Dynamic Response of an Active Filter Using a Generalized Nonactive Power Theory

Transcription

1 Dynmi Repone of n Aive Filer Uing Generlized Nonive Power heory Yn Xu Leon M. olber John N. Chion Fng Z. Peng yxu3@uk.edu olber@uk.edu hion@uk.edu fzpeng@mu.edu he Univeriy of enneee Mihign Se Univeriy Eleril nd Compuer Engineering Eleril nd Compuer Engineering Knoxville, N E Lning, MI Abr hi pper preen heory of innneou nonive power/urren. hi generlized heory i independen of he number of phe, wheher he lod i periodi or nonperiodi, nd wheher he yem volge re blned or unblned. By hooing pproprie prmeer uh he verging inervl nd he referene volge v p, he heory h differen form for eh peifi yem ppliion. hi heory i onien wih oher more rdiionl onep. he heory i implemened in prllel nonive power ompenion yem, nd everl differen e, uh hrmonod, reifier lod, ingle-phe pule lod, nd non-periodod, re imuled in MALAB. Uniy power for or pure inuoidl oure urren from he uiliy n be hieved ording o differen ompenion requiremen. Furhermore, he dynmi repone nd i imp on he ompenor energy orge requiremen re lo preened. Keyword nonive power, reive power, non-periodi urren, hun ompenor, SACOM. I. INRODUCION Nonliner lod drw highly diored urren from he uiliy well ue diorion of he volge. Some lod inrodue hrmoni ino he yem; ome drw irregulr urren whih re no periodi; ome hve ubhrmoni whoe frequenie re no ineger muliple of he fundmenl frequeny; ome re ingle-phe lod or unblned whih ue ymmery in hree-phe four-wire yem. Vriblepeed moor drive, r furne, ompuer power upplie, nd unblned ingle-phe lod re he mo ommon nonliner lod in power yem. A rnien diurbne my lo be onidered one kind of non-periodi urren from he ompenion poin of view. he diurbne my be ued by he udden hnge of lrge lod uh ring moor, ful, or udden lod hnge. he ompenor i ofen required o hve lrger power ring, lrger energy orge, nd fer wihing frequeny if i i reponible o miige uh diurbne. ime-bed innneou nonive power heory w fir formuled in he 930 by Fryze [], nd he inreing re of nonliner lod require more omprehenive heory o deribe, meure, nd ompene hee lod. However, mo of he previou effor hve foued on periodi noninuoidl yem, rher hn non-periodi yem []. he p-q heory propoed in [3] i vlid for hree-phe hree-wire yem wih hrmoni, nd i h been exended o hreephe four-wire yem [4-5]. In [6], Hilber pe ehnique re doped for he definiion nd ompenion of reive power. However, i inrodue new hrmoni o he ive urren whih i no deired in nonive power ompenion. Non-ineger muliple hrmoni re defined non-periodi urren in [7] nd he ompenion i diued. Nonperiodi urren re lo diued in [8]. he diveriy of he feure of non-periodi urren mke i diffiul o ge one definiion h fi ll iuion, nd he ompenion of uh urren i quie diffiul. However, from pril poin of view, regrdle of he lod, fundmenl inuoidl oure urren in phe wih he yem volge i uully he preferred objeive of ompenion. he heory propoed in hi pper i generlized one whih i independen of he number of phe in he yem, pplie wheher he volge re blned or unblned, nd o boh periodi nd non-periodod. Applied o prllel (hun) ive filer, hi heory provide flexibiliy in nonive power ompenion. By hnging he verging inervl nd he referene volge v p, he ive filer n ompene he nonive omponen in he lod urren o h he oure urren will be fundmenl inuoidl, or hve he me wveform he yem volge, or ny deired wveform, wheher he yem volge i diored or no. Combined wih he dire urren onrol heme, boh edy e nd dynmi repone re udied. I i hown h n ive filer wih he propoed nonive power heory h f dynmi repone whih i wihin one fundmenl yle. Severl for reled o he definiion ielf nd he implemenion re diued. hee for inlude he verging inervl C, he oupling indune L C, he DC link volge v d, nd he pine requiremen C of he ive filer. hey re deermined by he hrerii of he lod, he ring limi of he ive filer, nd he deired ompenion reul. II. INSANANEOUS NONACIVE POWER HEORY he heory w fir preened in [9]. he volge veor v() nd urren veor i() re defined, repeively, v ( ) [,,..., ], () v v v m

