI controllers after transformaton (5.9) are delvered to a Space Vector Modlator (SVM). Fg. 5.. Power estmaton block Fg. 5. shows an nstantaneos powers estmaton block. The γ Ψ angle s calclated sng estmated vrtal flx components Ψ Sa,Ψ Sb

61 #"# Fg. 5.. VF-DPC scheme wth Actve Flterng Fncton (AFF) block Fg. 5.. Power estmaton block - 6 -

62 In ths scheme of Fg. 5. measred npt converter crrents ca, cb and the estmated vrtal flx components Ψ Sa,Ψ Sb are sed for the power estmaton Fg. 5.. For a PWM rectfer operaton the reference actve power p ref (generated by the oter PI DC voltage controller) and reactve power q ref (set to zero for nty power factor) vales are compared wth estmated nstantaneos p and q vales, respectvely. The errors are delvered to PI controllers, whch elmnates steady state error. The otpt sgnals from PI controllers after transformaton pq/αβ : Cα snγ S cos Ψ γ ΨS Cp = Cβ cosγ S snγ Ψ ΨS Cq where: ( ) ( ) (5.6) sn γ Ψ = Ψ / Ψ Ψ (5.7a) S Sβ Sα Sβ ( ) ( ) cos γ Ψ = Ψ / Ψ Ψ. (5.7b) S Sα Sα Sβ are sed for swtchng sgnals generaton by Space Vector Modlator. Here a modfed algorthm based on vrtal flx, whch operates drectly on nstantaneos actve and reactve power components s presented [5.6]. The nstantaneos actve and reactve powers are estmated sng crrents ntended to compensate la, lb, lc and vrtal flx Ψ Sa,Ψ Sb accordng to Eqs (5.a and b) as: p = ω ( Ψ Ψ ) (5.8a) A Sα lβ Sβ lα q = ω ( Ψ Ψ ) (5.8b) A Lα lα Lβ lβ The calclated actve power (p A ) and reactve power (q A ) are delvered to the hgh pass flter (HPF) to obtan vales of the nstantaneos actve power ( p A ) and reactve power ( q A ) whch fnally are sed as a compensatng components. Addng actve flterng fncton wll case stable dstorton of npt PWM rectfer crrent, whch wll assre almost snsodal lne crrent. It permts to se PWM rectfer as a crrent harmoncs elmnatng devce

63 Fg Instantaneos power waveforms for dfferent crrent shapes. a) crrent n phase wth voltage b) crrent wth phase shft c) dstorted crrent From the top: grd voltage, grd crrent, actve and reactve power Fg. 5.3 presents smlated examples of actve and reactve powers for dfferent crrent shapes. It s obvos that for snsodal voltage and n phase crrent an actve power has a certan vale and reactve power s eqal (Fg. 5.3a). In case that grd crrent s not n phase wth grd voltage bt s stll snsodal, the actve power wll have the same level, bt non zero vale of reactve power wll appear (Fg. 5.3b). If the crrent become a dstorted one, n actve and reactve powers a plsaton component wll be vsble (Fg. 5.3c). Smmarzng, for hgher harmoncs elmnaton two hgh pass flters are needed, one for each power component. For hgher harmoncs elmnaton and reactve power compensaton, only one hgh pass flter n actve power s reqred (swtch n Fg. 5.). #"#. Fg VF-DPC control block

64 Fg Power estmaton block The nonlnear load crrent L s not measred Fg. 5.b. It s reconstrcted by the converter as a reslt of AC-lne crrent sensor locaton at pont of common coplng (PCC), where the system controls the crrent to be snsodal and may be determned by consderng the smmaton of crrents at the PCC. C = S L (5.9) The grd crrents sa, sb and the estmated vrtal flx components Ψ Sa,Ψ Sb are sed for estmaton of power components. The reference actve power p ref and reactve power q ref vales are compared wth the estmated nstantaneos p and q vales, respectvely. The errors are delvered to PI controllers. The otpt sgnals from PI controllers after transformaton pq/αβ are sed as a reference sgnals for Space Vector Modlator

65 6. Dmensonng of Power Converters Ths chapter s devoted to dmensonng of power converters. Ths s obvos, that proper dmensonng s very crtcal sse for desgnng and selecton of PWM Rectfer. Man power scheme of parallel connected conventonal dode rectfer fed Adjstable Speed Drve (ASD) and modern PWM rectfer/nverter fed system s shown n Fg.6.. It s very smple to see that PWM rectfer after some smple modfcatons n hardware and software can addtonally have actve flterng fncton. Therefore, power relatons between those two schemes: dode and PWM rectfers are very mportant for a desgn process. S = P Q H D D D D S = P Q H C C C C Fg. 6.. Power system scheme nder consderaton Smlated deal crrents for Shnt Actve Flter (SAF) operaton are presented n Fg. 6.b and for PWM Rectfer havng Actve Flterng Fncton (AFF) operaton n Fg. 6.a. a) b) Fg. 6.. The system crrents a) PWM rectfer wth Power Factor Correcton, b) Actve Power Flter. Smlatons nder deal condtons From the top: lne crrent, nonlnear load crrent, PWM converter npt crrent It s reqred to calclate a proper power rato of PWM Rectfer, especally when t wll have an Actve Flterng Fncton. Therefore, f t wll be calclated wrongly a converter wll not be able to delver demanded power to the load or to proper compensaton of nonlnear load. Contrary, n the case of excesses dmenson, t wll be expensve for end ser

66 6. PWM Rectfer Ratng In ths chapter a PWM Rectfer operaton only s consdered. Therefore, ths converter spples only ts own load, and does not compensate for dode rectfer/pwm nverter system (Fg. 6.3). S = P Q H D D D D S C = P C Fg PWM Rectfer operaton Among the power losses n the PWM converter are: Power transstors swtchng losses, AC-sde ndctor losses, Heatng losses, etc. It wll be consdered an deal PWM rectfer nder deal AC lne condtons. The apparent power of PWM rectfer s gven sng an RMS vale of AC-sde voltage and crrent as: S = 3 rms rms (6.) For ths expresson, only fndamental components of PWM rectfer npt crrent and voltage are taken nto accont. S = P Q, (6.) C C C where: P C = 3RI, Q C = 3X I, S C L C = 3Z I and, C L C Z = R X L (6.3) For any deal npt ndctance (R=), the apparent power can be expressed as follows: S = P Q = 3 ( X ) (6.4) C C C L C If we consder a nty power factor operaton and omts converter losses, the npt crrent C can be calclated as follows:

67 P = 3, = 3, then C C S LL S C PC = (6.5) 3 LL Fnally the expresson for ratng of PWM rectfer can be presented n the form: S C X P L C = PC ( ) (6.6) LL where: P C s load actve power, X L reactance of the npt flter, LL lne to lne voltage. The graphcal representaton of eqaton (6.6) s shown n Fg.6.4. Fg PWM rectfer ratng as a fncton of npt ndctance L C and DC-sde load power P C a) low power b) hgh power applcaton

68 It can be seen that the power rato of PWM rectfer strongly depends and ncrease wth ncreasng otpt power P C and npt ndctor vale L C. Ths s becase, the converter spply actve power to AC drve and reactve power to the npt ndctor. Therefore, the npt ndctor vale shold be kept n reasonable vale, otherwse for hgh power applcatons, hgh vale of npt ndctor wll ncrease demanded power rato S C of the converter even tmes. 6.. Shnt Actve Power Flter (SAF) Ratng Ths chapter deals wth dmensonng of power converter workng as a Shnt Actve Flter (SAF). Therefore, ths converter compensates only neghborhoods nonlnear loads and does not spply actve power P C = (Fg. 6.4). S = P Q H D D D D S = Q H C D D Fg Actve Flterng operaton The Actve Power Flter operaton reqres dfferent kva ratng. It s calclated only for compensaton of hgher harmoncs of crrent, whch typcally for dealzed dode rectfer wth ndctor on DC-sde. For consderatons n ths secton followng assmptons are made: - Snsodal grd voltage, - A dode rectfer operates n deal condtons and commtaton effect s neglected, - A phase shft between a grd voltage and fndamental harmonc of dode rectfer npt crrent changes n the range from to 3 (dsplacement factor). Therefore, for calclatons of the SAF kva ratng followng ponts shold consder: - THD of an dode rectfer npt crrent, - dsplacement power factor, - Inpt ndctor vale

69 Consderng an deal waveform of dode rectfer npt crrent (rectangle waveform, Fg. 6.b), we have: sn ( ) sn 5( ) sn 7( ) 3 ωt ϕ ωt ϕ ωt ϕ 5 7 L ( ωt) = IDC (6.7) π sn( ωt ϕ ) sn3 ( ωt ϕ )... 3 where I DC π P = 3 6 cosϕ D S In the case of deal compensaton, all harmoncs and the reactve power wll be elmnated. So n ths case the lne crrent S can be presented as follows: 3 S ( ωt) = I DC sn ( ωt) (6.8) π Then, from Eqs.(6.7)-(6.8) the npt crrent of PWM Rectfer wth actve flterng fncton s expressed as: sn ( ) sn ( ) sn 5( ) sn 7( ) 3 ωt ωt ϕ ωt ϕ ωt ϕ 5 7 C ( ωt) = Idc π sn( ωt ϕ ) sn3 ( ωt ϕ )... 3 (6.9) The RMS vale of npt crrent, f consderng only 5 th, 7 th, th, 3 th harmoncs, s obtaned as: C RMS P D =.75 3cos ϕs (6.) The RMS vale of npt voltage on PWM Rectfer havng actve flterng fncton can be calclated sng followng expresson: π dc ( ωt) C RMS = S ( ωt) X L d( ωt) π (6.) d( ωt) Therefore, fnally the kva ratng s calclated n ths form: S = (6.) 3 C RMS C RMS

70 5 4 Apparent power S [VA] Otpt power Pc/Pd [W] Fg SAF converter power ratng S C verss dode rectfer otpt power P D Fg. 6.6 shows converter power ratng of SAF wth few dfferent dsplacement factors verss dode rectfer otpt power P D. The waveforms show that SAF ratng s lower then PWM Rectfer ratng (for the same load condtons). An SAF ratng sbstantally ncreases wth dsplacement factor ncreasng. However, a dsplacement factor practcally s not hgher than 3 degrees, therefore, s shown that for low power applcatons power ratng of PWM Rectfer s always hgher than power ratng of SAF. 6 5 Apparent power S [VA] Indctance Lc [mh] Fg Converter power ratng verss npt flter ndctance - 7 -

71 Fg. 6.7 shows converter power ratng S C verss npt flter ndctance L C. A comparson of an example of PWM Rectfer (5kW load) wth AFF (compensatng 5kW loaded dode rectfer) s presented. As shown a PWM Rectfer for low power applcatons s not senstve for npt flter changes, whle SAF s more senstve for ncrease of npt flter ndctance. Moreover, for the same load condtons an SAF reqres lower power ratng than PWM Rectfer. A power ratng of SAF depends strongly on dsplacement factor (phase shft between grd voltage and st harmoncs of dode rectfer npt crrent) and ncreases together wth t PWM Rectfer wth Actve Flterng Fncton Ratng Ths chapter consder a power converter spplyng ts own load (P C ) and n the same tme compensatng neghborhoods nonlnear loads: dode rectfer/pwm Inverter (Fg. 6.8). S = P Q H D D D D S = P Q H C C D D Fg PWM Rectfer wth AFF operaton The kva ratng for PWM Rectfer havng actve flterng fncton s more complcated then for only rectfyng mode of operaton, becase t shold addtonally nclde a compensaton for a reactve Q D and harmonc H D powers generated by a dode rectfer. In the case of operaton wthot a PWM Rectfer load (P C =), the converter works as a Shnt Actve Flter. Consderng an deal waveform of dode rectfer npt crrent (rectangle waveform) expressed by Eq. 6.7 and assmng deal compensaton the lne crrent by Eq.6.8. Ideal npt PWM Rectfer crrent wrtten as follows: PC C ( ωt) = sn ( ωt) (6.3) 3 S The npt crrent of PWM Rectfer wth actve flterng fncton has followng form: - 7 -

