Sun, Yao; Hou, Xiaochao; Yang, Jian; Han, Hua; Su, Mei; Zapata, Josep Maria Guerrero

Transcription

1 Dwnlae fm bn.aau.k n: Januay 4, 09 Aalbg Uniesitet New Pespecties n Dp Cntl in AC MicGi Sun, Ya; Hu, Xiacha; Yang, Jian; Han, Hua; Su, Mei; Zapata, Jsep Maia Guee Publishe in: I E E E Tansactins n Inustial Electnics DOI (link t publicatin fm Publishe): 0.09/TIE Publicatin ate: 07 Dcument Vesin Ealy esin, als knwn as pepint Link t publicatin fm Aalbg Uniesity Citatin f publishe esin (APA): Sun, Y., Hu, X., Yang, J., Han, H., Su, M., & Guee, J. M. (07). New Pespecties n Dp Cntl in AC MicGi. I E E E Tansactins n Inustial Electnics, 64(7), Geneal ights Cpyight an mal ights f the publicatins mae accessible in the public ptal ae etaine by the auths an/ the cpyight wnes an it is a cnitin f accessing publicatins that uses ecgnise an abie by the legal equiements assciate with these ights.? Uses may wnla an pint ne cpy f any publicatin fm the public ptal f the pupse f piate stuy eseach.? Yu may nt futhe istibute the mateial use it f any pfitmaking actiity cmmecial gain? Yu may feely istibute the URL ientifying the publicatin in the public ptal? Take wn plicy If yu beliee that this cument beaches cpyight please cntact us at bn@aub.aau.k piing etails, an we will eme access t the wk immeiately an inestigate yu claim.

2 New Pespecties n Dp Cntl in AC MicGi Ya Sun, Membe, IEEE, Xiacha Hu, Stuent Membe, IEEE, Jian Yang, Membe, IEEE, Hua Han, Mei Su, an Jsep M. Guee, Fellw, IEEE Abstact Vitual impeance, angle p an fequency p cntl play imptant les in maintaining system stability, an la shaing amng istibute geneats (DGs) in micgi. These appaches hae been eelpe int thee ttally inepenent cncepts, but pesent stng eleance. In this lette, thei similaities an iffeences ae significantly eeale. Sme new finings ae establishe as fllws: ) angle p cntl is intinsically a itual impeance meth; ) itual impeance meth can als be egae as a special fequency p cntl with a pwe eiatie feeback; 3) the cmbinatin f itual impeance meth an fequency p cntl is equialent t the pptinal eiatie (PD) type fequency p, which is intuce t enhance the pwe scillatin amping. As a whle, these analgus elatinships pie the new insight int the esign f these thee cntlles. Inex Tems Dp cntl, micgi, itual impeance. M I. INTRODUCTION ICROGRID is a futue ten f integating enewable geneatin units in istibutin enegy system, which geneally cnsists f aius inetebase istibute geneats (DGs). In islane micgi, the ltage/fequency stability an accuate la shaing ae tw imptant tasks. As thee minate slutins, itual impeance, angle p an fequency p cntl hae been sepaately eelpe f e a ecae. Vitual impeance meth is ealy intuce t shape esie utput impeances in uninteuptible pwe systems []. Then, it s wiely utilize t ecuple PQ an eliminate eactiepwe iffeences in micgi ue t the line impeance mismatch [][3]. The angle p cntl is eelpe t ensue ppe la shaing in a ual istibutin netwks with highly esistie lines [4]. As it iectly egulates the cnete utput ltage angle, a significant steaystate fequency p is aie. The cnentinal Pω fequency p cntl is fistly ppse t achiee pwe shaing in paallel inetes withut cmmunicatin [5]. The basic iea f this cntl manne is t mimic the behai f synchnus geneats [6]. In aitin, a lage alue f p gains impes pwe shaing accuacy, but inceases the eiatin f fequency/ltage fm thei nmal alues, esulting in a taeff [7]. Geneally, itual impeance meth, angle p an fequency p cntl ae utilize with iffeent pupses in micgi. But, smetimes they puce simila effects: ) bth itual impeance an angle p cntl ae pacticable t the highly esistie lines f micgi; ) the eactie pwe shaing can be ameliate by egulating itual impeance an QV p gain, espectiely. T explain these phenmena, the analgus elatinships amng them ae iscusse in this lette. Fistly, this stuy pies a new insight t teat itual impeance. In fact, itual impeance can be egae as a Pδ an QV feeback cntl, which is simila t angle p. Secnly, afte taking the eiatie fm f angle p, the equialent chaacte f itual impeance is inheently a eiatie type Pω fequency p an pptinal type Q V p cntl. Thily, by cmbining fequency p an itual impeance meth, a mifie PD type Pω fequency p cntl is btaine t impe tansient stability. II. COMPARING VIRTUAL IMPEDANCE WITH DROOP CONTROL A. Funamental Cncept f Fequency Dp The cnentinal fequency p cntl is expesse as fllws in the inuctie wies f AC micgi [5]. ω = ω mp () V = V nq whee ω an V ae the angula fequency an ltage amplitue efeences f a ltage suce inete (VSI), espectiely. ω an V epesent alues f ω an V at n la, an m an n ae p gains f Pω an QV, espectiely. P an Q ae the utput aeage actie an eactie pwe f VSI. VSI Output Vltage Refeence L f C f Equialent Vltage Suce V δ X Real Output Vltage Equialent Line Impeδance R L V l R δ l i Vg δ g S = P jq Fig.. Equialent utput ltage suce cnsieing itual impeance. B. Equialence f Vitual Impeance an Angle Dp The itual impeance meth is use t shape the utput impeance f a VSI, as shwn in Fig. []. It ps the utput ltage efeence pptinally t the utput cuent. = Zi (3) whee Z = R jx is the itual impeance. = V δ an i ae the utput ltage an cuent, espectiely. = V δ is the ltage efeence f ltagecuent ual clse lp. Accing t Fig., we hae V δ V δ V δ( ) P jq R jx () = (4) By substituting utput pwe f utput cuent in (3), pwe flwing thugh itual impeance yiels the assciate ltage p V an phase angle iffeence δ. Simplifying (4) yiels the fllwing equatins RP XQ V = V V (5) V XP RQ δ = δ δ VV (6)