2 i i i m i () [,,..., ], () where m i he number of phe. he innneou ive urren i () nd he innneou nonive urren i n (), repeively, re defined P () i() v (), (3) p V () p in() i() i (). (4) where P() i he verge vlue of he innneou power p() over he verging inervl [-, ]: P( ) p( ) d ( ) ( ) d τ τ = v τ i τ τ. (5) Le v p () denoe he referene volge, whih n be he oure volge v() ielf, or ome oher referene uh he fundmenl omponen of v(). V p () i he rm vlue of he referene volge v p (), given by Vp( ) vp( ) vp( ) d τ τ τ. (6) Bed on he definiion for i () nd i n (), he innneou ive power p () nd innneou nonive power p n () re defined, repeively, p () v() i () (7) pn () v() i n(). (8) where p () nd p n () ify, p( ) = p ( ) + pn ( ). (9) I(), I (), nd I n () re he rm vlue of i(), i (), nd i n (), repeively. i () nd i n () re orhogonl o h, I ( ) = I ( ) + I n ( ). (0) For periodi yem wih period, nd hooing = /, nd v p () = v(), he verge ive power nd nonive power ify P ( ) = ( τ) ( τ) dτ P( ) v i, () Pn ( ) = ( ) ( ) d 0 v τ i τ τ. () n Over he ime inervl, P (), he verge vlue of p (), i equl o P(), he verge vlue of p(); nd P n (), he verge vlue of p n (), i zero. I indie h innneouly p() h boh ive nd nonive omponen, bu on verge, P() h only he ive power, whih i equl o P (). he verge vlue of p n () i zero, whih indie h he nonive power p n () flow bk nd forh, nd over he ime inervl, here i no energy uilizion. hi i onien wih he onvenionl definiion of ive power nd nonive power. By injeing he me moun of urren he innneou nonive urren i n () ino he yem, Uiliy i Inverer v i L wihing ignl i v d v d Conrol Lod i Nonive urren lulion v d Fig.. Syem onfigurion of hun nonive power ompenion. ompenor n ompleely ompene he nonive omponen in he lod urren wihou ny energy oure. Unlike mny oher nonive power/urren heorie, hi heory doe no hve ny limiion on he volge v() nd urren i(). I i generl definiion independen of he number of phe, wheher he volge i inuoidl or noninuoidl, nd wheher he lod i periodi or non-periodi. More peifilly, he definiion i pplible o ingle-phe, hree-phe hree-wire, nd hree-phe four-wire yem. For eh differen e, i i onien wih he rdiionl definiion nd ke on peifi form, by vrying he referene volge v p () nd he verging inervl. he referene volge v p () deermine he hpe of he innneou ive urren wveform, hown in (3). If P() nd V p () re onn, whih n be hieved wih = / for periodi yem wih period, i () h exly he me wveform v p (). In prie, v p () i hoen bed on he volge v(), he urren i(), nd he deired ive urren i (). By hooing differen referene volge, i () n be rehped o h he unwned omponen in i() re elimined; furhermore, he eliminion of eh hrmoni omponen i independen of eh oher. heoreilly, ould be hoen rbirrily from zero o infiniy. Prilly, for non-periodi yem, i hoen finie number bed on he ompenion objeive. For periodi yem wih period, i hoen o be one hlf or full period of, i.e., = / or, whih will ompleely ompene he nonive omponen in he lod urren. III. IMPLEMENAION IN A SACOM A previouly menioned, he heory i pplible o hreephe hree-wire, hree-phe four-wire, nd ingle-phe yem. A hree-phe four-wire prllel ompenion yem i hown in Fig.. he oure urren i i he um of he lod urren nd he ompenor urren i. he gol of ompenion i o mke he ompenor upply he nonive omponen of he lod urren, i.e., i () = i n (), o h he uiliy only provide he ive urren, i.e., i () = i (). In he propoed heory, he ompenion yem i umed o be lole, however in rel yem, loe exi in he wihe, he pior nd he induor. herefore erin moun of ive power i drwn o regule DC link pior volge. For hun ive filer, volge oure

