Key words: Wind Power generation, active and reactive power dispatch, non-linear optimization, mixed integer programming, wind power forecast.

Transcription

1 A Unt Commtment an Dspatch for a Wn ark Consern Wn ower Forecast C.F. Moyano 1, J. A. eças Lopes 1,2 1 Insttuto e Enenhara e Sstemas e Computaores o orto, orto, ortual 2 Faculae e Enenhara a Unversae o orto, orto, ortual Campus a Feup, Dr. Roberto Fras 378, orto Tel , Fax , e-mal: cmoyano@nescporto.pt, pl@fe.up.pt Abstract. The present paper escrbes an optmzaton stratey, to be aopte at the wn park control level, especally for those wth lare power output, that allow to efne the commtment of the wn turbnes an ther actve an reactve set ponts follown requests from the wn park spatch centers, assumn that nvual wn turbnes short term wn power forecasts are known an are expresse as power avalablty. Ths approach was also evelope wth a concern on the mnmzaton of the connecton / sconnecton of the nvual wn enerators, for a ven tme horzon, an takes also nto account restrctons n the lmts for reactve power enerate at the wn turbnes. Key wors: Wn ower eneraton, actve an reactve power spatch, non-lnear optmzaton, mxe nteer prorammn, wn power forecast. 1. Introucton A herarchcal montorn an control approach s ben evelope an aopte n several systems to eal wth the nees mpose by the lare ncrease of wn power penetraton n power systems. Ths control approach requres the control of the wn parks output power (actve an reactve) trouh a ecentralze spatch center archtecture, where orers are ssue from a central spatch that has the lobal vson of the system. Wn Generaton Dspatch Centers (actn as Generaton Areaton Aents) wll be nstalle n the ortuuese system, aoptn for ths purpose a herarchcal control archtecture. Havn n mn that wn eneraton can nect power ether n the transmsson network or n the strbuton rs, communcaton lnks must be establshe between the Wn Generaton Dspatch Centers an the Transmsson System Operator (TSO) or the Dstrbuton System Operators (DSO) [1]. If one assumes also, the partcpaton of wn eneraton n the market, smlar communcaton lnks must be establshe wth the market operator. In the Spansh case, all the enery proucton nstallatons wth nomnal power up 10 MW shoul to be assocate to a control center, whch receves from the Gr Operator nstructons an transmt ts nstructons to the fferent nstallaton owners [2]. Ths leslaton also mposes the necessty of wn parks to nform a forecast of the wn power proucton 30 hours before, wth a maxmum error of 20%. Uner ths scenaro, wn enerators are expecte to be able to control ther actve an reactve power outputs. Double fe nucton wn enerators (DFIG) controlle by statc converters an varable spee synchronous enerators wth full electronc r nterface are presently alreay capable of assurn such nvual control capabltes [3]. Rearn DFIG, a reat varety of control stratees can be use n the operaton of these machnes as t can be seen from [4, 5, 6 an 7]. In these works, stratees to control actve an reactve power wn park outputs also were propose. In these researches wn park control moels are bult-up wth a herarchcal moular structure: a central wn park controller sens out reference snals to each local wn turbne controller. Amon these works, reference [7] escrbes an optmzaton stratey to be aopte at a supervsory wn park control level wth the obectve of assurn that wn park actve an reactve power outputs atten the requests efne by system operators. However t consers wn velocty constant an equal for all the wn turbnes an oes not consers wn power forecastn errors. In [8] a spatch moule for a wn park s escrbe, assumn however that wn enerator s spatch s performe as a proportonal vson of operator s request throuh all the wn turbnes. Wn power forecast nees to be taken nto account n the formulaton of the optmzaton stratey. A methooloy for short-term wn power forecasts s escrbe n [9]. Ths approach nclues the evaluaton of confence ntervals wth a confence level. The present paper escrbes an optmzaton stratey, to be aopte at the wn park control level that allows to efne the commtment of the wn turbnes an ther RE&J, ol. 1, No.5, March 2007

