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2 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability Libao Shi 1, Zheng u 1, Chen Wang 1, Liangzhong Yao and Yixin Ni 1 1 Gaduate School at Shenzhen, Tinghua Univeity Shenzhen , Altom Gid Reeach & Technology Cente, Staffod, ST17 4L, 1 China United Kingdom 8 1. Intoduction In ecent yea, the inceaing concen to envionmental iue demand the each fo moe utainable electical ouce. Wind enegy can be aid to be one of the mot pominent enewable enegy ouce in yea to come (Ackemann, 005). And wind powe i inceaingly conideed a not only a mean to educe the CO emiion geneated by taditional foil fuel fied utilitie but alo a pomiing economic altenative in aea with appopiate wind peed. Albeit wind enegy cuently upplie only a faction of the total powe demand elative to the foil fuel fied baed conventional enegy ouce in mot pat of the wold, tatitical data how that in Nothen Gemany, Denmak o on the Swedih Iland of Gotland, wind enegy upplie a ignificant amount of the total enegy demand. Specially it hould be pointed out that in the futue, many countie aound the wold ae likely to expeience imila penetation level. Natually, in the technical point of view, powe ytem enginee have to confont a eie of challenge when wind powe i integated with the exiting powe ytem. One of impotant iue enginee have to face i the impact of wind powe penetation on an exiting inteconnected lage-cale powe ytem dynamic behaviou, epecially on the powe ytem mall ignal tability. It i known that the dynamic behavio of a powe ytem i detemined mainly by the geneato. So fa, nealy all tudie on the dynamic behavio of the gid-connected geneato unde vaiou cicumtance have been dominated by the conventional ynchonou geneato wold, and much of what i to be known i known. Intead, the intoduction of wind tubine equipped with diffeent type of geneato, uch a doublyfed induction geneato (DFIG), will affect the dynamic behaviou of the powe ytem in a way that might be diffeent fom the dominated ynchonou geneato due to the intemittent and fluctuant chaacteitic of wind powe in natue. Theefoe, it i neceay and impeative to tudy the impact of intemittent wind geneation on powe ytem mall ignal tability. It hould be noticed that mot publihed liteatue ae baed on deteminitic analyi which aume that a pecific opeating ituation i exactly known without conideing and eponding to the uncetaintie of powe ytem behavio. Thi ignificant dawback of deteminitic tability analyi motivate the eeach of pobabilitic tability analyi in which the uncetainty and andomne of powe ytem can be fully undetood. The

3 16 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct pobabilitic tability analyi method can be divided into two type: the analytical method, uch a point etimate method (Wang et al., 001); and the imulation method, uch a Monte Calo Simulation (Rueda et al., 009). And mot publihed liteatue elated to pobabilitic tability analyi ae baed on the uncetainty of taditional geneato with implified pobability ditibution. With inceaing penetation level of wind geneation, and conideing that the uncetainty i the mot ignificant chaacteitic of wind geneation, a moe compehenive pobabilitic tability eeach that conideing the uncetaintie and intemittence of wind powe hould be conducted to ae the influence of wind geneation on the powe ytem tability fom the viewpoint of pobability. Geneally peaking, the conideed wind geneation intemittence i caued by the intemittent natue of wind ouce, i.e. the wind peed. Coepondingly, the intoduction of the pobability ditibution of the wind peed i the key of olution. In ou wok, the wellknown Weibull pobability denity function fo decibing wind peed uncetainty i employed. In thi chapte, accoding to the Weibull ditibution of wind peed, the Monte Calo imulation technique baed pobabilitic mall ignal tability analyi i applied to olve the pobability ditibution of wind fam powe output and the eigenvalue of the tate matix.. Wind tubine model In modelling tubine oto, thee ae a lot of diffeent way to epeent the wind tubine. Function appoximation i a way of obtaining a elatively accuate epeentation of a wind tubine. It ue only a few paamete a input data to the tubine model. The diffeent mathematical model may be moe o le complex, and they may involve vey diffeent mathematical appoache, but they all geneate cuve with the ame fundamental hape a thoe of a phyical wind tubine. In geneal, the function appoximation epeenting the elation between wind peed and mechanical powe extacted fom the wind given in Equation (1) (Ackemann, 005) ae widely ued in modeling wind tubine. P m 0 V V 0.5 ρ A C (, ) V V < V V = p Vated < Vw < Vcut off 0 Vw Vcut off w cut in 3 wt p β λ w cut in w ated whee P m i the powe extacted fom the wind; i the ai denity; C p i the pefomance coefficient; λ i the tip-peed atio (v t /v w ), the atio between blade tip peed, v t (m/), and wind peed at hub height upteam of the oto, v w (m/); A wt = R i the aea coveed by the wind tubine oto, R i the adiu of the oto; V w denote the wind peed; and β i the blade pitch angle; V cut-in and V cut-offt ae the cut-in and cut-off wind peed of wind tubine; V ated i the wind peed at which the mechanical powe output will be the ated powe. When V w i highe than V ated and lowe than V cut-off, with a pitch angle contol ytem, the mechanical powe output of wind tubine will keep contant a the ated powe. It i known that the pefomance coefficient C p i not a contant. Uually the majoity of wind tubine manufactue upply the owne with a C p cuve. The cuve expee C p a a function of the tubine tip-peed atio λ. Howeve, fo the pupoe of powe ytem (1)