3 Uiliy i i v L Compenor Lod he ive urren of he ompenor i i mll frion of he whole ompenor urren i, o he ive omponen n be negleed, i.e., in i, nd in i, where i i he n nonive urren luled bed on he nonive power/urren heory diued in Seion II. he referene of he ompenor nonive urren i nd he referene of he n ompenor oupu volge v ify di L = v v (6) v d V d () Equivlen irui of he ompenion yem Nonive Curren Clulion PI i n -i i d (b) Conrol digrm of he hun ompenion yem i L PI Fig. Conrol heme of he ompenion yem. inverer wih pior i moly ued. here re wo omponen in he ompenor urren i, he nonive omponen i n o ompene he lod urren nd he ive omponen i o mee he ompenor loe by reguling he DC link volge v d, nd i = in + i. (3) A PI onroller i ued o regule he DC link volge v d, hown in Fig. b [0]. he ive urren needed o mee he loe i in phe wih. he mpliude of he ive urren i onrolled by he differene beween he referene volge V d nd he ul DC link volge v d. i i in phe wih nd i luled follow i = v KP( Vd vd ) + KI ( Vd vd ), (4) 0 where K P nd K I re he proporionl nd inegrl gin of he PI onroller. he equivlen irui of he hun ompenion yem i hown in Fig., where i he yem volge, v i he oupu volge of he inverer, L i he oupling indune, nd i i he ompenor urren. di L = v v (5) v h i, he referene ompenor oupu volge L ABLE I. PARAMEERS OF HE SACOM Syem volge, line-o-line rm (V) 08 DC link volge V d (V) DC link pine (µf) Coupling indune (mh) 0 Swihing frequeny (Hz) 0,000 v i di v = + v. (7) Subr (5) from (6), d( i i) L = v v. (8) Se he onrol inpu v ording o di v = v + L + L KP( i i) + KI ( ) i i (9) 0 where K P nd K I re he proporionl nd inegrl gin of he PI onroller. Fig. b i he omplee onrol digrm of he hun ompenion yem. he inner loop i he ompenor urren onrol whih onrol he oupu volge of he ompenor ording o he required nonive urren i. he ouer loop onrol he ive urren drwn by he ompenor by reguling he DC link volge v d, nd ombine he ive urren i ogeher wih he nonive urren i n. IV. CASE SUDIES OF DYNAMIC RESPONSE A Simulink model h been e up bed on he digrm in Fig.. he prmeer of he yem re hown in ble I. Some prmeer, uh he DC link volge v d, he DC link pine C, nd he oupling indune, vry ording o differen ompenion requiremen. o illure he generlized hrerii of he propoed heory, four nonliner lod re imuled, nd he imulion reul re nlyzed. A udden lod hnge i pplied o eh e o udy he dynmi repone of he ompenion yem.

4 () () (b) (b) lod urren of phe, il() lod urren of phe, il() oure urren of phe, i(), Vd =.5Vll oure urren of phe, i() () () ompenor urren of phe, i(), Vd =.5Vll DC link volge vd Fig. 3. Simulion of hrmonod ompenion. A. hree-phe Hrmoni Lod hi i he mo ommon nonliner lod in power yem. In hi e, he lod urren h hrmoni hown in Fig. 3, nd for lriy, only phe i hown. For ompenion of periodi urren wih fundmenl period, hooing differen lone doe no hnge he oure urren hrerii. Wih referene o (3) nd (4), he rm vlue of periodi quniy doe no depend on he ime verging inervl if i i n ineger muliple of /. So wih = /, he oure urren fer ompenion i hown in Fig. 3b. In region A, he ompenor i off, o h he oure urren i equl o he lod urren, whih onin hrmoni nd fundmenl nonive power. In region B nd region C, he ompenor i working nd he nonive omponen in he lod urren i ompleely ompened, nd he oure urren now i fundmenl inuoid nd in phe wih he fundmenl omponen of yem volge. he lod urren h udden hnge = 0.5. he nonive omponen of he inree i provided by he ompenor, nd he ive omponen of he inree i provided by he uiliy, whih i hown in region C, Fig. 3b. he udden inree of oupu power ue volge drop on he DC link pior hown in Fig. 3. Compred o he edy-e operion, he DC link volge vriion i muh lrger, whih demnd higher pine o preven he volge from dropping o low level. In Fig. 3, he volge vriion in region C rger hn he one in region B, beue fer he lod hnge, lrger moun of nonive urren i required from he ompenor. (d) DC link volge vd, Vd =.5Vll (e) oure urren of phe, i(), Vd = 3Vll Fig. 4. Simulion of reifier lod