Initialization of DFIG based wind generating system

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1 Intalzaton of DFIG bae wn geneatng ytem N.Amutha an B. Kalyan Kuma, membe, IEEE Electcal Engneeng epatment Inan Inttute of Technology Maa Chenna, Ina 636 Emal: Abtact Doubly fe nucton geneato (DFIG) ha to be popely ntalze fo pefomng ynamc analy. Even though DFIG ha nepenent eal an eactve powe contol, the eal an eactve powe output of DFIG epen both on the machne e paamete le wn pee an lp an netwo e paamete le g voltage etc. Th pape popoe a metho fo obtanng powe flow oluton ncopoatng DFIG bae wn geneaton wth only fou vaable a unnown vaable a compae to othe lteatue whee moe numbe of unnown vaable ae conee fo olvng the powe flow nclung the DFIG. The mulaton eult of the popoe metho fo IEEE 14-bu ytem ae peente. Inex Tem Powe flow, Doubly fe Inucton Geneato (DFIG), Slp, Newton-Raphon (NR) metho I. INTRODUCTION In ecent ay, becaue of nceae n powe eman, many enewable ouce ae nclue nto the g an uppotng the conventonal ouce of geneaton n mantanng the upplyeman ato. Among the enewable enegy ouce, wn enegy ytem upple 3% of the wol electcty eman [1]. Depenng upon the oto pee of nucton geneato, wn geneaton ytem ae categoze a fxe an vaable pee wn geneatng ytem. Inucton geneato bae vaable pee wn geneatng ytem ae futhe clafe bae on the metho of achevng the vaable pee uch a DFIG bae an full-cale convete bae. DFIG bae wn geneaton occupe the ft poton wth 5% of total wn powe geneaton []. In oe to pefom any ynamc analy, coect an accuate teay tate opeatng conton of any electcal ytem neceay. In cae of DFIG, the value of teay tate vaable uch a, magntue an angle of tato an oto voltage an magntue an angle of tato an oto cuent ae etemne fom powe flow. Eale lteatue [3]-[7] conee an nclue only the moel of fxe pee wn geneatng ytem nto the conventonal powe flow analy wheea the vaable pee wn geneatng ytem wee conee a PQ bu. Even though DFIG ha nepenent eal an eactve powe contol mla to conventonal ynchonou geneato, the eal an eactve powe epen on the wn pee, lp an the netwo conton. Hence, the DFIG moel cannot be conee mply a PQ o PV bu an alo cannot be neglecte n powe flow analy /14/$31. c 14 IEEE In [8], teay tate opeatng conton of DFIG wee obtane by coneng opt moel of wn tubne an teay tate moel of DFIG nto powe flow. In [8], all the vaable of DFIG uch a magntue an angle of tato voltage an cuent, oto voltage an cuent an lp wee taen a unnown vaable an the wn pee, eal an eactve powe wee conee a nown vaable fo olvng the powe flow nclung DFIG. Refeence [9] popoe a metho of ntalzng DFIG by coneng the bac to bac convete temnal a one ntenal bu an the powe flow oluton wa obtane. In efeence [8] an [9], moe vaable wee conee a unnown ue to whch the ze of loa flow Jacoban wa nceang whle ntalzng DFIG. In the peent wo, an attempt have been mae to ntalze the DFIG only ung fou vaable a unnown vaable. II. CONVENTIONAL NEWTON RAPHSON POWER FLOW METHOD Intalzaton an mpotant tatng tep whle ealng wth ynamc of a ytem. Incoect ntal value may lea to eo n tablty etmaton an ncoect ugment of atng of potecton equpment whch may lea to g collape ung emegency tuaton. Intalzaton of any ytem one ung loa flow tue [1]. Loa flow an optmzaton poblem, whee the netwo paamete uch a voltage an angle houl be foun out, o that all the netwo contant ae atfe. It etemne the vaable of the powe ytem netwo uch a voltage magntue an angle, eal powe necton an eactve powe necton by mnmzng the ffeence between the pecfe eal an eactve powe an thoe fom calculate eal an eactve powe necton at all bue n the netwo. In oe to o loa flow analy, out of voltage magntue, angle, eal powe necton an eactve powe necton, two vaable mut be nown an ae pecfe at each bu. Bae on the pecfe vaable at the bu, bue ae categoze a thee type: PQ bu, whee eal powe an eactve powe necton at bu ae nown an the voltage magntue an angle ae the unnown whch have to be etemne fom loa flow analy; PV bu, whee the the eal powe necton an voltage magntue at bu ae nown an the eactve powe an voltage angle ae unnown; Slac bu, whee the voltage magntue an angle at bu ae nown an the eal powe an eactve powe necton ae unnown.