4 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 163 tability analyi of lage powe ytem, numeou eeache have hown that C p can be aumed contant. Fig. 1 (Akhmatov, 00) give the cuve of pefomance coefficient C p with changing of otational peed of wind tubine at diffeent wind peed condition (βi fixed). Accoding to Fig. 1, by adjuting the otational peed of the oto to it optimized value ω m-opt, the optimal pefomance coefficient C pmax can be eached. Fig. 1. Cuve of C p with changing of ω m at diffeent wind peed In thi chapte, we aume that fo any wind peed at the ange of V cut-in < V w V ated, the otational peed of oto can be contolled to it optimized value, theefoe the C pmax can be kept contant. 3. Mathematical model of DFIG The configuation of a DFIG, with coeponding tatic convete and contolle i given in Fig.1. Two convet ae connected between the oto and gid, following a back to back cheme with a dc intemediate link. Fig. give the efeence fame, whee a, b and c indicate tato phae a, b and c winding axe; A, B and C indicate oto phae A, B and C winding axe, epectively; x-y i the ynchonou otation coodinate ytem in the gid ide; θ i the angle between q axi and x axi. Applying Pak tanfomation, the voltage equation of a DFIG in the d-q coodinate ytem otating at the ynchonou peed ω, in accodance with geneato convention, which mean that the tato and oto cuent ae poitive when flowing towad the netwok, and eal and eactive powe ae poitive when fed into gid, can be deducted a follow in a pe unit ytem. U 1 dψ d = R I ψ + () ω dt d d q

5 164 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct G I P U P g +jq g U t I P P g,q g contolle Fig.. Schematic diagam of DFIG with convete and contolle Fig. 3. Refeence coodinate fo DFIG U 1 dψ q = R I + ψ + (3) ω dt q q d 1 dψ d Ud = RId ψ q + (4) ω dt 1 dψ q Uq = RIq + ψ d + (5) ω dt

6 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 165 ψ = I I (6) d d m d ψ = I I (7) q q m q ψ = I I (8) d d m d ψ = I I (9) q q m q P = P + P = ( U I + U I ) + ( U I + U I ) (10) g d d q q d d q q Q = Q + Q = ( U I U I ) + ( U I U I ) (11) g q d d q q d d q d H Te Tm dt = (1) Whee U, I, Ψ denote the voltage, cuent and flux linkage; P and Q denote the eal and eactive powe output of wind geneato, epectively; T m and T e denote the mechanical and electomagnetic toque of wind geneato, epectively; R and denote eitance and eactance, epectively; the ubcipt and denote the tato and oto winding, epectively; the ubcipt g mean geneato; H i the inetia contant, and t tand fo time; i the lip of peed. The eactance and can be calculated in following equation. = + (13) σ m = + (14) σ m Whee σ and σ ae the leakage eactance of tato and oto winding, epectively; m i the mutual eactance between tato and oto. The afoementioned equation decibe the electical dynamic pefomance of a wind tubine, namely, the aynchonou machine. Howeve, thee equation ae not uitable fo mall ignal analyi diectly. It i neceay and impeative to deduce the implified and pactical model. The following aumption ae peented to model the DFIG. a. Magnetic atuation phenomenon i not conideed duing modelling; b. Fo the wind tubine equipped with DFIG, all otating mae ae epeented by one element, which mean that a o-called lumped-ma o one-ma epeentation i ued; dψ dψ d q c. The tato tanient and tato eitance ae negligible, i.e. = 0, = 0, and dt dt R =0 in Eq () and (3). Futhemoe, the tato flux-oiented contol tategy (Tapia et al., 006) i adopted in thi wok, which make the tato flux ψ line in accodance with d-axi, a depicted in Fig.3., i.e. ψ = ψ (15) d ψ q = 0 (16)