ompenion. B. hree-phe Diode Reifier Lod A hree-phe diode reifier i lo ypil nonliner lod. he urren of diode reifier i hown in Fig. 4 (phe ). I i periodi wveform wih he me period he fundmenl period of he yem volge, hu he urren n be deompoed ino fundmenl omponen nd hrmoni. However, differen from he hrmonod diued in he previou ubeion, he urren drwn by diode-bed reifier i no oninuou, nd he vriion of he urren wih ime di/ i very lrge (di/ = A/ in hi exmple). herefore, here re peil iue in he ompenion of reifier lod. A = 0.04, here i udden lod hnge whih ue he lod urren o inree (he eond dh line in Fig. 4). In Fig. 4b, region A how i() upplying he full lod urren when he ompenor i off; when he ompenor i on,

5 region B how h i () oe o inuoid, nd region C i i () fer he udden lod hnge. Fig. 4 how he nonive urren whih i provided by he ompenor, whih i highly diored. he lod hnge h n imp on he DC link volge, whih drop bou 50 vol when he lod hnge. o regule v d, ome ive urren i drwn. he udden lod hnge require lrger pine hn edy lod. he oure urren i () in Fig. 4b h ome pike, whih i ued by he lrge vriion of he urren wih ime. Aording o (5), he ompenor oupu volge v i given by di v = v + L. A lrge di / require lrge v ; however, if he DC link volge doe no mee hi requiremen, he ompenor i unble o provide he nonive urren required by he nonive power heory, nd pike our in he oure urren ordingly. Fig. 4b nd Fig. 4e how he oure urren when he DC link volge V d i.5v ll nd 3V ll, repeively, where V ll i he pek vlue of he yem line-o-line volge. he pike in Fig. 4e re mller hn hoe in Fig. 4b, whih how h oure urren wih le pike n be hieved by inreing he DC link volge. However, higher DC link volge require higher volge ring of he ompenor nd reul in higher ompenor loe. In prie, he DC link volge n be hoen beween V ll o V ll. C. Single-phe Pule Lod If ingle-phe lod i onneed o he hree-phe uiliy, he ingle-phe urren drwn from he yem ue n unblne of he yem. Non-inuoidl lod urren, or individul high mpliude pule lod urren lo inrodue high nonive omponen o he yem. In hi e, he lod urren i ingle-phe pule urren in phe, wih period of 3 ( i he fundmenl period of he volge). he pule lod urren i hown in Fig. 5. he volge i hree-phe fundmenl ine wve. Afer ompenion, he uiliy oure urren h urren in ll he hree phe, even hough he lod urren i only in phe. hey re in phe wih he yem volge, nd he mpliude re muh mller hn he pek vlue of he lod urren, hown in Fig. 5b. he mll moun of urren beween wo pule i he ive urren drwn o mee he ompenor loe. Unlike he previou wo e, he verging inervl i riil for o he ompenion in hi e. Fig. 5b, 5, nd 5d how he hree-phe oure urren fer ompenion where i /,, nd 3, repeively. Wih longer, ) i oer o ine wve; ) he hree phe re more blned; 3) i i lwy in phe wih he volge; nd 4) he mgniude of i i dereing. he overhoo in he urren re beue he ul ompenor urren doe no exly rk he referene nonive urren, whih i hrp ringle in hi e, nd he DC link volge onrol drw ive urren o mee he loe nd o reover he lrge volge drop well. However, by inreing, he () Single-phe pule lod urren. (b) Soure urren i ( = /). () Soure urren i ( = ). (d) Soure urren i ( = 3). Fig. 5. Simulion of ingle-phe pule lod ompenion. ompenor urren i lo inree, nd onequenly, he pine ring nd wihing urren ring mu inree well. Depending on he lod hrerii, ompenor requiremen, nd he ompenion reul deired, n uully be hoen o mee ll he objeive. In hi e for exmple, = h good oure urren wihou oo high of ompenor ring. D. Non-periodi Lod heoreilly, he period of non-periodod i infinie ( period muh lrger hn he fundmenl period of he uiliy volge). he nonive omponen in lod nno be ompleely ompened by hooing / or, or even everl muliple of. Fig. 6 how hree-phe non-periodi urren. Fig. 6b- 6d how he oure urren fer ompenion, wih = /,, nd 0, repeively. Wih = / (Fig. 6b), here i ill ignifin nonive omponen in i wih vrible pek vlue nd non-inuoidl wveform. In Fig. 6, he vriion of he mpliude of i i mller, nd in Fig. 6d, i oe o ine wve wih le nonive omponen. Here, longer moohe he oure urren wveform. heoreilly, i ould be pure ine wve if goe o infiniy, bu in prie, uh nno be implemened nor i i neery. If i

