Analysis of D-Q Small-Signal Impedance of Grid-Tied Inverters

Transcription

1 Analy o D-Q Small-Sgnal Impeane o r-te Inerter Bo Wen, Member, IEEE, Duhan Boroyeh, Fellow, IEEE, Rolano Burog, Member, IEEE, Paolo Mattaell, Fellow, IEEE, an Zhyu Shen, Member, IEEE Abtrat Th paper analyze the mall-gnal mpeane o three-phae gr-te nerter wth eebak ontrol an phae-loke loop () n the ynhronou reerene (-) rame. The reult unel an nteretng an mportant eature o three-phae gr-te nerter namely, that t - hannel mpeane behae a a negate nremental retor. Moreoer, the paper how that th behaor a oneuene o gr ynhronzaton, where the banwth o the etermne the reueny range o the retor behaor, an the power ratng o the nerter etermne the magntue o the retor. Aane, urrent, an power ontrol tratege o not hange th eature. An example how that uner weak gr onton, a hange o the banwth oul lea the nerter ytem to untable onton a a reult o th behaor. armon reonane an ntablty ue an be analyze ung the propoe mpeane moel. Smulaton an expermental meaurement ery the analy. Inex Term Impeane, nerter, negate retane rut, Nyut tablty, tablty, ynhronzaton I. INTRODUCTION r-te nerter are the key omponent that eler renewable energy to the gr [], []. They are typally ontrolle a urrent oure njetng urrent to the gr. Wth the nreang prealene o renewable energy reoure, power ualty an tablty ue nue by gr-te nerter beome more an more mportant [3] [7]. armon polluton oul happen ue to the nteraton between nerter an gr mpeane [3], [5], [7]. Large gr mpeane oul etablze the nerter ytem [4], [8]. In orer to eler power to the gr, reueny an phae angle o nerter output urrent houl ynhronze wth gr oltage, whh uually ere by Phae-Loke Loop () [9], []. Some reent lterature oere that ha a negate mpat on ytem tablty [8], [] [4]. Manurpt reee Augut 8, 4; ree Noember 4, 4; aepte January, 5. Date o urrent eron *******, 5. Th work wa upporte by the Center or Power Eletron Sytem (CPES) Renewable Energy an Nanogr (REN) mn-onortum. Reommene or publaton by Aoate Etor ****. Bo Wen wth Department Engneerng, Eletral Engneerng Don, Unerty o Cambrge, Cambrge, CB3 FZ, U (e-mal: bw37@am.a.uk). Duhan Boroyeh, Rolano Burgo, an Zhyu Shen are wth the Center or Power Eletron Sytem, the Braley Department o Eletral an Computer Engneerng, Vrgna Teh, Blakburg, VA 46 USA (e-mal: uhan@t.eu; rolano@t.eu; henzy@t.eu). Paolo Mattaell wth Unerty o Paoa, Italy (e-mal: paolo.mattaell@unp.t ). Color eron o one or more o the gure n th paper are aalable onlne at Dgtal Objet Ienter **************** In the pat, ntablty ue o power eletron relate ytem are manly belee to be aue by the negate nremental retor o -, -a onerter n ytem [5] [7] an a- onerter n a ytem [8] []. The negate nremental retor are reult o the output oltage regulaton o thee onerter. Together wth the hgh eeny eature o thee onerter, they beome ontant power loa (CPL), whh onume a xe amount o power regarle what the upply oltage. The nput urrent nreae when the upply oltage ereae, an e era. The negate retor n ombnaton wth other omponent n the ytem an uner ertan onton onttute a negate retor ollator, an the orgn o the ytem potental ntablty [6] []. Th kn ntablty an be analyze by applyng Nyut tablty rteron to the mpeane rato between oure an loa n ytem [6]. For a three-phae a ytem, no operaton pont ext n the tatonary rame. By ong a tranormaton rom the tatonary rame to the ynhronou reerene (-) rame, a three-phae a ytem beome two ouple ytem. Small-gnal mpeane n the - rame an then be ere by ong tratonal lnearzaton [8], [] [3]. Derng rom mpeane o - onerter, mpeane o three-phae a onerter are - by- matre. The CPL behaor an negate nremental retor behaor oun n the - hannel mpeane (Z ) o the matre [8], [9]. Meaurement tehnue an ee or - rame mpeane are alo eelope [4] [8]. Small-gnal tablty o the three-phae a ytem an then be analyze bae on - mpeane an generalze Nyut Crteron [9] [34], [36]. r-te nerter are not CPL. They are typally ontrolle a urrent oure ung ngle output urrent eebak ontroller or power oure ung both urrent an power ontroller a hown n Fg.. Intablty n gr-te nerter ytem wa not analyze ung the negate nremental retor onept n the pat [3] [7]. Reently, Re. [8] moel the eet o by ntroung ytem an onerter - rame. It how that hgh banwth nreae the negate real part o the nerter output mpeane, whh oul etablze the ytem [8], []. Re. [] ge the ull mpeane moel o the gr-te nerter onerng urrent eebak ontrol an n - rame. The moel how that hape - hannel output mpeane (Z ) o the gr-te nerter a a negate nremental retor wthn t banwth. Later on, Re. [] alo how the ame onluon, ung a moel that gnore the ouplng eet between -hannel an -

