Transient Stability Enhancement in Power System Using Static VAR Compensator (SVC)

Transcription

1 Leonaro Journal of Sciences ISSN Issue, July-December p. 9- ransien Sabiliy Enhancemen in Power Sysem Using Saic VAR Compensaor (SVC) Youssef MOULOUDI *, Abellah LAOUFI an Bousmaha BOUCHIBA Deparmen of Elecrical Engineering, Bechar Universiy, Bechar, Algeria. * Corresponing auhor moulouiyoussef@yahoo.fr Absrac In his paper, an inirec aapive fuzzy exciaion an saic VAR (uni of reacive power, vol-ampere reacive) compensaor (SVC) conroller is propose o enhance ransien sabiliy for he power sysem, which base on inpu-oupu linearizaion echniue. A hree-bus sysem, which conains a generaor an saic VAR compensaor (SVC), is consiere in his paper, he SVC is locae a he mipoin of he ransmission lines. Simulaion resuls show ha he propose conroller compare wih a conroller base on raiion linearizaion echniue can enhance he ransien sabiliy of he power sysem uner a large suen faul, which may occur nearly a he generaor bus erminal. Keywors Feeback linearizaion; SVC conroller; generaor exciaion; inirec aapive fuzzy. Inroucion An inerconnece power sysem basically consiss of several essenial componens. hey are namely he generaing unis, he ransmission lines, he loas, he ransformer, saic VAR compensaors an lasly he HVDC (High Volage Direc Curren) lines. During he hp://ljs.acaemicirec.org/ 9

2 ransien Sabiliy Enhancemen in Power Sysem Using Saic VAR Compensaor (SVC) Youssef MOULOUDI, Abellah LAOUFI A an Bousmaha BOUCHIB operaion of he generaors, here may be some isurbances such as susaine oscillaions in he spee or perioic variaions in he orue ha is applie o he generaor. hese isurbances may resul in volage or freuency flucuaion ha may affec he oher pars of he inerconnece power sysem. Exernal facors, such as lighning, can also cause isurbances o he power sysem. All hese isurbances are erme as fauls. When a faul occurs, i causes he moor o lose synchronism if he naural freuency of oscillaion coincies wih he freuency of oscillaion of he generaors. Wih hese facors in min, he basic coniion for a power sysem wih sabiliy is synchronism. Besies his coniion, here are oher imporan coniion such as seay-sae sabiliy, ransien sabiliy, harmonics an isurbance, collapse of volage an he loss of reacive power. Differen approaches for exciaion conrol are available in lieraure such as aapive fuzzy exciaion conrol of power sysems base on inpu-oupu linearizaion echniue [], nonlinear exciaion conrols base on feeback linearizaion conrol (FBLC) concep [,3], nonlinear SVC conrol for improving power sysem sabiliy [4], an coorinae conrol of generaor exciaion an SVC [5,6]. Aapive nonlinear exciaion conrol for inerconnece power sysem is repore in [7]. Sabiliy enhancemen is of grea imporance in power sysem esign. Exciaion conrol an saic VAR compensaor (SVC) play imporan roles in sabiliy enhancemen of power sysems. SVCs are increasingly applie for various reasons by he uiliies in moern power sysems wih long ransmission lines an remoe sources of generaions. Since SVCs can achieve fas an precise regulaion of erminal volage, SVC conrol schemes arac increasing aenion in recen years. In aiion o is funcions for rapi conrol of volage, SVC insallaions serve o improve he ransien sabiliy of power sysem following a major isurbance o he sysem [8]. A hree-bus sysem, which conains a generaor an an SVC, is consiere in his work. he SVC is locae a he mipoin of he ransmission lines. A nonlinear feeback law for he generaor exciaion is foun which linearizes an ecouples he power sysem moel. A new coorinae exciaion an SVC conrol scheme is propose base on linearize moel. he new coorinae conroller consiss of wo conrollers, an exciaion conroller an an SVC conroller. he conrollers for he generaor exciaion an SVC are esigne separaely base only on local measuremens. his paper presens an inirec aapive fuzzy exciaion conrol base on inpu-oupu

