Effect of neglecting stator transients in squirrel cage wind generator model.

Transcription

1 Effect of neglecting stato tansients in squiel cage wind geneato odel. S. Matín, M.P. Coech, S.Booy, M. Gacía-Gacia CIRCE-Depataento de Ingenieía Eléctica de la Univesidad de Zaagoza C/ Maía de Luna nº 3, Zaagoza (España) Eail: Abstact. The study of the ipact of the wind geneation in the electical gid is acquiing special ipotance in the last yeas. Fo these studies it is necessay to analyse its influence in the dynaics of the electical systes of powe. Theefoe, it is necessay to obtain suitable dynaic odels fo each study. In this pape two odels of wind tubine geneating systes ae pesented: a 5th ode and a 3d ode odel. The behaviou of both detailed odels ae descibed and copaed. Both odels atch up with the squiel cage technology. Key wo Wind enegy, siulation odels, powe syste dynaics, squiel cage wind tubine, copaison of odels. 1. Intoduction The powe syste dynaic is evaluated by siulation, and copanies usually use the dynaical odule of softwae package as PSS/E [2], Euostag, Nueous odels to epesent wind tubine geneating systes can be found in the liteatue. Howeve, ost of the cannot be applied easily fo fundaental fequency siulations because they contain tie constants which ae too shot to be taken account in fundaental fequency siulations [3]. The odels pesented in this wok have been ipleented in PSS/E. This dynaic siulation tool is widely used by the electical copanies in the wold. Coonly the use of the 5 th ode geneato odel is ecoended. The tie siulation of the 5 th ode odel with PSS/E is geate than the 3 d ode odel. In this pape a copaison of these two odels behaviou is ade. As a esult of the inceasing cae fo the envionent, the enewable enegies ae acquiing special ipotance in the last yeas. The wind enegy is one of the ost ipotant ways to geneate electicity fo enewable souces, and the nube of wind tubines will be inceased quickly ove the next 10 yeas. Nowadays, the ain poble is to deteine the influence of this geneation on the dynaics of electical powe systes by inteacting with conventional geneation equipent. Thus, the wind enegy ipact on the dynaics of the powe systes becoes an ipotant atte in electical and wind enegy copanies, and so, it is studied by eans of powe syste dynaic siulations [1]. Theefoe the odels behaviou should be nea the eality to get oe accuate esults. 2. Wind tubine odel Next the odel of squiel cage induction geneato developed is descibed in detailed fo. The odel ust conside the pefoance of all the pats of the wind tubine: The blades catch the echanical powe of the wind and they behave accoding to thei powe cuve. The echanical set consides the syste inetias. The geneato tansfos the dynaic enegy fo the axis in electical enegy RE&PQJ, Vol. 1, No.3, Mach 2005