2 hannel. Th moel pret the nerter mpeane well or unty power ator applaton where the ouplng eet an be gnore. oweer, or a three-phae ytem wth reate power, the ouplng eet between an hannel gnant; th moel annot pret the mpeane uner th onton. V ab θ P re Q re PWM Current Controller re Power re Controller P Q L ab R L Power Cal. Samplng ab θ Power Stage Samplng ab a b θ Controller Fg.. r-te nerter wth eebak ontrol an. Intea, th paper propoe a ull analytal moel or the output mpeane o the three-phae gr-te nerter n the - rame, onerng the eet o, an eebak ontrol a hown n Fg.. Ung the propoe moel, nerter mall-gnal mpeane are haraterze wth erent ontrol tratege. Speally, mpeane alue are hown n the orm o Boe plot, whh learly emontrate the negate retor behaor o Z. An analytal expreon or the negate retor gen. The moel how that a hgher banwth wll proue a wer reueny range o the negate retor, an a hgher power ratng o the nerter wll reult n a lower magntue o the retor. The moel ere by meaure mpeane. The moel alo nate that uner weak gr onton, the negate nremental retor o Z oul lea the ytem to untable onton. Small-gnal mpeane o power onerter are the lnearzaton aroun ther operaton pont. Reently, mall-gnal mpeane an tablty analy o threephae onerter were alo eelope n the tatonary rame ung harmon lnearzaton on a gnal [5], [3], [35]. Th paper oue on the tratonal - mpeane analy n the ynhronou reerene rame. The ret o th paper nlue een eton. Seton II how the power tage mall-gnal moel o the gr-te nerter. Seton III moel the eet o on nerter mpeane. Seton IV moel the nerter mpeane wth urrent eebak ontrol. Seton V moel the eet o power eebak ontrol on nerter mpeane. Seton VI how the tablty analy ung the propoe moel. Seton VII how the expermental eraton o the propoe moel. Seton VIII the onluon. II. POWER STAE SMALL-SINAL MODEL Fg. how the mall-gnal rut moel o the grte nerter power tage n the ytem - rame [], [8]. Aume the nput o the gr-te nerter upple by a t oure, whh oul be a - onerter or olar applaton or an a- onerter or wn applaton. Then, the ynam rom the nput an be neglete. The mallgnal rut moel then an be repreente by the traner unton matrx low hart hown n Fg. 3. the traner unton matrx rom uty rato etor nutor urrent etor the power tage. = = IL, D L Z out = = or Zout = IL D L = or to the output mpeane o L V D L V D R L R L L ωl L L ωl L Z out Fg.. Small-gnal rut moel o nerter n ytem - rame. - Z out Fg. 3. Inerter power tage mall-gnal moel. The open loop output mpeane wthout an be ere by orng perturbaton o the uty rato an oltage to zero a hown n Fg.. The expreon o the power tage output mpeane : Z Z L R L L Z out_ol Z Z L L R () L Note that mpeane o the three-phae onerter n the - rame a -by- matrx. Z repreent the oltage repone n hannel when hannel urrent perturbe. Z repreent the hannel oltage repone when hannel urrent perturbe. E. () how that Z an Z are the ame a the mpeane o the nerter a nutor. Z an Z repreent the ouplng eet between the an hannel. The traner unton matrx between the uty rato etor an nutor urrent etor an be ere by orng

3 perturbaton o gr an oltage to zero a hown n Fg.. The expreon o : L R L () V L L R L L L R L III. INFLUENCE OF Output mpeane o a - onerter nluene by t power tage parameter an eebak ontroller [6]. Derng rom a - onerter, a gr-te onerter uually nee to ynhronze wth the gr []. Tratonal an eebak ontrol o the gr-te nerter are ormulate alo n the - rame. Reently, other ynhronzaton an eebak ontrol tratege were alo eelope. Thee nlue tratege uh a power ynhronzaton [37], ontroller n tatonary rame [] an een a ontrol o gr-te nerter a a ynhronou generator [38]. Note that thee top are out o the ope o th paper. Beaue o, the nerter ytem ha two - rame: one the ytem - rame, an another the ontroller - rame [8] a hown n Fg. 4. r oltage ene the ytem - rame. The ontroller - rame ene by the, whh etmate the reueny an angle o gr oltage to n the poton o the ytem - rame. In a teay tate, the ontroller - rame algne wth the ytem - rame. When mall-gnal perturbaton are ae to the gr oltage, the poton o the ytem - rame hange. The ontroller - rame no longer algne wth the ytem - rame beaue o the ynam (PI regulator o ). The angle between two - rame a hown n Fg. 4. Voltage an urrent etor n the ytem - rame are rotate to the ontroller - rame or eebak ontrol by matrx T. The uty yle omman generate by eebak ontrol are then rotate to the ytem - rame by the nere o matrx to ontrol the power emonutor. Δθ Fg. 4. Sytem an ontroller - rame. T, n o o T n T, L T (3) T (4) Small-gnal perturbaton o the ytem oltage propagate to the output angle, an urther to the urrent an uty rato etor n the ontroller - rame. Perturbaton then go to the oltage generate by the nerter power tage an nally to the output urrent o the nerter []. Th mean ynam nluene the output mpeane o the gr-te nerter. el ontroller - rame - Z out ytem - rame Fg. 5. Inerter mall-gnal moel wth. In orer to moel the mall-gnal propagaton path through, traner unton matre, an are ene. perturbaton path rom ytem oltage to oltage n the ontroller - rame. moel the mall-gnal perturbaton path rom ytem oltage to uty yle n the ontroller - rame. moel the mall-gnal moel the mall-gnal perturbaton path rom ytem oltage to urrent n the ontroller - rame. Fg. 5 how the traner unton matrx low hart repreentaton o a gr-te nerter mall-gnal moel wth. the lter traner unton matrx or oltage an urrent gnal ontonng. repreent the tme elay ( ) ue to gtal ontrol an PWM [39]. Note that, n the moel hown n Fg. 5, ang the major erene to the moel hown n Re. [8]. n n n (5) n n n el T el.5t el.5t el el.5t el (6).5T el a b T k ppll k pll / Fg. 6. SRF. ω θ

