Autonomous Voltage Security Regions to Prevent Cascading Trip Faults in Wind Turbine Generators

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1 Downloaded from orbt.dtu.dk on: Nov Autonomous oltage Securty Regons to Prevent Cascadng Trp Faults n Wnd Turbne Generators Nu Tao; Guo Qngla; Sun Hongbn; Wu Quwe; Zhang Bomng; Dng Tao Publshed n: IEEE Transactons on Sustanable Energy Lnk to artcle DOI: 1.119/TSTE Publcaton date: 216 Document erson Peer revewed verson Lnk back to DTU Orbt Ctaton (APA): Nu T. Guo Q. Sun H. Wu Q. Zhang B. & Dng T. (216). Autonomous oltage Securty Regons to Prevent Cascadng Trp Faults n Wnd Turbne Generators. IEEE Transactons on Sustanable Energy 7(3) DOI: 1.119/TSTE General rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts. Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research. You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan You may freely dstrbute the URL dentfyng the publcaton n the publc portal If you beleve that ths document breaches copyrght please contact us provdng detals and we wll remove access to the work mmedately and nvestgate your clam.

2 Autonomous oltage Securty Regons to Prevent Cascadng Trp Faults n Wnd Turbne Generators Tao Nu Qngla Guo Senor Member IEEE Hongbn Sun Senor Member IEEE Quwe Wu Senor Member IEEE Bomng Zhang Fellow IEEE Tao Dng Member IEEE Abstract Cascadng trp faults n large-scale wnd power centralzed ntegraton areas brng new challenges to the secure operaton of power systems. In order to deal wth the complexty of voltage securty regons and the computaton dffculty ths paper proposes an autonomous voltage securty regon () for each wnd farm and the pont of common couplng () substaton whose voltage can be controlled n a decoupled way. The computaton of the can be completed usng a stepwse search method exchangng voltage and power nformaton between the control center and the wnd farms. At each wnd farm an s determned to guarantee the normal operaton of each wnd turbne generator (WTG) whle n the control center each regon s desgned n order to guarantee secure operaton both under normal condtons and after an N-1 contngency. A real system n Northern Chna was used to carry out case studes to verfy the effectveness of the s proposed and good performance was demonstrated usng the Monte Carlo method. Index Terms autonomous voltage securty regon () N-1 contngency voltage control wnd power ntegraton p q w w NOMENCLATURE The autonomous voltage securty regon () of pont of couplng (POC) bus n wnd farm The of pont of common couplng () bus n Number of wnd unts n wnd farm N w Number of wnd farms N g Number of conventonal generators N s Number of scenaros Actve and reactve power of wnd unt n wnd farm under normal condtons oltage magntude of wnd unt n wnd v w farm under normal condtons Q Total reactve power regulaton of wnd Manuscrpt receved October ; revsed February ; accepted March Ths work was supported n part by Natonal Natural Scence Foundaton of Chna ( ) and Natonal Key Basc Research Program of Chna (213CB22826). Paper no. TSTE Tao Nu Qngla Guo Hongbn Sun and Bomng Zhang are wth the Department of Electrcal Engneerng Tsnghua Unversty Beng Chna. (emal: guoqngla@tsnghua.edu.cn) Quwe Wu s wth Techncal Unversty of Denmark Department of Electrcal Engneerng Elektrove 325 Kgs. Lyngby DK 28 Tao Dng s wth X an Jaotong Unversty Department of Electrcal Engneerng No.28 Xannng West Road X an Shanx CN 7149 Q gm A s Q svc s s farm under normal condtons (The superscrpt denotes normal condtons) Total reactve power regulaton of conventonal power plant m n the control center under normal condtons Total reactve power regulaton of statc voltage compensators (SCs) n wnd farm n scenaro s oltage magntude of POC bus n wnd farm under normal condtons and n scenaro s oltage magntude of bus under normal condtons and n scenaro s I. INTRODUCTION S the most promsng renewable energy source (RES) wnd power s wdely used over the world. There are several voltage-related challenges for accommodatng large-scale wnd power such as voltage fluctuatons and the voltage stablty under dsturbances. In order to address these operaton ssues n wnd power grd a number of technques have been developed to enhance the wnd power hostng capacty and stablty of the power system [1-5] mantan the voltage of the wnd power ntegraton area wthn lmts [6-11] and mantan an approprate voltage profle wth the help of on-load tap changes (OLTCs) and capactor/reactor banks [25-27]. Furthermore statc methods such as P curves and contnuaton power flow (CPF) are used to analyze the rsk of voltage nstablty from the perspectve of voltage stablty n wnd systems. There are also some researches focus on mprovng the voltage stablty [12-14] of the power system wth wnd power. One of the maor challenges for large-scale wnd power n Chna s cascadng trp faults. Durng 211~214 several severe cascadng trp ncdents occurred n Chna due to the normal but not safe operaton state [19]. Once a trp fault occurs other wnd farms voltage wll sgnfcantly ncrease and cannot be kept wthn a normal voltage lmt. As a consequence wnd turbne generators (WTGs) n other wnd farms are trpped by hgh-voltage protecton systems. As more WTGs trp wnd farm voltages become hgher resultng n cascadng trp faults. Here a cascadng trp ncdent n Zhangbe Wnd Power Base n Northern Chna on Feb 26 th 212 was recorded n Fg. 1 by synchronzed measurements from deployed phasor measurement unts (PMUs). As shown n Fg. 1 the cascadng faults were trggered by short-crcut faults n wnd farm GT whch