3 [ Leonaro Journal of Sciences Issue, July-December ISSN p. 9- linearizaion. he inirec aapive conrol use fuzzy logic sysems o moel he plan an consruc he conrollers assuming ha he fuzzy logic sysems represen he rue plan, herefore fuzzy IF-HEN rules escribing he plan can be irecly incorporae ino he inirec aapive fuzzy conroller. Maerial an Meho o simplify he iscussion, a simplifie moel for a generaor an an SVC sysem, which forms a hree bus sysem shown in Figure (Xl =Xl 3 ) is consiere. Generaor G ransformer 3 Xl Xl 3 V S Xl Xl 3 Faul SVC Figure. A simplifie generaor an SVC hree bus moel Mechanical euaion []: () = w() Δ δ () D w w& () = w() ( Pe Pm ) () H H Generaor elecrical ynamics. he plan moel can be wrien as:. x. x. x 3 = x = ( Dx M = ( x3 o + (x + (x x' )i i x' )i + E x i f ) 3 + Pm) (4) where x = δ is he relaive roor posiion, x = w is he relaive spee an x 3 = E ' is he ransien EMF in he uaraure axis. he mechanical power inpu P m is assume consan an he elecrical power oupu P e is given by:

4 ransien Sabiliy Enhancemen in Power Sysem Using Saic VAR Compensaor (SVC) Youssef MOULOUDI, Abellah LAOUFI A an Bousmaha BOUCHIB P = E i + x i (5) e ' 3 E ' = (x x ) i (6) ' An he irec an uaraure axis currens are given by: i i = (g cosδ + b sin δ)e' + (b cosδ g sin δ)x = (b cosδ g sin δ)e' + (g cosδ + b sin δ)x 3 3 (7) an: y = g + jb (8) Anoher variable of ineres in power sysem sabiliy suies is he generaor erminal volage. he erminal volage is obaine as: V = V + V, where V = E' + ix' an V = E i x' [7,9]. ' Saic VAR Compensaor he applie SVC is shown in Figure, which is a fixe capacior an hyrisor conrolle reacor (FC/CR) ype an locae a he mipoin of each ransmission line. he magniue of he SVC amiance is obaine by [,]: B B s L L( α) Bc = B (9) π α + sin α α = () πx ( ) L Accoring o he variaions in erminal volage an angular spee, he suscepance of he inucor B L an hen B S can be regulae as shown in Figure 3 []. B C B L V svc V ref KB S+ R B L Figure. FC/CR ype of SVC Figure 3. Block iagram of he SVC conroller he SVC ynamic moel can be expresse as follows:

5 [ Leonaro Journal of Sciences Issue, July-December ISSN p. 9- B = L C B B () () ( B () + B k u () ) L + R Where B L () is he suscepance of he inucor in SVC; B C he suscepance of he capacior in he SVC; R he ime consan of he SVC regulaor, K B, he gain of he SVC regulaor an u B () is he inpu of he SVC regulaor. he configuraion of he SVC is shown in Figure, he faul we will consier in his paper is a symmerical 3-pahse o groun shor circui faul, which accurse a he ransmission lines. λ is he fracion of he faule line o he lef of he faul. If λ = he faul is a he generaor bus erminal. λ =.5 pus he faul in he mile of he line beween bus an bus, an so on. Feeback Linearizaion In his secion, he esign principles using he irec feeback linearizaion (DFL) echniue o esign a nonlinear coorinae conroller for he power sysem shown in Figure is consiere [3]. he ynamic moel given in Euaion () can be wrien in he following form [7]: ẋ = f (x) + g(x)u y = h(x) () where: f g. ( ) D ' x = x ( ) + x x ii ix3 + Pm M M ' ( x + ( x x ) i ). ( x) = u E,h(x) = f x o = an [ ] o 3 x x = x. x x3 he feeback linearizing an ecoupling conrol is hen efine as [4]: [ v α( x) ] ( x) u = (3) β 3