2 actve an reactve set ponts follown requests from the wn park spatch centers, assumn that nvual wn turbnes short term power forecasts are known an are expresse as power avalablty accorn to [9]. 2. The optmzaton formulaton The optmzaton problem of the wn park manaement can be solve n a smlar way as the one use to manae conventonal eneraton n a power system, throuh the soluton of two nterrelate optmzaton problems. A Unt Commtment problem s solve frst, n orer to etermne the turbnes scheule, an the techncal spatch output s performe to etermne set ponts to each turbne n a secon step. Y For the wn park case, we can assume that an X, Z are respectvely bnary varables that moele the status (on/off), the startup an shutown of each wn turbne. The obectve functon for ths subproblem s to mnmze the number of turbnes n operaton an status chanes, n orer to reuce mantenance cost for wn turbnes an swtchn evces. The Unt Commtment problem can be solve throuh a mxe nteer problem [10], as formulate bellow. n Mn ( b X + c Y + Z ) (1) s.t. where, A A b, A MaxS ( X ) ( X mn S ) Loss Loss 0 (2) (3) 1 ( X X ) Y 0 (4) Y 0 (5) ( + 1 X X ) Z 0 (6) Z 0 (7) c an are cost assocate to mantann the unty actve an ts cost of startup an shutown for turbne at pero. In Wn ower Generaton these costs can be consere as constants for an actve turbne for a efne nterval. Cost for startup an shutown are consere as relate to mantenance costs. MaxS an S mn are respectvely the maxmum avalable actve power lmt of enerator at nterval th, as result of the approach shown n [9], an the mnmum actve power for each enerator at th nterval, resultn from the mnmum techncal eneraton lmt of the each turbne. s the actve power requre by the r operator at the connecton bus at nterval. As the power forecast s base n the approach escrbe n [9], that mples n assumn a confence nterval efne by the operator for each unt commtment. Coeffcents b, c an can be use to mprove fferent stratees to commt the wn turbnes by mofyn the relaton between coeffcents b an c an n the obectve functon. On the other han, when a unt nees to be n an off state, for a etermne pero, the corresponent b assumes a hh value an the nterval of avalable power assumes a mnmum value to avo ts commtment. Equatons (2) an (3) represent the feasblty contons an equatons (4) to (7) represent the operatonal restrctons assne to the startup an shutown for each wn turbne. Losses are consere at ths stae as approxmatons, represente by n Loss equatons (2) an (3), assumn a raal wn park confuraton. The Unt Commtment problem can become unfeasble f the sum of the actve power requeste by the operator plus the wn park nternal losses s reater than the total avalable wn power or f the sum of the operator request plus the wn park nternal losses s lower than the mnmum techncal lmt of one enerator. Ths kn of nfeasblty nees to be checke before startn the problem soluton. The wn park spatch s obtane throuh the soluton of a NL sub-problem, consern the operatonal constrans an the mnmzaton of the msmatch between the total wn park eneraton output (actve an reactve) an wn park spatch center requests. The man fference of the NL approach presente n ths work from the one presente n [7] s that the characterstcs of the wn turbne operaton are consere nto ths formulaton. Wn turbne reactve power lmts are suppose to follow a lnear relaton wth the actve power enerate as MaxS M = k an mn S m M m = k, were k an k are the parameters of that lnear relaton. The obectve functon aopte conssts n the wehte sum of varables an that represents the percentae of the non-elvere actve an reactve power outputs at nterval (respectvely an ) rearn the spatch center request. Constrans relate wth the actve an reactve power enerator lmts an voltaes n all the noes are also consere [12]. Other terms can be ae to the obectve functon to moel fferent stratees [7]. The non-lnear optmzaton sub-problem s formulate RE&J, ol. 1, No.5, March 2007

3 for each pero as: Mn s.t. σ + σ (8) ( 1 ) + (, θ ) = 0 (9) ( 1 ) + (, θ ) = 0 (10) C 0 (11) 0 (12) mn S MaxS (13) m M k k (14) mn Max (15) where equatons (9) an (10) represent the actve an reactve power balance equatons n each wn park bus, parameterze by an as n [11 an 12]. an are vectors, wth a menson equal to the number of buses of the wn park, havn only one non-zero element representn the actve an reactve power requeste at the nterconnecton bus. an are vectors that contan the actve an reactve power enerate at each wn park bus, an (, θ ) an (, θ ) are the actve an reactve power balance vectors as functon of voltaes ( ) an anles (θ ) of the wn park buses. C represent the capactors eneraton present n the wn park. Lmts are mpose n equatons (11) an (12) to varables an, corresponn = 0 an = 0 to the stuaton where the requests from the wn park spatch center are fully carre out. If ths lmt s not consere, an can assume neatve values, an the wn park output woul be reater than the requeste [11]. Wn enerator operatonal lmts are consere n equatons (13)-(14). In the case of reactve power lmts, they are rectly nclue as actve power enerate functons. Fnally, voltae lmts ( are consere n equaton (15). ) for all the buses The NL sub-problem s solve usn the prectorcorrector verson of the rmal-dual Non-Lnear Interor onts Metho, as escrbe n [13]. 3. Results Fure 1: Wn ark schematc Results are presente next to llustrate the capabltes of ths approach, usn a small wn park wth 10 turbnes (660 kw nomnal capacty) an 21 lnes formn two feeers connecte to the r nterconnecton bus, as shown n fure (1). For each wn enerator the reactve power lmts are consere as ± 40% of actve power enerate. oltae lmts () are assume to be wthn the rane p.u. No capactor evce was consere for ths case. Consern the approach escrbe n [9], the proceure was teste usn 4 tme ntervals of 15 mnutes each. In Table I, maxmum estmate eneraton powers an mnmum techncal lmts for each wn turbne ( max an mn ) are shown. Estmate enerate powers at turbnes numbers 22 (pero 1), 18 (pero 2), 16 (pero 3), 12 an 22 (pero 4) are zero because the forecaste wn spee s not enouh to keep the machne n operaton (cut-off zone). In a frst case, the actve an reactve power System Operator requests are respectvely 2MW an 0.6 MAr for all peros. Table II shows the status of the wn turbnes for each pero. As t can be seen, turbnes 16 an 22 are out of servce for all peros an turbnes 12 an 18 chane ther status, nfluence by the enerators n the cut-off zone. The status of the turbnes wth eneraton levels uner ther mnmum techncal lmts was set to zero n the unt commtment step usn a lare value for coeffcents b n these ntervals (1000 n ths case). Meanwhle the others b coeffcents were set equal to 1. alues of c an n ths case were set to 5. The wn park nternal actve power losses were estmate as 10% of the wn park actve power output. Althouh ths may be consere as an overestmaton t enables the soluton feasblty for the problem RE&J, ol. 1, No.5, March 2007