3 caused the very low voltage. Unfortunately most of the WTGs n Chna were not equpped wth effectve low-voltage rde through (LRT) control so these WTGs were shut down. Combned wth the capactors that were not swtched off n tme ths led to a sudden large amount of redundant reactve power. Due to the fact that the wnd power pool area was connected wth a relatvely weak power grd afterwards the voltage profle n ths ntegraton area sgnfcantly ncreases durng.4s~2.s resultng n great wnd generaton loss. Accordng to the data from State Electrcty Regulatory Commsson of Chna there are 193 large-scale cascadng trp ncdents durng January to August n 211 n Northern Chna and the most severe wnd power loss n an ncdent was 5 MW whch brngs great challenges to power system operaton. oltages / p.u GT trpped frst Tme / s Fg. 1. Typcal trp-off process voltage durng a cascadng falure We can conclude from the cascadng trp process that the statc voltage profles are crucal to secure operatons and the most mportant reason leadng to cascadng trp s the mproper statc voltage magntude profles. Thus n order to deal wth the large-scale cascadng trp problems and keep the wnd farms workng under normal and safe state voltage securty regon s then proposed to determne voltage operaton ranges for all the mportant buses n the wnd pool area. When the wnd farms operate wthn these regons once a wnd farm trps other wnd farms can stll operate at an acceptable voltage level and wll not lead to cascadng trp. There s some prelmnary research on statc voltage securty regon [15-17] however some challenges stll reman. Frstly large-scale wnd pool areas usually nclude dozens of wnd farms wth thousands of WTGs and all the voltage of the area shall be taken nto account. Otherwse any trp ncdent may result n cascadng trp faults. A control center can hardly model all the detals to guarantee each WTG s operaton constrants both under normal condtons and N-1 contngences. Secondly the boundary of statc voltage securty regon s complex due to the ntermttent and stochastc characterstcs of wnd power. Therefore the computaton of voltage securty regon for onlne applcaton s also a great challenge. Several studes have proposed methods for reducng the computatonal burden of the boundary. Based on the two-level wnd automatc voltage control (AC) system n [18-19] an approxmate N-1 GT WLS voltage securty regon boundary encompassed by cuttng planes for centralzed multple wnd farms s presented n [2] and [21]. However wth the lnearzaton assumpton the accuracy s sacrfced to reduce the computaton burden. Last but not least for practcal applcatons the herarchcal wnd-ac system uses an autonomous voltage controller n each wnd farm and a synergc voltage controller n the control center [19]. It s more promsng and practcal for wnd farms to ndependently control themselves wthout consderng the detals of other wnd farms operaton. The prevous research [22] ddn t produce decoupled voltage operaton ranges for wnd farms. Therefore a concept of (autonomous voltage securty regon) s proposed n ths paper. The defnton of the n the wnd power grds s: If the control center controls the pont of common couplng () bus and wnd farms control ther own pont of couplng (POC) buses n ther own certan ranges each wnd farm can control all the WTGs wthn normal operaton ranges under both normal condtons and any N-1 contngency wthout consderng the operaton detals of other wnd farms. The set of these voltage operaton ranges for bus and POC buses s defned as the. The concept of autonomous means each wnd farm can control ther voltages by themselves wthout consderng other wnd farms.e. the produces decoupled voltage control strateges for each wnd farm. The n ths paper s proposed from the perspectve of securty ams to deal wth the large-scale cascadng trp faults caused by hgh-voltage protecton systems of WTGs when the termnal voltages of WTGs exceed ther upper bounds after an N-1 contngency. Accordng to the analyss of cascadng trp process n Fg. 1 we can conclude that the how to compute autonomous voltage securty regon () to acqure voltage securty control ranges of each wnd farm and avod cascadng trp s a statc voltage securty problem and the computaton of should be based on statc power flow equatons. The ASR computed here could be adopted as constrants for the voltage controllers that are deployed n wnd farms and control center. Durng the control process of course the dynamc models are crucal especally the dynamc reactve power reserve of SCs/SGs wll greatly nfluence the voltage profles when contngences happen [3]-[31]. In future work we wll further research how dynamcs models nfluence the (e.g. the optmal allocaton of SC/SGs) n wnd farms. Ths paper ams to extend the prevous work to propose the statc and focus on acceleratng the computaton. And the contrbutons of the paper can be summarzed as follows. (1) The for the bus and the POC bus n each wnd farm s proposed and can be used for decoupled voltage control among all wnd farms and the bus. That s the most mportant contrbuton. (2) In prevous studes [22] an teratve method for the system-wde computaton was proposed. The stepwse search method proposed n ths paper does not requre teraton and the necessary constrant nformaton s exchanged only once between the control center and each wnd farm resultng n less necessary computaton tme.