4 T o 3 n To ere, o 3 n 3, an o 3 n 3 (7), the trategy n the ynhronou reerene (-) rame (SRF) [9] hown n Fg. 6 onere rtly. The SRF tranormaton matrx hown n E. (7). In the - rame, the aerage moel o hown n Fg. 7, an the eraton begn rom the teay-tate relatonhp o arable n two rame a hown n E. (8). T Δθ k ppll k pll / ω Fg. 7. Aerage moel o SRF., V V I I, E. (8) nate that the angle between etor n the ontroller rame an the etor n ytem rame ; ung the rotaton matrx T, E. (8) an be rewrtten a: o() n() V V, n() o() o() n() I I, n() o() (9) D D o() n() D D n() o() A mall-gnal perturbaton to E.(9): V o( ) n( ) V V n( ) o( ) V Δθ (8) () By ong a mall angle approxmaton o trgonometr unton, an anelng the teay tate alue, the relatonhp between oltage etor n the ontroller rame, ytem rame, an output angle an be ere a: V V V V V V () () Reall that output angle : t (3) Where, t k k ppll pll (4) Subttute E. (3) to (), E. (5) how the euaton repreentng the relaton between output angle an hannel oltage. t V t (5) Dene Then, a: For oltage, V V Then, t V t ene a: V V (6) (7) (8) V V (9) For uty rato, mlar mall-gnal analy an be one, whh yel: D D () Then, ene a: D D () A mlar euaton an be ere or nutor urrent a hown n E. (): I I () ene a: I I (3) Solng the euaton repreente by Fg. 5, the output mpeane o an nerter wth workng on open loop : Z Z out_ol_ out el (4)

5 a b T - DC () - DC T - (-) LPF LPF LPF LPF Fg. 8. DDSRF. k ppll k pll / ω θ Then DD, t, an t V V beome wth DDSRF, an they are:, DD (33), an DD V V DD V V (34) D D DD D D (35) T Δθ k ppll k pll / ω Δθ I I DD I I (36) Fg. 9. Aerage moel o DDSRF. One mportant ue n egn the ouble lne reueny rpple aue by three-phae unbalane. Deouple Double SRF (DDSRF) [4], a hown n Fg. 8, an eete trategy to mgrate the ouble lne reueny rpple. The ynam o the eouplng term moele a traner unton matrx n Fg. 9. The expreon o an be oun n Re. [4], an hown rom E. (5) to (9). (5) Where, (6) When DDSRF ue, E. (4). IV. replae by DD IMPEDANCE WIT CURRENT CONTROL AND el ontroller - rame - Z out ytem - rame n (7) e - _re = 4 ( ) The Low-Pa Flter (LPF) n Fg. 8 : LPF (8) (9) (3) Wth DDSRF, the relaton between output angle an gr oltage : (3) Where, t t V V (3) Fg.. Small-gnal moel wth an urrent eebak ontrol. The urrent ontroller an be mplemente n ether ynhronou rame or tatonary rame. Statonary rame urrent regulator an be tranorme to ynhronou rame ung the tranormaton proe by [4]. Moelng o the mpeane o a oltage oure onerter wth a tatonary rame urrent regulator hown n [43]. The nluene o erent urrent regulator wll not be elaborate upon; only the urrent ontroller n ynhronou rame onere n th paper. Fg. how the mall-gnal moel o the grte nerter wth urrent eebak ontrol. The urrent ontroller matrx. e the eouplng term. k k p k (37) k p

6 3L V e 3L (38) V Solng the euaton repreente by Fg., the output mpeane o a gr-te nerter ytem wth workng uner a loe-loop onton : Z Z out_l_ out I el el e When DDSRF ue, replae by DD e n E. (39). replae by DD (39) an Table I n the Appenx how the parameter o the nerter prototype ytem. Ung thee parameter an E. (4), Fg. how the Boe plot o nerter power tage open loop output mpeane (Zout_ol) oer plotte wth output mpeane open loop wth (Zout_ol_). Clearly, Z o Zout_ol_ hape a a negate retor at low reueny. Ung thee parameter an E. (39), Fg. how the Boe plot o nerter output mpeane wth urrent eebak ontrol an erent egn. The mpeane are alulate up to hal wthng reueny where t al to o o. Magntue (B) Phae (eg) Magntue (B) Phae (eg) Z Z Zout_ol Zout_ol_ -8 4 Freueny (z) 4 Z Z behae a a negate nremental retane wthn banwth. Three erent egn n whh banwth ( bw_) are rom 5 z to z (lne reueny et to be 4 z n orer to allow a we range o banwth) are hoen to how the nluene o. The reult how that a hgher banwth ae yel a wer reueny range o negate retane behaor. The magntue o the retane relate to the power ratng o the nerter. Epeally, a hown n Fg. 3, the urrent etor o the nerter ynhronze wth the gr oltage etor, whh algne n hannel to njet real power to the gr. When oltage turbane happen n hannel, the oltage etor beome. Beaue o, the urrent etor wll rotate to keep ynhronzaton wth the oltage etor. Meanwhle, the urrent ontroller keep urrent magntue n hannel unhange. Then, urrent etor beome L ue to the hannel oltage perturbaton. Note that the mall-gnal repone o hannel urrent n the oppote reton o hannel oltage perturbaton, o, rom Fg. 3, Z an be alulate by E. (4) wthn the banwth o. Th onluon alo ere by the magntue o Z n low reueny a hown n Fg.. Aorng to E. (4), an nerter wth a hgh urrent ratng ha low mpeane n - hannel; th hown n Fg. 4, n whh mpeane wth three erent hannel urrent reerene are plotte. Magntue (B) Phae (eg) Magntue (B) Phae (eg) Z Z 4 4 Freueny (z) Z log( V I / ) =9. B bw_ = 5 z bw_ = z bw_ = z kppll = 4.46 kpll = 99 kppll = 8.9 kpll = 3964 Z kppll = 7.84 kpll = 586 Fg.. VSI power tage mpeane (Z out_ol) an open loop wth mpeane (Z out_). Fg.. Impeane o nerter wth urrent ontrol an erent banwth. Z V I (4) A t an be obere n Fg., Z how the urrent oure behaor. In low reueny range, t hape by the urrent ontroller ntegrator; n hgh reueny range, Z the mpeane o the a nutor. Z an Z are ery mall wthn the urrent ontroller banwth beaue o unty power ator ontrol. In hgh reueny range, they behae a the power tage mpeane alue a hown n E. (). Z _ L I _ V Fg. 3. Phaor agram o nerter wth urrent eebak ontrol an when perturbaton happen n hannel.