2 The complex powe necte at an th bu gven a, Ŝ P Q V Ī ; 1,...,n bue (1) Ī Ŷ V () 1 Whee, S, P, Q ae the appaent, eal an eactve powe necte at the th bu. V an Ī ae the complex bu voltage an cuent necte at th bu. Ŷ the th ow, th column element of the ytem amttance matx. The eal an eactve powe necte can be expee n tem of netwo bu voltage, angle an amttance a, P Y V V co(θ + θ θ ) (3) 1 Q Y V V n(θ + θ θ ) (4) 1 The eal powe necte pecfe at all the bue except at the lac bu. Hence, the pecfe eal powe necte can be wtten a P pec P G P L...,n bue (5) Whee, P G the eal powe geneate at bu an P L eal powe eman o loa at bu. n the numbe of bue. Smlaly, the eactve powe pecfe at all the loa bue an gven a, Q pec Q G Q L m +1...,n bue (6) Whee, m the numbe of geneato bue exclung lac. Snce at loa bu Q G zeo, Q pec Q G Q L Q L m +1...,n bue (7) The man poblem of loa flow analy that the voltage an angle of the netwo bue houl be choen uch that ΔP m ΔQ m P pec Q pec P cal...,n bue (8) Q cal m +1...,n bue (9) Whee, P cal, Q cal ae the value compute fom (3) an (4) wth the choen value of voltage an angle. Becaue of fat convegng natue an accuacy, Newton-Raphon (NR) metho wely ue to olve the above equaton. NR metho olve the non-lnea algebac equaton teatvely by computng the ft evatve of Taylo ee expanon of (8) an (9). At th teaton, [ Δθ ΔV [ θ V ] ] +1 J 1 [ ] θ V [ ] ΔP m + ΔQ m [ ] Δθ ΔV (1) (11) Th teatve poce epeate tll [ ] nom ΔP m ΔQ m ɛ (1) Whee, ɛ the expecte eo n mmatch an J the acoban matx fome by the ft evatve of ytem vaable. III. STEADY STATE MODELING OF DFIG Upon neglectng the tanent n tato flux lnage, the oubly fe nucton geneato moele a a ffth oe ynamc ytem n ynchonou efeence fame [11] an ecbe by the followng algebac ffeental equaton, v q q x + E q (13) v + x q + E (14) E q T e 1 ω [E q q + E ] (15) 1 t ω b ω T [E q +(x x ) ]+E + x m v x (16) E 1 t ω b ω T [E (x x ) q ] E q x m v q x (17) ω 1 t ω b ω H [T e T m ] (18) Whee, E q x m x ω ψ, x x x m x, E x m x ω ψ q, T x. Snce -ax aume to lag behn the q-ax by 9, the phao fom of voltage an cuent equaton ae gven by, Ê E q + E (19) ˆV V q + V () Î q + (1) ˆV V q + V () In teay tate [1], the evatve tem n (16)-(18) wll become zeo. Thu, afte eaangng Ê (x x )Î xm x ˆV (1 + T ) (3) Î (1 + T ) ˆV + xm x ˆV ( x T + x ) (4) ˆV ( + x )Î + Ê (5)

3 IV. MODIFIED NEWTON RAPHSON POWER FLOW METHOD INCLUDING DFIG In conventonal loa flow, the geneato bu ha ynchonou geneato connecte to t, whee eal powe an voltage magntue ae contolle paamete an hence, pecfe. Moeove, the voltage magntue of ynchonou geneato can be pecfe nepenent of netwo conton a the excte of ynchonou geneato mantan a contant temnal voltage magntue. Hence, t eay to calculate the ntal value of ynchonou geneato. Wheea n cae of DFIG, even though DFIG ha nepenent eal an eactve powe contol mla to conventonal ynchonou geneato, the eal an eactve powe epen on the