4 (3) The detaled networks of each wnd farm are taken nto account and a complete power flow model s used nstead of a tradtonal senstve model n each wnd farm. Thus the results are more accurate. (4) DstFlow format [23] s used to compute optmal power flow (OPF) n each wnd farm. Ths model s completely equvalent to power flow model wth polar coordnates format n radal networks [23] whch guarantees the computaton accuracy. The stepwse method proposed n ths work needs repeated computaton and the DstFlow model sgnfcantly saves computaton tme due to the hgher lnearty. The paper s organzed as follows. The voltage feasble regon (FR) for an ndvdual wnd farm s frst descrbed n Secton II. Based on these FRs the s computed. Sx necessary steps to acqure the and the nformaton exchange between wnd farms and the control center are gven at the end of Secton II. Secton III presents case studes of a smple system and a real system. The effectveness of the proposed stepwse method s demonstrated by Monte Carlo smulaton n Secton III followed by conclusons. II. IN WIND POOL AREA A. Computaton structure of Unlke hydro and thermal power plants wnd farms are often dstrbuted over large areas and the wnd powers are then connected to a hgh-voltage bus (11/22 k-level) va several feeders (35 k-level) n wnd farms. The hgh-voltage bus n each wnd farm s the POC bus. Several wnd farms are then connected to a bus n a substaton at a hgher voltage level (22/5 k) va transmsson lnes then centrally ntegrated nto the power grd. A typcal structure for centralzed ntegraton of wnd farms n Northern Chna s shown n Fg. 2. nto account the wnd farm's parameters and ams to acqure both maxmum and mnmum voltage magntudes for each POC bus n a centralzed ntegraton area. For the control center a synergstc control strategy s desgned to coordnate all dstrbuted POC buses whch uses the securty-constraned optmal power flow (SCOPF) and ensures that the voltage of all wnd farms satsfes the operatonal constrants under both normal condtons and after an N-1 contngency. B. FR for an ndvdual wnd farm The typcal structure of an ndvdual wnd farm s shown n Fg. 3. In each wnd farm the detaled network topology of dfferent knds of devces s taken nto account. Frst for an ndvdual wnd farm t s supposed to fnd the FR for the POC bus ( POC ) and the ( ) bus. Note that the voltage of each WTG n a wnd farm s a state varable and the reactve power of each devce s a control varable. In each wnd farm for a specfed actve power (1-f) and the gven voltage of (1-g) we only use the reactve power control capablty of ts own wnd farm (1-d) to prevent all WTGs from trppng-off (1-e). The cascadng trp ncdents may happen f (1-e) s volated. The maxmum and mnmum value of POC (1-a)~(1-b) are supposed to be obtaned for voltage control of the wnd farm. When POC operate wthn [ POC POC ] all WTGs can operate normally only by usng the control capablty of the wnd farm. conventonal power plants P Q other wnd farms bus POC POC bus perspectve vew of the ndvdual wnd farm Fg. 3. Perspectve vew of an ndvdual wnd farm Fg. 2. Typcal structure for centralzed ntegraton of wnd farms n Northern Chna Accordng to the herarchcal wnd-ac system [19] the voltage of the bus s controlled by the control center whle the voltage of POC bus s controlled by wnd farms. Therefore t s feasble to fnd a decoupled voltage control range (the ) for the control center and each wnd farm. Accordng to the AC system the s computng structure s desgned as follows. For each wnd farm an autonomous control strategy s desgned to keep the POC bus wthn ther own range whch takes st mn qw qw (1-a) max (1-b) l l.. w f p q p q v I (1-c) q q q (1-d) w w w v v v (1-e) w w w p p (1-f) SP w w (1-g) SP n

5 voltage of POC bus n wnd farm ( ) The radal network feature of wnd farms s fully consdered to mprove computaton performance. Here (1-c) expresses the power flow model n DstFlow [24] format whch nclude three lnear constrants (1-c-1)~(1-c-3) and one quadratc constrant (1-c-4). The hgher lnearty of the DstFlow model results n consderable tme savng for the stepwse method below wth repeated computaton [23]. b b 2 2 p p I r p v G (1-c-1) 1 1 q q I x q v B (1-c-2) b b b b v v 2 r p x q I r x (1-c-3) p q v I (1-c-4) b 2 b b b In wnd farm p and q denote actve and reactve power of branch p and q denote actve and reactve power load of node I denotes the current of branch. Actually s controlled by the control center and not fxed. So from the wnd farm sde let ncrease and decrease respectvely stepwse by.1 p.u. from current value the correspondng POC and POC are computed for each gven SP by solvng (1) and these soluton ponts are combned together to acqure the maxmum and mnmum curves for POC as shown n Fg. 4. The regon bounded by the two curves s the FR of an ndvdual wnd farm whch s the set of all feasble operatonal ponts and guarantees normal operaton of all WTGs under normal condtons. POC voltage of bus ( ) Fg. 4. Stepwse search method n an ndvdual wnd farm It should be noted that: 1) Decreasng the search step wll