72 sn ( ωt ϕ ) sn 5( ωt ϕ ) sn 7( ωt ϕ ) P 3 C C ( ωt) = Idc sn ( ωt) Idc 3S π π sn( ωt ϕ ) sn3 ( ωt ϕ )... 3 (6.4) where I DC π P = 3 6 cosϕ D S The RMS vale of npt crrent, f consderng only 5 th, 7 th, th, 3 th harmoncs, s obtaned as: C RMS P C PC P D P D =.75 3cos S 3cos S ϕ ϕ S S (6.5) The RMS vale of PWM Rectfer havng actve flterng fncton npt voltage can be calclated sng Eq 6. and the kva ratng sng Eq. 6., respectvely. '!!"#$"%& ( Fg Power ratngs of the PWM converter - constant PWM Rectfer load power and varable dode rectfer load power (-5kW) As shown n Fg. 6.9 the apparent power of the PWM Rectfer wth Actve Flterng Fncton depends on dode rectfer power and npt ndctor vale. For hgher vales of dode rectfer power the apparent power of the converter ncrease nonlnearly. It shows that for hgher vales of npt ndctor a hgher power s reqred. Ths s reslt of hgher voltage drop across ndctor. Fg. 6.6 gves a vew for the reqred apparent power of the PWM Rectfer - 7 -

73 wth AFF n case of constant ts own load power and varable power of a dode rectfer. As show, the apparent power s hgher then demanded PWM Rectfer load. A dfference shows how mch power s reqred for AFF verss a dode rectfer power. 6.4 Desgn of passve components The VSC connected to the grd needs an ndctor monted between VSC and a grd whch operates as a voltage sorces. The smplest and most common s an L-flter, whch contans three seres ndctances, one n each phase. The LC-flter contans the same ndctances and n addton, has three parallel copled capactors, bt problems can be occrrng de to resonances. The resonance freqency depends on capactor and grd ndctance vales, whch vares on tme. The man advantages of sch a flter are: Low grd crrent dstorton, Reactve power prodcton. Redcton of the crrent harmoncs arond swtchng freqency and mltplcaton of swtchng freqency s the man goal to get hgh performance PWM rectfer, whch flflls IEEE standards n relaton to EMC. Hgh vale of ndctance n the frond of rectfer can solve ths problem, however ths blky and expensve solton, redce dynamcs and operaton range. It means voltage drop across the ndctance, whch has nflence for the crrent, s controlled by npt voltage of the PWM rectfer bt maxmal ampltde s lmted by the DC-lnk voltage. Conseqently, a hgh crrent (hgh power) throgh the ndctance reqres ether a hgh dc-lnk voltage or low ndctance..#)#% #% AC sde L and LC npt flter The npt ndctor has to be desgned careflly becase low ndctance wll gve a hgh crrent rpple and wll make the desgn more dependng on the lne mpedance. The hgh vale of ndctance wll gve a low crrent rpple, bt smltaneosly redce the operaton range of the rectfer. The voltage drop across the ndctance has nflence for the lne crrent. Ths voltage drop s controlled by the npt voltage of the PWM rectfer bt maxmal vale s lmted by the DC-lnk voltage. Conseqently, a hgh crrent (hgh power) throgh the ndctance reqres ether a hgh DC-lnk voltage or a low ndctance (low mpedance)

74 a) b) Grd sde Rectfer sde L C L Fg. 6.. Inpt flters a) L type, b) LC type The am of the npt flters s to redce the hgh harmoncs at the grd sde. The npt flter desgn procedre shold take nto accont followng aspects: power ratng, lne and swtchng freqency. Inpt ndctor vale has to be calclated n % of the base vales. Therefore, on the begnnng base vales shold be calclated. Base mpedance: Z Base capactance: C b ( EmLL ) =, (6.6) P b C = ω Z, (6.7) S b Where: E mll lne to lne rms voltage, f s grd freqency, P C actve power absorbed by the converter n rated condtons, The maxmm vale of npt mpedance defned as: L max % Z = b, (6.8) ω S Therefore, the maxmal ndctance can be determnate as: U DC U f L 3 (6.9) ω I m L [mh] I [A] Fg. 6.. Lne ndctor vale verss rated npt crrent calclated from Eq.(6.9)

75 Or n the other hand where no load condtons are consdered, bt the npt crrent rpples are taken nto accont. U LL L =,where rpple =5% f (6.) 6 f S rpple L [mh] I [A] Fg. 6.. Lne ndctor vale verss rated npt crrent calclated from Eq.(6.) An LC flter conssts also a capactor, whch together wth an npt ndctor create a low pass flter. A gven ct-off freqency f ct-off s sed for calclaton of capactance n ths way: C = (6.3) π f L ct off DC-lnk capactor For balanced three-phase system wth neglected swtches losses the DC-lnk model express d by: C dt DC P 3 C Spd p (6.3) p= U DC = where d p s a swtchng fncton. For balanced three-phase system 3 Spd p s eqal to one. p= For known acceptable peak rpple voltage of capactor can be fond as: C mn U LL 3 U DC = PC 3U U f LL DC s dc and swtchng freqency, the mnmm (6.3)

76 C [F] P [kw] Fg DC-sde capactor vale verss the otpt power.#)#" #" A selecton of npt ndctance for APF proceeds wth dfferent condtons then t was taken for PWM Rectfer. The man dfference s the APF shold be able to force crrents wth hgh parameter, to be capable compensate hgher harmonc crrents prodced by dode t rectfers. Therefore, the smplest eqaton for an npt ndctance vale has followng form: U L f DC s I (6.33) L [mh] I [A] Fg Lne ndctor vale verss rated npt crrent calclated from Eq.(6.33) Whle, a DC lnk capactor mnmal vale can be calclated sng eqaton presented below: C = P o m ε ω U DC (6.34) where: P m ampltde of power plsaton, ε - U DC voltage error, ω o - freqency of plsaton

77 C [F] U [V] Fg DC-lnk capactor vale verss DC-lnk voltage Fg. 9.6 shows a vale of reqred DC-lnk capactor vale verss demanded DC-lnk voltage. As mentoned the capactance decreases for DC-lnk voltage vale. Tab. 6.. Eqatons for passve elements desgn Parameter PWM Rectfer Actve Flter Dode Rectfer Inpt dc E U m DC 3 L Indctance L fs I ω I m Inpt U LL L = Indctance 6 fsrpple U max L Ls d dt L = S π fi DC Capactance C mn = P C U 3 U LL DC 3U U f LL DC s C = ~ P o m ε ω U DC C = P C π 54 f U U S LL DC A PWM Rectfer and SAF have the same converter topology, both of them reqre an passve elements lke: npt ndctance (that shapes the npt crrents) and DC-lnk capactance (energy storage devce). A DC-lnk capactance of the SAF compared to a PWM Rectfer DC-lnk capactance s always smaller, snce the SAF has smaller peak npt crrent and no real power delvery. A sze of dode rectfer DC-lnk capactance s mch larger than of PWM Rectfer or the SAF. For gven (the same) peak rpple voltage reqrement, the frst two converters operates wth swtchng freqency, whle a dode rectfer operate wth sgnfcantly smaller grd freqency. The typcal DC-lnk capactance vale of SAF s above 5% smaller than that of PWM Rectfer. Whle a dode rectfer DC-lnk capactance can be abot 5 tmes larger than that of PWM Rectfer

78 .#)#$&'( As mentoned n Chapter 3 a mnmal vale of DC-lnk voltage for PWM converters can be calclated from followng eqaton: U 3 =, 45 (6.35) DC mn S ( rms) S ( rms) A mnmal DC-lnk voltage U DCmn s eqal to 56 V. Therefore, typcally t s set to 6 V. For SAF applcatons to obtan hgh vale of T S S, a hgh vale of DC-lnk voltage s reqred. S U = DC (6.36) T S L C Above mentoned eqaton, determne a DC-lnk voltage for gven npt ndctance L C and T S S parameter (condtoned by a dode rectfer, descrbed n Chapter ). Therefore, the SAF s not stable for hgh power applcatons de to ther hgh DC-lnk voltage reqrements. 6.5 Conclsons SAF reqres lower power ratng than PWM Rectfer (for low power applcatons) A power rato of PWM rectfer S C strongly depends on otpt power P C and npt ndctor L C vale, A power ratng of SAF depends on dsplacement factor (phase shft ψ between grd voltage and st harmoncs of dode rectfer npt crrent), a dode rectfer load as well as on npt ndctor vale, Demanded apparent power of a PWM Rectfer S C wth AFF wll always be hgher then t reslts from ts own load vale P C and depends on dode rectfer load P, as well as on phase shft angle ψ, The kva ratng of SAF s more than two tmes less then ratng of PWM Rectfer (for the same load condtons)

79 7. Smlaton and Expermental Reslts The operaton of VOC (Voltage Orented Control) and VF-DPC (Vrtal Flx based Drect Power Control) schemes nder dfferent grd voltage condtons for PWM Rectfer and Shnt Actve Flterng (SAF) operaton has been smlated sng the MATLAB/SIMULINK and SABER software. Expermental reslts were obtaned n laboratory set-p descrbed n Appendx. The man electrcal parameters of the power crct are gven n Table I. Tab. 7. Basc parameters of the system nder stdy Parameters Smlaton Experment Resstance of reactors R: mω mω Indctance of reactors L: mh mh DC-lnk capactor: 45 F 45 F Samplng freqency: khz khz Swtchng freqency f: khz khz Phase voltage V: 3 RMS 5 RMS DC-lnk voltage: 6 V 4V PWM rectfer load resstance R: 5 Ω 5Ω Dode rectfer load resstance R: 5 Ω / 5 Ω 5 Ω / 5 Ω The smlaton and expermental stdy has been performed wth few man objectves: - Presentng and explanng the PWM Rectfer operaton, wth an deal snsodal and dstorted nbalanced grd voltage, as well as comparson of VF-DPC wth conventonal VOC control algorthm. The reslts present the steady state and dynamc performance of the system, - Introdcng the actve flterng fncton (AFF) for PWM Rectfers, both for VOC and VF-DPC control algorthms. A VOC consst of two dfferent methods of compensaton hgher crrent harmoncs: the frst smple one, non selectve and the second one called the selectve compensaton s compared wth VF-DPC wth a compensaton of harmoncs based on p-q theory, - Addtonally, a closed loop control method wll be ntrodced and compared wth open loop control, - Introdcton of possble grd voltage dstrbances, - Operaton of dode rectfer nder dfferent grd voltage condtons,

80 - Introdcton of advanced Synchronos Doble Reference Frame Phase Locked Loop (SDRF-PLL) approach whch makes control system nsenstve for a majorty of grd voltage dstrbances, - Introdcton of passve elements nflence for operaton of PWM Rectfer. The expermental reslts were measred on laboratory setp wth ds3 DSP board. Both control strateges were mplemented n a system wth samplng and swtchng freqency khz and non deal grd voltage condtons. The chosen samplng freqency was khz to acheve effectve actve flterng operaton. It s well known that for good extracton of hgher harmoncs content, a hgh samplng freqency s reqred. The man harmoncs prodced by dode rectfers are: 5, 7, and 3. A 3 th harmonc freqency s 65, for khz swtchng freqency t gves only 5 samples per perod. Therefore, khz seems to be a mnmal vale of samplng freqency from the pont of vew of effectve flterng. Fg. 7.. General system scheme - 8 -

81 7. Voltage Orented Control (VOC) :#%#% a) Smlaton b) Smlaton Fg. 7.. Statonary operaton of VOC PWM Rectfer a) deal grd condtons b) dstorted grd 5% of 5 th harmonc From the top: grd voltage, npt crrent, DC-lnk voltage, FFT of npt crrent a) Smlaton b) Experment Fg Dynamc state operaton: smlaton load step change From the top: grd voltage, npt crrent, d and q axs crrent, DC-lnk voltage - 8 -

82 a) Smlaton b) Experment sa sa ca la Fg Steady state operaton of the system contanng of PWM Rectfer and dode rectfer From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) a) Smlaton b) Experment Fg PWM Rectfer load step change marked wth vertcal lne From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) Fg. 7. presents a steady state operaton of VOC scheme (presented n Fg. 5.3) of PWM Rectfer for deal grd condtons (a) and 5% of 5 th harmonc dstorted grd voltage (b). As shown the VOC scheme n case of dstorted grd voltage and wthot any addtonal PLL has sgnfcantly dstorted npt crrent (THD=9%). In Fg. 7. a load step change s presented and a coplng between d and q axs can be observed. Some decoplng technqes to elmnate for ths effect are presented n Appendx