7 Magntue (B) Phae (eg) Magntue (B) Phae (eg) Z Z re = -6A; re = A re = -A; re = A re = -A; re = A Freueny (z) 4 Z Z Magntue (B) Phae (eg) Magntue (B) Phae (eg) SRF DDSRF Freueny (z) 4 Fg. 4. Impeane o nerter wth urrent ontrol an erent re. Fg. 6. Impeane wth urrent ontrol an erent tratege. Magntue (B) Phae (eg) Magntue (B) Phae (eg) Z Z w/o eouplng w/ eouplng Freueny (z) 4 Z Z Magntue (B) Phae (eg) Magntue (B) Phae (eg) Z Z Freueny (z) 4 Z Z re = -A; re = -6A re = -A; re = A re = -A; re = 6A Fg. 5. Impeane o nerter wth an wthout eouplng ontrol. Fg. 5 how the mpeane o the nerter wth an wthout eouplng ontrol. Wth eouplng ontrol, Z an Z are reue. Th expete, beaue eouplng ontrol reue the ouplng between an hannel, whh relete by Z an Z. The ue o eouplng ontrol oe not hange the negate retane behaor o Z. Fg. 6 how the mpeane wth erent tratege, whh nate that ue o DDSRF oe not hange the negate retane behaor o Z. The gr-te nerter an njet reate urrent to upport the gr. Fg. 7 how the mpeane o the grte nerter wth erent reate power njeton. The blue lne how the mpeane o the apate power njeton ae; the green lne how the mpeane o no reate power njeton, an the re lne how the nute power njeton ae. Note that reate power njeton wll nreae the mpeane o ro ouplng term Z ; the ret o the mpeane are the ame wth the unt power ator ae. The negate retane eature reman unhange when the gr-te nerter njet reate power to the gr. Fg. 7. Impeane o nerter wth erent reate urrent njeton. V. INFLUENCE OF POWER FLOW CONTROL LOOP el ontroller - rame - Z out ytem - rame e PQ - PQ - PQ P re Q re = Fg. 8. Inerter mall-gnal moel wth, urrent an power ontrol. On top o the urrent ontroller, a power low ontroller an be ae to ontrol the real an reate power aurately generate by the nerter. The mall-gnal moel

8 Magntue (B) Phae (eg) Magntue (B) Phae (eg) hown n Fg. 8 or the power low ontrol ae. PQ the traner unton matrx o the power low ontroller: kpq k ppq PQ k (4) PQ k ppq PQ an PQ are mall-gnal traner unton matre o power alulaton n - rame: P Q By ong lnearzaton to E. (4), ere: PQ an PQ (4) V V PQ V V (43) I I PQ I I (44) Solng the euaton repreente by Fg. 8, the output mpeane o the gr-te nerter ytem wth an power eebak ontrol : Z Z out PQ PQ el PQ PQ e I out_pq el PQ When DDSRF ue, by, by DD n E. (45). DD PQ replae by Z Z DD e (45) are replae, an replae bw_ = 5 z -4 bw_ = z -8 bw_ = z Freueny (z) Z Z Fg. 9 how the mpeane o the nerter prototype wth power eebak ontrol ung the nerter power tage parameter lt n Table I an the ontroller parameter lt n Table II n the Appenx. Note that the ntegrator gan o urrent ontroller n Table II nreae ompare to what hown n Table I n orer to loe the power eebak ontrol loop. One the power low ontroller apple, wthn t banwth, Z beome a pote retane, an Z tll a negate retane. banwth tll nluene the reueny range o the negate retane behaor o Z a hown n Fg. 9. Z an Z are tll low n the low reueny beaue o the unty power ator ontrol. Magntue (B) Phae (eg) Magntue (B) Phae (eg) B.7 B Pre = -5W; Qre = -5Var Pre = -5W; Qre = Var Pre = -5W; Qre = 5Var.7 B Z Z.7 B 8.7 B.7 B Freueny (z) Fg.. Impeane o nerter wth power eebak ontrol an erent reate power njeton. When njetng reate power nto the gr, all our mpeane hange along wth the real an reate power ratng, a hown n Fg.. In orer to unertan the mpeane matrx when a power ontroller apple, or, n other wor, to unertan the mpeane eature o a ontant power oure, the ollowng eraton are hown []: P Q (46) E. (46) a goo approxmaton at the reuene that are below the power regulaton banwth where P an Q are ontant. Then the oltage etor an be ere a E. (47) rom E. (46). It an be lnearze ung the twoarable Taylor ere up to the eon term a hown n E. (48). Then, the mpeane matrx when reueny zero hown n E. (49). It an be ere by omparng t reult wth the alue hown n Fg. or erent reate njeton onton. Z Z Fg. 9. Impeane o nerter wth an power eebak ontrol.