2 A. Blades In the fist place, the tubine blades catch the echanical enegy of the wind. In this case, the odelled tubine does not have pitch contol and the contol will be ade by eans of stall contol. In noal opeation with stall contol, laina flow is obtained at the oto blades. Hee the lift values coesponding to the angle of attack ae eached at low dag coponents. Thus, the patial loading anges a high degee of aeodynaic efficiency is attained. If the wind speed appoaches the value at which the geneato eaches its ated powe, fathe toque developent at the oto ust be inhibited. Extensive igid coupling with the gid enables the geneato to keep the tubine at alost constant speed. Wind spee exceeding ated levels cause highe angles of attack and thus to stalling, when the aiflow unsticks fo pat of the blade pofile, this causes a lowe oto toque and lowe pefoance coefficients. Hub Geabox Geneato v s i s The powe coefficient epesents the elation between the powe extacted by the wind tubine espect to the total powe tanspoted by the wind. In this case, as the Pitch angle is constant, the powe coefficient only depen on λ, the tip step atio. The powe cuve epesents the electical to powe poduced by the wind tubine fo each wind speed in peanent egie. The powe cuve is a basic chaacteistic of the achine. This cuve is an initial data given by the anufactue. The powe cuve allows calculating the enegy poduced by the achine fo the wind distibution of the zone. The Fig 2 epesents the powe cuve of the odelled tubine. Seveal sections can be defined in the powe cuve: - Fo cal (0 /s) to a speed fo 3 to 5 /s the achine does not poduce enegy. - Fo the stating speed (3 to 5 /s) to the noinal speed (~12 to 14 /s), is a section of inceasing powe. Due to the blade stall in geneatos CSCF, the cuve has a chaacteistic section called coonly "hup", in which is eached the axiu powe, followed by a section of highe spee and salle powe poduced. - When the wind speed is geate than a value aound 25 /s, the geneatos stops to poduce electical enegy to avoid pobles of echanical oveload. Vw Blades Fig 1. Wind tubine configuation. The wind tubine capacity fo extact the enegy fo the wind depen on thee factos: - The wind powe available. Its value depen on the wind distibution, which is a chaacteistic of the wind fa location. - The powe cuve of the achine which is function of the type of achine. - The good behaviou of the achine to espond to fluctuations in the wind speed. This is a chaacteistic of tubine technology. The echanical powe extacted fo the wind is expessed as following: 3 1/ 2 A Cp( ) Vw P = ρ λ (1) Whee ρ is the ai density (coonly kg/ 3 ) A is the swept aea V w is the wind speed (/s) Cp is the powe coefficient. P (kw) B. Mechanical set Wind speed (/s) Fig 2. Powe cuve. In the dynaic odels fo stability studies the inetia constant of the echanical set ust be consideed t. In this odel the value of the oent of inetia is the total of the syste. It includes the blades, the geabox, and the geneato. The wind kinetic enegy is caught by the blades of the wind tubine. The blades ae ade of coposite ateial (polyeste, glass and cabon fibbe aong othes) which allows obtaining a high esistance with a educed weight. The blades ae the ost flexible eleent of the set, but fo this kind of studies infinite igidity is usually consideed RE&PQJ, Vol. 1, No.3, Mach 2005

3 The blades tun at an alost constant speed of appoxiately p. Due to the fact that this speed is clealy insufficient to poduce electical enegy, a ultiplie is used to elevate the speed of 40 to 100 ties the speed of the blades, so that noinal speed is obtained in the output axis (aound the 1500 p). The axis is jointed to the geneato though a clutch. Due to the ipotant igidity of both axes (blades and geneato) and the ultiplie, infinite igidity is consideed fo the set. Only the clutch elasticity and daping can be no despicable, ainly in the geatest achines. Geneato n = 1500 p As it can be appeciated, H is the elation between the kinetic enegy of the geneato at the synchonis speed and the powe base of the achine. C. Geneato odel equations The dynaic behaviou of the squiel cage induction geneato can be descibed by eans of the behaviou equations. In these equations the thee-phase windings of stato and oto ae epesented by eans of two gaes of othogonal fictitious windings. In the pesented odel the following suppositions have been taken: Blades n = 20 p Fig 3. Geabox layout. The est of the fictions (viscous and static) ae vey sall and its existence does not affect the dynaic behaviou of the geneato fo this study. The stato cuent is positive when it flows fo the achine towa the netwok. The epesented equations ae in the synchonous efeence fae. Q axis is advanced 90º of axis D in the otation diection as shown in Fig 4. Q axis The set has an elevated inetia. The eleents that contibute oe ae the blades, due to the fact that the ass is vey fa fo the otate axis and its weight, although low fo thei spead, is eally consideable (~2 tons/blade). In this pape it has been consideed an equivalent inetia oent equals to the su of inetia of the geneato, ultiplie, bushing and blades, all efeed the axis of the geneato: Whee and J = J + J + J + J (2) eq J ' gen geabox hub blades ( 1/ ) 2 blades + hub = Jblades + hub (3) Fig 4. Diect (D) and quadatue (Q) axis Fo powe systes study is desiable to use the pe unit epesentation. Fig 5 shows the geneato equivalent cicuit in the synchonous efeence fae. I QS + V QS - v D axis R s s R DS s x DR L ω b V QR=0 I QR = n / n (4) geneato blades I DS Q axis R s s R I DR Whee J epesents the inetia of the diffeent pats fo the syste, is the elation of the geabox and n the spee of the eleent. + V DS s x QR V DR=0 QS In stability studies, the constant of inetia H is the fundaental vaiable. It gives an idea of the achine electoechanical esponse tie befoe tansitoy event. It is efeed to the powe base of the achine, and can be defined as: ( 2πf / p) 1/ 2 J netwok H = (5) S b 2 D axis Fig 5. Equivalent cicuit of the asynchonous geneato in axes DQ Next, the voltage equations of the induction achine ae pesented. All the aounts ae in p.u except the angula fequency (ω b =2πf ated ) RE&PQJ, Vol. 1, No.3, Mach 2005