7 166 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct Then the tato voltage equation can be ewitten a U U = 0 (17) d = ψ = U (18) q t Whee U t i the teminal voltage; Fom Fig. 3, the vecto of tato voltage U =U t i alway align with q axi with the tato flux-oiented contol tategy. And accoding to the tato flux linkage equation (6) and (7), the tato cuent I d and I q can be epeented a the function of oto cuent and teminal voltage U t, i.e. 1 Id = ( Ut + mid ) (19) Subtituting equation (8) and (9) in equation (4) and (5), we find I q 1 = miq (0) di U = R I + I (1) d d d q ω dt di U = R I I + () q m q q d ω dt ψ Whee = - m /. Conide that the gid-ide convete of DFIG alway opeate at unity powe facto, i.e. Q = 0, the eactive powe Q g i equal to the tato eactive powe Q, i.e. Q g =Q. In the teady tate analyi, in accodance with the expeion of tato powe and the oto powe, it can be poved that P =-P, and P g =P /(1-). Accodingly, the eal and eactive powe equation and the toque equation can be ewitten a Ut P = P /(1 ) = I (1 ) g m q (3) Ut Qg = Q = ( Ut + mid) (4) d m H = Te Tm = ( ψdiq + ψqid) Tm= UtIq Tm (5) dt Finally, the equation (17-18), (1-), (3-5) contitute the 3 d ode implified pactical DFIG model. 4. Mathematical model of DFIG Convete A hown in Fig., the model of DFIG fequency convete ytem conit of oto-ide convete, gid-ide convete, the dc link and the coeponding convete contol. In thi

8 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 167 chapte, it i aumed that the gid-ide convete i ideal and the dc link voltage between the convete i contant duing analyi. Thi decouple the gid-ide convete fom the oto-ide convete. The oto-ide convete i aumed to be a voltage-contolled cuent ouce, and the tato flux-oiented contol tategy i employed to implement the decoupled contol of the eal and eactive powe output of DFIG. The oveall convete contol ytem conit of two cacaded contol loop, i.e. the inne contol and the oute contol. The inne contol loop implement the oto cuent contol, and the oute contol loop implement the powe contol (Tapia et al., 006). In ode to implement the decoupled contol of the eal and eactive powe output of DFIG, two new vaiable, U ˆ d, U ˆ q ae intoduced which ae defined a: ˆ d d q U = U I (6) ˆ m U = U + I ψ (7) q q d The newly intoduced vaiable can fully make the dynamic of d and q axe decoupling. Accodingly, the oto voltage equation can be ewitten a di = (8) ˆ d d RId ω dt U Uˆ q diq = RIq (9) ω dt In thi chapte, two pecial PI contolle ae deigned to implement the decoupled contol of the eal and eactive powe output of DFIG. The block diagam of oto-ide convete including the inne and oute contol loop expeed in d and q axe ae given in Fig.4 and Fig.5. In the oto cuent contol loop, T = /R, T i the time contant of oto cicuit; I def, I qef ae the oto cuent efeence in d and q axe, epectively; K and T ae the contol paamete of PI contolle. In the powe contol loop, P ef, Q ef ae the eal and eactive powe efeence; K 1, T 1 ae the contol paamete of PI contolle. It hould be noted that the pecific value of K 1, T 1, K and T can be detemined though pole placement method (Tapia et al., 006). In accodance with Fig. 4, the coeponding tato eal powe contol model can be decibed a diqef dp dp ef T1 K1T1( ) = K1( P Pef ) (30) dt dt dt duˆ q diq diqef T + KT( ) = K( Iq Iqef ) (31) dt dt dt T di ω dt q Uˆ q = Iq (3) R

9 168 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct P ef K 1 T 1 I qef K T Û q 1/ R 1+ T /ω I q P K K 1 U t m Fig. 4. Block diagam of eal powe contol ytem in oto-ide convete Q ef Q K 1 T 1 I def K T Û d 1/ R 1+ T /ω I d K1 K U t / m Fig. 5. Block diagam of eactive powe contol loop in oto-ide convete P U t ψ = miq (33) Similaly, the coeponding tato eactive powe contol model can be decibed a didef dq dq ef T1 K1T1( ) = K1( Q Qef ) dt dt dt (34) duˆ d di di d def T + KT( ) = K( Id Idef ) dt dt dt (35) T ˆ did Ud = Id (36) ω dt R