6 () Lod urren () (b) Soure urren i (), = / () Soure urren i (), = (d) Soure urren i (), = 0 Fig. 6. Simulion of non-periodod ompenion. lrge enough, inreing furher will no ypilly improve he ompenion reul ignifinly. ypilly, here i no need o inree o lrger vlue he mll deree in HD i ofen no worh he lrger pil o (higher ring of he ompenor omponen nd herefore higher pil expene). V. DISCUSSION In nonive power ompenion, here re everl for whih hve ignifin influene on he hoie of ompenor ype, he power ring of he ompenor, he energy orge requiremen of he ompenor, nd he ompenion reul. Some of hee for re reled o he nonive power heory ielf, whih inlude he verging inervl, nd he referene volge v p, while oher re pril iue reled o he implemenion of he ompenion yem. In hi pper, he oupling indune L, he power ring of he ompenor, he pine of he DC link, nd he DC link volge v d hve been ken ino oniderion. A. Averging Inervl If here re only hrmoni in he lod urren, in Subeion IV.A nd IV.B, doe no hnge he ompenion reul long i i n inegrl muliple of /, where i he fundmenl period of he yem. Here he nonive urren i ompleely ompened, nd purely inuoidl oure urren i hieved. However, in oher e, uh in Subeion IV.C nd IV.D, h ignifin influene on he ompenion reul, nd he power nd energy orge ring of he ompenor omponen. Wih longer, beer oure urren will be hieved, bu he o of higher power ring for he wihe nd pine. here i rdeoff beween beer ompenion nd higher yem ring (i.e., o). On he oher hnd, longer doe no neerily yield beer oure urren wveform. For peifi yem, here i n pproprie wih whih he ompenion n be hieved []. For exmple, in Subeion 4C, he hoie of depend on he period of he pule. B. Coupling Indune L he oupling indune L beween he power yem nd he ompenor ould be he indune of ep-up rnformer or oupling reor. I he filer of he ompenion urren i, whih h high ripple onen due o he ompenor PWM onrol of he wihe. If L i oo mll, i nno filer he ripple in he ompenion urren i ; nd if L i oo lrge, he imeonn of he yem will be o lrge h i nno rk he referene, whih reul in indeque operion of he ompenion yem. L i inverely proporionl o he rm vlue of lod urren (I l ) when he ripple in he oure urren imied o peifi perenge (5% in hi work), i.e., where K i onn. L = K / I (0) l C. DC Link Cpine C Aording o he diuion in Seion II, he verge power of he ompenor P () over i zero. Energy i neiher genered nor onumed by he ompenor. herefore, he energy ored in he pior i onn red DC link volge V d given by E = CV d. () However, he innneou power i no neerily zero. he ompenor generlly h pior for energy orge, nd hi pior opere in wo mode, i.e., hrge nd dihrge. Differen pine vlue re required o fulfill differen ompenion k. he mximum energy vriion in he pior i he inegrl of v()i () beween ime mx when he pior goe from dihrge o hrge, nd min when he pior goe from hrge o dihrge, or vie ver. hu,

7 mx E = v( ) i ( ). () min he energy vriion on he DC link pior ue he volge vriion, h i E + E = C( Vd + Vd ). (3) he DC link volge vriion i mll frion of V d, V d = V d, where 5%. he pine requiremen i derived from () - (3): E C =. (4) ( + / ) Vd For differen ppliion, he energy vriion E i differen, whih deermine he pine ring, for given DC link volge vriion. For ppliion oher hn hrmonod, E lo hnge wih [3]. bed on he generlized nonive power heory. A onrol heme i developed o regule he DC link volge of he inverer nd o genere he wihing ignl for he inverer bed on he required nonive urren. he ompenion yem i imuled nd differen e re udied. he imulion reul how h he heory propoed in hi pper i pplible o he nonive power ompenion in hreephe four-wire