9 Z out_pq V () P P Q Q P (47) F F OF I I Q I I Z out_pq I I I P I Q Q I I I I I I P I Q P I I I I I I I P I Q I I I I P I Q I I (48) (49) Current (A) a b Stable k ppll hange rom.5 to Tme () (a) Untable VI. STABILITY ANALYSIS USIN TE PROPOSED MODEL Although th paper oue on mpeane analy o the three-phae gr-te nerter, th eton ge a bre uon o tablty analy ung the propoe moel. Th example alo how that nreang banwth oul aue ntablty o the gr-te nerter ytem uner weak gr onton. r V g Z g PCC Z o Z VSI Loa A nterae Z L Freueny (z) pll Stable k ppll hange rom.5 to 3 Untable Tme () Fg.. One lne agram o the nerter ytem wth loal loa. One lne agram repreentaton o the nerter ytem uner tuy hown n Fg.. In th ytem, the threephae nerter onnete to the pont o ommon ouplng (PCC) together wth the three-phae pae loa. Th nerter ynhronze wth PCC oltage by SRF. Only urrent eebak ontrol apple n orer to ontrol the amount o power njeton to PCC. Eah phae o the pae loa ont o a parallel onnete retor an apator. The gr onnete to PCC through mpeane, ontng o an nutor an retor. The etale parameter o th ytem are hown n Table III n the Appenx. Fg. how the tme oman mulaton reult o the nerter ytem. In the mulaton, wthn the tme range rom to eon, the ytem runnng uner table onton. At eon, proportonal gan (k ppll) o PI regulator nreae rom.5 to 3; both nerter output urrent a hown n part (a) o Fg. an output reueny o VSI a hown n part (b) o Fg. tart to ollate. The whole ytem beome untable. (b) Fg.. (a) Inerter output urrent; (b) output reueny. In orer to pret table an untable onton o the ytem ung the mpeane-bae metho, an a nterae oun at the termnal o the nerter a hown n Fg.. A reporte by Re. [7], when ung mpeane-bae tablty analy or a gr-te nerter ytem, the nerter houl be treate a loa, an Nyut tablty rteron houl be apple to the mpeane rato between the gr e mpeane an nerter mpeane a hown n E. (5). L Z o Z (5) R g L g C Loa R Loa Fg. 3. One phae agram o Z o n tatonary rame. From a mall-gnal pont o ew, Zo the parallel o gr mpeane Zg an loa mpeane ZL. The one phae agram o Zo n tatonary rame hown n Fg. 3.

10 Deraton o Zo n - rame ue n Re. [33], ung the parameter lte n Table III, Zo n - rame plotte n Fg. 4 a a ol blak lne. Magntue (B) Phae (eg) Magntue (B) Phae (eg) 4 - Z -4 Z o_ -6 Z u 8 Z 9 Z o_ Z u k ppll =.5 - Z k ppll =3 Z -4 Z o_ Z o_ -6 Z u Z u k ppll =.5 k ppll = Freueny (z) Freueny (z) Fg. 4. Impeane o gr e an VSI. Ung E. (39) an nerter parameter lte n n Table III, Z alulate an plotte n Fg. 4 a a ahe re lne or table onton (k ppll =.5) an a ol re lne wth a rle marker or untable onton (k ppll = 3). The hange o egn oe not hange Z _ n Fg. 4. Sgnant hange ha been ntroue n Z _. There are mall araton on Z _ an Z _, but ompare to Z _, thee araton an be gnore, ne they are oer 3B maller than Z _. Wth bgger alue o k ppll, reueny range o negate retor o Z _ extene. Intablty aue by Z _. Ung Zo an Z an applyng generalze Nyut rteron (NC) to mpeane rato L, tablty onton o the example ytem an be prete orretly a hown n Fg. 5. In part (a) o Fg. 5, when k ppll.5, none o the ytem haratert lo enrle the rtal pont (-, ), an the ytem table. In part (b) o Fg. 5, when k ppll 3, one o the ytem haratert lo (λ ) enrle the rtal pont, whh nate the ytem untable. In th example, gr-te nerter ontrolle wth urrent ontroller, the negate retor only obere on Z, not Z. Z an Z are ontrolle wth ery mall magntue uner unty power ator. Intablty o the ytem manly ue to Z. More etale tablty analy ung NC an be oun n Re. [9] [34]; th paper wll not elaborate on th partular analy. When the nerter njet reate power, magntue o Z beome gnant, but t tll not negate retor. When power ontroller are ae an nerter njet reate power, Z an Z oul alo behae a negate retor a hown n Fg.. The mpat o Z an Z on ytem tablty uner thee onton nee more uon n the uture. Imagnary Ax - - Real Ax (a) Imagnary Ax - - Real Ax Fg. 5. NC plot: (a) table ae (k pll =.5); (b) untable ae (k pll = 3). (b) VII. EXPERIMENTAL VERIFICATION In orer to ery the propoe moel, a low power prototype o the three-phae gr-te nerter an - mpeane meaurement eupment [44] are bult a hown n Fg. 6. All the mpeane were meaure rom 4 z to kz (hal wthng reueny o the nerter) wth pont. For the ae wth urrent eebak ontrol an SRF, an nerter prototype wth parameter lte n Table I ue or meaurement. For the ae wth power eebak ontrol, the parameter lte n Table II are ue or meaurement. Fg. 7 how the meaure mpeane oer-plotte wth reult alulate ung propoe E. (39) or unt power ator ontrol, where hannel urrent reerene - A an the SRF banwth z. The reult how goo auray o the propoe moel. Fg. 8 how Z wth a erent SRF banwth. The meaurement reult learly how the negate mpeane behaor o Z an t araton along wth banwth. Fg. 9 an Fg. 3 how the meaurement reult wth nute an apate reate power uner urrent eebak ontrol wth z SRF banwth. Fg. 3 how the meaurement reult wth power eebak ontrol where P re -5 W an Q re Var. All the meaurement reult math wth the reult prete by the moel ery well. VSI IBT Moule Controller o Z Teter A Inutor Control Boar Senor Boar Power Ampler Power Ampler Power Ampler 3 Fg. 6. Expermental ytem. Z Teter D Power Supply