10 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 169 Q ψ = ( ψ + I ) (37) m d So fa, baed on the tato flux-oiented contol tategy, and conideing the decoupled contol of the eal and eactive powe output of DFIG, the whole educed pactical electomechanical tanient DFIG model conit of the following 7 th ode model U = 0 (38) U d q = U (39) t d = (40) m H U t I q T m dt di dt ω ω = I ˆ d U T d d (41) di U ( ) ( ) def m ω 1 m ω ˆ K1 t = KU 1 q Id + KU 1 q Ud + Qef dt T T 1 T1 (4) duˆ 1 ω K ω ˆ dt T T d = K( ) Id Idef K Ud T di dt ω ω = I ˆ q U T q q (43) (44) di ω 1 ω ˆ K qef m m 1 = KU 1 q ( ) Iq + KU 1 q Uq Pef dt T T 1 T1 duˆ 1 ω K ω ˆ dt T T q = K( ) Iq Iqef K Uq T (45) (46) 5. Model of wind fam of DFIG type In thi chapte, a imple aggegated model of lage wind fam in the mall ignal tability analyi i employed. We aume that cuently the opeating condition of all wind geneato in a wind fam ae ame, and the wind fam i conideed to be fomed with a numbe of wind geneato jointed in paallel. Theefoe, the wind fam can be educed to a ingle machine equivalent. Fo a wind fam conited of N wind geneato, the value of tato and oto voltage ae ame a the value of ingle machine. The tato and oto cuent ae N time lage than the ingle machine. The tato and oto eitance and eactance a well a K ae 1/N lage than the ingle machine. The emaining contol paamete ae ame a the ingle machine.

11 170 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct 6. Small ignal tability analyi incopoating wind fam of DFIG type Small ignal tability i the ability of the powe ytem to maintain ynchonim when ubjected to mall ditubance (Kundu, 1994). In thi context, a ditubance i conideed to be mall if the equation that decibe the eulting epone of the ytem may be lineaized fo the pupoe of analyi. In ode to analyze the effect of a ditubance on a linea ytem, we can obeve it eigenvalue. Although powe ytem i nonlinea ytem, it can be lineaized aound a table opeating point, which can give a cloe appoximation to the ytem to be tudied. The behavio of a dynamic autonomou powe ytem can be modelled by a et of n fit ode nonlinea odinay diffeential equation (ODE) decibed a follow (Kundu, 1994) dx =f(x,u) (47) dt 0=g(x,u) (48) whee x i the tate vecto; u i the vecto of input to the ytem; g i a vecto of nonlinea function elating tate and input vaiable to output vaiable. The equilibium point of ytem ae thoe point in which all the deivative x 1, x,..., x n ae imultaneouly zeo. The ytem i accodingly at et ince all the vaiable ae contant and unvaying with time. The equilibium point mut theefoe atify the following equation dx 0 =f(x 0,u 0 )=0 (49) dt 0=g(x 0,u 0) (50) Whee (x 0, u 0 ) ae conideed a an equilibium point, which coepond to a baic opeating condition of powe ytem. Coeponding to a mall deviation aound the equilibium point, i.e. x=x 0 +Δx (51) u=u 0 +Δu (5) The function f(x,u) and g(x,u) can be expeed in tem of Taylo eie expanion dx dt 0 dδx + =f(x 0,u 0)+AΔx+BΔu+O( Δx,Δu ) (53) dt u +Δu=g(x, u ) +CΔx+DΔu+O( Δx, Δu ) (54) With tem involving econd and highe ode powe in Eq(53-54) neglected, we have Δx=AΔx+BΔu (55) 0=CΔx+DΔu (56)

