An Adaptive Control of Static Var Compensator on Power Systems

Transcription

1 An Adapive Conrol of Saic Var Compensaor on Power Sysems N.F.DJAGAROV Zh.G.GROZDEV M.B.BONEV G.D.GEORGIEV Elecrical Deparmen Technical Universiy, Sudenska sr, Varna BULGARIA Absrac: The sysem means of compensaing has been used for oscillaion damping in power sysems. In resen years he FACTS devices are exensively used. In he paper is suggesed an adapive SVC conrol using opimal singular observer. Like regulaing he inducive par of L-C sysem device are improve he main indexes of ransien processes a differen oscillaions in power sysems. Key words: FACT devices, SVC, adapive conrol, opimal singular adapive observer Inroducion Power sysem oscillaions can be damped using a wide variey of devices. Power sysem sabilizers nave been successfully applied o auomaic volage regulaors and speed conrollers [,2,3,4]. Power sysem sabilizers design represens a formidable challenge since general echniques canno be applied. Using of adapive observers is opimal soluion for his problem [5,6,7]. FACTs devices (saic var compensaors, hyrisor conrolled series capaciors, hyrisor conrolled phase angle regulaor, ec.) have been suggesed also [8,9,]. FACT devices can be used o conrol he power flow and enhance sysem sabiliy. The parameers in he ransmission line, i.e. line impedance, erminal volages, and volage angle can be conrolled by hese devices. I is used for independen conrol of real and reacive power in ransmission lines. Moreover, he FACTs can be used for volage suppor and damping of elecromechanical oscillaions. Advances in high power hyrisor echnology and elecronics circuiry have promped he developmen of conrollable saic var sources, ofen called var generaors. Saic Var Compensaors or SVCs were o provide fas, coninuous or sep like volage conrol for large, flucuaing indusrial loads, such as elecric arc furnace. They are primarily used o rapidly conrol volage a a weak poin in power ransmission and large indusrial neworks. A conroller regulaing he ac sysem volage wih respec o a reference volage wih some droop characerisic varies he SVC curren and reacive power. The droop value is seleced according o he desired sharing of reacive power generaion among various sources, as well as oher needs of he sysem such as providing for an adequae margin for ransien volage sabiliy. The capacior banks in a SVC are raed for full capaciive oupu, whereas he reacor banks are raed for full inducive oupu; he coupling ransformer and elecronic circui could be dimensioned o wihsand he sum of he maximum capaciive and inducive oupu. I should be emphasized ha he SVC capaciy for compensaion is solely deermined by he size of is reacive componens implying significan physical size and mainenance. A SVC can conrol only one of he hree principal parameers, volage, phase angle, or impedance, which deermines he power flow in ac power sysems []. Therefore, i does no posses he capabiliy o independenly conrol acive and reacive power in he ransmission line. Fixed or mechanically swiched capaciors and reacors ogeher wih synchronous compensaor have long been employed o increase seady sae power ransmission by conrolling he volage profile along he ransmission lines. I has been demonsraed ha boh he ransien and seady sae sabiliy (i.e., firs swing sa-

2 biliy and damping) of a power sysem can be enhanced if he compensaion device can reac quickly by using solid-sae, hyrisor swiches and elecronic conrol. The funcion of SVC is o minimize he magniude and duraion of sysem disurbances by regulaing erminal volage and damping power oscillaions. To accomplish his, an conrol is employed ha derives he necessary reference signals for he inernal conrol of SVC o produce he desired reacive power oupu for he ac sysem o counerac he disurbances. The main problem is choosing of series device for damping which should performed normal work during all differen saes and power disurbance. The bes choice for he problem is an adapive conroller. During he pas years an adapive neuro-fuzzy conrollers are used, bu heir main problem remains - he ime for uning-raining is oo long. In he paper is presen a direc classical mehod for idenificaion by using an opimal singular adapive observer (OSA), which calculae direc he linear algebraic sysem equaions [8]. One of he imporan advanages of OSA esimaors is ha heir rue poles may no coincide wih he desired pole and ha i doesn inerfere wih heir accuracy. Neiher does he fac ha he objec being observed and idenified may be insable. Anoher big advanage is avoiding synhesis of sysem wih pole assignmen, which is compulsory wih Luenberger s observers. Excep for ha he OSA observer is robus o ha coincidence. By using he OSA observers has been creaed a family of adapive OSA sabilizers, which effecs on he auomaic volage regulaor (AVR) and on he governor of he synchronous generaor [3, 4, 5]. 2 Power sysem model Figure show he invesigaed sysem which included synchronous generaor conneced o infiniy bus hrough line produced by equivalen resisances Z l = rl + jll. On he generaor erminal is conneced alernae 3- SG I G Z l I l bus Z L Tr I L Measuremen I CSVC C SVC TH I LSVC TH 2 L SVC zero deecion Swiching logic ampliude u con U ref SVC conrol b L (k) z(k) OSA observer x,a ˆ ˆ u ST (k) Fig.. Invesigaion power sysem