11 Magntue (B) Phae (eg) Magntue (B) Phae (eg) Z Meaure Z Moel Z Meaure Z Moel Z Meaure Z Moel Z Meaure Z Moel Freueny 3 4 (z) Freueny 3 (z) 4 Magntue (B) Phae (eg) Magntue (B) Phae (eg) Z Meaure Z Moel Z Meaure Z Moel Z Meaure Z Moel Z Meaure Z Moel Freueny (z) 4 Freueny 3 (z) 4 Fg. 7. Meaurement reult ompare wth moel or re = -.A, re = A, bw_ = z. Fg. 3. Meaurement reult ompare wth moel or re = -.A, re = - 6 A, bw_ = z. Magntue (B) Phae (eg) bw_ = 5 z Meaurement bw_ = 5 z Moel bw_ = z Meaurement bw_ = z Moel bw_ = z Meaurement bw_ = z Moel -8 3 Freueny (z) 4 Magntue (B) Phae (eg) Magntue (B) Phae (eg) Z Meaure Z Moel Z Meaure Z Moel Z Meaure Z Moel Z Meaure Z Moel Freueny (z) 4 Freueny 3 (z) 4 Fg. 8. Meaurement reult wth erent banwth ompare wth moel or re = -.A, re = A. Fg. 3. Meaurement reult ompare wth moel or P re = -5.W, Q re = Var, bw_ = z. Magntue (B) Phae (eg) Magntue (B) Phae (eg) 4 - Z Meaure Z Meaure Z Moel Z Moel Z - Meaure Z Meaure Z Moel Z Moel Freueny 3 (z) Freueny 3 (z) 4 Fg. 9. Meaurement reult ompare wth moel or re = -.A, re = 6 A, bw_ = z. VIII. CONCLUSION Th paper preent an analy o gr-te nerter mall-gnal mpeane n - rame uner erent ontrol tratege. Inluene o, an urrent an power eebak ontrol to the nerter mpeane are ue. Some mportant eature o nerter mpeane are ue. Thee eature nate that a gr-te nerter workng a a urrent oure oul etablze the ytem ue to the negate nremental retor o Z. Th negate nremental retor behaor a reult o an urrent njeton. Inreang o banwth exten the reueny range o th behaor, an nreae o nerter power leel ereae the abolute alue o the retor. A bre mulaton example how that uner weak gr onton, a mall nreae o the banwth oul lea the ytem to untable onton. The example alo how how the propoe moel an be ue to pret uh ntablty. arware meaurement ery the propoe moel. The moel ge nght nto the gr-te nerter