yem, ingle-phe yem, lod urren wih hrmoni, nd non-periodod urren. hi heory i dped o differen ompenion objeive by hnging he referene volge v p () nd he verging inervl. he pril iue uh he DC pine ring, he oupling indune, nd he DC link volge re lo diued. ACKNOWLEDGMEN We would like o hnk he Nionl Siene Foundion for prilly upporing hi work hrough onr NSF ECS D. DC Link Volge v d he minimum vlue of he DC link volge v d i he pek vlue of he line-o-line yem volge (V ll ) []. In prie, higher v d i required o llow he PI onroller beer performne. Here.5V ll i ued in he imulion. If here i udden lod hnge or here i high urren vriion (di/) in he lod urren, higher DC link volge i required o h he ompenor h he biliy o ompene uh high urren vriion, whih i illured in Subeion IV.B. Beide ll he for diued bove, he wihing frequeny i lo n imporn for whih need o be onidered. If he lod urren h very high frequeny hrmoni, higher wihing frequeny i required o elimine he high frequeny hrmoni. VI. CONCLUSIONS A generlized nonive power heory h been preened in hi pper for nonive power ompenion. he innneou ive urren i (), he innneou nonive urren i n (), he innneou ive power p (), nd he innneou nonive power p n () re defined in yem whih doe no hve ny limiion uh he number of phe, wheher he volge nd he urren re inuoidl or non-inuoidl, nd wheher he lod i periodi or nonperiodi. By hnging he referene volge v p () nd he verging inervl, hi heory h he flexibiliy o define nonive urren nd nonive power in differen e. I i generlized heory h oher nonive power heorie diued in [] ould be derived from hi heory by hnging he referene volge nd he verging inervl. he flexibiliy i illured by pplying he heory o differen e uh hree-phe periodi yem wih hrmoni, diode reifier lod, ingle-phe pule lod, nd yem wih non-periodi urren. hi heory i implemened uing hun ompenor. he urren h he ompenor mu provide i luled REFERENCES [] S. Fryze, Aive, reive, nd ppren power in non-inuoidl yem, Przegld Elekro, no. 7, 93, pp (In Polih) [] L. M. olber,. G. Hbeler, Survey of ive nd non-ive power definiion, IEEE Inernionl Power Eleroni Congre, Oober 5-9, 000, Apulo, Mexio, pp [3] H. Akgi, Y. Knzw, A. Nbe, "Innneou reive power ompenor ompriing wihing devie wihou energy orge omponen," IEEE rn. Ind. Appl., vol. 0, My/June 984, pp [4] F. Z. Peng, J. S. Li, Generlized innneou reive power heory for hree-phe power yem, IEEE rnion on Inrumenion nd Meuremen, Vol. 45, Feb. 996, pp [5] H. Akgi, Aive filer nd energy orge yem opered under nonperiodi ondiion, IEEE Power Engineering Soiey Summer Meeing, Sele, Whingon, July 5-0, 000, pp [6] H. Lev-Ari, A. M. Snkovi, Hilber pe ehnique for modeling nd ompenion of reive power in energy proeing yem, IEEE rnion on Cirui nd Syem, vol. 50, April 003, pp [7] E. H. Wnbe, M. Arede, Compenion of non-periodi urren uing he innneou power heory, IEEE Power Engineering Soiey Summer Meeing, Sele, Whingon, July 5-0, 000, pp [8] L. S. Czrneki, Non-periodi urren: heir properie, idenifiion nd ompenion fundmenl, IEEE Power Engineering Soiey Summer Meeing, Sele, Whingon, July 5-0, 000, pp [9] F. Z. Peng, L. M. olber, Compenion of non-ive urren in power yem - definiion from ompenion ndpoin, IEEE Power Engineering Soiey Summer Meeing, July 5-0, 000, Sele, Whingon, pp [0] M. D. Mnjrekr, P. Seimer,. A. Lipo, Hybrid mulilevel power onverion yem: ompeiive oluion for high power ppliion, IEEE rnion on Indury Appliion, vol. 36, no. 3, My/June 000, pp [] N. Mohn,. M. Undelnd, W. P. Robbin, Power Eleroni: Converer, Appliion, nd Deign, John Wiley nd Son, Seond Ediion, 995. [] Y. Xu, L. M. olber, F. Z. Peng, J. N. Chion, J. Chen, Compenion-bed non-ive power definiion, IEEE Power Eleroni Leer, vol., no., June 003, pp [3] L. M. olber, Y. Xu, J. Chen, F. Z. Peng, J. N. Chion, Compenion of irregulr urren wih ive filer, IEEE Power Engineering Soiey Generl Meeing, July 3-8, 003, orono, Cnd, pp