4 In these equations the capacitos batteies have not been consideed, since they have been consideed to be extenal to the geneato. In addition, the squiel cage induction geneato has the oto windings shotcicuited, and theefoe, the oto voltage in D and Q axes will be constant and equal to zeo. Wind tubine Bus1 Bus2 Bus4 Bus3 Electical netwok Whee: v v d q v = Rs + v = Rs + + = R d s QR + d = 0.0 = R q + s d + q = 0.0 ω d q = = = = ( s ) d ( s ) q + ( ) d + ( ) q b (6) (7) (8) (9) Fig 6. Double busba powe syste. Next, the esults obtained with the 5 th ode and the 3 d ode odel ae shown. The ade siulations have the following landaks: Flat siulation fo t = 0 s to t = 2 s. In t = 2 s a thee-phase shot cicuit in bus 4 is applied taking place a voltage dop of 80 % in the wind geneato bus. In t = 2.4 s is spightly the continuous lack and the siulation until t = 5 s. The next Figs show the behaviou of both odels. In geen colou the 5 th ode odel and in blue colou the 3 d ode. Coonly, these equations ae adapted fo investigations of dynaic sall-signal stability by dψ neglecting the stato flux tansients = 0 and dψ = 0 [4]. This siplified epesentation coespon to the 3d ode odel, and it is often applied also in tansient voltage stability [5] with lage fluctuations of the voltage at tansient gid distubances eseaches. Fig 7 shows the voltage esults obtained by eans of the siulation of both odels. The electoagnetic toque can be expessed by the following expession: T ( + ) = q d (10) With this sign convention the active and eactive powes ae: Fig 7. Response to a syste fault 3. Study P Q = v = v + v + v (11) Fig 8 and Fig 9 show in detail the esults obtained fo both odels in active and eactive powe. As it can be appaised, the odel of 3 d ode can be descibed as the suounding cuve of the esult obtained by eans of the 5 th ode. In ode to investigate and to copae the behaviou of the two odels, a double cicuit, double busba powe syste has been consideed, as shown in Fig 6. The syste shot cicuit level was assued to be 16 MVA and /R atio was assued to be RE&PQJ, Vol. 1, No.3, Mach 2005

5 Refeences [1] D. Gacía Gacía, M.P. Coech, M. Sanz, J.B. Aoyo, M. Gacía-Gacia. Study of wind powe liit fo a netwok bus. ICREPQ 03, Vigo (Spain), [2] PSS/E Powe Syste Siulato fo Engineeing, Powe Technologies Inc, vesion Fig 8. Reactive powe obtained fo the 5 th and 3 d ode odel [3] Slootweg, J.G., Polinde, H., Kling, W.L. Repesenting Wind Tubine Electical Geneating Systes in Fundaental Fecuency Siulations. IEEE Tansactions on Enegy Convesion, Vol 18, NO.4, Decebe [4] Feijóo, A., Cidas, J., Caillo, C. (2000). A thid ode odel fo the doubly-fed induction achine, Electic Powe Systes Reseach, vol.56, pp [5] Ledesa, P., Usaola, J., Rodíguez, J.L., Bugos, J.C. Copaison between contol systes in a doubly fed induction geneato connected to an electic gid. EWEC 99, Madid (Spain), Fig 9. Active powe obtained fo the 5 th and 3 d ode odel 4. Conclusions This pape shows the behaviou of a squiel cage induction wind tubine accoding to two geneato odels: the 5 th and the 3 d ode odel. In the squiel cage induction geneato, the fact of neglecting the stato tansients does not iply to lose pecision. In addition using the 3 d ode odel, the siulation tie is educed appoxiately to the fouth pat, eason why fo siulation with geat netwoks its use is advisable RE&PQJ, Vol. 1, No.3, Mach 2005