Controlled Switching Based on the Injection Method

Transcription

1 Conrolled Swiching Based on he Injecion Mehod C.D. Tsirekis, N.D. Haziargyriou, B.C. Papadias Elecric Energy Sysems Laboraory Deparmen of Elecrical and Compuer Engineering Naional Technical Universiy of Ahens, Greece 9 Heroon Polyehniou Sr., Zografou, Ahens, Greece sirekis@power.ece.nua.gr, nh@power.ece.nua.gr Absrac - Fundamenal requiremen for all conrolled swiching applicaions is he precise definiion of he desired swiching imes. This can be achieved by exhausive simulaions using for each nework ransien simulaion programs like EMTP/ATP. In his paper a new mehodology is proposed, based on he Injecion Mehod, ha eliminaes he need for exhausive simulaions by calculaing he exac ransien volage or curren expressions in parameric form. Circuibreaker s saisical characerisics, like conac operaion ime scaer and deviaion of he slope of he conac gap volage wihsand characerisic are aken ino accoun in his mehod. Keywords: Conrolled Swiching, Swiching Transiens, Opimum Swiching Insan, EMTP, Circui-Breaker. I. INTRODUCTION Conrolled swiching is a echnique ha auomaically adjuss he circui-breaker mechanism in such a way ha swiching operaion akes place a a poin-on-wave which minimizes swiching ransiens, such as he phase-o-earh overvolage, he inrush curren and he ransien recovery volage (TRV) across he breaker poles [3, 8]. One of he mos significan requiremens for proper conrolled swiching porformance is o reduce he saisical variaions of conac operaion imes. Circui-breaker echnology has improved hese saisical scaers, allowing hus uiliies and manufacurers o achieve conac operaion imes quie close o he preferable ones. This means ha a precise definiion of he desired swiching imes is required. This can be achieved by exhausive simulaions using for each nework ransien simulaion programs like EMTP/ATP [3]. This procedure is imposed by he necessiy of he invesigaion of he effecs of parameer changes (such as he rapped charge in a capacior bank or he impedance of a load) and he circui-breaker characerisics (such as he saisical variaions of he conacs operaing imes and he conacs gap characerisic of dielecric srengh) on he opimum swiching insan. In his paper a new mehodology is proposed, based on he Injecion Mehod, ha overcomes hese problems. The basic principle is he calculaion of he exac ransien volage or curren expressions in parameric form, as funcions of he swiching insans and he nework parameers. Circui-breaker characerisics, such as conacs gap volage wihsand characerisic and variaions in conacs operaing imes are considered. Wih he aid of arihmeic echiques, he exrema of hese funcions as well as he values of he swiching insans and he nework parameers for which hese exrema occur, can be easily calculaed. A series of sudy cases has been carried ou for he implemenaion of he mehod. I includes simple nework configuraions, for he easy confirmaion of he accuracy of he resuls. In all cases he opimum swiching insans are calculaed using exchausive EMTP simulaions and he Injecion Mehod and a comparison of he resuls is carried ou. II. THEORETICAL ISSUES A. Injecion Mehod Injecion mehod is he generalizaion of he already known Curren Injecion Mehod [1, ], which is based on superimposiion heorem and has been used for he calculaion of ransien currens and volages in swich opening cases, especially single-phase ones. The generalized Injecion Mehod is also applicable o swich closing cases. Furhermore, modern compuer faciliies allow he performance of he necessary calculaions in a sysemaic way, making Injecion Mehod a suiable mean for hreephase calculaions, no only for closing or opening cases, bu also for more complicaed swiching scenarios, like auoreclosing. In closing cases Injecion Mehod calculaes he ransien volages and currens produced when a volage Vin, wih equal magniude and opposie polariy o he one appearing across he open poles of he swich jus before he closing insan, is imposed, resuling in eliminaion of he volage across he swich jus afer he closing insan. Wih he assumpion ha he nework elemens are linear, his eliminaion can be simulaed wih he injecion of Vin o he swiching poin a he swiching insan. In Fig. 1 i is shown how he acual volage can be obained by he superimposiion of he volage Vin o he iniial one o be eliminaed. Similarly, in opening cases Injecion Mehod calculaes he ransien volages and currens produced when a curren Iin, wih equal magniude and opposie polariy o he one flowing hrough he closed poles of he swich jus before he opening insan, is imposed, resuling in eliminaion of he curren hrough he swich. Assuming again ha he nework elemens are linear, his eliminaion can be simulaed wih he injecion of Iin o he swiching poin a he swiching insan.