6 ransien Sabiliy Enhancemen in Power Sysem Using Saic VAR Compensaor (SVC) Youssef MOULOUDI, Abellah LAOUFI A an Bousmaha BOUCHIB he expressions for α(x) an β(x) are repore in he appenix. For racking he oupu o a esire reference y m, he new inpu v can be chosen as: = & y&& + a && e + a e& a e (4) v m 3 + where e is he racking error efine as e=(y m -y ) an a, a, a 3 are chosen such ha he polynomial ( s a s + a s + a ) + is sric Hurwiz an he sysem has poles a esire 3 locaions. he conrol law given by Euaions (3) an (4) resuls in feeback linearize an ecouple sysem wih he oupu y converging asympoically o he esire response. Consier he SVC moel () is linear, when a faul occurs, he SVC can help o enhance he sabiliy. Implemenaion of his conrol law reuires precise informaion abou he sysem parameer specifically he ransmission amiance y. However he y is usually imprecisely moelle or may vary ue o fauls in he power sysem. he aapive fuzzy conroller esigne nex mainains sabiliy an esire performance in he presence of uncerainy or unknown variaion in plan parameers an srucures. Aapive Fuzzy Conrol he fuzzy logic sysems wih cenre average efuzzifier, prouc-inference rule an singleon fuzzifier of he form [5]: y where ψ ( x) j M ( x) θ ψ ( x) = (5) = j n M j j j μ ( xi ) ' ( x ) ' i= Fi n ( μ i ) = i= F i wo main reasons arise for using he fuzzy sysem (5) as basic builing block of aapive fuzzy conrollers. Firs, he fuzzy sysems in he form of (5) are proven in [5] o be universal approximaors, i.e., for any given real coninuous funcion f on he compac se U, here exiss a fuzzy sysem (5) such ha i can uniformly approximae f over U o arbirary accuracy. herefore, he fuzzy sysems (5) are ualifie for moelling nonlinear sysems. Secon, he fuzzy sysems (5) are consruce from he fuzzy IF HEN rules using some specific fuzzy inference, fuzzificaion, an efuzzificaion sraegies. herefore, 4

7 [ Leonaro Journal of Sciences ISSN Issue, July-December p. 9- linguisic informaion from a human exper can be irecly incorporae ino he conroller [4]. Accoring o he efiniion in [5], aapive fuzzy approaches can be classifie as inirec fuzzy conroller an irec fuzzy conroller. An inirec fuzzy conroller uses fuzzy logic sysem as a moel of he plan an can incorporae fuzzy escripions of he plan irecly ino iself. From euaions (A-) an (A-) given in Appenix, we can see ha α ( x) an β( x) are funcion of parameers E, Δ δ an w (x, x an x 3 ). hese parameers are ifficul o measure, since E is physically unmeasurable herefore he approximaions of α ( x) an β( x) αˆ ( x θ ) = θ ψ( x) βˆ can be generae using he basis funcion expansion as follows: ( x θ ) = θ ψ( x) β α β α (6) θ α ^ α θ β ^ β Figure 4. Srucure of fuzzy sysems Using he cerainly euivalen principle, he conrol law (3) can be wrien in erms of αˆ ( x ) an βˆ ( x ) θ α u βˆ θ β as: [ αˆ ( x θ ) + y&& m + a e] ( x θ ) = α where a = [ a a a ] an e [ eee &&&] 3 β ( x) & (7) = wih he upae law for he parameers: θ = γ e α Pbψ (8) θ e β = γ Pbψ( x)u (9) 5

8 ransien Sabiliy Enhancemen in Power Sysem Using Saic VAR Compensaor (SVC) Youssef MOULOUDI, Abellah LAOUFI A an Bousmaha BOUCHIB he P marix is he uniue posiive efine 3 3 marix ha saisfies he Lyapunov euaion. We use Lyapunov sabiliy heory o rive conrollers parameers upae laws, which insure sabiliy of he close loop sysem an plan oupu o achieve racking performance []. Resuls an Discussion he suie sysem is illusrae in Figure ; which applie o a real nework in Algeria which conains a generaor place in he noe Naama, he SVC is locae a he mipoin of he ransmission lines an he noe Bechar. (Naama an Bechar in souhwes Algerian), he parameers use in simulaion are as follows: P m =, D = 5, M = 5., o = 6.8, X =.5, X =.4, X =.46, X =.546, δ = 4, X rf =.48, Xl = Xl =.33, B lo =.7, B C =.7, R =., K B = 5. he following faul seuence is consiere: Sage : he sysem is in a per faul seay-sae. Sage : A faul occurs a = sec. Sage 3: he faul is remove by opening he breakers of he faule lines a =. sec. Sage 4: he ransmission lines are resore wih he faul cleare a = sec. Sage 5: he sysem is in a pos faul-sae. We have sare he simulaion by inroucing he feeback linearizaion conrol o enhance ransien sabiliy for a power sysem. he response of he power angle uner ifferen faul locaion ( λ =.5,.,.8 an.5) are given in Figure 5. From he resul we can see ha since he physical limi of he FDL, when he faul occurs close o he generaor erminal ( λ =.5) he sysem canno mainain he synchronism. When a large faul occurs, i is very ifficul for FDL o aap he variaions in reacance of he ransmission lines. For his reason he SVC is aken ino consieraion, he SVC is locae a he mipoin of he ransmission line in a power sysem. he propose coorinae conroller consiss of wo conrollers, a generaor exciaion an SVC conroller. he response of he reacive power angle ( Δ δ( ) ) wih coorinae conroller, is given in Figure 6 where he faul is locae nearly a he erminal of he generaor bus ( λ =. ). 6