4 TABLE I Forecaste ower n each Turbne (MW) ero Bus max mn max mn max mn max mn Total Bus TABLE II Unt Commtment eros Turbne TABLE III Turbne spatch ((MW),(MAr)) eros Results from the spatch for each pero are shown n Table III. Turbnes 16 an 22 are not shown because they were not commtte. As t can be seen, the actve power enerate s strbute amon all the turbnes, an the reactve power prouce n enerators also mantans the pre-establshe relaton. Table I shows the moule an anle of the voltaes n all the buses of the wn park. oltae at bus 1 was fxe at 1 p.u., an t can be observe that the nternal reactve power proucton ncreases the voltae at wn turbnes buses. Buses 16 an 22 are not shown because they are not use n all the ntervals. Bus TABLE I Turbne spatch (, ) ero The mportance of the relatons between coeffcents b, c an s shown next by analyzn two cases, consern an operator request for each pero as shown n Table an the wn power forecaste shown n Table I. TABLE Operator request Operator eros Request (MW) (MAr) In a frst case, the coeffcents b are set as 1, except for the cases where the forecaste wn spee s not enouh to keep the machne proucn (cut-off zone), where lare values (equal to 1000) are consere, as n the prevous case. c an are set as 0.5, whch correspons to a stuaton where the mnmzaton of the number of turbnes n servce has prorty over the mnmum number of status chanes. Table I an II show respectvely the unt commtment an the actve an reactve power spatches of the wn turbnes for ths case RE&J, ol. 1, No.5, March 2007

5 Bus TABLE I Turbne Commtment eros Turbne TABLE II Turbne spatch ((MW),(MAr)) eros Total 2,23 0,75 1,57 0,63 2,86 0,69 2,26 0,73 In a secon case, for the actve power avalable shown n Table I, the coeffcents b are set as 1, except for the stuatons where the forecaste wn spee s not enouh to keep the machnes proucn (cut-off zone) whch requres usn lare values (1000) for these coeffcents, as n the prevous case. c an are set as 50 to llustrate the behavor of ths approach n a stuaton where the mnmzaton of the number of status chanes has prorty over the number of turbnes n servce. Table III shows the unt commtment for ths case. As can t can be seen, the man fferences of ths soluton from the prevous one conssts n swtchn on turbnes 4, 6 an 10 n pero 1 an swtch on turbnes 6 an 10 n pero 2 an 3. Turbne 12 remans sconnecte for all peros, whle n the prevous soluton was connecte at peros 1, 2 an 3. As expecte, n the peros where the forecaste wn spee s such that the turbnes are n the cut-off zone, the enerators are not commtte shown the effectveness of the propose alorthm. Actve an reactve power spatches for all wn turbnes can be seen at Table IX. When comparn these results wth the prevous ones, one can be see that the actve an reactve powers are more strbute. Ths fact can be use to mprove the control of the wn power output, reucn the epenence of wn park output from the wn power ntermttency. Table X shows the full avalable wn park output actve power for the two stratees presente, mnmum number of turbnes (MNT) an mnmum number of status chanes (MNC), shown that for the frst case there s no possblty of keepn the operator request output f a suen wn power ecrease takes place for peros 1, 2 an 3, because wn turbnes are spatche at ts maxmum level. TABLE III Turbne Commtment eros Turbne TABLE IX Turbne spatch ((MW),(MAr)) eros Bus Total 2,24 0,71 1,61 0,65 2,87 0,67 2,26 0,73 Case TABLE X Avalable ower eros MNT 2,23 1,62 2,86 2,32 MNC 3,38 1,79 3,22 2,32 Fnally, parameters an were analyse. For these cases, operator request of 6 MW an 2 MAr an RE&J, ol. 1, No.5, March 2007