83 Fg. 7.3 and 7.4 presents a steady state operaton and dynamc response of PWM Rectfer, respectvely. A PWM Rectfer operates n parallel wth dode rectfer. The npt crrent ca s controlled to be snsodal, bt together wth npt dode rectfer crrent la gves sgnfcantly dstorted grd crrent sa. After ntrodcng the actve flterng fncton the PWM Rectfer can drew a dstorted crrent to obtan a snsodal grd crrent. In the next secton two dfferent actve flterng approaches are presented. :#%#" 4 ; Fg. 7.5 and 7.6 presents an actvaton and steady state operaton of VOC scheme wth actve flterng (Fg.5.4). Frst two perods on Fg. 7.5 presents a PWM Rectfer operaton, where converter npt crrent s controlled to be a snsodal. Then the actve flterng fncton s actvated and snsodal waveform of the PWM Rectfer becomes adeqately dstorted to obtan snsodal shape of grd crrent. a) Smlaton b) Experment Fg Actvaton of AFF marked wth vertcal lne From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv)

84 a) Smlaton b) Experment sa sa ca la Fg Steady state operaton From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) :#%#$ 4 ; A block dagram of control algorthm nder stdy s presented n Fg Compared to total harmoncs compensaton (Fg.5.4), where the actve flterng fncton calclate total harmoncs content for compensaton, the selectve harmoncs method compensates the man harmoncs ndvdally. Therefore, t gves better reslts, however reqre more powerfl mcroprocessor for mplementaton. Fg. 7.7 and 7.8 presents the steady state and transents when Actve Flterng Fncton (AFF) s acheved. a) Smlaton b) Experment sa sa ca la Fg Steady state operaton From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv)

85 a) Smlaton b) Experment Fg Actvaton of AFF marked wth vertcal lne From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) a) Smlaton b) Experment Fg. 7.. Nonlnear load step change marked wth vertcal lne From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) :#%#)' Ths operaton gves a possblty of remove one par of crrent sensors (Fg. 5.6). Therefore, an electronc crct as well as a control algorthm becomes smpler. In ths staton wth a PWM Rectfer conventonal control strategy can overtake acton of actve flterng. The only

86 one change s a crrent sensors locaton, whch s moved from the converter s npt to the grd sde. Ths s sgnfcant smplfcaton of the system, bt t becomes hole system less stable. Addtonal, problems occr over crrent protecton are presented. a) Smlaton b) Experment sa sa ca la Fg. 7.. Steady state operaton From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) a) Smlaton b) Experment Fg. 7.. Nonlnear load step change marked wth vertcal lne From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv)

87 7. Vrtal Flx Based Drect Power Control (VF-DPC SVM) :#"#% 4 Fg. 7. and 7.3 presents the steady state and dynamc respond for PWM Rectfer operaton respectvely. As shown even for dstorted grd voltage grd crrent s almost snsodal. Ths reslt from natral low pass flter behavor of vrtal flx estmaton sed n nstantaneos actve and reactve power estmaton algorthm (Fg. 5.9). Note that, the coplng effect between actve and reactve powers practcally does not exst. Ths s reslt of very good behavor of the VF-DPC system descrbed n Chapter 5.. a) Smlaton b) Experment Fg. 7.. PWM rectfer operaton wth dstorted grd voltage - steady state From the top: grd voltage (U a ), grd crrent ( sa ) a) Smlaton b) Experment Fg PWM rectfer operaton wth dstorted grd voltage load change From the top: grd voltage (U a ), grd crrent ( sa ) spectrm of grd crrent, actve and reactve power

88 a) Smlaton b) Experment 4. Graph (V) : t(s) a. (V) (A) : t(s) a. (A) (A) : t(s) ca (A). -. (A) : t(s). la 5. (A) t(s) Fg PWM rectfer operaton at steady state From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) In Fg. 7.4 s presented staton, where a PWM Rectfer operates n parallel wth dode rectfer. The npt crrent c s controlled to be snsodal, bt together wth npt dode rectfer crrent l gves sgnfcantly dstorted grd crrent s. :#"#" 4 The Actve Flterng Fncton presented n Fg. 5.9 gves new advantages for a PWM Rectfer, lke compensaton of nonlnear load crrents. Fg. 7.5 shows a steady state for actve flterng operaton. A converter npt crrent s sgnfcantly dstorted, whle a grd crrent becomes almost snsodal. a) Smlaton b) Experment Fg Actve flterng operaton at steady state From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv)

89 a) Smlaton b) Experment Fg Start p of actve flterng marked wth vertcal lne From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) Fg. 7.6 presents waveform when the actve flterng fncton s swtched on. The left part shows conventonal PWM rectfer operaton, then after three perods actve flterng fncton was appled. Ths acton deforms converter crrent to provde almost snsodal grd crrent. The notches vsble on the grd voltage waveform (Fg. 7.6b) are generated by sgnfcantly dstorted crrents created by the system drng actve compensatng operaton. In Fg. 7.7 nonlnear load change s presented. The ampltde of npt dode rectfer s hgher, ths prodce hgher rpples n PWM converter npt crrent to obtan snsodal waveform of grd crrent. a) Smlaton b) Experment Fg Actve flterng operaton nonlnear load change marked wth vertcal lne From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv)

90 (-) :#"#$' a) Smlaton b) Experment 4. Graph5 (V) : t(s) a. (V) (A) : t(s) a. (A) (A) : t(s) ca. 5. (A) (-) : t(s) la t(s) Fg Actve flterng operaton at steady state From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) Fg. 7.7 and 7.8 presents a steady state and nonlnear load step change operaton respectvely. As mentoned n Chapter 5, ths control scheme ses crrent sensors located on the grd sde. Therefore, a mnmal nmber of crrent sensors s adopted. a) Smlaton b) Experment 4. Gra ph5 (V) : t(s ) a (A) : t(s ) a (A) : t(s ) c a (-) : t(s ) la t(s ) Fg Actve flterng operaton nonlnear load step change marked wth vertcal lne From the top: grd voltage (U a ), grd crrent ( sa ) (A/dv), converter crrent ( ca ) (A/dv), dstorted crrent ( la ) (A/dv) - 9 -

91 Fg. 7.9 shows a nonlnear load step change that reslts on hgher ampltde of a dode rectfer crrent. Hgher rpples on PWM converter npt crrent are vsble. As a reslt hgher ampltde of grd crrent s presented. 7.3 Smmary - Comparson of Compensatng Reslts Ths secton presents a compensaton reslts comparson. In Tab. 7. a THD and HD parameters are collected. Fg. 7. and 7. shows a graphcal representaton of data collected n Tab. 7. for VOC and VF-DPC SVM respectvely. Tab Comparson of compensaton methods: deal grd voltage, dstorted grd voltage THD sa HD [%] [%] 5h 7h h 3h No compensaton,47 9,6 3,6,88,9 Total compensaton 3,4,85,78,85,3 VOC Selectve compensaton,8,56,8,77,3 Closed loop 3,5,9,8,9,35 PQ based compensaton 3,5, VF-DPC Closed loop 3,8,,7,88,88 THD sa HD [%] [%] 5h 7h h 3h No compensaton,7, 3,38,98,4 Total compensaton 6,4,87,76,86,34 VOC Selectve compensaton 5,8,57,83,75,33 Closed loop 6,5,93,84,9,34 PQ based compensaton 4,, VF-DPC Closed loop 4,4,7,7,4,8-9 -

92 a) b) 8 Non compensated VOC fll VOC selectve compensaton VOC closed loop 8 Non compensated VOC fll VOC selectve compensaton VOC closed loop HD [%] 6 HD [%] Harmonc nmber Harmonc nmber Fg. 7.. HD reslts for VOC a) deal grd voltage, b) dstorted grd voltage a) b) Not compensated VF-DPC SVM open loop VF-DPC SVM closed loop Not compensated VF-DPC SVM open loop VF-DPC SVM closed loop 8 8 HD [%] 6 HD [%] Harmonc nmber Harmonc nmber Fg. 7.. HD reslts for VF-DPC SVM a) deal grd voltage, b) dstorted grd voltage For methods VOC and VF-DPC SVM the obtaned reslts are qte smlar and the HD ndex s less than % for all consdered hgher harmoncs. Ths can be a reslt of lmted samplng freqency ( khz). Sch a vale can be very hgh for a PWM Rectfers, especally for hgh power applcatons. However, t s rather small n case of Actve Flters. The hghest consdered harmonc nmber s 3. Ths means the 65 Hz, for khz samplng freqency that gves abot 5 samples per perod of 3 th harmonc, ths can be not enogh for proper recognton of harmonc content. Addtonal ncreasng of samplng freqency gves better reslts for compensaton of hgher harmoncs lke 3 th, 7 th, 9 th etc. 7.4 Rectfyng and Regeneratve Mode of PWM Rectfer Operaton The PWM Rectfer n most cases s appled n ASD when regeneratve mode of operaton s reqred. Also n energy savng applcatons t works n regeneratve mode, where the energy - 9 -

93 flows from the load to the grd. In ths staton a grd crrent wll be n phase wth a grd voltage to obtan a nty power factor. However, the ampltde of the grd crrent wll be n opposte phase. Fg. 7. presents smlaton reslts of a) PWM rectfer operaton mode and b) PWM Rectfer havng actve flterng fncton. It can be observed that the grd crrent Fg. 7.b compared wth Fg. 7.a becomes almost snsodal and s n phase wth grd voltage, whch provdes nty power factor. In ths staton converter npt crrent s more dstorted to compensate for hgher harmoncs of nonlnear load crrent. a) b) Fg. 7.. Smlaton reslts for rectfer operaton mode. a) PWM Rectfer operaton mode b) Actve flterng fncton of PWM Rectfer From the top: grd voltage, grd crrent, converter crrent, nonlnear load crrent. Fg. 7.4 shows a regeneratve operaton mode of PWM Rectfer wthot a) and wth b) actve flterng fncton actvated. In worst staton grd crrent can be more dstorted then presented n Fg. 7.3a and for eqal load condtons for dode and PWM rectfers cold be sgnfcantly dstorted lke n Fg That precsely shows that actve flterng fncton of PWM Rectfers can be very sefl n topc of harmoncs pollton control. Addtonally, t works correctly n both operatng modes of PWM Rectfer: rectfyng and regeneratng

94 Fg Smlaton reslts for regeneratve mode for eqal loads of dode and PWM Rectfer. From the top: grd voltage, grd crrent, converter crrent, nonlnear load crrent. a) b) Fg Smlaton reslts for regeneratve operaton mode. a) PWM Rectfer operaton mode b) Actve flterng fncton of PWM Rectfer From the top: grd voltage, grd crrent, converter crrent, nonlnear load crrent. Fg. 7.5 presents percentage content of hgher harmoncs n grd crrent for PWM Rectfer rectfyng mode (red), regeneratve mode (green) and appled actve flterng mode (ble). As shown actve flterng fncton redces harmoncs content even few tmes and HD factor s no hgher than %

95 8 6 Not compensated rectyfyng mode Not compensated regeneratve mode Flterng fncton appled 4 HD [%] Harmonc nmber Fg Percentage harmoncs content PWM Rectfer rectfyng and regeneratve operaton (nder 5% of 5 th harmonc grd voltage dstorton) Fg Crrent vector locs of: a) dode rectfer npt crrents, b) PWM Rectfer and c) grd crrents (where AFF s not appled), d) and e) PWM Rectfer crrents (where AFF s appled) for regeneratve and rectfyng operaton mode, f) grd crrents whle AFF appled. Fg. 7.6 shows crrent vector locs for oscllograms presented n Fg. 7. and 7.4. Sgnfcantly dstorted dode rectfer npt crrent s presented n Fg. 7.6a, whle a PWM Rectfer has almost deal crclar shape (Fg. 7.6b). Therefore, grd crrent (Fg. 7.6c) becomes dstorted. For AFF actvated, the PWM Rectfer crrents (rectfyng and regeneratng mode Fg. 7.6e and 7.6d respectvely) becomes dstorted, whle a grd crrent (Fg. 7.6f) s almost crclar

96 7.5 Typcal Grd Voltage Dstorton The power qalty problems [5., 5.6] can be demonstrated as: nonstandard voltage, crrent or freqency devaton, whch reslts n a falre or a dsoperaton of end-se eqpment. The most often appear grd voltage dstortons can be smmarzed as: Voltage sags (drop n voltage as a reslt of startng hgh power motors, few-cycles draton). Voltage swell (short-term ncrease n voltage of a few cycles draton as a reslt a sngle lne-to-grond falts or energzng a capactor bank). Interrpton (few-cycles draton). Harmoncs (prodced by appled nonlnear elements n power systems, sch as, power electronc swtches, satrated magnetc components). Typcal waveforms of grd voltage dstrbances are shown n 7.8. Fg Grd voltage emergency condtons: a) voltage nothng, b) mplsve, c) oscllatory, d) voltage sag, e) voltage swell, f) voltage nterrpton, g) voltage flcker