produce more accurate results but ths wll lead to a sgnfcant ncrease n computaton tme. Consderng both accuracy and effcency search step s set as.1 p.u. 2) For the gven SP t s not practcal for wnd-ac f the voltage operaton range [ POC POC ] s too small. Consderng both computaton amount and practcablty the stepwse search ends when the voltage operaton range [ POC.5 p.u. for each step for each step.1 p.u..5 p.u. current value of bus stepwse search POC ] s less than.5 p.u. as shown n Fg. 4 the green regon wll be used as the FR for each ndvdual wnd farm. 3) For each step once SP s gven POC s ncreasng n wnd farm s total reactve power Q (n Fg. 3). Thus for each gven SP wnd farm s correspondng total reactve control capablty Q and Q whch are used below for system-sde n (3) can be obtaned from optmal so- lutons of POC and POC respectvely by solvng (1). 4) On-load tap changers (OLTCs) and capactor/reactor banks are not consdered as optmal varables due to the followng two reasons: Frst n Chna most tap changers n wnd farms could not be onlne regulated n operaton. Few OLTCs are used to optmze the voltage profle only 3~5 tmes a day. In terms of capactor/reactor banks one of the reason leadng to the cascadng trps s the mproper swtches capactor/reactor banks whch are gradually replaced by SC/SGs n wnd farms n Chna. Thus ths paper manly focuses on the coordnaton of WTGs (wnd turbne generators) and SC/SGs. Second n order to guarantee secure and economc operatons of wnd farms n Chna some wnd farms may use the OLTCs and capactor/reactor banks to optmze the voltage scheme every 1~4 hours. But dfferent from OLTCs and capactor/reactor banks optmzaton the proposed s appled to real wnd systems onlne for 1~5 mnutes level. Therefore the control center wll refresh the after every operaton of the OLTCs and capactor/reactor banks. When wnd farm computes the operaton state of OLTCs and capactor/reactor banks remans unchanged thus they are not consdered as optmal varables n computaton model. 5) Due to the fact that the computaton tme of s always less than 2 seconds and the s appled to real wnd systems for 1~5mns level the computaton of s based on the assumpton that a short-term wnd speed forecastng model s known wth suffcent accuracy [28]-[29]. Thus the model uses the current actve power nterface. Thus the model uses the current actve power nterface. On the other hand the control center wll refresh the every 1~5mns onlne n wnd operaton whch also guarantees the accuracy of n a real wnd system. C. for multple wnd farms Based on the FRs for each ndvdual wnd farm above the s then proposed for POC buses of all wnd farms and the bus n the control center. The means: each wnd farm can autonomously control all ther WTGs wthn normal operaton ranges not only under normal condtons but also under any N-1 contngency (wthout consderng the operaton detals of other wnd farms) n a decoupled way as long as the control center controls wthn [ ] whle all wnd farms control ther POC wthn [ POC POC ]. Obvously the rregularly-shaped FR (green regons) n Fg. 5 cannot be used for decoupled voltage control between

6 voltage of POC bus n wnd farm ( ) voltage of POC bus n wnd farm N w ( ) voltage of POC bus n wnd farm 1 ( ) bus and each wnd farm because the operaton range for POC depends on the value of. Thus the rectangle-shaped regons can be used for decoupled control because the operaton range for POC s ndependent of. (operaton range for POC remans unchanged when changes.e. n the blue rectangles the voltage operaton range for POC s always [ POC POC ] as long as the voltage of remans wthn [ ]). As shown n Fg. 5 the blue rectangles n each fgure are the whch can be used for decoupled control between the bus and each wnd farm. POC1 POC N w POC 1 POC Fg. 5. for multple wnd farms POC POC N w POC N w 1 Fg. 6. Lnearzaton of FR s upper bound for wnd farm n wnd farm 1... wnd farm N w : voltage of bus ( ) To compute the the upper bounds and lower bounds of all wnd farms practcal FRs (green regons) are frst lnearzed by two lnes respectvely for practcal applcaton. As shown n Fg. 6 there are N operatonal ponts on FR s upper bound (from 1 to N). (the upper-left small subfgure n Fg. 6 s the voltage feasble regon.e. Fg. 4) The upper bound s voltage of bus ( ) n N n n : POC N N : POC N better approxmately lnearzed wth a larger square of the trangle 1 n N. It s assumed that n=n* s the optmal of total N ponts (2-a) then the two lnearzed constrants of the upper bound (lne 1 n and n N) can be expressed as (2-c). Smlar to the upper bound ths method can be also appled to the lnearzaton of the lower bound. There are also N operatonal ponts on FR s lower bound (from 1 to N). The square of the trangle 1 m N reaches the maxmum when m=m* (2-b) then the two lnearzed constrants of the lower bound (lne 1 m and m N) can be expressed as (2-d). ( m s on the lower bound) n* arg max (2-a) S n12... N 1 nn S m m N N m* arg max (2-b) n* n* 1 n* N N N n* N m* * 1 m m* N N N m* N (2-c) (2-d) Here and are set to the maxmum and mnmum value among all