12 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 171 Whee A, B, C and D ae called a Jacobian matice epeented in the following f(x, u) A= x f(x, u) B = u g(x,u) C = x g(x,u) D = u x 0,u0 x 0,u0 x 0,u0 x 0,u0 (57) (58) (59) (60) If matix D i noningula, finally we have dδx =(A-BD -1 C)Δx=ΛΔx (61) dt The eigenvalue and eigenvecto of the tate matix can eflect the tability of the ytem at the opeating point and the chaacteitic of the ocillation (Kundu, 1994). Accoding to the etablihed 7 th ode DFIG model decibed in Section 4, the tate vaiable ae I d, I def, Û d, Û q, I q, I qef and, epectively, and the algebaic vaiable ae U d, U q, I d, I q, epectively. In mall ignal tability analyi, when the wind fam i integated into the powe gid, thee algebaic vaiable mentioned above in d-q coodinate ytem need to be tanfomed to the ynchonou otating coodinate ytem (x-y coodinate ytem), i.e. thee algebaic vaiable will be ubject to U dq = T U (6) xy I dq = Τ I (63) xy inθ coθ Whee T i tanfomation matix, Τ = coθ inθ ; θ denote the phae angle of geneato teminal voltage U t, which can be obtained by the teady tate powe flow olution. Accodingly, we can obtain Whee A WF, B WF, C WF and D WF ae expeed a follow dδ x = A Δ x+ Δ U WF B WF xy (64) dt Δ I = C Δx+ D ΔU (65) xy WF WF xy

13 17 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct A WF ΔI ΔI ΔUˆ ΔI ΔI ΔUˆ Δ d def d q qef q ω ω T m ω 1 m ω KU 1 t ( ) KU 1 t T T 1 ω 1 K ω K( ) K T T T T = ω ω T 1 m m 1 t ( ) KU 1 t T T 1 KU ω 1 K K( ) T T T ω m Ut H ω ω K T (66) U d U q 0 0 m ω 1 ˆ m ω K1U t 0 KI 1 d ( ) + KU 1 d T T 1 T B WF = T (67) m ω 1 0 ˆ m ω KI 1 q ( ) + KU 1 q T T m 0 Iq m CWF = T (68) m DWF = T T (69) Hee, each geneato in a powe ytem to be tudied can be epeented a the afoementioned fom in accodance with the dynamic model of itelf. Fo a powe ytem

14 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 173 coniting of n geneato (including wind fam) with m tate vaiable, by eliminating ΔI xy, we can get the Jacobian matice of the whole ytem A, B, C and D (Wang et al., 008)a given in following [ ] AA = (70) G m m [ 0] BB = (71) G m N CG C = 0 (7) N m Whee YGG DG YGL D = Y Y LG LL N N (73) A B C G G G A1 = A WF An B1 = B WF Bn C1 = C WF Cn m m m n n m (74) (75) (76) D G D1 = D WF Dn n n Whee, Y GG and Y LL ae the elf-admittance matice of geneato node and non-geneato node; Y LG and Y GL ae the mutual admittance matice between them. (77)

15 174 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct Finally, the coeponding tate matix can be given in following: -1 Λ = A-BD C (78) 7. Pobabilitic mall ignal tability analyi with wind fam 7.1 Pinciple of Monte Calo imulation Monte Calo method i a cla of computational algoithm that ely on epeated andom ampling to compute thei eult. In uncetainty analyi, the elationhip between the dependent vaiable and independent vaiable can be decibed a Zh() = (79) whee = [x 1, x,, x m ] i the vecto of the independent vaiable and Z=[z 1,z,,z n ] i the vecto of the dependent vaiable. h=[h 1 (), h (),, h m ()] epeent the function elationhip between input vaiable and output vaiable. In geneal, if h i vey complex, it i had to olve the pobability ditibution of Z applying analytic way. In thi ituation, the Monte Calo method ae employed to calculate the dicete fequency ditibution which appoximately imulate it pobability ditibution. The eence of the uncetainty analyi i to etimate the tatitic popetie of Z baed on the tatitic popetie of and the function h (Fihman, 1996). The mot impotant tatitic popety in uncetainty analyi i the pobability ditibution, which i alway decibed by the pobability denity function (PDF). Pobability denity function decibe the pobability denity of a vaiable at a given value (Fihman, 1996). Theefoe, the main objective of uncetainty analyi i to etimate the PDF of the dependent vaiable on the bai of the PDF of independent vaiable and thei elationhip function. Monte Calo imulation i a epetitive pocedue: (1) The andom independent vaiable i geneated baed on it PDF; () Accoding to the elationhip function h, the vecto Z can be calculated; (3) Repeat (1) and (), the PDF of the dependent vaiable Z can be etimated when the ample ize (the numbe of epetition) i lage enough. The jutification of Monte Calo imulation come fom the following two baic theoem of tatitic: (i) The Weak Law of Lage Numbe and (ii) The Cental Limit Theoem. Baed on the above two theoem, it can be poved that with inceaing of ample ize, the PDF of the dependent vaiable obtained by Monte Calo imulation will appoach to that of the population. 7. Pobabilitic mall ignal tability incopoating wind fam The flow chat of the Monte Calo imulation technique fo powe ytem mall ignal tability analyi with conideation of wind geneation intemittence i given in Fig. 6. It i well known that the uncetainty of wind geneation i due to the uncetainty of wind peed, o we begin with the pobability ditibution of the wind peed. Fig. 7 how a Weibull ditibution function of wind peed with k = and c =10. When a andom wind peed i geneated, the mechanical powe output extacted fom the wind can be calculated via a king of wind tubine model uually given by function appoximation. If the wind peed V m i le than the cut-in peed V cut-in o i lage than the cut-off peed V cut-off, the wind fam will be tipped. If the cuent wind peed belong to the peed ange fom cut-in to cut-off, the wind fam will be kept connected to the gid in powe flow calculation and mall ignal tability analyi. The poce i epeated until the pe-et ample ize N i