wn pee, lp an the netwo conton. Hence, t neceay to ncopoate teay tate moel of DFIG nto the conventonal loa flow analy. The eal an eactve powe output of DFIG epen on fve vaable uch a lp,, magntue an angle of tato voltage, V θ an magntue an angle of oto voltage, V θ.in the peent wo, DFIG conee to be n MPPT opeatng moe. Hence, the mechancal powe an lp ae nown an ae taen a pecfe vaable. Snce, DFIG ha fou unnown vaable, that V,θ V,θ, fou equaton ae neee to olve the teay tate equaton of DFIG. Two of the equaton ae gven by the eal an eactve powe balance equaton at DFIG temnal. DFIG expecte to be opeate at pecfc powe facto. Hence, the th equaton obtane fom the powe facto angle, φ. The fouth equaton obtane fom the mechancal powe equaton, whch nothng but the eal powe output ae along wth tato an oto loe. In th wo, only oto powe lo, P l, conee a t aume that the tato etance neglgble. P DFIG P tato + P oto (6) Q DFIG Q tato + Q oto (7) F 1 DFIG Q DFIG co(φ) P DFIG n(φ) (8) P m P tato (1 )+P l (9) The eal powe flow n the tato an oto of DFIG then gven by, P tato P 1 + P eal( ˆV Î ) (3) P x m x ˆV ˆV (x T n(θ )+x co(θ θ )) x P 1 P x m x ˆV ˆV ( x T n(θ )+x co(θ θ )) (x + x T ) Q 1 Q xm x ˆV ˆV (x T co(θ ) x n(θ )) T x x Q 1 Q xm x ˆV ˆV (x T co(θ )+x n(θ )) P l Roto lo al + bl + cl ˆV V q + V θ θ θ al T (x x ) x m bl x ˆV cl al bl co(θ ) Snce, DFIG epen both on t vaable an netwo conton, the P G an Q G n equaton (5) an (6) ae eplace by P DFIG an Q DFIG of DFIG. Thu, the fou equaton at the bu whee DFIG connecte ae gven a, Whee, Q tato Q 1 + Q mag( ˆV Î ) (31) P oto P 1 + P eal( ˆV Î ) (3) Q oto Q 1 + Q mag( ˆV Î ) (33) ( x T ) + x (x x )T P 1 ΔP m ΔQ m (P DFIG P L ) P cal (34) (Q DFIG Q L ) Q cal (35) ΔF 1 m Q DFIG co(φ) P DFIG n(φ) (36) ΔF m P pec m P m (37) It aume that out of n numbe of bue, m numbe of bue ae conventonal ynchonou geneato an t numbe of bue ae nucton geneato bue. The mmatch equaton to be olve then gven by the followng equaton,

4 ΔP m ΔP m ΔQ m ΔQ m ΔF 1 m ΔF m J1 J3 Δθ Δθ J Δ V Δ V Δθ J4 Δ V (38) whee,...,n bue; m +1...,(n t) bue; (n t +1)...,n bue; The acoban matce nclung DFIG bu gven by, J1 θ θ θ θ θ θ θ P θ θ J Q θ V V V V P θ P V Q θ Q V V V P V V V Q V θ θ (x + x T ) θ (x + x T ) (x + x T ) θ θ θ θ (x x )T P DFIG θ co(φ) n(φ) co(φ) n(φ) θ θ P l (al + cl) P l (bl + cl) co(φ) θ n(φ) J3 F1 θ F θ F1 V F V J4 F1 θ F θ F1 V F V P l θ ( al bl n(θ )) P l θ P l θ V. SIMULATION RESULTS Whee, (x x )T + P DFIG (x x )T + P DFIG In oe to valate the popoe metho, IEEE-14 bu ytem [13], the ngle lne agam of whch hown n Fg. 1, conee fo powe flow tue. The bae value of IEEE-14 bu ytem ae taen a 1 MVA an 13.8 V. It aume that twenty x an thteen numbe of vaable pee DFIG bae wn geneaton ytem ae connecte at Bu-5 an Bu-1, epectvely, a hown n Fg.,1. The paamete of oubly fe nucton geneato DFIG-1 an DFIG- connecte at Bu-5 an Bu-1, epectvely ae gven n Table I.