wnd farms (2-e) as shown n Fg. 5. (2-e) For convenence (2-f) s used nstead of the FR s boundary constrants (2-c)~(2-e) expressng that the operaton pont ) s wthn the FR of wnd farm. ( POC f (2-f) (2) completes the lnearzaton of the FR whch s used n SCOPF (3). The for multple wnd farms can also be obtaned by usng stepwse search method. For each step at the gven the correspondng operaton range [ POC POC ] for POC n the ndvdual wnd farm can be computed by (1) above. But n multple wnd farms the normal operaton range for POC noted as [ POC(1) POC(2) (as shown n Fg. 7) due to the followng two reasons: ] s a subrange of [ POC POC ] 1) The operaton range [ POC POC ] of the ndvdual wnd farm s computed based on the assumpton that the control center has enough control capablty to control at the gven SP (1-g). But n multple wnd farms the control center may not have enough control capablty to control at SP whle wnd farms decoupled control ther POC at any value wthn [ POC POC ]. For example the voltage operaton pont

7 voltage of POC bus n wnd farm ( ) ( POC1 POC2 POC SP ) may not exst. 2) [ POC(1) POC(2) ] should both guarantee all WTGs normal operaton not only n normal condtons but also under any N-1 contngency. max s f1 f2 f 1 ΔQw ΔQg ΔQsvc 1 POC 2 POC 1 2 Ns s 2 POC k POC k k 1 s1 1 f s.t. g mk g mk g mk (3-a) Q Q Q (3-b) Q Q Q Q (3-c) current k k Ng current qv qv POC k pw m g m k ww k m1 1 S Q S Q Ng SP current qv qv pp m g m k wp k m1 1 S Q S Q POC (3-d) (3-e) Q Q Q (3-f) f s s s svc svc k svc s s k POC k s s current s qv s POC k ww svc k 1 s s current s qv s k wp svc k 1 S Q S Q N m N s N k 12 w s 1 g 2 (3-g) SP voltage of bus ( ) Fg. 7. oltage operaton range of wnd farm n the ndvdual wnd farm and SP n multple wnd farms for each gven Therefore for each gven SP (3-e) the control center ams to seek the largest voltage operaton range (f 1 n (3-a)) for the POC buses of all wnd farms. Under normal condtons the conventonal power plants use reactve power control capabltes (3-b) to control to the gven value SP (3-e) whle wnd farms use reactve power control capabltes (3-c) to mantan POC wthn [ POC POC ] (3-d). Wnd farms cannot operate normally f (3-d) s volated n the normal condtons. When a N-1 contngency happens the fast-response compensators such as SCs are regulated (3-f) n order to mantan POC buses voltage as much as they can (f 2 n (3-a)) whch also guarantees that the operaton ponts are wthn the FR (3-g) after N-1 contngency the volaton of constrants (3-g) may result n a cascadng trp. For a wnd pool area all ndvdual wnd farms trp faults should be consdered otherwse any trp fault s lkely to cause a cascadng trp fault trggered by the frst trp fault. Here S s the senstvty coeffcent e.g. S qv wp denotes the senstvty of s (p) voltage (v) to wnd farm (w) s reactve power (q) under normal condtons (superscrpt ). It should be noted: 1) α s the weght coeffcent for each wnd farm. The weght coeffcent for wnd farms wth a larger capacty of reactve power compensators s greater. 2) The weght coeffcent and α n multple obectve functon (3-a) must satsfy >> α =12 N w. For each step at the gven SP [ POC(1) POC(2) ] solved by (3) can guarantee decouplng and securty: (A) Decouplng: Wnd farm can realze decoupled control POC at any value wthn [ POC(1) POC(2) ] wthout consderng other wnd farms. (Proved below) (B) Securty: Normal operaton for all wnd farms under normal condtons and under any N-1 contngency. Proof of (A): Frstly let Δ g(k) denote the total voltage regulaton of conventonal generators at the current operaton state where ΔQ gm(k) qv g ( k ) S pw mqg mk m1 s constraned by (3-b) thus Δ g(k) s constraned Δ g Δ g(k) N g Δ g. It s assumed ( SP Δ (*) g(1) (*) (*) POC1(1) POC (1) Δ (*) (*) (*) g(2) POC1(2) POC (2)) s optmal of OPF (3). When the voltage of bus s fxed at SP for wnd farm the voltage of ts POC bus POC s strctly ncreasng n ts total reactve power regulaton ΔQ the strctly ncreasng functon s defned as F Q SP where ΔQ = Q Q current. For wnd farm (=12 N w) POC (*) [ POC(1) (*) POC(2) ] because the nverse functon Q F 1 SP s also strctly ncreasng as such current * * current 1 2 Q Q Q Q Q Q Q Q Q Q Q current And the senstvty coeffcent S qv wp s always postve then

8 voltage of POC bus n wnd farm ( ) SP current SP current * g g1 qv * qv qv * Swp Q 1 Swp Q Swp Q SP current * SP current g2 g N w SP current qv g wp g 1 S Q Due to the fact that ΔQ gm can be obtaned such that ΔQ gm are contnuous control varables S Q SP current qv g wp 1 Ng qv g g pw m g m g m1 S Q Qg m Qg m Qg m (*) (*) Thus POC [ POC(1) POC(2) ] a correspondng ΔQ can always be found for wnd farm ΔQ gm for conventonal SP generators whch satsfy all constrants at the fxed value of bus.e. the control center can use conventonal generators control capabltes to control the bus s voltage at SP when each wnd farm decoupled control ther POC buses (*) (*) voltage wthn [ POC(1) POC(2) ]. Ths completes the proof. POC for each step 1 for each step p 2 q 1 SP p SPq Fg. 8. for wnd farm.1 p.u..5 p.u. voltage of bus ( ) current