12 behaor n the gr. armon reonane an ntablty ue reporte n the lterature an be analyze ung the haraterze mpeane moel. APPENDIX TABLE I. PARAMETERS OF RID-TIED INVERTER PROTOTYPE Symbol Derpton Value V Inerter nput oltage 7 V V D hannel gr oltage 99.6 V V Q hannel gr oltage V re D hannel urrent reerene - A re Q hannel urrent reerene A ω Lne reueny π 4 ra/ L Inutane o nerter output nutor 97 µ R L Retane o nerter nutor el-retor mω w Swthng reueny kz k p Proportonal gan o urrent ontroller.3 k Integrator gan o urrent ontroller 5.59 ω n Natural reueny o gnal ontonng lter.3e6 ra/ ζ Dampng ator o gnal ontonng lter 4.74e-3 T el Tme elay ue to gtal ontrol an PWM.5/ w ω Cut o reueny o LPF n DDSRF 777 ra/ k ppll Proportonal gan o nerter Integral gan o nerter k pll TABLE II. PARAMETERS OF CURRENT AND POWER FEEDBAC CONTROLLER Symbol Derpton Value k p Proportonal gan o urrent ontroller.3 k Integrator gan o urrent ontroller 5.8 k ppq Proportonal gan o power ontroller.8 k PQ Integrator gan o power ontroller 7 P re Real power reerene -5 W Q re Reate power reerene Var TABLE III. PARAMETERS OF INVERTER SYSTEM FOR STABILITY ANALYSIS Symbol Derpton Value V g r lne-lne peak oltage 6 V ω g r oltage reueny π 6 ra/ L Inutane o nerter m V Inerter oltage 6 V w Swthng reueny o nerter kz I re hannel urrent o nerter -9 A I re hannel urrent o nerter A k p Proportonal gan o nerter urrent ontroller.5 k Integrator gan o nerter urrent ontroller.59 k ppll Proportonal gan o nerter.5 (table); 3 (untable) k pll Integral gan o nerter 3. Z L Loal pae loa R Loa: Ω; C Loa: 5 μf Z g r mpeane R g:. Ω; L g: m output reueny o nerter pll REFERENCES [] F. Blaabjerg, C. Zhe, an S. B. jaer, Power eletron a eent nterae n pere power generaton ytem, IEEE Tran. Power Eletron., ol. 9, pp , Sep. 4. [] J. Roabert, A. Luna, F. Blaabjerg, an P. Rorguez, Control o Power Conerter n AC Mrogr, IEEE Tran. Power Eletron., ol. 7, pp , No.. [3] J.. R. Enln an P. J. M. eke, armon nteraton between a large number o trbute power nerter an the trbuton network, IEEE Tran. Power Eletron., ol. 9, pp , No. 4. [4] M. Lerre, R. Teooreu, an F. Blaabjerg, Stablty o photoolta an wn turbne gr-onnete nerter or a large et o gr mpeane alue, IEEE Tran. Power Eletron., ol., pp. 63 7, Jan. 6. [5] M. Cepee an S. Jan, Renewable Energy Sytem Intablty Inolng r-parallel Inerter, n Pro. 4th Annu. Appl. Power Eletron. Con. Expo., Mar. 9, pp [6] E. Vttal, M. O'Malley, an A. eane, A Steay-State Voltage Stablty Analy o Power Sytem Wth gh Penetraton o Wn, IEEE Tran. Power Syt., ol. 5, pp , Feb.. [7] S. Jan, Impeane-Bae Stablty Crteron or r-connete Inerter, IEEE Tran. Power Eletron., ol. 6, pp , No.. [8] L. arneor, M. Bongorno, an S. Lunberg, Input-amttane alulaton an hapng or ontrolle oltage-oure onerter, IEEE Tran. In. Eletron., ol. 54, no. 6, pp , De. 7. [9] C. Se-yo, A phae trakng ytem or three phae utlty nterae nerter, IEEE Tran. Power Eletron., ol. 5, pp , May. [] F. Blaabjerg, R. Teooreu, M. Lerre, an A. V. Tmbu, Oerew o Control an r Synhronzaton or Dtrbute Power eneraton Sytem, IEEE Tran. In. Eletron., ol. 53, pp , Ot. 6. [] M. Cepee an S. Jan, Impeane hapng o three-phae grparallel oltage-oure onerter, n Pro. 7th Annu. Appl. Power Eletron. Con. Expo., Mar., pp [] B. Wen, D. Boroyeh, R. Burgo, P. Mattaell, an Z. Shen, Inluene o phae-loke loop on rame mpane o three-phae oltage-oure onerter an the mpat on ytem tablty, n Pro. 3 CPES Power Eletron. Con., Apr. 6 8, 3. [3]. M. Alawaa, Y. A. R. I. Mohame, an W. Xu, Moelng, Analy, an Suppreon o the Impat o Full-Sale Wn-Power Conerter on Subynhronou Dampng, IEEE Syt. J., ol. 7, pp. 7 7, De. 3. [4]. M. Alawaa, Y. A. R. I. Mohame, an W. Xu, Ate Mtgaton o Subynhronou Interaton Between PWM Voltage-Soure Conerter an Power Network, IEEE Tran. Power Eletron., ol. 9, pp. 34, Jan. 4. [5] N. Sokal, Sytem ollaton rom negate nput retane at power nput port o wthng-moe regulator, ampler, / onerter, or /a nerter, n Pro. IEEE Power Eletron. Spe. Con., Sep. 973, pp [6] R. D. Mlebrook, Input lter oneraton n egn an applaton o wthng regulator, n Pro. IEEE In. Applat. So. Con., Ot. 976, pp [7] M. Cepee, X. Le, an S. Jan, Contant-Power Loa Sytem Stablzaton by Pae Dampng, IEEE Tran. Power Eletron., ol. 6, pp , Jul.. [8]. Mao, D. Boroyeh, an F. C. Lee, Noel reue-orer mallgnal moel o a three-phae PWM reter an t applaton n ontrol egn an ytem analy, IEEE Tran. Power Eletron., ol. 3, no. 3, pp. 5 5, May 998. [9] M. Belkhayat, Stablty rtera or a power ytem wth regulate loa, Ph.D. ertaton, Purue Un., Wet Laayette, IN, De [] N. Bottrell, M. Proano, an T. C. reen, Dynam tablty o a mrogr wth an ate loa, IEEE Tran. Power Eletron., ol. 8, no., pp , No. 3. [] T. Meo, J. Jokp, A. Maknen, an T. Sunto, Moelng the gr ynhronzaton nue negate-retor-lke behaor n the output