3 phase symmerical load ZL = rl + jl L, by means is simulaed he differen oscillaions - shor cu, connecing/disconnecing of saic load. The assumed posiive curren direcions for corresponding elemens are shown by arrows. SVC is presen like damping shun inducive LC device. The reacor conduciviy is regulaed by he adapive conroller, which conrol firing angle (α) for hyrisors TH and TH 2. The adapive conroller is consising of Opimal Singular Adapive (OSA) observer, SVC conrol and conrol signal resricor. On he inpu of observer is feed a sabilizaion signal (like erminal volage, roor speed, load angle, ec.). The esimaions of variables and parameers on he model xˆ, aˆ are calculaed by OSA observer. On his basis SVC conrol block creae he conrol signal, which is ransformed in firing angle for hyrisors α by definie mehod. 2. Synchronous generaor model Equaions of he generaor are wrien of own coordinae sysem, which is fixed for is roor. In his manner a variable coefficiens are ignored. Equaions of he oher elemens (saic load, line, SVC) are wrien in synchronous roaing coordinae sysem. A creaion of equaions for connecions he curren equaions of generaor are ransformed ino d,q, axes. The synchronous generaor is modeled by is complee model in he d,q, frame is used, wrien in Cauchy form [6]: d I s H s Bss Bsr U s. ; d = + I r H r Brs Brr u f () d ωk = ( T T T G); d T m where subscrip s refers o he saor parameers and variables, and subscrip r - roor; I [ ] [ ] [ ] s = i d,iq ; I r = i f,ig,ih ; U s = ud, uq ;he elemens of marices and vecors H and В are funcion of he saor and roor resisance and inducive impedance and he roor angular speed (axes d,q,) - ω k ; T T - urbine orque; T G = xad.( id + i f + ig).iq xaq.( iq + ih). i d - he generaor elecromagneic orque; T m - he urbine and generaor mechanical ime consan; u f - field volage; generaor parameers in p.u.: Since he equaions of power sysem are wrien in axes d,q,, which are roaing synchronous, he saor marix and vecors are ransformed in same coordinae sysem wih he help of nex expressions: B ss = b T b Bss ; H s = T b H b s ; I s T b I b = s ; cos δb ; sin δb T b = ; (2) sin δb ; cos δij δ b = θ k θ kb = ω k ω 2.2 Saic RL load model d I L = H L + BL.U (3) d Where: he elemens of vecor H L and marix B L are funcions of load parameers; U - generaor erminal volage vecor. 2.3 Reacor model for SVC d I LSVC = H LSVC + BLSVC.U (4) d Where: he elemens of H LSVC and marix B are funcion of load parameer. LSVC kb d 2.4 Condenser model for SVC d U = ACSVC. I CSVC + U d Where: he elemens of marix funcion of condenser parameer; I CSVC = ( I G + I L + I LSVC + I l). 3 SVC conrol (5) A CSVC are 3.. Conrol signal creaing The basic idea of sabilizer is, ha he conrol objec can be coninuously esimae by linear model of low order and creae addiional conrol signal. The invesigaions presen [3] ha for he sabilizer he minimal models of 2 nd order migh be used, which provides a grea