16 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 175 eached. Finally, the pobabilitic-tatitical analyi can be conducted baed on the eult fom diffeent wind peed condition mentioned above to eveal the impact of wind geneation intemittence on powe ytem mall ignal tability. Weibull ditibution of wind peed Fequency ditibution of wind peed baed on MC Wind tubine model Fequency ditibution of wind fam powe output baed on MC Set ample ize N i =1 Geneate andom wind peed V m i =i+1 Wind fam tipped Y Powe flow calculation w/o wind fam integated SSS analyi w/o wind fam integated V m <=V cut-in? o V m >=V cut-off? N Powe flow calculation with wind fam integated SSS analyi with wind fam integated i<=n? N Y Pobability tatitic analyi Fig. 6. Flow chat of Monte Calo baed pobabilitic mall ignal tability analyi incopoating wind fam

17 176 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct PDF Fig. 7. Weibull ditibution with k = and c = Application example Wind peed (m/) The IEEE New England (10-geneato-39-bu) ytem wa employed a benchmak to tet the popoed model and method. The ingle line diagam of the tet ytem i given in Fig. 8. In thi ytem, the claical geneato model i applied to the ynchonou geneato G. The 4 th ode geneato model with a implified 3 d ode excite model i applied to the emaining 9 ynchonou geneato. It hould be noticed that thee i no any powe ytem tabilize conideed in the tet ytem. All imulation wee implemented on the MATLAB TM envionment. G G1 G G G3 G5 G4 G9 G6 G Fig. 8. Single line diagam of IEEE New England tet powe ytem A wind fam with 00 MW DFIG i integated into the non-geneato bue, i.e. bu1- bu9. The coeponding paamete of wind tubine and DFIG ae given in Table 1.

18 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 177 Accoding to the pocedue given in Fig. 6, the fequency ditibution of wind peed by applying Monte Calo method to the Weibull pobability ditibution of wind peed can be calculated a depicted in Fig. 9. The ample ize i et to be 8000 duing imulation. Paamete Value 1.35 kg/m 3 R 45 m C p V cut-in 3m/ V cut-off 5m/ V ated 10.8m/ R l l m R H 3.5 K T K T Table 1. Paamete of wind tubine and DFIG with MW capacity Fequency Wind peed / m/ Fig. 9. Fequency ditibution of wind peed Next, in accodance Eq. (1) and the fequency ditibution of wind peed a hown in Fig.9, fo the wind fam with 00*MW capacity, the pobability ditibution of wind fam powe output can be finally obtained a hown in Fig. 10. Fom Fig.10, thee exit two

19 178 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct concentation of pobability mae in the ditibution: one coepond to the value of zeo, in which the wind fam i cut off; the othe coepond to the value of 400MW, in which the ated powe output i geneated by the wind fam Fequency Wind fam powe output (MW) Fig. 10. Pobability ditibution of wind fam powe output Fig. 11 how the fequency ditibution of the eal pat of eigenvalue when the wind fam i connected to bu Fequency Small ignal table egion Real pat value Fig. 11. Pobability ditibution of eal pat of eigenvalue with wind fam integation into bu0