13 mpeane o a three-phae photoolta nerter, n Pro. 4th IEEE Int. Symp. Power Eletron. Dtrb. eneraton, Jul. 3, pp. 7. [] S. t, V. Vlatko, D. Boroje, an F. C. Lee, A new ontrol algorthm or three-phae PWM buk reter wth nput plaement ator ompenaton, IEEE Tran. Power Eletron., ol. 9, pp. 73 8, Mar [3] B. Wen, D. Boroyeh, P. Mattaell, Z. Shen, an R. Burgo, Inluene o phae-loke loop on nput amttane o three-phae oltage-oure onerter, n Pro. 8th Annu. Appl. Power Eletron. Con. Expo., Mar. 3, pp [4]. Jng,. A. Corzne, an M. Belkhayat, Small-gnal mpeane meaurement o power-eletron-bae a power ytem ung lne-to-lne urrent njeton, IEEE Tran. Power Eletron., ol. 4, pp , Feb. 9. [5] Y. A. Famlant,. Jng,. A. Corzne, an M. Belkhayat, New tehnue or meaurng mpeane haratert o three-phae a power ytem, IEEE Tran. Power Eletron., ol. 4, pp. 8 8, Jul. 9. [6]. Fran, R. Burgo, D. Boroyeh, F. Wang, an. arm, An algorthm an mplementaton ytem or meaurng mpeane n the - oman, n Pro. Energy Coner. Congr. Expo., Sep., pp [7] S. Zhyu, M. Jak, P. Mattaell, D. Boroyeh, J. Verhult, an M. Belkhayat, Degn an mplementaton o three-phae a mpeane meaurement unt (IMU) wth ere an hunt njeton, n Pro. 8th Annu. Appl. Power Eletron. Con. Expo., Mar. 3, pp [8] V. Vala, A. Lazaro, A. Barrao, P. Zumel, C. Fernanez, an M. Sanz, Impeane entaton proeure o three-phae balane oltage oure nerter bae on tranent repone meaurement, IEEE Tran. Power Eletron., ol. 6, pp , De.. [9] A.. J. MaFarlane an I. Potlethwate, The generalze Nyut tablty rteron an multarable root lo, Int. J. o Control, ol. 5, pp. 8 7, 977. [3] Z. Yao, P.. Theron, an B. Daat, Stablty analy o power ytem by the generale Nyut rteron, n Pro. Int. Con. on ontrol, Mar. 994, pp [3] J. Sun, Small-gnal metho or a trbute power ytem A Rewew, IEEE Tran. Power Eletron., ol. 4, no., pp , No. 9. [3] R. Burgo, D. Boroyeh, F. Wang,. arm, an. Fran, On the a tablty o hgh power ator three-phae reter, n Pro. Energy Coner. Congr. Expo., Sep., pp [33] M. Shwezer an J. W. olar, Shtng nput lter reonane an ntellgent onerter behaor or mantanng ytem tablty, n Pro. Int. Power Eletron. Con. ECCE Aa, May, pp [34] A. A. A. Rawan an Y. A. R. I. Mohame, Analy an atempeane-bae tablzaton o oltage-oure-reter loa n gr-onnete an olate mrogr applaton, IEEE Tran. Sutanable Energy, ol. 4, pp , Jul. 3. [35] M. Cepee an J. Sun, Impeane moelng an analy o gronnete oltage-oure onerter, IEEE Tran. Power Eletron., ol. 9, pp. 54 6, Mar. 4. [36] B. Wen, D. Boroyeh, P. Mattaell, R. Burgo, an Z. Shen, Impeane-bae analy o gr-ynhronzaton tablty or threephae parallele onerter, n Pro. 9th Annu. Appl. Power Eletron. Con. Expo., Mar. 4, pp [37] L. Zhang, L. arneor, an. P. Nee, Power-Synhronzaton Control o r-connete Voltage-Soure Conerter, IEEE Tran.Power Syt., ol. 5, pp. 89-8, May. [38] Q. C. Zhong, P. L. Nguyen, Z. Ma, an W. Sheng, Sel- Synhronze Synhronerter: Inerter Wthout a Deate Synhronzaton Unt, IEEE Tran. Power Eletron., ol. 9, pp , Feb. 4. [39] P. Mattaell, F. Polo, F. Dal Lago, an S. Saggn, Analy o Control-Delay Reuton or the Improement o UPS Voltage-Loop Banwth, IEEE Tran. In. Eletron., ol. 55, pp. 93-9, Aug. 8. [4] P. Rorguez, J. Pou, J. Berga, J. I. Canela, R. P. Burgo, an D. Boroyeh, Deouple Double Synhronou Reerene Frame or Power Conerter Control, IEEE Tran. Power Eletron., ol., pp , Mar. 7. [4] R. Teooreu, M. Lerre, an P. Rorguez, r Conerter or Photoolta an Wn Power Sytem. Pataway, NJ: Wley-IEEE Pre. [4] D. N. Zmoo, D.. olme, an.. Boe, Freueny-oman analy o three-phae lnear urrent regulator, IEEE Tran. In. Appl., ol. 37, no., pp. 6 6, Apr.. [43] B. Wen, D. Boroyeh, R. Burgo, an P. Mattaell, Input mpeane o oltage oure onerter wth tatonary rame lnear urrent regulator an phae-loke loop, n Pro. Energy Coner. Congr. Expo., Sept. 3, pp [44]. Fran, R. Burgo, D. Boroyeh, F. Wang, an. arm, An algorthm an mplementaton ytem or meaurng mpeane n the - oman, n Pro. Energy Coner. Congr. Expo., Sep., pp

14 本文献由 学霸图书馆 - 文献云下载 收集自网络, 仅供学习交流使用 学霸图书馆 ( 是一个 整合众多图书馆数据库资源, 提供一站式文献检索和下载服务 的 4 小时在线不限 IP 图书馆 图书馆致力于便利 促进学习与科研, 提供最强文献下载服务 图书馆导航 : 图书馆首页文献云下载图书馆入口外文数据库大全疑难文献辅助工具