5 Fg. 1. Smplfe agam of IEEE-14 bu ytem TABLE I INDUCTION GENERATOR PARAMETERS Man Paamete (n pe unt) DFIG 1 DFIG Rate powe MW MW Rate voltage 69V 69V No. of pole 4 4 Rate fequency 5 Hz 5 Hz Stato etance.48 pu.11 pu Roto etance.18 pu.8 pu Stato leaage eactance.75 pu.74 pu Roto leaage eactance.1 pu.1761 pu Magnetzng eactance 3.8 pu.766 pu The DFIG-1 at bu 5, aume to be opeatng at a wn pee of 1 m/ an the mechancal powe an lp, coeponng to the MPPT of 1 m/, ae gven by.57 pu an.4, epectvely. The DFIG-1 aume to be opeatng at laggng powe facto of.95. Wheea, DFIG- at bu 1, aume to be opeatng at a wn pee of 8 m/ an a leang powe facto of.95. The mechancal powe an lp, coeponng to the MPPT of 8 m/, ae gven by.67 pu an.17, epectvely. TABLE II POWER FLOW RESULTS Bu Voltage(pu) P (pu) Q(pu) Roto Voltage(pu) The powe flow mulaton eult ae gven n Table II. Fom the Table II, t can be een that, at bu 5, the eal powe necte.49 pu an eactve powe abobe.7 pu. Bu 5 have a local loa wth eal powe eman of.76 pu an eactve powe eman of.16 pu. Thu, the DFIG-1 elveng eal powe of.568 pu an abobng eactve powe of.1867 pu. The eactve powe beng abobe a DFIG-1 elveng the ate powe an alo opeatng at laggng powe facto. The oto voltage.484 at an angle of Fom the Table II, t can be een that, at bu 1, the eal powe abobe.4 pu an eactve powe necte.364 pu. Bu 1 have a local loa wth eal powe eman of.9 pu an eactve powe eman of.58 pu. Thu, the DFIG- elveng eal powe of.658 pu an nectng eactve powe of.16 pu. The oto voltage.159 at an angle of The oto loe of DFIG-1 an DFIG- ae.4 pu an.1 pu, epectvely. Thu, the teay tate opeatng conton of DFIG ae thu obtane ung only fou vaable. VI. CONCLUSION The peent wo popoe a metho fo ntalzng DFIG bae wn geneaton ytem connecte to the g. The pape mofe the conventonal Newton-Raphon powe flow algothm to nclue the DFIG. The powe flow fo IEEE 14-bu ytem wa pefome nclung the DFIG an the eult ae peente. The popoe metho tae only fou vaable a unnown vaable when compae to metho popoe n othe lteatue whee about even o eght vaable ae taen a unnown vaable fo olvng the teay tate opeatng conton of DFIG. REFERENCES [1] [Onlne]. Avalable: [] M. Khaaou an M. Elleuch, Compaon between optlp an fxe pee wn enegy conveon ytem, n 5th Intenatonal Mult- Confeence on Sytem, Sgnal an Devce, Jul. 8, pp [3] Stana loa moel fo powe flow an ynamc pefomance mulaton, IEEE Tanacton on Powe Sytem, vol. 1, no. 3, pp , Aug [4] A. Feoo an J. Ca, Moelng of wn fam n the loa flow analy, IEEE Tanacton on Powe Sytem, vol. 15, no. 1, pp , Feb.. [5] K. Dvya an P. N. Rao, Moel fo wn tubne geneatng ytem an the applcaton n loa flow tue, Electc Powe Sytem Reeach, vol. 76, no. 6, pp , 6. [6] L. M. Cato, C. R. Fuete-Equvel, an J. Tova-Henaez, A unfe appoach fo the oluton of powe flow n electc powe ytem nclung wn fam, Electc Powe Sytem Reeach, vol. 81, no. 1, pp , 11. [7] U. Emnoglu, A new moel fo wn tubne ytem, Electc Powe Component an Sytem, vol. 37, no. 1, pp , 9. [8] J. F. M. Pan an A. E. F. Loenzo, Calculatng teay-tate opeatng conton fo oubly-fe nucton geneato wn tubne, IEEE Tanacton on Powe Sytem, vol. 5, no., pp. 9 98, May 1. [9] S. L, Powe flow moelng to oubly-fe nucton geneato (DFIG) une powe egulaton, IEEE Tanacton on Powe Sytem, vol. 8, no. 3, pp , Aug. 13. [1] I. J. Nagath an D. P. Kotha, Moen Powe Sytem Analy. McGaw-Hll, [11] P. Kunu, Powe ytem tablty an contol. McGaw-Hll New Yo, 1994, vol [1] M. K. Pal, Lectue note on powe ytem tablty, Tech. Rep. [13] F. Mlano, Powe Sytem Moellng an Scptng. Spnge, 1.