97 Presented grd voltage dstrbances have tremendos mpact on proper operaton of electronc eqpment lke a dode or PWM Rectfers. Therefore, those dstrbances n a grd system can case malfncton or damage of electronc eqpment. :##%& a) THD = [%] b) THD = 5[%] c) Unbalanced voltage Fg Operaton of dode rectfer for a) deal grd voltage condtons, b) dstorted of 5 th harmoncs grd voltage, c) nbalanced grd voltage. From the top: grd voltage, grd crrent, DC-lnk voltage. As shown n Fg. 7.8 nbalanced grd voltage has a negatve nflence on grd crrents as well as on DC-lnk voltage. Srprsng s, that for harmoncs dstorted grd voltage obtaned reslts are a bt better, then for deal grd condtons. It s s reason of hgher grd voltage, therefore a grd crrent looks more sqared and a DC-lnk voltage s smoother. a) -[%] b) [%] Fg Operaton of dode rectfer for a) voltage swell, b) voltage sag. From the top: grd voltage, grd crrent, DC-lnk voltage

98 Fg. 7.9 presents operaton of a dode rectfer nder voltage swell (a) and voltage sag (b). As shown a grd crrent decrease and ncrease respectvely. Moreover, a DC-lnk voltage ncreases and decreases respectvely Fg Operaton of dode rectfer for one phase voltage nterrpt. From the top: grd voltage, grd crrent, DC-lnk voltage. Fg. 7.3 presents operaton of dode rectfer for one phase voltage nterrpt. It s well vsble, that n ths staton a dode rectfer becomes a one phase H type brdge, sppled from lne to lne voltage. A decreasng effect of DC-lnk voltage s present and voltage level flctatons appears. Phase A Phase B Phase C I m [ A ] t [s] I m [ A ] t [s] I m [ A ] t [s] 6 4 I m [ A ] THD = 7.56[%] 4 THD = 35.93[%] 4 THD = 39.99[%] I m [ A ] I m [ A ] f=n*5 [Hz] f=n*5 [Hz] f=n*5 [Hz] Fg Operaton of dode rectfer for nbalanced grd voltage condtons. From the top: grd voltage, grd crrent, st -harmonc of grd crrent, FFT of grd crrent

99 Fg. 7.3 shows nbalanced grd voltage mpact for dode rectfer operaton. As shown each phase s dstorted ndvdally, whch ntrodce an nsymmetrcal condtons. :##" A PWM Rectfer wth VF-DPC SVM scheme s not robst for all types of grd voltage dstortons. As shown n Fg. 7.3 for nbalanced grd voltage, sgnfcantly npt crrents are obtaned. Addtonally, DC-lnk voltage flctatons are presented. Therefore, an addtonal PLL system s reqred for complete protecton of the system from grd voltage dstrbances Fg Operaton of PWM Rectfer nder dstorted and nbalanced grd voltage condtons From the top: Grd voltage, grd crrent, DC-lnk voltage. The advanced PLL algorthm presented n [9.3] were selected and mplemented n VF-DPC SVM control algorthm. v a v b v c [ T αβ ] v α vβ [ T dq ] θ ' v d vq k p k v d ω' θ ' sn - Fg Synchronos Doble Reference Frame Phase Locked Loop (SDRF-PLL) [9.3] The reslts obtaned wth (SDRF-PLL) are mch promsed, the control system s robst aganst of most grd voltage dstrbances. Ths assre proper operaton of the system for

100 abnormal and falre grd condtons. Bellow are presented selected smlaton reslts wth llstrate VF-DPC SVM scheme wth advanced PLL system operaton. Fg Operaton of PWM Rectfer nder dstorted and nbalanced grd voltage condtons From the top: grd voltage, grd crrent. Fg Operaton of PWM Rectfer nder grd voltage sag. From the top: grd voltage, grd crrent. Fg Operaton of PWM Rectfer nder grd voltage swell. From the top: grd voltage, grd crrent. - -

101 Fg Operaton of PWM Rectfer nder grd voltage momentarly one phase nterrpton. From the top: grd voltage, grd crrent. In fgres operaton of PWM Rectfer nder several dfferent grd voltage dstortons are presented. All of them show three phase grd voltage (pper waveform) and three phase PWM Rectfer npt crrent (lower waveform). Fg presents the 5% dstorton of 5 th harmonc and % nbalance. Fg and 36 shows % voltage sag and swell respectvely. Fnally, Fg shows momentarly nterrpton n one phase. Those reslts llstrate stable operaton of PWM Rectfer nder dfferent grd voltage condtons s garanteed. 7.6 Inflence of Passve Components, DC-lnk Voltage and Converter Power Varatons :#.#% ' 7 Ths chapter presents reslts of VF-DPC-SVM for dfferent parameters varatons. 8 rectfer operaton actve flterng 7 THD [%] C [F] Fg Grd crrent THD verss vale of DC sde capactor - -

102 As presented n Fg a grd crrent THD decreases wth ncreasng vale of DC-sde capactor. Ths can be a reslt of storage bgger vale of energy n capactor. 8 rectfer operaton actve flterng 6 THD [%] L [mh] Fg Grd crrent THD verss vale of AC-sde ndctor Fg shows grd crrent THD verss vale of AC-sde ndctor. As shown n Fg the VF- DPC SVM s not mch senstve for npt ndctance changes, bt for actve flterng fncton ths parameter changes. :#.#"&'( 7' 8 rectfer operaton actve flterng THD [%] U DC [V] Fg Grd crrent THD verss vale of DC-voltage - -

103 Fg. 7.4 presents a grd crrent THD verss vale of DC-voltage. It s well vsble that hgh vale of DC voltage mpose low vale of grd crrent THD for both PWM and actve flterng operaton. 9 8 Lne crrent THD [%] Actve power of PWM Rectfer[kVA] Dode Rectfer crrent [A] Fg Grd crrent THD verss: a) actve power of PWM Rectfer and b) dode rectfer power 7.7 Dscsson on Dgtal Sgnal Processor Implementaton :#:#%' ' 8 Dfferences between the control technqes wth respect to the comptaton complexty are presented n Fg. 7.4 and 7.4. Frst one presents the nmber of nstrctons per sample cycle, the second one shows comptaton ntensty (dspace 3) Nmber of nstrctons per sample tme VOC VF-DPC VF-DPC PQ VOC Total VOC Selectve Fg Nmber of nstrctons per sample tme - 3 -

104 6 5 Comptaton ntensty dspace 4 3 VOC VF-DPC VF-DPC PQ VOC Total VOC Selectve Fg Comptaton ntensty dspace :#:#%6 6 < A samplng tme T S selecton s very mportant from the dgtal control pont of vew. Frst of all, hgh samplng tme T S s reqred for the proper reconstrcton and selecton of hgher harmoncs content. For a chosen mnmal reqred nmber of samples per perod and lmted hgher harmonc, the mnmal samplng tme can be selected (Tab. 7.3). Tab Selecton of samplng tme T S Harmonc nmber Correspondng freqency [Hz] Ts (mn) [khz] For the parameters presented n Tab. 7.3 a mnmal reqred nmber of samples were 5. Indrectly, a samplng tme T S has an nflence for compensaton capablty ( t resltng from a dode rectfer operaton, mentoned n Chapter ) specally, when a samplng freqency s not eqal to swtchng freqency of the modlator. In case when a samplng freqency s hgher then a swtchng freqency, the modlator can loose some nformaton from the control algorthm. The response of the modlator n ths case can be not complete or delayed. That may case n malfncton of the compensaton

105 7.8 Conclsons Ths chapter presents smlaton and expermental reslts of two dfferent control strateges: conventonal control strategy for PWM rectfers - Voltage Orented Control (VOC), and novel grd voltage sensorless Vrtal Flx based Drect Power Control (VF-DPC) wth constant swtchng freqency sng Space Vector Modlator (SVM). Steady state and dynamc behavor as well as harmonc compensaton effectveness of VOC strategy depends on appled crrent control technqe (see Appendx A.5). In case of nbalanced grd voltage the PLL s strongly reqred to obtan possbly close snsodal grd crrent. In contrast performance of VF-DPC SVM depends strongly on accracy of nstantaneos actve and reactve estmaton, whch n the case of VF based calclatons, s more robst to hgher harmoncs n grd voltage. However, both VOC and VF-DPC SVM are very senstve for nbalanced grd voltage (Fg. 7.3). Therefore, to compensate for nbalanced voltage, a SDRF-PLL [9.-9.3] system has been appled. A VF-DPC control strategy s addtonally eqpped on SDRF-PLL approach, whch makes control system robst for a majorty of grd voltage dstrbances (Fg. 7.7). Regardng the dynamc performance n VOC scheme a coplng effect between d and q crrents can be observed. Ths can be compensated for sng decoplng algorthm presented n Appendx A.5. On the other hand n VF-DPC scheme the coplng between nstantaneos actve and reactve power practcally does not exst (see Fg. 7.6). In the case when PWM Rectfer shold be extend wth Actve Flterng Fncton, t can be mplemented n two ways: open (Fg. 5..a) or closed loop (Fg. 5..b). For both open and closed loop control strateges two control sses are presented. The open loop control strategy reqres addtonal crrent sensors and modfcaton of control algorthm. The closed loop control strategy operates lke a PWM rectfer wth only changed locaton of crrent sensors. However, the open loop strategy allows controllng crrent harmoncs content and grd power factor ndependently (see Fg. 5.). So, the power factor compensaton can be sed as an opton. The Actve Flterng Fncton (AFF) for both control strateges has been presented. Ths s stable solton, whch extend fnctonalty of PWM Rectfer. A devce can work as typcal PWM rectfer or/and operate as Shnt Actve Flter (SAF). After small modfcaton of hardware and software as well as approprate ncrease of PWM converter kva power, t s possble to compensate for neghborng non-lnear power loads sppled at the PCC. For VOC method there are proposed two dfferent hgher harmoncs compensaton strateges: total (Fg. 5.4) and selectve (Fg. 5.5) harmoncs compensaton methods. A VF-DPC ses only one compensaton method based on pq power - 5 -

106 theory (Fg. 5.). The effectveness of the crrent harmonc redcton depends strongly on the sed control strategy, bt also on grd voltage dstorton. VF-DPC SVM scheme wth AFF performs mch better (abot two tmes) as VOC (n depended on harmonc compensaton method: total or selectve) nder dstorted grd voltage (see Tab. 7.). However, nder pre snsodal grd voltage both control methods gves smlar reslts. Note that n the case of VOC scheme selectve harmonc compensaton s lghtly better as total compensaton. The regeneratve mode of operaton (Fg. 7.) s very crtcal n the case f the nonlnear load crrent and regeneratve crrent of PWM Rectfer are at the same vale (Fg. 7.3). However, the AFF s able to elmnate ths phenomenon (Fg. 7.4). Addtonally, nflence of passve elements and DC-lnk voltage vales s ntrodced and dscssed, as well as selecton of samplng tme. Tab Comparson of VOC SVMAFF wth VF-DPC SVMAFF parameter VOC AFF VF-DPC AFF Grd voltage sensor No No Crrent control loops Yes No Power control loops No Yes Robst for hgher harmoncs n grd voltage No Yes Possble se of dfferent SVM strateges Yes Yes Oter DC-lnk voltage reglaton Yes Yes Tab Comparson of conventonal and smplfed VF-DPC AFF parameter VF-DPC AFF open loop VF-DPC AFF closed loop Addtonal crrent sensor Yes No Grd voltage sensor No No Addtonal modfcaton of control algorthm Yes No Grd crrent harmoncs content control () Yes Yes Power factor correcton () Yes Yes Independent control of () and () Yes Yes Precse over crrent protecton Yes No Based on smlaton stdy carred-ot n SABER smlaton package as well as expermental reslts measred n the laboratory setp the man featres and advantages of VF-DPC SVM PWM Rectfer wth AFF can be smmarzed as: No lne voltage sensors are reqred, - 6 -