value of bus Therefore the stepwse search method can be used to obtan the. Smlar to the FR above from the wnd farm sde let ncrease and decrease stepwse respectvely from current value the correspondng POC(1) and POC(2) s computed for each gven SP by solvng (3) then combne these soluton ponts together to acqure the voltage securty regon curves as shown n Fg. 8. Consderng both accuracy and effcency the frst several steps n the computaton are set to.5 p.u. whle other steps are set to.1 p.u.. Apparently there are many dfferent rectangles wthn the blue curves n Fg. 8. It s therefore mportant to seek the largest for the wnd pool area. To fnd the largest SP POC(1) and POC(2) are frst normalzed for each gven n Fg. 7 usng (4). k k k 12 Then the square of can be computed usng (5) the superscrpt p and q represent step p and q as shown n Fg. 8. The can be obtaned from the maxmum S(pq) expressed n (6) where the stars follow p or q represent the maxmum soluton of all steps. Another pont should be noted s the requrement of accuracy. In addton to decreasng the search step n Fg. 4 and Fg. 8 lnear nterpolaton can be used between two adacent steps n Fg. 8 to get more data ponts n order to obtan a larger. N w SPq SPp p q q* p* POC 1 POC POC 2 S p q (5) SPp* SPq* D. The computaton process of n a wnd pool area The process of acqurng can be dvded nto sx steps as shown n table I the nformaton exchange and sx computaton steps between system-sde and wnd-farm-sde are shown n Fg. 9. TABLE I FLOW CHART TO COMPUTE FLOW CHART Step 1 All the ndvdual wnd farms use stepwse search method for each gven SP to compute the correspondng [ POC POC ] by (1). Step 2 Each ndvdual wnd farm sends the data set Step 3 Step 4 Step 5 Step 6 { (4) (6) SP POC POC Q Q } to control center. The control center uses (2) to lnearze the upper bounds and lower bounds of all wnd farms. The control center uses stepwse search method SP for each gven to compute the correspondng [ POC(1) POC(2) ] by (3). Normalze each POC(k) usng (4) and obtan the largest usng (5). The result of s expressed as (6). The control center sends [ POC POC ] back to each wnd farm for voltage control. The control center should control the voltage of bus wthn [ ].

9 oltage of bus voltage of POC bus n wnd farm ( ) Fg. 9. Informaton exchange and sx computaton steps of between system-sde and wnd-farm-sde For more clear llustraton and understandng we put all regons and curves nto Fg. 1 whch also shows the corres pondng step n table I to compute or get these regons and curves. POC Step 6 Wnd Farm Step 2 Control Center feasble regon curve (step 1) applcable feasble regon lnearzed feasble regon (step 3) securty regon curve (step 4) (step 5) Step 5 Step 4 Step 3 Step 1 Step voltage of bus ( ) Fg. 1. Illustraton of dfferent knds of regons and curves III. CASE STUDIES A. A smple system wth two wnd farms POC 1 POC 1 Step 2 Fg. 11. for two wnd farms and bus Wnd Farm N w POC 2 Step 6 N-1 secure N-1 not secure POC 2 A smple system wth two wnd farms was studed to verfy the proposed method usng Monte Carlo smulaton. Frst the Monte Carlo smulaton method was used to generate 1 smulaton ponts that guarantee normal operaton under N- condtons thereafter all N-1 contngences based on each operaton pont were computed. The N-1 secure ponts were plotted green whle N-1 not secure ponts were plotted red n Fg. 11. Then the (blue cube) was computed for ths smple system and plotted n Fg. 11. The smulaton results demonstrate three characterstcs of : 1) Securty: All operatonal ponts n the were green ponts ( N-1 secure ponts ). 2) Accuracy: N-1 securty cannot be guaranteed f operatonal ponts are located outsde the blue cube n Fg. 11. Some red ponts ( N-1 not secure ponts ) exst outsde but near to the cube boundary whch shows that the boundary of computed s near to the real boundary of securty regon. 3) Autonomous (Decouplng): The operaton ponts fll all space of the blue cube.e. wnd farm 1 and wnd farm 2 can controls ts own POC bus s voltage to any value wthn [ POC1 POC1 ] and [ POC2 POC2 ] by tself as long as the bus controls ts voltage wthn [ ] wthout consderng voltage operaton detals of the other wnd farm and the bus. Therefore the proposed n ths paper can be used for voltage control n a decoupled way. B. A real system wth eght wnd farms n Northern Chna A real system wth eght wnd farms comprsng the ZB Wnd Power Base n North Chna as Fg. 2 shows was studed to verfy the effectveness of the s proposed n ths study. Frstly the tme and frequency computed once for wnd farms are recorded n table II. Due to the hgher lnearty DstFlow model n wnd farms and only once necessary nformaton exchange the computaton does not take a lot of tme. Fg. 12 shows the voltage devaton n the ZB wnd power base after dfferent N-1 contngences. There are eght black lnes whch represent eght dfferent contngences for eght wnd farms. If eght wnd farms and the substaton operate wthn ther own then after an N-1 contngency even f the voltages of other wnd farms and the substaton ncrease they wll not volate the voltages upper and lower bounds of normal operaton. TABLE II COMPUTATION TIME AND FREQUENCY FOR WIND FARMS OPF/ Computng Computng Computaton Place Each Indvdual Wnd Farm SCOPF Frequency Tme LY s CNG s GT s DJH s WLS s GH s WHP s QSY s Total Tme 7.653s Control Securty s s Center Regon Other computatons (nclude boundary lnearzaton.245s