9 [ Leonaro Journal of Sciences ISSN Issue, July-December p. 9- relaive roor angle in eg Lama=.5 Lama=.5 Lama=. Lama= ime in sec Figure 5. he response of power angle a ( λ =.5,.,.8 an.5) Relaive roor angle in eg Figure 6. he response of power angle a ( λ =. ) he simulaion resul shows ha he propose conroller can enhance he ransien sabiliy of he power sysem, uner a large suen faul, which may occur nearly a he generaor bus erminal, bu local measuremens are reuire. his work presens an inirec aapive fuzzy exciaion conrol base on inpu-oupu linearizaion. In inirec aapive conrol, he parameers of he plan are esimae an he conroller is chosen assuming ha he esimae parameers represen he rue values of he plan parameers. he comparison of he response of he relaive power angle ( Δ δ() ) uner he case coorinae conrol wih an wihou inirec aapive fuzzy conroller is given in Figure 7. 7

10 ransien Sabiliy Enhancemen in Power Sysem Using Saic VAR Compensaor (SVC) Youssef MOULOUDI, Abellah LAOUFI A an Bousmaha BOUCHIB Relaive roor angle in eg 6 4 Feeback Linearizaion FBL Aapive Fuzzy Conroller AFLC Figure 7. Response of he relaive power angle ( Δ δ () ): () wih aapive fuzzy conroller, () wihou fuzzy a ( λ =. ) he responses of he relaive roor spee (w()) an he generaor bus erminal volage (V ()) uner he case wih inirec aapive fuzzy conroller are given in Figures 8 an 9, where he faul is locae a ( λ =. ). he seay-sae erminal volage is a funcion of he reference operaing poin. hus he erminal volage can be brough o an accepable limi by moving he operaing poin, once he sysem has sele o a seay-sae operaion. Relaive roor spee in pu Figure 8. Response of he relaive roor spee (w()) wih aapive fuzzy conroller a ( λ =. ) Generaor erminal volage V Figure 9. Response of he generaor bus erminal volage (V()) 8

11 [ Leonaro Journal of Sciences Issue, July-December ISSN p. 9- he response of he volage a SVC, he reacance conrolle by he SVC (B L ()) an he response of elecric power (P e ) for he sysem using inirec aapive fuzzy conroller are shown in Figures o Vsvc Figure. Response of he volage (V svc ()) a SVC.5 BL Figure. Response of he (B L ()) 3 Pe Figure. Response of he elecric power (P e ) 9

12 ransien Sabiliy Enhancemen in Power Sysem Using Saic VAR Compensaor (SVC) Youssef MOULOUDI, Abellah LAOUFI A an Bousmaha BOUCHIB U Figure 3. he inpu conrol using inirec aapive fuzzy conroller. Ub Figure 4. he inpu of he SVC Conclusions In his paper, he ynamic ineracion beween he generaor exciaion an he SVC is aken ino accoun in he conroller esign. I presens an applicaion of aapive fuzzy conrol o esign a non linear excier for a power sysem o enhance is performance when subjece o abnormaliies such as hree-phase o groun fauls. he propose inirec aapive fuzzy conrol is base on inpu-oupu linearizaion. Simulaion resuls show ha he propose conroller can enhance ransien sabiliy of he power sysem uner a large suen faul, even in he case where a faul occurs nearly a he generaor bus erminal.