107 Smple control algorthm wthot several coordnate transformaton, No crrent control loops, the system operates drectly on nstantaneos actve and reactve powers, Good dynamcs and practcally no coplng between actve and reactve power, Snsodal lne crrents for deal and dstorted lne voltage, thanks to the natral lowpass flter behavor of the ntegrators sed n flx estmator, Constant swtchng freqency thanks to se of Space Vector Modlator (SVM), Proposed system can operate as a PWM rectfer, Shnt Actve Flter or t can take the role of PWM rectfer havng actve flterng fncton. Ths extends tasks of PWM rectfer on elmnatng of hgher harmoncs n lne crrent. In ths case PWM rectfer spply ts load and at the same tme compensate for harmoncs AC lne crrent, Thanks to actve flterng fncton t s possble to se non polltng eqpment what s PWM rectfer as a crrent harmoncs elmnatng devce, t s also possble to add ths fncton to crrently exstng PWM rectfers, The system has been verfed by the smlaton and expermental stdy, Compared to standard PWM rectfer, t has to be dmensoned for a larger power rato

108 8. Smmary and Closng Conclsons The thess has been devoted to analyse, control and desgn of PWM Rectfers wth addtonal Actve Flterng Fncton (AFF). Varos problems were addressed and dscssed as follows: Open (4 crrent sensors Fg. 5.a) and closed ( crrent sensors Fg. 5.b) loop for grd crrent hgher harmonc netralzaton, Control strateges for actve and reactve power control wth specal emphass on Drect Power Control wth Space Vector Modlaton (DPC-SVM) scheme, Algorthms for Actve Flterng Fncton (AFF), Rated power condtons, Passve components desgn, To analyze and comparatve stdy two smlaton models, were developed: sng SABER software package and Matlab/Smlnk. These models allow stdyng both power converters wth control loop and harmonc netralzaton methods. For expermental valdaton a laboratory set-p based on 5kVA Danfoss dode and PWM converters wth dspace controller has been constrcted. Among mportant reslts of the thess are: 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), Proposed system can operate as a PWM Rectfer, Shnt Actve Flter (SAF) or t can take the role of PWM Rectfer havng AFF. Ths extends tasks of PWM Rectfer on elmnatng of hgher harmoncs n grd crrent. In ths case PWM Rectfer spply ts load and at the same tme compensate for AC grd crrent harmoncs of neghborhood nonlnear loads, Thanks to AFF t s possble to se a PWM Rectfer as a non polltng eqpment and crrent harmoncs elmnatng devce. Also t s possble to add ths fncton to crrently workng PWM rectfers, - 8 -

109 Compared to standard PWM Rectfer, t has to be dmensoned for a hgher power rato. Therefore, desgnng process for converter power rato calclatons (dependng on applcaton PWM Rectfer, Shnt Actve Flter, and PWM Rectfer wth Actve Flterng Fncton) was elaborated. As mentoned n Chapter 6 applcaton of PWM Rectfer or PWM Rectfer s proftable for hgh power applcatons (>5 kw), whle adopton of Shnt Actve Flters s advantageos for low power applcatons. Varos control strateges for crrent harmonc netralzaton were presented and verfed n smlatons and expermental. Demonstrated reslts confrm seflness of Actve Flterng as an extended fncton of PWM Rectfer control algorthm. Above mentoned control strateges were nvestgated n smlatons and expermentally. Obtaned reslts, confrms eqty of argment of ths thess. In the athor opnon the reslts of ths thess can be sed n desgn and development of modern PWM rectfers wth actve harmonc netralzaton fncton as well as shnt actve power flters

110 Appendx A. Harmoncs #%#% =>? 3 Harmoncs n a three-phase system transformed to the αβ-frame wll rotate n dfferent drectons dependng on the harmonc nmber [6]. For nstance, the fndamental crrent wll rotate conter-clockwse: the 5 th harmonc crrent wll rotate clockwse and the 7 th harmonc crrent wll rotate conter-clockwse. The three voltage vectors n the αβ-frame are shown bellow. β 7 ω ( t g ) 5 ω ( t g ) ( t) (7) ( t) (5) ( t) () ω ( t g ) α Fg. A... Representaton of harmonc vectors rotaton n dq reference frame Harmoncs of orders n=3k, k=,,3, are of a zero seqence. In the αβ-frame ths harmonc vector wll not rotate. In a three-phase grd wthot a netral leader, zero-seqence harmoncs wll not occr. Harmoncs of the order n=6k, K=,,3 are of a postve seqence. Ths, the harmonc vector n the αβ-frame wll rotate conter-clockwse. The postve-seqence harmoncs are the 7 th, 3 th, 9 th, etc. Harmoncs of the order n=6k-, K=,,3 are of a negatve seqence. Ths, the harmonc vector n the αβ-frame wll rotate clockwse. The negatve-seqence harmoncs are the 5 th, th, 7 th, etc. The rotatng vector n below s defned for each harmonc n, sng a three lne crrents: e e j 3 π 4π j j 3 3 n = an bn cn = αn β n (A..) - -

111 #%#"5 3 When transformng rotatng vectors from the αβ-frame to the dq-frame, a conter-clockwse rotaton of the αβ-frame wth fndamental anglar freqency wll occr. The crrent vector ( ) αβ s transformed sng: π j( ω ) ( ) gt dq ( αβ ) = e (A..) The fndamental crrent vector n the αβ-frame wll be transformed to a statonary vector n the dq-frame. Postve-seqence harmoncs wll rotate slower n the dq-frame. For negatveseqence harmoncs, the vectors n αβ-frame wll rotate faster n the dq-frame. The harmoncs transformaton from αβ-frame to dq-frame s shown n table bellow. Tab. A.3. Harmoncs representaton n αβ statonary and rotatng dq frames Harmonc type Harmonc nmber n αβ-frame dq-frame Fndamental n= π ( αβ ) j( ωgt ) ( t) = ( dq) e ( t) = Postve seqence n=6k, k=,,3 π ( αβ ) jn( ωgt ) ( t) = e ( ) ( )( π dq j n ωgt ( t) = e ) Negatve seqence n=6k-, k=,,3 π ( αβ ) jn( ωgt ) ( t) = e ( ) ( )( π dq j n ωgt ( t) = e ) n n () ( n) () n n () ( n) ( n) - -

112 A. Basc Harmonc Dstorton n Power System The specfcaton of power system harmonc, conventonal and nstantaneos power theores wll be revewed nder deal and dstorted condtons [4]. A waveform s dstorted when a voltage or crrent n power system contans other freqences than the fndamental freqency of the mans. The dstortng components of waveforms nder steady state condtons are sally nteger mltples of the fndamental power freqency. #"#%' = Accordng to the above descrpton perodcal sgnal of voltage, crrent and power can be represented as Forer seres ( t) ( t) = n= = n= U I n n sn( ω t ψ ) n sn( ω t ψ ϕ ) n n n n (A..) (A..) where ϕ = U, I ) - phase angle between n-th voltage and crrent harmoncs n ( n n ω n = nω ; ω n s the anglar freqency of the nth harmonc πn ω n = πnf = (A..3) T U n and I n are the rms (root mean sqare) vale of the nth harmonc voltage and crrent respectvely: X n = T T x ( t) dt n (A..4) based on Parseval theorem the rms vale of the dstorted voltage and crrent s gven by: T U rms = ( t) dt = U n = U U U... (A..5) T T I rms = ( t) dt = I n = I I I... (A..6) T - -

113 The total harmonc dstorton factor (THD) s most commonly sed to characterze the magntde of the dstorted sgnals. The THD gves the rato between the geometrc sm of the magntdes or rms of the harmoncs and the magntde (or rms vale) of the fndamental component: n= X n THD =. (A..7) X The man dsadvantage of the THD s that the detaled nformaton abot harmonc spectrm s lost. The nstantaneos power s defned as: p(t) = (t) (t) (A..8) Classcal approaches defne that actve power s an average vale of nstantaneos power T P = p( t) dt ( t) ( t) dt P T = T = T n= n = U I n= U n I n cosγ n T S = U rms I rms = ( t) dt ( t) dt = U I n (A..9) T T Q = S P D T n= n n= For a typcal three-phase system wthot netral wre, U I wll be zero snce a zero seqence components of the crrent system do not exst. Therefore, the eqatons (A..9) posses only AC components: P = P = U I cosγ (A..) n= n n= n= n= n n n S = U n I (A..) n= n= n Q = Q = U I snγ (A..) n n n n - 3 -

114 Where the actve power P wll ths represent a measre of the average energy flow even n a dstrbed power system. The apparent power S s sally sed to specfy the sze of reqred power system eqpment. The apparent power S s consdered as representng the maxmm actve power, whch can be delvered by a voltage sorce whle the lne losses are mantaned constant. The reactve power Q s of nterest for specfyng the sze of compensaton eqpment n power system sch as PWM converters and actve power flters. From the comparson of Eqs. (A..8), (A..) wth (A..9) can be seen that as dstnct from snsodal sgnals the sqare sm of actve and reactve power s not eqal to apparent power. Therefore, to complete the defntons a dstorton power D has been ntrodced (Fg.A.A..). The separate power are connected n eqaton D = S P Q (A..3) S D Q P Fg. A..4. Graphcal representaton of power components A.3 Instantaneos decomposton of powers Instantaneos power for three-phase system s sally consdered n orthogonal coordnates α-β- then n three-phase coordnate a-b-c. Therefore, the Clarke transformaton C and ts reverse transformaton C - defne the relatonshp between the three-phase system a-b-c and the statonary reference frame α-β- are descrbed as: x x x α β = 3 / / / 3 / / x 3 / x / x a b c (A.3.a) where x denotes crrents or voltages - 4 -

115 - 5 - = / 3 / / / 3 / / / 3 x x x x x x c b a β α (A.3.b) The α-β components can be represented n the Cartesan plane by a space vector x αβ : β α αβ jx x x = (A.3.) where the α-axs and the a-axs have the same orentaton. The β-axs leads the a-axs wth 9. For a three-phase power system, nstantaneos voltages a, b, c and nstantaneos crrents a, b, c are expressed as nstantaneos space vectors and = c b a and = c b a (A.3.3) For three-phase voltages and crrents a, b, c and a, b, c the α, β and components are expressed as: [ ] = c b a C β α and [ ] = c b a C β α (A.3.4) For the typcal three-phase system wthot netral wre, zero seqence component of the crrent system does not exst ( = c b a ). It gves fnally smple realzaton of sgnal processng thanks to only two sgnals n α-β coordnate what s the man advantage of abc/αβ transformaton. Wth ths assmpton the eqatons (A..5) can be descrbed as: = c b a 3 / / 3 / / 3 β α (A.3.5) and

116 - 6 - = c b a 3 / / 3 / / 3 β α (A.3.6) General three-phase for-wre system s represented as separated: three-phase three-wre system and a sngle-phase system, whch represents the zero seqence components. ) ( ) ( t p t p p T c b a T c b a = = = β α β α (A.3.7) The nstantaneos zero seqence power p (t) s only observable f exst both zero seqence components (, ). ) ( v t p = (A.3.8) #$#%< #$#%< #$#%< #$#%< The Takahash defne the nstantaneos actve power p as scalar prodct between the threephase voltages and crrents and nstantaneos reactve power q as vector prodct between them: c c b b a a abc abc p = = ) ( ) ( (A.3.9) c c b b a a abc abc q ' ' ' ) ( ) ( = = (A.3.) where a, b, c s 9 lag of a, b, c respectvely. The same eqatons can be descrbed n matrx form as: = c b a c c b b a a q p ' ' ', (A.3.) where = = ba ac ca a b c a b c c b a 3 3 ' ' '. (A.3.)