6 MW an 4 MAr are teste consern the avalable power forecastn presente n Table I for pero 1. As the operator request s reater than the maxmum capablty of wn park at ths pero, wn park output can not follow the operator request. In these cases, actve an reactve power output s reuce, consern the nternal wn park actve an reactve power losses. For both operator requests the wn power output are reuce to 4.95 MW an 1.50 MAr. Snce the full actve power avalable s spatche n the two cases, althouh the parameterzaton of actve an reactve power s nepenent, the lnear relaton between actve/reactve powers enerate mposes ths result. Table XI shows the wn turbne spatch for both operator requests. alues for an are an for the requeste 6 MW an 2 MAr, an an Bus 4. Conclusons an are respectvely TABLE XI Turbne spatch (MW) (MAr) Total enerate Wn ark output In ths paper, an optmzaton stratey was evelope to prove the commtment of wn turbnes n a wn park, as well as to entfy the actve an reactve power set ponts that result from a local spatch, applyn concepts from classcal unt commtment an spatch an takn nto account the characterstcs of the turbnes an eneraton lmts obtane from wn power forecasts. Ths stratey allows wn parks to follow requests from a System Operator or from a wn park spatch center, rearn actve/reactve power to be enerate. Such functonalty allows wn park eneraton to become qute flexble allown ther partcpaton n electrcty markets an ther response to System Operator requests when a network restrcton emans the reucton of eneraton n a eoraphcal area. References [1] A. Estanquero, R. Castro, J.R. Meeros nto, R. Rorues, J. eças Lopes; How to repare a ower System for 12% Wn Enery enetraton: The ortuuese Case Stuy. Norc Wn ower Conference, Espoo, Fnlan, May, [2] (2004) Royal Decree 436/2004, Date March 12th, Establshn the Methooloy to Upate an Oranze the Leal an Economc roceures for Electrcty Generaton Belonn to the Specal Reme. [Onlne]. Avalable: [3] J. L. Roruez-Ameneo et al., Automatc eneraton control of a wn farm wth varable spee wn turbnes, IEEE Trans. Enery Convers., olume 17, no. 2, pp , Jun [4] J. Wk, J. O. Gere, T. Geneal, an M. Gustafsson, Steay state power system ssues when plannn lare wn farms, ower Enneern Socety Wnter Meetn, IEEE olume 1, Jan pp: vol.1. [5] A. Tapa, G. Tapa, J. X. Ostolaza, J.R. Saenz, R. Crao, J. L. Berasateu, Reactve ower Control of a Wn Farm mae up wth Doubly Fe Inucton Generators (I an II), n roc IEEE orto ower Tech Conference l0th 13th September, orto, ortual. [6] R. G. e Almea, J. A. eças Lopes, an J. A. L. Barreros, Improvn power system ynamc behavor throuh oubly fe nucton machnes controlle by statc converter usn fuzzy control, IEEE Trans. ower Syst., vol. 19, no. 4, pp , Nov [7] R.G. e Almea, E.D. Castronuovo, an J.A. eças Lopes, Optmum Generaton Control n Wn arks When Carryn Out System Operator Requests. IEEE Transactons on ower Systems, ol.21, Nº 2, May [8] A.D.Hansen,. Sørensen, F. Iov, F. Blaaber, Centralse power control of wn farm wth oubly fe nucton enerators. Renewable Enery 31 (2006) [9]. nson, G. Karnotaks, On-lne assessment of precton rsk for wn power proucton forecasts. Wn Enery, olume 7, Nº 2, Aprl/June 2004, [10] M. Carrón; J.M. Arroyo ; A Computatonally Effcent Mxe-Inteer Lnear Formulaton for the Thermal Unt Commtment roblem. IEEE Trans. ower Syst. olume 21, Issue 3, Au ae(s): [11] C. F. Moyano, R.S. Salao, Auste OF Soluton Usn arameterze Moel, Automaton an Control Maazne Brazlan Automaton Socety, ol.17 no.2/aprl, May an June 2006 (n ortuuese). [12] S. Granvlle; J.C.O. Mello; A.C.G. Melo; Applcaton of nteror pont methos to power flow unsolvablty. IEEE Trans. ower Syst., vol 11, no 2, pp , May [13] E. D. Castronuovo, J. M. Campanolo, an R. Salao, New versons of nonlnear nteror pont methos apple to the optmal power flow, n roc. IEEE T&D Latn Amerca, São aulo, Brazl, Apr RE&J, ol. 1, No.5, March 2007