20 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 179 Accoding to the tatitical analyi baed on Fig. 11, we found that thee i a pobability of oughly 39.1% (318 out of 8000 in imulation) that the eal pat of the eigenvalue will be poitive, in which ituation the ytem i mall ignal untable. Theefoe we can conclude that the tability pobability of the tet ytem i 60.9% in cuent opeating condition. Futhemoe, thee exit two concentation of pobability mae in the ditibution: the left one coepond to the ituation that the wind fam i cut off; the ight one coepond to ituation that wind tubine geneate ated powe. Unde the ame wind peed condition, the wind fam i connected to the bu1-9, epectively. The coeponding eult ae given in Table. Bu No. of wind geneato Stable Pobability % Othe % Table. Small ignal table pobability with diffeent wind fam integation poition Electo-mechanical ocillation mode can be picked out accoding to the electo-mechanical elative coefficient o the fequency of ocillation, i.e. >1 o 0.1<f<.5Hz (Wang et al., 008). The mean and tandad eo of the mode popetie: fequencie, Electo-mechanical elevant atio, damping atio, and the paticipating facto ae given in Table 3. We found that the 9 th EM ocillation mode i untable with a pobability of 39.1%, and it i actually the pai of eigenvalue that detemine the mall ignal tability pobability of the whole ytem. In ummay, accoding to the imulation eult dicued above, we can conclude that the deteminitic mall ignal tability analyi can be conideed a a pecial cae tudy in the pobabilitic mall ignal tability analyi. Epecially, the pobabilitic mall ignal tability baed on the Monte Calo method can evaluate the tet powe ytem moe objectively and accuately. 9. Concluion Thi chapte addee the impact of intemittent wind geneation on powe ytem mall ignal tability. Fitly, the well-known Weibull pobability ditibution i employed to eveal wind peed uncetainty. Accoding to the Weibull ditibution of wind peed, the Monte Calo imulation technique baed pobabilitic mall ignal tability analyi i applied to olve the pobability ditibution of wind fam powe output and the eigenvalue of the tate matix. Finally, the IEEE New England tet powe ytem i tudie a benchmak to demontate the effectivene and validity of the popoe model and method. Baed on the numeical imulation eult, we can detemine the intability pobability of the powe ytem with the uncetainty and andomne of wind powe conideation. And fom viewpoint of mall ignal tability, the mot uitable integation poition fo wind fam can be detemined a well.

21 180 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct EM mode Fequency Damping atio EM elevant atio Mean Std Mean Std Mean Std Mot elevant geneato Stability G8 100% G7 100% G4 100% G8 100% G 100% G6 100% G9 100% G6 100% G % Table 3. Popetie of EM ocillation mode with wind fam integation into bu0 10. Refeence Ackemann, T. (005). Wind Powe in Powe Sytem, Wiley, ISBN , Chichete Akhmatov, V. (00). Vaiable-peed wind tubine with doubly-fed induction geneato pat i: modelling in dynamic imulation tool. Wind Engineeing, Vol. 6, No., , ISSN de Alegía, IM.; Andeu, J.; Matín, JL.; Ibañez, P.; Villate, JL. & Camblong, H. (007). Connection equiement fo wind fam: A uvey on technical equieement and egulation, Renewable and Sutainable Enegy Review, Vol.11, No.8, , ISSN Feijóo, A.; Cidá, J. & Caillo, C. (000). A thid ode model fo the doubly-fed induction machine, Electic Powe Sytem Reeach, Vol.56, No., 11-17, ISSN Fihman, G. (1996). Monte Calo: Concept, Algoithm, and Application, Spinge-Velag, ISBN , New Yok Joelin, H. G.; Iniyan, S.; Seevalan, E. & Rajapandian, S. (007). A eview of wind enegy technologie, Renewable and Sutainable Enegy Review, Vol.11, No.6, , ISSN Kundu, P. (1994). Powe Sytem Stability and Contol, McGaw-Hill, ISBN , New Yok