3 whee V,an δ ae magnitue an angle f the efeence ltage, espectiely. V an δ ae magnitue an angle f the utput ltage, espectiely. F simplicity, V an V ae eplace by V because thei ltage magnitue lie in the acceptable ange f the nminal ltage eiatin. Mee, when the itual impeance is pue inuctance, (5)(6) ae gien by = mp (7) V = V nq whee X X m = ; n (9) = V V Fm (7) an (8), itual impeance is egae as a Pδ an QV feeback cntl. Especially, the fm f (7) is equialent t angle p in [4], an the fm f (8) is the cnentinal QV p cntl. Refeence [4] has pe that lage cefficients m an n can geatly impe the pwe shaing. Actually, it means that a lage itual inuctance is apte t ameliate line impeance mismatches. Thus, the equialence pies a physicalbase insight t tune the paametes f angle p cntl. C. Analgy between Angle Dp an Fequency Dp By taking the eiatie fm the bth sies f (7), the equialent chaacte f itual inuctance is gien by P ω = ω m (0) t whee is the angula fequency f ltage efeence. ω Usually, a pue eiatie tem f actie pwe is eplace by a highpass filte t suppess intefeence. Thus, the tansient p functin (0) takes the fm ω ms = ω P s ω c (8) () whee ωc is the cutff fequency f the highpass filte. Fm (), itual inuctance meth can be iewe as a special Pω fequency p cntl, whse p gain is a washut highpass filte [8]. In cntast t the static feeback f (), the washut filtebase actie pwe shaing esn t cause the fequency eiatin. In aitin, it shul be nte that the ppse washut filtebase eactie pwe shaing in [8] cannt impe the eactie pwe shaing. D. Impe Dp Cntl by Cmbining Vitual Impeance Meth an Fequency Dp Usually, itual impeance an fequency p cntl ae simultaneusly apte. Theefe, a mifie p cntl is pesente as fllws by substituting ()() int (8)(0) P ω = ω mp m () t V= V ( n n) Q (3) Clealy, the Pω p is change t a PD type fequency p cntl in (). Accing t (3), an equialent QV p gain n esulting fm itual impeance, is ae t impe eactie pwe shaing. III. SMALL SIGNAL ANALYSIS Smallsignal analysis f () is an effectie tl t eflect the pwe angle espnse. Accing t Fig., the utput actie pwe f VSI is expesse as [] VV g Vg P = cs( θ δl ) cs θ (4) Z Z whee Z anθ ae the magnitue an phase f the utput line impeance. Vg δ g is the cmmn bus ltage. δl is the pwe angle, expesse as δl = δ δg (5) Using the lineaize mel (4)(5), the cespning tansient mel aun the steaystate is fme. P = k P δ δ l ; δ l = δ δ g = ( ω ω g ) (6) s whee kpδ = P/ δlis a iffeential cefficient. In cnsieatin f the lwpass pwe filte, the utput chaacteistic f mifie p in () is gien by m ms ω = ω P (7) τ s Substituting (7) in (6) yiels ( τ s ) kp P = ( ω ω ) (8) g τ s ( mkp) s mkp F a typical secne mel f chaacteistic equatin in (8), the amping ati ζ is btaine mk P ζ = (9) mkpτ By tuning paametes, τ an m, the tansient espnse can be egulate apppiately withut cmpmising steay state. The functin f the eiatie feeback is t enhance the amping f pwe scillatin an ynamic stability.