10 voltage of POC bus n wnd farm ( ) oltage / p.u. normalzaton by (4) acqure the largest by (5)) Total Computaton Tme 16.46s Lower Bound.95 CNG DJH GT LY QSY SY WLS WHP (ZB) POC buses n each Wnd Farm and bus Fg. 12. oltage of wnd farms and the bus wthn an after N-1 contngences Fg. 13 shows the voltage of each WTG n an ndvdual wnd farm n whch each whte star represents a WTG. If a wnd farm operates wthn ts as shown n Fg. 13 (a.1) and (a.2) then the WTGs operate at a lower voltage level before a trp fault. After other wnd farms trp fault the voltage of all WTGs wll ncrease but they wll not exceed the upper bound (1.1 p.u.). However the stuaton s dfferent f the wnd farm operates wthout the whch s shown n Fg. 13 (b.1) and (b.2). Before the trp fault although each WTG can operate normally WTGs n the whte cycle operate at a hgher voltage level and are close to the upper bounds (1.1 p.u.). After other wnd farms trp fault all WTGs voltage ncreases and some (WTGs n the whte cycle) exceed ther upper bounds leadng to cascadng trp faults. (a.1) Before trp fault (a) wthn (b.1) Before trp fault (b) wthout normal condton dfferent N-1 contngences Upper Bound (a.2) After trp fault exceed 1.1 p.u. (b.2) After trp fault Fg. 13. oltage magntude of wnd unts n a wnd farm wthn or wthout the after an N-1 contngency C. Comparson wth other works Here we compare the proposed wth recent relevant researches from eght aspects n table III. By comparson the advantages of the proposed method can be summarzed as follows. 1) oltage securty regons (SR) are decoupled or not: For each wnd farm the proposed [ POC POC ] can be used for decoupled voltage control whle other works compute the SR [ ] whch cannot be used for decoupled voltage control. (As shown n Fg. 14) 2) The proposed also provded decoupled securty voltage ranges [ ] for substaton but other works ddn t. 3) In each wnd farm the power flow model (n DstFlow format) s used. Thus the result of the proposed method wll be more accurate. 4) The stepwse search method proposed n ths paper does not requre teraton and the necessary constrant nformaton s exchanged only once between the control center and each wnd farm resultng n less necessary computaton tme. Here we use 1 dfferent power flow nterfaces to compute SR of the real system (as Fg. 2 shows) usng dfferent methods. The average total computaton tme was recorded n table III and the proposed method observes faster computatons than other works. POC Fg. 14. Comparson between proposed n ths paper and SR n relevant works TABLE III COMPARISON AMONG DIFFERENT METHODS Comparson Ths paper [22] [2] [21] Results of securty regon for wnd farms Wnd farms can decoupled control ther voltages? Provde decoupled securty voltage ranges for substaton? [ POC POC ] [ ] [ ] Yes No No [ ] No No Man computaton method Stepwse search Iteraton Model and Accuracy Wnd Farms Control Center voltage of bus ( ) Power flow model n DstFlow format Senstve model Senstve model Approxmate boundary Senstve model

11 Accuracy better average average Average total computaton tme for 1 computatons 15.25s 16.11s 15.48s Necessary nformaton Requre exchange durng computatons Only once teratons Only once Consder randomness of wnd power? No Yes No I. CONCLUSIONS Due to the complexty of voltage securty regons and the dffculty of computaton ths paper proposes the and a stepwse search method for ts computaton. At each wnd farm an s desgned to guarantee the normal operaton of each WTG whle n the control center each regon s desgned n order to guarantee normal operaton both under normal condtons and after N-1 contngences. If the control center controls bus wthn ts and all the wnd farms POC buses operate n ther own each wnd farm can realze decoupled control of all the WTGs wthn normal operaton ranges both under normal condtons and under any N-1 contngency wthout consderng the operaton detals of other wnd farms. Compared wth the prevous methods the results are more accurate because the power flow model s used nstead of a tradtonal senstve model n each wnd farm. It wll not take a lot of computaton tme because ths method does not requre teraton and uses power flow model wth the DstFlow format n each wnd farm. Case studes wth s smple system and a real system verfy the accuracy and effectveness of the method and good performance usng a Monte Carlo smulaton. Wth ncreased wnd power penetraton s may not exst. Thus how to curtal wnd power and acqure maxmum securty regons wll be studed n a future study. Indeed t s also mportant to deal wth the randomness of actve power due to the forecast errors. Compared wth the proposed n ths paper the robust to actve wnd power randomness s much more complcated and the computaton must take more tme. Based on the proposed usng the specfc current actve power nterfaces n ths paper the robust to actve wnd power randomness wll be studed n the future works. 