22 Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability 181 Mei, F. & Pal, B. C. (005). Modelling and mall-ignal analyi of a gid connected doubly-fed induction geneato, IEEE Powe Engineeing Society Geneal Meeting, pp , ISBN , San Fancico, June 005, IEEE, New Jeey Mendonca, A. & Lope, J. A. P. (005). Impact of lage cale wind powe integation on mall ignal tability, Futue Powe Sytem Intenational Confeence, pp. 1-5, ISBN , Amtedam, Nov. 005, IEEE, New Jeey Rouco, L. & Zamoa, J. L. (006). Dynamic patten and model ode eduction in mallignal model of doubly fed induction geneato fo wind powe application, IEEE Powe Engineeing Society Geneal Meeting, pp. 1 8, ISBN , Monteal, July 006, IEEE, New Jeey Rueda, J. L.; Colome, G. D. & Elich, I. (009). Aement and enhancement of mall ignal tability conideing uncetaintie. IEEE tanaction on Powe Sytem, Vol. 4, No. 1, , ISSN Slootweg, J. G.; Polinde, H.; & Kling, W. L. (001). Dynamic modelling of a wind tubine with doubly fed induction geneato, IEEE Powe Engineeing Society Summe Meeting, pp , ISBN , Vancouve, July 001, IEEE, New Jeey Tapia, G.; Tapia, A. & Otolaza, J.. (006). Two altenative modeling appoache fo the evaluation of wind fam active and eactive powe pefomance. IEEE Tanaction on Enegy Conveion, Vol. 1, No. 4, , ISSN Tapia, A.; Tapia, G. & Otolaza, J.. & Saenz, J.. (003). Modeling and contol of a wind tubine diven doubly fed induction geneato. IEEE Tanaction on Enegy Conveion, Vol. 1, No., , ISSN Touakia, G.; Nomikob, B. M. & Vounaa, C. D. (009). Effect of wind pak with doubly fed aynchonou geneato on mall-ignal tability, Electic Powe Sytem Reeach, Vol.79, No.1, , ISSN Wang, C.; Shi, L.; Wang, L. & Ni, Y. (008). Modelling analyi in powe ytem mall ignal tability with gid-connected wind fam of DFIG Type, Wind Engineeing, Vol.3, No.3, 43 64, ISSN Wang, K. W.; Chung, C. Y.; Te, C. T. & Tang K. M. (001). Pobabilitic eigenvalue enitivity indice fo obut PSS ite election. IEE Poceeding- Geneation, Tanmiion and Ditibution, Vol. 148, No. 4, , ISSN Wang, K. W.; Chung, C. Y.; Te, C. T. & Tang, K. M. (000). Impoved pobabilitic method fo powe ytem dynamic tability tudie, IEE Poceeding- Geneation, Tanmiion and Ditibution, Vol.147, No.1, 37-43, ISSN Wang,. F.; Song Y. H. & Iving, M. (008). Moden Powe Sytem Analyi, Spinge, ISBN , New Yok Wu, F.; Zhang,. P.; Godfey, K. & Ju, P. (006). Modeling and contol of wind tubine with doubly fed induction geneato, IEEE Powe Sytem Confeence and Expoition, pp , ISBN , Atlanta, Nov. 006, IEEE, New Jeey

23 18 Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct u, Z.; Dong, Z. Y. & Zhang, P. (005). Pobabilitic mall ignal analyi uing Monte Calo imulation, IEEE Powe Engineeing Society Geneal Meeting, pp , ISBN , San Fancico, June 005, IEEE, New Jeey

24 Off Poduct Edited by D. Geche Kaue ISBN Had cove, 18 page Publihe InTech Publihed online 04, Apil, 011 Publihed in pint edition Apil, 011 Thi book i a timely compilation of the diffeent apect of wind enegy powe ytem. It combine eveal cientific dicipline to cove the multi-dimenional apect of thi yet young emeging eeach field. It bing togethe finding fom natual and ocial cience and epecially fom the extenive field of numeical modelling. How to efeence In ode to coectly efeence thi cholaly wok, feel fee to copy and pate the following: Fom Tubine to Wind Fam - Technical Requiement and Spin- Libao Shi, Zheng u, Chen Wang, Liangzhong Yao and Yixin Ni (011). Impact of Intemittent Wind Geneation on Powe Sytem Small Signal Stability, Fom Tubine to Wind Fam - Technical Requiement and Spin-Off Poduct, D. Geche Kaue (Ed.), ISBN: , InTech, Available fom: InTech Euope Univeity Campu STeP Ri Slavka Kautzeka 83/A Rijeka, Coatia Phone: +385 (51) Fax: +385 (51) InTech China Unit 405, Office Block, Hotel Equatoial Shanghai No.65, Yan An Road (Wet), Shanghai, 00040, China Phone: Fax:

25 011 The Autho(). Licenee IntechOpen. Thi chapte i ditibuted unde the tem of the Ceative Common Attibution-NonCommecial- ShaeAlike-3.0 Licene, which pemit ue, ditibution and epoduction fo non-commecial pupoe, povided the oiginal i popely cited and deivative wok building on thi content ae ditibuted unde the ame licene.