4 TABLE I. The Analgus Relatinships Amng Vitual Impeance Meth, Angle Dp an Fequency Dp In AC Micgi Equialent feeback cntl Aantages Ptential awbacks Vitual impeance cntl (3) Angle p cntl (7) Washut filtebase meth () Fequency p Vitual impeance ()(3) PD type fequency p (3) Withut cmmunicatin Cnstant fequency egulatin Impe pwe shaing pefmance Nt affecte by the physical paametes Withut cmmunicatin Accuacy actie pwe shaing Satisfacty tansient pgess Rbust t system paametes Futheme, as itual inuctance nly pies ne egee f feem (DOF) in (9), m an n ae epenent. Theefe, tansient espnse an eactie pwe shaing cannt be sepaately egulate by itual inuctance. Altenatiely, the mifie p cntl in ()(3) shul be apte. On the whle, the analgus elatinships amng these cntl stategies ae pesente in Table I. IV. SIMULATION RESULTS T eify the unifie cntl law between the cnentinal p cntl with itual impeance an the mifie p cntl ()(3), the cntl scheme an simulatin mel with thee paallelcnnecte DGs ae built in Fig.. Fistly, the fequency p cntl ()() with gains 4 3 m = 3 0 an n = 0 is teste as shwn in Fig. 3(a.) (c.). Secnly, itual eactance X = 0.9 Ω is ae in Fig. 3(a.)(c.). Finally, accing t equialent elatinship f (9), 5 3 m = 0 an n = 3 0 ae apte,instea f itual impeance, whse esults ae shwn in Fig. 3(a.3)(c.3). Fig.3 eeals that fequency p plus itual impeance hae the equialent functins t the mifie p ()(3) in espects f imping the tansient espnse an eactie pwe shaing accuacy. V. CONCLUSION Afte cmpaing thee iffeent cncepts, itual impeance meth, angle p an fequency p cntl, the inheent elatinships ae establishe in this lette. Thee imptant One DOF Tw DOF One DOF Tw DOF Cannt guaantee accuacy pwe shaing Requie glbal psitining system (GPS) signals t synchnize DGs Maginally stable system, p bustness Slw ynamic espnse Fequency eiatin Requie elatiely high banwith f cntlle iewpints ae pinte ut: ) itual impeance, angle p an washut filtebase meth ae equialent each the; ) itual impeance is in cnsistency with the QV p gain t impe pwe shaing; 3) an impe fequency p with a pwe eiatie feeback is intuce t amp the pwe scillaty an impe the tansient espnse. VI. REFERENCES [] J. M. Guee, L. GaciaeVicuna, an J. Matas, "Output impeance esign f paallelcnnecte UPS inetes with wieless lashaing cntl," IEEE Tans. In. Electn., l.5, n.4, pp.635, Aug.005. [] J. He an Y. Li, "Analysis, esign, an implementatin f itual impeance f pwe electnics inteface istibute geneatin," IEEE Tans. In. Appl., l.47, n.6, pp , N. 0. [3] H. Mahm, D. Michaelsn, an J. Jiang, "Accuate eactie pwe shaing in an islane micgi using aaptie itual impeances," IEEE Tans. Pwe Electn., l.30, n.3, pp , Ma.05. [4] R. Majume, G. Lewich, A. Ghsh, S. Chakabati, an F. Zae, "Dp cntl f cneteinteface micsuces in ual istibute geneatin, " IEEE Tans. Pwe Del., l. 5, n. 4, pp , Oct. 00. [5] M. C, Chanka, D. M. Dian, an R. Aapa, "Cntl f paallel cnnecte inetes in stanalne ac supply systems," IEEE Tans. In. Appl., l.9, n. pp.3643, Jan.993. [6] S. D Ac an J. A. Suul, "Equialence f itual synchnus machines an fequencyps f cnetebase micgis, " IEEE Tans. Smat Gi, l. 5, n., pp , Jan. 04. [7] J. M. Guee, J. C. Vasquez, J. Matas, L. G. e Vicuna, an M. Castilla, "Hieachical cntl f pcntlle AC an DC micgis A geneal appach twa stanaizatin," IEEE Tans. In. Electn.,l. 58, n., pp. 587, Jan. 0. [8] M. Yazanian an A. MehiziSani,"Washut filtebase pwe shaing," IEEE Tans. Smat Gi, l.7, n., pp , Ma.06. P Q ms s Dp Cntl ()() n Pwe Cntl Lp Aeage Pwe Calculatin RefeenceVltage w V s Vltage Cntl Lp Xs s 50 Vitual Impeance DG Cuent Cntl Lp P W M VSI i f Output Vltage L f 3mH C i f 0mF Line Impeance 0.3 j0.44w Cmmn La g R line L line 0.4 j6w Bus Vltage R line3 L line3 j0.63w DG DG3 Fig.. Cntl schematic an test mel f simulatins in Matlab/simulink.

5 Actie Pwe Reactie Pwe (kva).5 Cnentinal Fequency Dp ()() Fequency Dp Vitual Reactance ()() (3) Mifie Fequency Dp ()(3) (a.) (c.) P P Q Q (b.) x 03 g g 5 3g 0 Pwe Angle (a) Actie Pwe (a.) 0 3 Reactie Pwe (kva).5 P P Q Q (b.) 0 x 03 g g g 4 (c.) Pwe Angle (a) Fig. 3. Cmpaisns f (a) actie pwe, (b) eactie pwe, an (c) pwe angle une thee meths. Actie Pwe (a.3) Reactie Pwe (kva).5 P P Q Q (b.3) 0 x g g 8 3g 6 4 (c.3) Pwe Angle (a)