117 Addtonal nformaton can be obtaned by defnng an nstantaneos complex power p(t) n the Cartesan plane: p( t) = ( t) ( t) = a a b b * = Re #$#" { p( t) } Im{ p( t) } cc j [( b c) a 3 = p( t) jq( t) = ( c ) a b ( a ) ] b c (A.3.3) The most freqently referred power theory was proposed by Akag [9] when the three-phase voltages and crrents are transformed nto α-β coordnates, and addtonally the three-phase voltages and crrents excldng zero-phase seqence components. Therefore, nstantaneos power on the three-phase crct can be defned as follows: p = (A.3.4) α α β β In order to defne the nstantaneos reactve power, Akag ntrodced the nstantaneos magnary power space vector defned by: q = (A.3.5) α β β α (magnary axs vector s perpendclar to the real plane on the α-β coordnates) The conventonal nstantaneos power p and the above defned nstantaneos magnary power q, whch s the ampltde of space vector q are expressed by: p α = q β β α α β (A.3.6) α α and β β obvosly mean nstantaneos power becase they are defned by prodct of the nstantaneos voltage n one axs and the nstantaneos crrent n the same axs. Therefore, p s the real power n the three-phase crct and ts dmenson s [W]. Conversely, α β and β α are not nstantaneos power, becase they are defned by the prodct of the nstantaneos voltage n one axs and nstantaneos crrent not n the same axs bt n the perpendclar axs. The α-β crrents can be obtaned as follows: - 7 -

118 - 8 - = q p α β β α β α (A.3.7) and gves fnally = q p α β β α β α β α (A.3.8) #$#$ #$#$ #$#$ #$#$ The theory proposed by Peng [4] defnes vector q desgnated as the nstantaneos reactve (or nonactve) power vector of the three-phase crct. The magntde (or the length) of q s desgnated as the nstantaneos reactve power that s = = b a b a a c a c c b c b c b a q q q q (A.3.9) and c b a q q q q q = = (A.3.) Next the nstantaneos actve crrent vector p, the nstantaneos reactve crrent vector q, the nstantaneos apparent power s and the nstantaneos power factor λ are defned as: p def cp bp ap p = = (A.3.) q def cq bq aq q = = (A.3.) s def = and s p def = λ (A.3.3) where

119 = = and a b c = = (A.3.4) a b c are the nstantaneos magntdes (or norms) of the three-phase voltage and crrent, respectvely. A.4 Smlatons and Expermental envronments #)#%69 Fg. A.4.. Saber model The control algorthms of PWM rectfer was mplemented n SABER, whch provdes analyss of the complete behavor of analog and mxed-sgnal systems, ncldng electrcal sbsystems. The man electrcal parameters of the power crct and control data are gven n the Table 7.. The example of PWM rectfer model s shown n Fg. A.4.. The electrcal elements are taken from lbrary, bt control algorthm has been wrtten n MAST langage

120 #)#"6 Fg. A.4.. Smlnk based smlaton model Addtonally, the smlnk models were sed. The power system elements were modeled n Power System Toolbox. The control strctre was bld sng blocks from the lbrary. Fg. A.4.3. Plecs based smlaton model The Plecs power system elements were also consdered nto smlatons and some comparson between Power System Toolbox and Plecs were done. #)#$9 9&6%%/$ Laboratory setp conssts of two parts: power crct, control and measrement systems. - -

121 PWM Rectfer TM PWM Inverter TM 3 Phase Grd IPC IPC Optc fber Optc fber recever recever 3 DC lnk 3 AC Voltage&Crrents Measrements Optc fber 6 DC Voltage Measrements Optc fber 6 AC Voltage&Crrents Measrements Measrement Eqpment DSP Interface Pentm TM DS3 dspace Master : PowerPC 64e Slave: DSP TMS3F4 AC Motor Host Compter Fg. A.4.4. Confgraton of laboratory setp Power crct The laboratory setp (Fg. A.4.4) conssts of two commercal Danfoss nverters VLT 5 seres (Table A.) wth a resstors as a passve load. Table A. General parameters of VLT55 nverter U LN I LN I VLT,N S VLT,N P VLT,N Effcency [V] [A] [A] [kva] [kw] , 5,5 3,,96 where: U LN - lne voltage, I LN - lne crrent, I VLT,N - otpt crrent, S VLT,N - otpt power, P VLT,N - power on shaft. Control and measrement systems Ths part of system conssts of followng elements: dspace DS3 board nserted nto a PC-Pentm, nterface board and measrement system, Software. - -

122 Measrement Eqpment Measrement Eqpment AC&DC Voltages&Crrents AC&DC Voltages&Crrents Optc Fber Recevers Optc Fber Recevers Optc Fbers Isolaton Amplfers LEM-55 Converters and Isolaton Amplfers Optc Fber Drvers Optc Fber Drvers START STOP START STOP DA Converters AD Converters Inpt/Otpt Sgnals PWM Sgnals DS3 DS3 Fg. A.4.5. Block dagram of DSP nterface The power converters are controlled by the dspace DS3 board nserted nto a PC-Pentm. The mxed RISC/DSP/CAN dgtal controller based on two mcroprocessors (PowerPC64e 333MHz and TMS3F4 MHz) and for hgh-resolton analog-to-dgtal (A/D) converters (.8µs - bt) provde a very fast processng for floatng pont calclatons. It makes possble real tme control. Fg. A.4.6. DS3 nsde the Pentm PC Basc parameters of DS3: master processor - Motorola PowerPC64e/333MHz slave processor fxed pont DSP of TI s TMS3F4 6 channels of ADC 6 bt (resolton) 4 )s (samplng tme), V 4 channels of ADC bt.8 )s, V - -

123 8 channels of DAC 4 bt - 5 )s, V ncremental Encoder Interface 7 channels 3 dgtal I/O lnes Control Desk software The DSP sbsystem, based on the Texas Instrments TMS3F4 fxed pont processor, s especally desgned for control of power electroncs. Among other I/O capabltes, the DSP provdes one three-phase PWM generator and for sngle phase PWM generators. The other CAN sbsystem based on Semens 8C64 mcrocontroller s sed for connecton to a CAN bs. The PPC has access to both the DSP and the CAN sbsystems. The PPC s the master, whereas the DSP and the CAN mcrocontroller are slaves. The followng fgres gve an overvew of the fnctonal nts of the DS3 PPC. a) b) ISA Bs nterface conector (Host ntrface) Master PPC Decrementer, Tmebase Tmer A & B Interrpt Control DPMEM DPMEM ADC Unt DAC Unt Incremental Encoder Interface Bt I/O Unt Seral Interface I/O Unts I/O Connectors P, P, P3 CAN Sbsystem Slave MC CAN Controller Slave DSP CAN Sbsystem ADC Unt Tmng I/O Unt (PWM, CAP) Bt I/O Unt Fg. A.4.7. a) Block scheme of DS3; b) Placement of man components DSP nterface provde galvanc solaton between control board DS3 and power crct. All PWM sgnals are generated by DS3 and send sng optc fbers to the Interface and Protecton Card IPC that s monted on the front panel of the nverter, nstead of orgnal Danfoss control board. The IPC ncldes: optc fber recevers, 4MHz modlaton of gate - 3 -

124 sgnals and protectve fncton reqred by the VLT,.e. short-crct, shoot-trogh of the DC lnk, over voltage and over temperatre. Software Operaton on DS3 s provded by an ntegrated Control Desk program (see Fg. A.4.9). Thanks to ths applcaton t s possble to change strctre and parameters n real tme. For algorthms applcaton t s possble to se: assembler, C langage and Smlnk. Fg. A.4.8 Screen of Control Desk software A.5. Revew and desgn of Crrent and Power Controllers A.5. Crrent Control Technqes Crrent control (CC) [,.,.] creates the ntegral control and therefore qalty of CC s most mportant for the qalty of the whole control and flterng fncton. ##%#% %#%' ' '' A.5... Basc Reqrements and Defntons Most applcatons of three-phase voltage-sorce PWM converters - AC motor drves, actve flters, hgh power factor AC/DC converters, nnterrptble power spply (UPS) systems and AC power spples - have a control strctre comprsng an nternal crrent feedback loop. Conseqently, the performance of the converter system largely depends on the qalty of the appled crrent control strategy

125 U DC Ac Bc Cc - - ε Α ε Β ε C PWM Crrent Controller S A S B S C - C B A AC sde (load) Fg. A.5.. Basc block dagram of crrent controlled PWM converter The man task of the control scheme n CC-PWM converter (Fg. A.5.) s to force the crrents n a three-phase AC load to follow the reference sgnals. By comparng the command Ac ( Bc, Cc ) and measred A ( B, C ) nstantaneos vales of the phase crrents, the CC generates the swtchng states S A (S B,S C ) for the converter power devces whch decrease the crrent errors ε A (ε B,ε C ). Hence, n general the CC mplements two tasks: error compensaton (decreasng ε A,ε B,ε C ) and modlaton (determnaton of swtchng states S A,S B,S C ). A.5... Basc reqrements and performance crtera The accracy of the CC can be evalated wth reference to basc reqrements, vald n general, and to specfc reqrements, typcal of some applcatons. Basc reqrements are: no phase and ampltde errors (deal trackng) over a wde otpt freqency range, to provde hgh dynamc response of the system, lmted or constant swtchng freqency to garantee safe operaton of converter semcondctor power devces, low harmonc content, good dc-lnk voltage tlzaton. The followng parameters of the CC system dynamc response can be consdered: dead tme, settlng tme, rse tme, tme of the frst maxmm and overshoot factor. The foregong featres reslt both from the PWM process and from the response of the control loop. For example, for dead tme the major contrbtons arse from sgnal processng (converson and calclaton tmes), and may be apprecable especally f the control s of the dgtal type. On the other hand, rse tme s manly affected by the AC sde ndctances of the converter. The optmzaton of the dynamc response sally reqres a compromse, whch depends on the - 5 -

126 specfc needs. Ths may also nflence the choce of the CC technqe accordng to the applcaton consdered. In general, the compromse s easer as the swtchng freqency ncreases. Ths, wth the speed mprovement of today's swtchng components (e.g. IGBT's), the peclar advantages of dfferent methods lose mportance and even the smplest one may be adeqate. Nevertheless, for some applcatons wth specfc needs, lke actve flters, whch reqre very fast response or hgh power converters where the nmber of commtatons mst be mnmzed, the most stable CC technqe mst be selected. A Presentaton of CC Technqes Exstng CC technqes can be classfed n dfferent ways. In ths Chapter, the CC technqes are dvded nto two man grops (Fg. A.5.): Controllers wth open loop PWM block (Fg. A.5.3a) and On-Off controllers (Fg. A.5.3b). PWM Crrent Control Methods On-Off Controllers Separated PWM block Hysteress Delta Modlacton On lne Optmzed Lnear Controllers Fzzy Logc and ANN PI State Feedback Fg. A.5.. Crrent Control technqes Resonant Controllers Predctve and Deadbeat In contrast to the On-Off controllers (Fg. A.5.3b), schemes wth open loop PWM block (Fg. A.5.3a) have clearly separated crrent error compensaton and voltage modlaton parts. Ths concept allows s to explot the advantages of open loop modlators (snsodal PWM, space vector modlator, optmal PWM) whch are: constant swtchng freqency, well-defned harmonc spectrm, optmm swtch pattern and good DC lnk tlzaton. Also, fll ndependent desgn of the overall control strctre as well as open loop testng of the converter and load can be easly performed

127 c S ε v A c S Controller PWM B - S C Control Part Modlaton Part Voltage Sorce Converter AC Sde (Load) c - ε On-Off Controller Control Modlaton Part S A S B S C Voltage Sorce Converter AC Sde (Load) Fg. A.5.3. a) Controller wth open loop PWM block b) On-Off Controller A Introdcton to Lnear Controllers - Basc strctres of lnear controllers Two man tasks nflence the control strctre, when desgnng crrent control scheme: reference trackng and dstrbance rejecton abltes. Conventonal PI controller a) PI Controller d Plant r e y C(s) G(s) - b) c) K K /T K Fg. A.5.4. a) Feedback controller, b) and c) Two forms of PI controller strctre The npt-otpt relaton of the control scheme presented n Fg. A.5.4a can be descrbed by: C( s) G( s) G( s) y( s) = r( s) d( s), (A.5.) C( s) G( s) C( s) G( s) or n the form: y ( s) = T ( s) r( s) S( s) d( s), where: C(s) controller transfer fncton (Fg. A.5.4b and Fg. A.5.4c), here C( s) K st = K = K, where s st K T = (A.5.) K G(s) plant transfer fncton, K proportonal gan, - 7 -

128 T(s) reference transfer fncton, K ntegral gan, S(s) dstrbance transfer fncton, T ntegratng tme, r - reference sgnal, d dstrbance sgnal, y otpt sgnal, s Laplace varable, For good reference trackng t shold be: C( s) G( s) T ( s) =, (A.5.3) C( s) G( s) and for effectve dstrbance rejecton: S ( s) =, (A.5.4) C( s) G( s) The above condtons can be flflled for low freqency range. However, n hgher freqency range the performance s detorated. Moreover, PI controller parameters nflence both reference trackng and dstrbance rejecton performance and are not possble to nflence the characterstcs separately. Table A.3. Controller parameters accordng to standard rles (for fast samplng T S ) Integratng tme T Method Plant Proportonal gan K Integratng gan K Remarqes Optmal Modls Crteron (For T >> τ ) a o K e st sτ O a K = Ta K τ O o K T = T a = K O τo - 4% overshoot n response to step change of reference - Very slow dstrbance rejecton Optmal Symmetry Crteron (For T >> τ ) ) a ( T b O sτ KOe st ( st ) a b K = K O Ta ( T τ ) b o K T = 4( T b o = τ ) T a 8KO ( Tb τ o ) - Fast dstrbance rejecton - 43% overshoot n response to step change of reference. -A n npt flter s reqred (T F =T ) Dampng Factor Selecton ξ = (For τ = ) O K e st sτ O a K = 4 T K T = ξ ( a O K O ) ( K ) O K = 4ξ Ta KO - Well damped Rle of the Thmb K = K T = T s = T s - Only for very roghly desgn T s samplng tme Some of sch a standard rles commonly sed n power electroncs and drves control practce are gven n Table A.3. For T a < 4τ o the modls crteron s more sefl, whereas for T a >> τ o t s better to apply the symmetry crteron. The rles of Table A.3 are vald for contnos or fast sampled (T s ) dscrete systems. For slow (T s T a ) or practcal (T s < T a ) samplng, the samplng tme T s has to be nclded n controller parameters. It shold be noted, - 8 -