13 [ Leonaro Journal of Sciences ISSN References Issue, July-December p. 9-. Yousef H.A., Wahba M.A., Aapive fuzzy nonlinear exciaion conrol of power sysem, s Conference on Inernaional Feeraion of Auomaic Conrol, ACCS 5, March 5.. Wang Y., Xie L., Hill D.J., Robus nonlinear conroller esign for ransien sabiliy enhancemen of power sysems, in Pro.3 h Conference on Decision an Conrol, ucson, AZ, Dec. 99, p Mak F.K., Design of nonlinear generaor exciaions using ifferenial geomeric conrol heories, in Pro. 3 h Conference on Decision an Conrol, ucson, AZ, Dec. 99, p Ma Y., Chen S., A suy on nonlinear SVC conrol for improving power sysem sabiliy, IEEE ENCON 93 / Beijing 993, China, p Cong L., Wang Y., ransien sabiliy an volage regulaion enhancemen via coorinae conrol of generaor exciaion an SVC, Elecrical Power Energy Sysems, 5, p Mahran A.R., Hogg B.W., Coorinae conrol of synchronous generaor exciaion an Saic VAR Compensaor, IEEE ransacions on Energy Conversion, 99, 7(4), p Jain S., Khorrami F., Faranesh B., Aapive nonlinear exciaion conrol of power sysems wih unknown inerconnecions, IEEE ransacion on conrol sysem echnology, 994, (4), p Wang Y., an Y.L., Robus nonlinear coorinae generaor exciaion an SVC conrol for power sysems, Elecrical Power Energy Sysems,, p Anerson P.M., Foua A.A., Power sysem conrol an sabiliy, Iowa Sae Universiy Press, Ames, Iowa, Ghazi R., Azemi A., Aapive fuzzy sliing moe conrol of SVC an CSC for improving he ynamic performance of power sysems, Conference publicaion No.485, AC-DC power ransmission, 8-3 November, IEE, p Canizares C.A., Analysis of SVC an CSC conrollers in volage collapse, IEEE ransacions on Power Sysems, 999, 4(), p Milano F., Power Sysem Analysis oolbox, Documenaion for PSA version..,

14 [[ ransien Sabiliy Enhancemen in Power Sysem Using Saic VAR Compensaor (SVC) Youssef MOULOUDI, Abellah LAOUFI A an Bousmaha BOUCHIB January 6, Li S., Applie nonlinear conrol, USA, Prenice-Hall, ang S., Li H.X., Wang W., Observer base aapive fuzzy conrol for SISO nonlinear sysems, Fuzzy Ses an Sysems, 4, p Wang L.X., Fuzzy sysem an conrol, esign an sabiliy analysis, Englewoo cliffs, NJ: Prenice Hall, 99. Appenix he expressions for α ( x) an β ( x) are:. i x3 + ( x x' ) i x 3 3 o D α( x) = x ( ) + g [(( x x' ) i x )( E' cos( x + δ ) x sin( x + δ )) M M M x + ( x x' ) i ( x x' ) i ( E' sin( x + δ ) x cos( x + δ ))] + g ( )((( x x' ) i x )cos( x + δ ) Mo b ( x x' ) isin( x+ δ)) + x[(( x x' ) i x3)( E' sin( x+ δ) + x 3cos( x+ δ)) + ( x x' ) i M x3 + ( x x' ) i ( E' cos( x+ δ) x 3sin( x+ δ))] + b( )[(( x x' ) i x3)sin( x+ δ) + ( x x' ) Mo i cos( x + δ ) (A-) i b β( x) = + g [(( x x' ) i x )cos( x + δ ) ( x x' ) i sin( x + δ )] + [(( x x' ) i x ) M M M 3 3 o o o sin( x + δ ) + ( x x' ) i cos( x + δ )] (A-) Lis of Symbols VAR: Vol-ampere reacive power (is a uni use o measure reacive power in an Alernaive curren (AC) power sysem); HVDC: High Volage Direc Curren; Δδ : he relaive power angle of he generaor; ω : he relaive spee of he generaor; P e : he acive elecric power elivere by he generaor; P m : he mechanical inpu power; D: amping consan; M: ineria consan; E : he EMF in he uaraure axis; E f : he exciaion conrol inpu. o : he roor circui ime consan; x : he irec axis reacance; x : he irec axis ransien reacance; x : he uaraure axis reacance; x : he uaraure axis ransien reacance; g: he euivalen conucance beween he generaor an he infinie bus; X rf : he ransformer reacance; X rl : he ransmission line reacance; B L : he suscepance of he inucor in SVC; B C : he suscepance of he capacior in he SVC; R : he ime consan of he SVC regulaor; k B : he gain of he SVC regulaor; y : he ransmission amiance; Xl, Xl 3 : reacance of ransmission lines