4 speed and sufficien correcness. A single-inpu single-oupu (SISO) adapive observer is being used in invesigaion sysem. A fig.3 is seen ha for OSA observer inpus discree pars of inpu u ST ( k ) and oupu B L( k ) for resuling induciviy are fed, also a signal z ( k ), which represen a limied inpu sequence for idenificaion is fed oo. The observed sysem migh be presen by a following ype of a linear model in he sae space: x( k + ) = A.x( k) + b. [ ust ( k) + z( k) ] =, = A.x( k) + b.v( k) x()=x, (6) y( k ) = c.x( k), k=,,2,.; (7) Where: x(k) is an unknown curren sae vecor; x() is an unknown iniial sae vecor; u ST (k) is an inpu signal; z(k) is a limied inpu sequence for idenificaion; A, b and c are unknown marix and vecors of he following ype: b A = = ; b = a ; a a2 b 2 c =. (8) The inpu/oupu daa are shaped on he Hankel and Toepliz marices [2]: y () y( 2) Y = ; y y( 4) Y 2 = ; y 3 Y 3 = ; y 5 η ηˆ ( ) = ; (9) η2 u() u() U = ; U 2 = u ; u 2 u ( 3) u( 2) ( 4) u( 3) u U 3 = u The vecor esimaion ĥ is calculaed hrough he following vecor-marix expression: ĥ = N.Y 32.Y 22.Y 2 N 2.Y 3 () където: - - N 2 = U 3 Y 32.Y 22. U 2. The vecor â is calculaed hrough he following expression: ( ) aˆ = Y 22 Y 22 U 2 N 2 Y 32 Y 22 Y 2. () - - Y 22. U 2. N 2. Y 3 The vecor esimae is calculaed η ˆ : ˆ η = Y + U. N 2. Y 32. Y 22. Y 2- U. N 2. Y 3.) (2) The vecor esimae bˆ is calculaed by he linear sysem equaions of following ype: T. bˆ = ĥ, (3) Where: T = is Toepliz marix. â2 The iniial vecor esimae is calculaed by he opimal esimaor of following ype: xˆ( ) = ηˆ( ) + U ( ˆ ˆ. h-b) (4) The curren vecor is esimaed by he degenerae OSA observer: xˆ( k+ ) = A.x ˆ ˆ( k ) +b.u ˆ ( k ), xˆ( ) = x, k=,, 2,, (5) The conrol signal will calculaed by esimae sae vecor and model parameers [2]: bl ( p) = aˆ ( p).ˆ x( p) = â.xˆ â2. xˆ 2 (6) Where: p=k,k+,,k+n. α [deg] b Lp [p.u.] Fig.2. Used funcion for hyrisor conrol Afer he conrol signal b L has been deermined ough o ransformaion of specific values for b L ino real values for hyrisor firing angle α in degrees. b = 2 2α / π + sin 2α / π (7) [ ] nom Lp b L.

5 Where: b Lp are values of b L se o real sysem in p.u.; b L.nom nominal value of b L. Figure 2 shows he modificaion of firing angle α in dependence of b Lp. 3.2 Thyrisor conrol The hyrisor model (fig.3) [7] is simulaed as a resisor Ron, an inducor Lon, and a DC volage source represening he forward volage Vf, conneced in series wih a swich. The swich is conrolled by a logical signal depending on he volage Vak, he curren Iak, U T [p.u.] А U AK I AK K R ON L ON U f К Fig.5. Generaor erminal volage. Q SG А Gae К Swiching logic Fig.3. Thyrisor model. and he gae signal g. The Thyrisor block also conains a series Rs-Cs snubber circui ha can be conneced in parallel wih he hyrisor device. 4 Simulaion sudy Differen disurbances causing ransien processes have been simulaed. The represen simulaions are aken by hree-phase ground U T [p.u.] G U AK I AK Fig.4. Generaor erminal volage Fig.6. Generaor reacive power. ω SGdev [p.u.] x Fig.7. Generaor roor speed deviaion. shor cu for ime a ms, afer ha he proecion is acivae. The follow simulaions are

6 compared wih same sysem, which include compensaor from fixed condenser and reacor. α [deg] Fig.8 Firing angle for hyrisor α [deg] Wih blue lines on following figures are shown resuls when he OSA observer is acive, wih red lines sysem wih fixed capacior and in- δ [deg] ducor. Fig. Generaor load angle Fig.9 Firing angle for hyrisor 5 Conclusion Using he adapive conrol of FACTS is opimal soluion power flow conrol in power sysems. Oherwise hese devices can damping he oscillaions and improve he qualiy of ransien processes. The suggesed adapive conrol for SVC is simple herefore minimal compuing devices are needed, which define very good damping properies. The obained simulaion sudies prove is qualiy and perspecives for conrol and regulaing of ransien processes and improve power sysem sabiliy. Q [p.u./mva] 23 References Fig. Reacive power of SVC [] De Mello F.P., Concordia C. Conceps of synchronous machine sabiliy as affeced by exciaion conrol. IEEE Trans. of Power Apparaus and Sysems, v.pas-88, N4, Apr., 969, pp [2] Chen G.P., Malik O.P., Qin Y.H., Xu G.Y. Opimizaion echnique for he design of linear opimal power sysem sabilizer. IEEE Trans. on Energy Conversion, v.7, N3, Sep., 992, pp

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