129 however, that controller parameters calclated often on the bass roghly estmated plant data, can only be sed as broadly ndcatve of the vales to be employed. ##%#"*'' %#"*'' A.5... Ramp Comparson Controller The Ramp Comparson Crrent Controller, ses three PI error to prodce the voltage commands Ac, Bc, Cc for a three-phase snsodal PWM (Fg. A.5.4) Ac Bc - Cc - - Carer Ac Bc Cc S A S B S C U DC A B C AC sde Fg. A.5.4. Ramp comparson controller In keepng wth the prncple of snsodal PWM, comparson wth the tranglar carrer sgnal generates control sgnals S A,S B,S C for the nverter swtches. Althogh ths controller s drectly derved from the orgnal sbosclaton PWM, the behavor s qte dfferent, becase the otpt crrent rpple s fed back and nflences the swtchng tmes. The ntegral part of the PI compensator mnmzes errors at low freqency, whle proportonal gan and zero placement are related to the amont of rpple. The maxmm slope of the command voltage Ac ( Bc, Cc ) shold never exceed the trangle slope. Addtonal problems may arse from mltple crossng of tranglar bondares. As a conseqence, the controller performance s satsfactory only f sgnfcant harmoncs of crrent commands and the load EMF are lmted at a freqency well below the carrer (less than /9)

130 Smlaton reslts a) b) 4 3 x ref x 4 3 x ref x x, y x, y y ref y y ref y,3,35,4,45,5,55,6 tme Lne voltage 4,3,35,4,45,5,55,6 tme Lne voltage 4 Lne crrent and lne voltage - Lne crrent Lne crrent and lne voltage - Lne crrent -4-4,3,35,4,45,5,55,6 tme,3,35,4,45,5,55,6 tme Fg. A.5.5. Smlated transent to the step change of reference crrent (at.4 s): A 3A, and the lne voltage drop (at.55 s) a) dampng factor selecton ξ =.77, b) ξ = A.5... Statonary Vector Controller In three-phase solated netral load topology (Fg. A.5.), the three phase crrents mst add to zero. Therefore, only two PI controllers are necessary and the three-phase nverter reference voltage sgnals can be establshed algebracally sng two-to-three phase converson blocks αβ/abc. Fg. A.5.7 shows the block dagram of a PI crrent controller based on statonary coordnates α,β varables. The man dsadvantage of the PI controller actng on AC components, namely the nonzero steady state crrent error, stll remans. Crrent controller Phase Converson U DC αc - βc - K K K K v α v β αβ ABC PWM modlator β α αβ ABC A B C AC sde (Load) Fg. A.5.5. Statonary PI controller operatng n αβ coordnates wth AC components - 3 -

131 A Synchronos Vector Controller (PI) In many ndstral applcatons an deally mpressed crrent s reqred, becase even small phase or ampltde errors cases ncorrect system operaton (e.g. vector controlled AC motors, actve power flters). In sch cases the control schemes based on space vector approach are appled. Fg. A.5.6 llstrates the Synchronos Controller, whch ses two PI compensators of crrent vector components defned n rotatng synchronos coordnates x-y. Thanks to the coordnate transformatons, sx and sy are dc-components, and PI compensators redce the errors of the fndamental component to zero. xc - - yc x y Crrent controller K K K K Coordnate transformaton and Phase Converson v x v α xy αβ PWM v modlator v β y αβ ABC sn ω s t cos ω s t xy αβ A B αβ C ABC U DC AC sde (Load) Fg. A.5.6. Synchronos PI controller workng n rotatng coordnates x,y wth DC components However, the synchronos controller of Fg. A.5.6 s more complex as the statonary controller (Fg. A.5.7). It reqres two coordnate transformatons wth explct knowledge of the synchronos freqency ω s. As shown, the nner loop of the controller (consstng of two ntegrators and mltplers) s a varable freqency generator whch prodces always reference voltage V αc, V βc for the modlator (PWM), even when n the steady states the crrent error sgnals are zero. Hence, ths controller solves the problem of non zero steady state error nder ac components. However, the dynamc s generally worst than that of the statonary controller becase of the cross coplng between α,β components

132 Example Synchronos Crrent Controller for PWM Rectfer Desgn Based on Standard Rles The block dagram of a synchronos crrent controller workng n x-y coordnates for PWM rectfer s shown n Fg. A.5.3A. Inpt Flter PI Controller Processng Delay PWM Rectfer U L AC sde ndctor xyc st F - ε st K st stµ p K c sto V R R L sl L xy xy Samplng/Feedback Delay stf A. Open loop transfer fncton Fg. A.5.7 Block dagram of synchronos crrent controller The followng smplfyng assmptons are made: the cross-coplng effect between the x and y axes de to ndctance L s neglected, the dead tme of the power converter (also processng and samplng) s approxmated by a frst-order nerta element: e sto, (A.5.5) st o the sm of small tme constants s defned as: τ = T T T (A.5.6) Σ µ p o f where: T µp processng/execton tme of algorthm, T o power converter dead tme, T f tme delay of the feedback flter and samplng. Note that wth swtchng freqency f s the statstcal delay of the PWM nverter s (.5)/f s, delay of the tme dscrete sgnal processng /f s and feedback delay (avarager) (.5)/f s. So, the sm of the small tme constant τ Σ s the ramge (.5)/f s to /f s. The open loop transfer fncton s gven by the eqaton: st KGo ( s) = K st sτ Σ Ko st L (A.5.7) where K, T proportonal gan and ntegral tme of PI controllers, L K O = K C K L, K L =, TL = - gan and tme constant of the lne reactor, (A.5.8) R R K C power converter (PWM) gan, L L - 3 -

133 The choce of optmal crrent controller parameters depends on the lne reactor tme constant T L relatve to the sm τ Σ of all other small tme constants. B. For T L >>τ Σ controller parameters selecton accordng symmetry crteron T = 4τ Σ, TL K =, (A.5.9) Koτ Σ whch sbsttted n, yelds open-loop transfer fncton of the form: T KGo ( s) = K s4τ K T s4τ s4τ Σ 3 s 8τ L Σ O L Σ oτ Σ s4τ Σ( sτ Σ) stl τ Σ s4τ Σ( sτ Σ) stl s 8τ Σ For the closed-loop transfer fncton we obtan: Σ Σ 3 Σ 3 Σ (A.5.) s4τ KG ( s) = (A.5.) 3 s4τ s 8τ s 8τ Σ To compensate for the forcng element n the nmerator, se s made of the npt nerta flter G ( s) =, (A.5.3) F s4τ so that expresson becomes KG cf ( s) = KG C or approxmately KG cf Σ ( s) G F ( s) = s4τ Σ ( s) = s4τ st eq Σ s 8τ Σ, (A.5.4) 3 s 8τ 3 Σ, (A.5.6) where T eq = 4τ Σ s the eqvalent tme constant of the closed crrent control loop optmzed accordng to the symmetry crteron. C. Calclatons Data U I f L L L = V = 4A = 5Hz f = khz U t DC Slope condtons = 7V R L L = mh L =. T =. f S = s U I πf U.5U L L DC L L L T = = 4 f t Converter gan M =.9 K C Load MU = U DC T = 3.5 V

134 LL TL = R K L L =. = = R L Sm of the small tme constants τ = T =. Σ S Open loop gan K O = K LKC = 35 Controller parameters desgn sng Symmetry Crteron TL K = =.8 K τ K Σ O T = 4τ =.8 Σ TL = 8K ( τ ) o Σ = 99 D. Smlaton reslts a) b) 4 3 x ref x 4 3 x ref x x, y y ref y x, y y ref y,3,35,4,45,5,55,6 tme Lne voltage 4,3,35,4,45,5,55,6 tme Lne voltage 4 Lne crrent and lne voltage - Lne crrent Lne crrent and lne voltage - Lne crrent -4-4,3,35,4,45,5,55,6 tme,3,35,4,45,5,55,6 tme Fg. A.5.8. Smlated transent to the step change of reference crrent (at.4s): A 3A, and the lne voltage drop (at.55s) a) wthot npt flter b) wth npt flter E. Decoplng control So far the cross-coplng effect de to lne ndctance L was neglected. However, t can be easy compensated for sng a decoplng network nsde or otsde the controller []. Fg. A.5. llstrates n expanded tme scale mprovements by the decoplng network

135 crrents 5 5 crrents ,4,45,55,6-5,4,45,55,6 tme tme Fg. A.5.9. Synchronos PI controller a) wthot decoplng, b) wth decoplng nsde of controller (see Fg. A.5.4.b). wthot npt flter, wth npt flter T F = T ##"6 ' The transfer fncton of the standard PI compensator sed n synchronos controller workng n rotatng coordnates wth DC components can be expressed as: G( s) K st = K = K, where s st K T =, (A.5.7) K As shown n [36], an eqvalent sngle phase statonary AC crrent controller whch acheves the same DC control response centered on the AC control freqency can be calclated as follows: sk G( s) = [ g( s jω ) g( s jω )] = K, (A.5.8) s ω s The last eqaton can be seen to be a Resonant Controller wth nfnte gan at the resonant freqency ω s. Crrent controller Phase Converson U DC αc - βc - K K K K v α v β αβ ABC PWM modlator β α αβ ABC A B C AC sde (Load) Fg. A.5.. Statonary Resonant Controller

136 Example: Desgn of Statonary Resonant Crrent Controller for PWM Rectfer. The block dagram of a statonary resonant crrent controller for PWM rectfer (only phase A) s shown n Fg. A.5.3. Resonant Controller PWM Rectfer U L AC sde ndctor I Ac - I A ε sk K s ω s K C V R R L sl L I A Fg. A.5.. Smplfed block dagram of crrent control loop wth resonant controller (small tme constatns are neglected and K c = ) A. Open loop transfer fncton Transfer fncton of the resonant controller gven by Eq (A.5.9) can be expressed as follows: G ( s) C sk c c s c s = K = (A.5.9) s ω s s ωs where: c = K ω, c = K, c = K s The open loop transfer fncton s gven: KG c c s c s O ( s) = s ω s R sl L L B. Controller desgn based on Nasln polynomal The characterstc polynomal of the closed-loop transfer fncton can be calclated as: (A.5.) D( s) = c c s c s ( R sl )( ω ) (A.5.) L L s s The parameters of the controller can be compted based on 3 nd order Nasln polynomal: 3 s s s P N ( s) = a( ) (A.5.) 3 ω αω α ω From two last eqatons one obtans: 3 3 c = L ω α R ω L L c = L ω α R L L L L s 3 c = L ω α R ω or n the form: s K = L ω α R L ω = αω L L L s 3 K = L ω α L ω C. Calclatons Data s (A.5.3) (A.5.4)

137 R L L = mh L ω = 34rad / s s =. Selectng the Nasln polynomal parameter α = ω = ω = a 34rad / s rad s / Controller parameters c = c = 95A.5.7 c = A.78 or n the form K = A.87 K = 95A.5.7 D. Smlatons reslts s 4 3 x ref x x, y y ref y,3,35,4,45,5,55,6 tme Lne voltage 4 Lne crrent and lne voltage - Lne crrent -4,3,35,4,45,5,55,6 tme Fg. A.5.. Smlatons for Resonant Controller ##$4 $4( < >>'' >'' The block scheme of a dgtal ANN-based crrent controller for three-phase PWM converter s shown n Fg The controller operates wth components defned n stator orented coordnates α-β. Ths, the coordnate transformaton s not reqred. The otpt voltages αc, βc are delvered to the space vector modlator, whch generates control plse S A, S B, S C for power transstors of the PWM converters