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12 [26] Daratha N Das B Sharma J. Coordnaton between OLTC and SC for voltage regulaton n unbalanced dstrbuton system dstrbuted generaton IEEE Trans. Power Del. vol. 29 no. 1 pp [27] awan F A Karlsson D. oltage and reactve power control n systems wth synchronous machne-based dstrbuted generaton. IEEE Trans. on Power Del. vol. 23 no. 2 pp [28] Ye R Suganthan P N Srkanth N. A comparatve study of emprcal mode decomposton-based short-term wnd speed forecastng methods. IEEE Trans. Sustanable Energy vol. 6 no. 1 pp [29] Sngh Rohan Sahay Kshan Bhushan Srvastava Shubhankar Aseet. Short-term wnd speed forecastng of Oak Park Weather Staton by usng dfferent ANN algorthms Smart Grd Technologes - Asa (ISGT ASIA) 215 IEEE Innovatve 215 pp [3] Neumann T.; Wnhoven T.; Deconnck G.; Erlch I Enhanced Dynamc oltage Control of Type 4 Wnd Turbnes Durng Unbalanced Grd Faults IEEE Trans. Energy Converson. vol. 3 no. 4 pp [31] De Rcke S Ergun H an Hertem D et al. Grd Impact of oltage Control and Reactve Power Support by Wnd Turbnes Equpped Wth Drect-Drve Synchronous Machnes. IEEE Trans. Sustanable Energy vol. 3 no. 4 pp Tao Nu receved hs Bachelor degree from the Department of Electrcal Engneerng Tsnghua Unversty Beng Chna n 214. He s pursung the Ph.D. degree at Dept. of Electrcal Engneerng at Tsnghua Unversty. Hs research nterests nclude voltage securty regon automatc reactve power voltage control and renewable generaton ntegraton. (CET) Department of Electrcal Engneerng Techncal Unversty of Denmark (DTU) Kgs. Lyngby Denmark from November 29 to October 21 an Assstant Professor from November 21 to August 213 and has been an Assocate Professor snce September 213 wth the same centre. Bomng Zhang (SM 95 F 1) receved the Ph.D. degree n electrcal engneerng from Tsnghua Unversty Beng Chna n Snce 1985 he has been wth the Electrcal Engneerng Department Tsnghua Unversty promoted to a Professor n Hs nterest s n power system analyss and control especally n the EMS advanced applcatons n the Electrc Power Control Center (E). Tao Dng (S 13 M 15) receved the degree n mathematcs from Southeast Unversty Nanng Chna the B.S.E.E. and M.S.E.E. degrees from Southeast Unversty Nanng Chna and the Ph.D. degree from Tsnghua Unversty Beng Chna n and 215 respectvely. From 213 to 214 he was a stng Scholar at the Department of Electrcal Engneerng and Computer Scence Unversty of Tennessee Knoxvlle TN USA. He s currently an Assocate Professor wth the State Key Laboratory of Electrcal Insulaton and Power Equpment and the School of Electrcal Engneerng X an Jaotong Unversty X an Chna. Hs research nterests nclude electrcty markets power system economcs and optmzaton methods and power system plannng and relablty evaluaton. He was the recpent of the Outstandng Graduate Award of Beng Cty. Qngla Guo (SM 214) was born n Jln Cty Jln Provnce n Chna on Mar He graduated from the Department of Electrcal Engneerng Tsnghua Unversty Beng Chna n 2 wth B.S degree. He receved hs PhD degree from Tsnghua Unversty n 25 where he s now an assocate professor. He s a member of CIGRE C2.13 Task Force on oltage/ar support n System Operatons. Hs specal felds of nterest nclude smart grds cyber-physcal systems and electrcal power control center applcatons. Hongbn Sun (SM 212) receved hs double B.S. degrees from Tsnghua Unversty n 1992 the Ph.D from Dept. of E.E. Tsnghua Unversty n He s now Changang Scholar of Educaton Mnstry of Chna full professor of electrcal engneerng n Tsnghua Unv. and assstant drector of State Key Laboratory of Power Systems n Chna. From 27.9 to 28.9 he was a vstng professor wth School of EECS at the Washngton State Unversty n Pullman. He s a Fellow of IET. He s a member of IEEE PES CAMS Cascadng Falure Task Force and CIGRE C2.13 Task Force on oltage/ar support n System Operatons. In recent 15 years he led a research group n Tsnghua Unversty to develop a commercal system-wde automatc voltage control systems whch has been appled to PJM nterconnecton the largest regonal power grd n USA and to more than 6 large-scale power grds n Chna. He publshed more than 3 academc papers. He won the Chna Natonal Technology Innovaton Award n 28 the Natonal Dstngushed Teacher Award n Chna n 29 and the Natonal Scence Fund for Dstngushed Young Scholars of Chna n 21. Hs research nterests nclude smart grds renewable generaton ntegraton and electrcal power control center applcatons. Quwe Wu (S 4 M 8-SM 15) receved the B.Eng. and M.Eng. degrees n power system and automaton from Nanng Unversty of Scence and Technology Nanng Chna n 2 and 23 respectvely and the Ph.D. degree n power system engneerng from Nanyang Technologcal Unversty Sngapore n 29. He was a Senor R&D Engneer wth ESTAS Technology R&D Sngapore Pte Ltd. Sngapore from March 28 to October 29. He was a Postdoc wth the Centre for Electrc Technology