138 U DC αc βc βc αc ANN β ANN α βc αc Vector modlator S A S B S C Converter A B C error β error α α β αβ/abc A B RLE Fg..A.5.3. On-lne traned ANN crrent controller of PWM converter To assre a fast response and hgh performance of crrent control, the confgraton of ANN s based on lnear adaptve flter topology. Fg. A.5.4 shows the ANN controller for one component (phase A). As npt of the controller s reference crrent Ac (n), whch s sampled by delay blocks Z-, and otpt s sampled voltage command Ac (n). There are L nts n the npt layer and the nmber L s set to be the same as the samplng nmber n a perod of the reference crrent so that the nformaton of harmoncs n the reference crrent s known to the network. Ac (n) Ac (n) W OUT Z - Ac (n-) W OUT Z - Ac (n-) W 3 OUT 3 Ac (n) Z - Ac (n-l-) OUT W L L e (n) Fg. A.5.4. ANN topology for one components (phase) The relatonshp between the otpt and npt s: Ac = Ac ( n ) w Ac ( n w (A.5.5) ( n) = ) where: =,,...,L s nts nmber, Ac (n)={ Ac (n),...,i Ac (n-l)} T, s command crrent vector, w ={w,...,w L } T, s weght vector The ANN conssts of two layers:

139 Inpt layer: n ths layer there are L nts V, V,...,V L. The otpts of these nts are OUT, OUT,..., OUT L, whch are connected whch the otpt layer throgh the weghts w, w,..., w L. Otpt layer: ths layer conssts of one nt only. The npts to ths layer are otpts OUT L from the npt layer. Ths layer acts as a fan-ot layer and hence the otpt of ths layer s reference voltage Ac (n). The error sgnal ser for learnng of ANN can be expressed as follows: e( n) = ( χ δz )( ( n) ( n)) (A.5.6) R where : χ = K RT, δ = ε, ε = exp( s ) ε L R, L - are load parameters, K s the gan of the PWM nverter. The weghts vector w (n) are modfed by the rle : Ac A w ( n) = w ( n ) e( n) ( n) (A.5.7) µ A Example: On-lne ANN based crrent controller for PWM rectfer ANN CR smlaton reslts for PWM Rectfer ANN parameters: khz samplng freqency - levels U DC =6V, R L =.Ω, L L =mh, f t =khz, Reference crrent step change: A to 3A Fg. A.5.5. Smlnk - smlaton panel

140 ANN - smlaton reslts 35 Reference Load 3 5 d 5 5 5,4,5,6 Reference Load 5 q 5-5 4,4,5,6 Lne crrent 3 Lne crrent ,,,3,4,5,6,7 tme Fg. A.5.6. Smlaton reslts The ANN s on-lne traned controller and t needs tme to learn reference sgnal waveform. To mprove transent response a proportonal controller P wth a control gan K P s connected n parallel wth the ANN, as shown n Fg. A.5.7. P αc ANN α Fg. A.5.7. ANN wth parallel P controller Ths combnaton provdes faster learnng (Fg. A.5.8(a) and (b)) and mproves dynamc response of the controller (Fg. A.5.8(c) and (d))

141 a) b) Reference crrent Load crrent Reference crrent Load crrent crrent crrent ,,,,,, tme tme c) d) Reference crrent Load crrent Reference crrent Load crrent crrent crrent ,,3,4,4,5,6 tme tme Fg. A.5.8. Learnng process and response of the ampltde change of the ANN crrent controller (fsw=5khz) (a) and (c) ANN wthot proportonal gan (b) and (d) ANN wth proportonal gan K P =7 (learnng rate µ=.) Learnng and adaptaton (can learn the reference shape) abltes are the man advantages of the on-lne traned ANN crrent controller. However, hgh samplng freqency (for good reference trackng) and tme consmng desgn procedre s reqred to assre hgh performance crrent control. ##)> 4(4' 4' A.5.4. Introdcton Ideally mpressed crrent n an ndctve load cold be mplemented sng an deal comparator operated as On-Off controller. In sch system, however, the converter swtchng freqency wll be nfnty, and as conseqence, of hgh swtchng losses the semcondctor power devces wll be damaged. Therefore, n practcal schemes swtchng freqency s lmted by ntrodcng: hysterese wth wdth h or sample and hold (S&H) block wth samplng freqency f S (Fg. A.5.9). Ths creates two classes of controllers whch wll be dscssed n the next sectons

142 a) b) h c - ε Ideal Comparator S A c - ε Ideal Comparator S&H f s S A Fg. A.5.9. Two methods to lmt the swtchng freqency of crrent control system wth deal comparator a) Hysteress controller, b) Delta Modlator A.5.4. Hysteress Crrent Controllers Hysteress control schemes are based on a nonlnear feedback loop wth two-level hysteress comparators (Fg. A.5.9a). The swtchng sgnals S A,S B,S C are generated drectly when the error exceeds an assgned tolerance band h (Fg. A.5.9b). U DC a) b) Ac Bc Cc S A S B S C β B state Hysteress band state A B C S C -h h Three-phase Load Fg. A.5.. Two levels hysteress controller: block scheme (a), swtchng trajectory (b) Althogh the constant swtchng freqency scheme s more complex and the man advantage of the basc hysteress control - namely the smplcty - s lost, these soltons garantee very fast response together wth lmted trackng error. Ths, constant freqency hysteress controls are well sted for hgh-performance, hgh speed applcatons. A Delta Modlaton (DM) The basc scheme, the Delta Modlaton-Crrent Controller (DM-CC), s shown n Fg. A

143 A c Bc Cc SH SH SH 3 A S&H S A S B S C U DC B C Three-phase Load Fg. A.5.. Delta modlaton crrent controller - basc block scheme It looks qte smlar to that of a hysteress CC, bt the operatng prncple s qte dfferent. In fact, only the error sgn s detected by the comparators, whose otpts are sampled at a fxed rate so that the nverter stats s kept constant drng each samplng nterval. Ths, no PWM s performed; only basc voltage vectors can be generated by the converter for a fxed tme. Ths mode of operaton gves a dscretzaton of the nverter otpt voltage, nlke the contnos varaton of otpt voltages whch s a partclar featre of PWM. A Analog and Dscrete Hysterese When the hysteress controller s mplemented n dgtal sgnal processor (DSP), ts operaton s qte dfferent as n the analog scheme. Fgre A.5. llstrates typcal swtchng seqence n analog (a) and dscrete (b) mplementaton (also called sampled hysterese). (a) (b) S / H c h /Ts c c - h t t t 3 T s T s T s Fg. A.5.. Operaton of the analog (a) and dscrete (b) hysteress controller In the analog controller the crrent rpples are kept exactly wthn the hysteress band and swtchng nstance are not eqal. In contrast, the dscrete system operates at fxed samplng tme T s, the controller operates rather lke Delta modlator

144 Fgre A.5.53 llstrates operaton of dfferent crrent controllers for the same nmber of swtchngs (N = 6). It s clearly to see that for hysterese band h = A, the dscrete controller (Fg. A.5.3c) reqres 3.3µs samplng tme (3 khz) to exactly copy the contnos hysterese behavor (Fg. A.5.3b). Wth longer samplng tme 33µs (3 khz), operaton of dscrete hysteress controller (Fg. A.5.3d) s far from those of contnos one (Fg. A.5.3b). a ) b ) T m e c ) d ) Tm e T m e T m e Fg. A.5.3. Crrent control wth: a) Delta modlator Ts = 67µs; b) contnes hysterese h = A; c) dscrete hysterese h = A, Ts = 3.3µs; d) dscrete hysterese h = A, Ts = 33µs. A.5. Power Controllers The synthess of the actve and reactve power controllers can be done analytcally sng a smplfed model. In ths model the swtchng waveforms created by the PWM converter are replaced by ts average vale wthn the swtchng perod. A model n dq coordnates has the followng eqatons: Ld Lq = R = R where, Lq Ld = U = Ld Lq dld L dt dlq L dt ωl ωl Lq Ld Sd Sq (A.5.8) (A.5.9)

145 and p = U q = U Lq Ld That gves, the model smplfes: = R Ld U = R Lq d Ld L dt d L dt Lq ωl ωl Lq Ld Sd Sq (A.5.3) (A.5.3) Introdcng PI controllers for actve power p and reactve power q the block dagram of Fg. A.5.4 s obtaned. U Ld q - PI - Ls R Ld ωl ωl p - PI - - Ls R Lq Lq U Fg. A.5.4. Smplfed block dagram The actve and reactve power controllers are copled by the cross therms. The synthess of the PI parameters shold be done n order to get a good response and to mnmze those effects. Consderng the reactve power nll, that s Ld =, the actve power control loop becomes dsconnected of the reactve power. The nflence of the reactve power on ths control loop shold be analyzed later. The block dagram s, p* - st n st - sq - U RLs p U Fg. A.5.5. Actve power control block dagram

146 The lne voltage s seen as a constant pertrbaton, and s compensated by the ntegral part of the PI controller. In ths way, the zero of the PI controller s placed over the pole of the system. So, the open loop tme constant T ol can be expressed by: L T n = = T ol (A.5.3) R The closed loop transfer fncton s: U p( s) Geq st R = = = pref ( s) G U st eq R st R U (A.5.33) The closed loop tme constant T cl s gven by: T R Tcl = (A.5.34) U And can be a specfcaton of the controller desgn. So UTcl T = (A.5.35) R The parameters of the PI controller can be gven by: k p = Tn L T = U T, cl R k = T = U T (A.5.36) cl The specfcaton of T cl shold be done n order to get good response and decoplng between p and q powers. The rato of k p /k for dfferent closed loop tme constant T cl s constant and eqal to open loop tme constant T ol. Becase the actve and reactve power control loops are smlar, eqatons (A.5.33) are vald for both controllers. Fg. A.5.6 obtaned n MATLAB/Smlnk presents a step change on the reference actve power. The reference of the reactve power s constant and eqal to zero. Ths fgres shows that effectvely there s a pertrbaton on the reactve power. Note that the pertrbaton s elmnated dependng of the open loop tme constant. Redcng the closed loop tme constant, the maxmm vale of the pertrbaton s redced as shown n Fg. A.5.A

147 Actve power [kw] Reactve power [kvar] 6 4 Response to step changes on actve power Tme (ms).8.6 T cl=.5ms.4. T cl=.ms T cl=.5ms T cl=.ms Tme (ms) Fg. A.5.6 Step change of the reference actve power for dfferent T cl

148 References Books and PhD Thess. M. P. Kazmerkowsk, R. Krshnan, F. Blaabjerg Control n Power Electroncs Academc Press. R. Barlk, M. Nowak Technka tyrystorowa WNT H.Tna, R.Barlk Teora przekształtnków skrypt PW, Warszawa 3 4. M.Malnowsk Sensorless Control Strateges for PWM Rectfers, PhD Thess, Warsaw Unversty of Technology, 5. J. Hafner On the redcton of Harmoncs n Power Systems A New Hybrd Power Flter Approach, PhD Thess, Techncal Unversty of Berln, M. Lserre Innovatve control technqes of power converters for ndstral atomaton, PhD Thess, Poltecnco d Bar, 7. R. Strzeleck, H. Spronowcz Współczynnk mocy w systemach zaslana prd przemennego metody jego poprawy Ofcyna Wydawncza PW, Warszawa 8. A. Olszewsk Mkroprocesorowe systemy sterowana fltrów aktywnych PhD Thess, Poltechnka Warszawska,. J. Lasoweck Elementy magnetyczne w kładach napedowych WNT 98. M. Aredes Actve Lne Power Condctoners PhD Thess TU Berln 996. S. Hansen Harmonc Dstorton of Rectfer Topologes for Adjstable Speed Drves PhD Thess Aalborg Unversty. M. M. Kal Drect Flx Control for Hgh-Power Actve Front Ends wth Low Swtchng Freqency PhD Thess Rhr-Unversty of Bochm 3 3. P. Baloskorsk Analza pracy prostownka sterowanego o wspolczynnk mocy rownym jednosc PhD Thess, Warsaw Unversty of Technology R. Teoflak Kompensatorowa praca napd elektrycznego o reglowanej prdkoc obrotowej PhD Thess, Warsaw Unversty of Technology 997 Crrent Control Technqes [.] S. Bso, L. Malesan, P. Mattavell Comparson of crrent control technqes for actve flter applcaton, IEEE Trans. on Ind. Electroncs, vol. 45, no. 5, October 99. [.] M. P. Kazmerkowsk, L. Malesan Crrent control technqes for three-phase voltage-sorce PWM converters: a srvey, IEEE Trans. on Ind. Electroncs, vol. 45, no. 5, pp ,

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