2 V() 1 1 Vin() Va() 1 (a) - Iniial volage V() 1 (b) - Injeced volage Vin() (c) - Acual volage as he resul of superimposiion of Vin o V Fig. 1. Diagrams illusraing he Volage Injecion Mehod in a case of swich closing a he insan =1 B. Opimum Swiching Insan. The definiion of wha Opimum Swiching Insan means in his mehod is of grea imporance. The significance of his definiion is necessary if i is clear ha he swiching insan which leads o he minimizaion of a resuling volage or curren of ineres somewhere in he nework, may be more or less differen from he swiching insan which leads o he minimizaion of ineresing volages and/or currens a he same or a oher nework locaions. Furhermore, he oal number of hree-phase swiching operaions in each applicaion, considering he opening or closing of each pole as separae swiching operaion, is usually no less han hree and herefore he opimum swiching insan for one swiching operaion may refer o a differen poin-on-wave han he opimum swiching insan of oher operaions. Therefore, we have o alk abou opimum swiching insan combinaion raher han opimum swiching insan. This is defined as he combinaion of insans corresponding o he respecive poins-on-wave, so ha when each swiching operaion akes place, he following objecive funcion is minimized: A ( ) = X V ( ) + Y I ( ) (1) 1 i i j j i j where V i and I j he ineresing p.u. volages and currens o be conrolled, X i and Y j he respecive user-defined weighing facors which deermine he degree of significance of each conrolled quaniy and he vecor of he swiching insans for each operaion. The soluion of he problem of minimizaion of he above objecive funcion is achieved arihmeically for a large number of possible swiching insans combinaions over a user-defined range of values of elemens. Saisical disribuion of conrolled circui-breaker characerisics makes he problem of invesigaion of opimum swiching insans combinaion much more complicaed [3, 8]. The way hese saisical characerisics are aken ino accoun in he proposed mehod for closing or opening cases, is described in he nex paragraphs. 1) Closing In mos cases he closing swiching insan (named making insan) does no coincide wih he insan of mechanical closing of he circui-breaker conacs (arge insan). Making insan is deermined by he inersecion of he waveform of he volage across he circui-breaker conac and he conac gap dielecric srengh characerisic, he rae-of-decay of which (RDDS) is infiniy only in ideal (and hus non-acual) swiches. Saisical deviaions of he operaing ime (he ime inerval unil he iniiaion of conac movemen), he conac velociy and he conac gap dielecric srengh affec he arge insan and he slope, resuling in a parallel shifing o boh sides of he volage wihsand characerisic and a deviaion of is slope [3, 4, 7, 8]. Thus, insead of a simple making insan and he respecive arge insan, i is more realisic o alk abou a window of making insans and he respecive arge insans, as illusraed in Fig. [3]: Absolue value of volage (p.u.) 1.5 Lef limi of making poin Nominal volage wihsand characerisic (VWC) Volage across breaker pole Lef & righ limis of VWC Righ limi of making poin Targe insan window Nominal making poin Fig.. Diagram illusraing he making insan window for a case where arge insan corresponds o zero volage. For each arge insan window combinaion for all closing cases (including he individual poles closing of he same circui-breaker), a maximum value of A( ) is obained, named Am. The opimum arge insan window combinaion resuls arihmeically from he minimum Am of all possible arge insan window combinaions. Noe ha he procedure is quie complicaed because of he possible dependence of waveforms of he volages across he circui-breaker poles from he arge insans of previously closed poles, as i may

3 occur in sysems wih ungrounded neural. ) Opening Similarly o closing, he swiching insan in opening cases (named breaking insan) does no coincide wih he insan of mechanical separaion of he circui-breaker conacs (here his is he arge insan). Breaking insan is eiher he insan of he nex physical zero curren or he insan of a possible curren chopping. Curren chopping complicaes he problem, because heoreically i may occur a any curren level, especially in vacuum circui-breakers [5, 6]. Assuming for simplificaion ha arc exinguishing a physical zero curren is equivalen o a zero curren chopping, i is assumed ha curren chopping will occur in any case. Curren chopping leads o higher overvolages han hose resuling from breaking a a physical zero curren. However, bibliography shows [5, 6, 7, 8] ha curren chopping is raher less severe for dangerous overvolages han reigniions. Therefore, he basic principle for conrolled opening is he avoidance of reigniions. Reigniion will occur whenever he ransien recovery volage (TRV) across he opening circui-breaker conacs inersecs he volage wihsand characerisic of he breaker conac gap. Conrary o he closing cases, he volage wihsand characerisic is absoluely consecuive in opening cases and iniiaes a he conac separaion insan (arge insan), as illusraed in Fig. 3 [5, 6]: Targe (conac separaing) insan window Lef & righ limis of VWC Inducive curren Source volage Chopping curren TRV Nominal volage wihsand characerisic (VWC) Fig. 3. Diagram illusraing he breaking insan window for a case of successful inducive curren inerrupion. For each arge insan window combinaion for all opening cases (including he individual poles opening of he same circui-breaker), a maximum value of A( ) is obained, named Am. This maximum value is exraced for all possible chopping currens for each arge insan, excluding hose which lead o reigniion. In he laer case for all possible chopping currens, an exremely large value is se for A( ). The opimum arge insan window combinaion resuls arihmeically from he minimum Am of all possible arge insan window combinaions. III. ALGORITHM The algorihm can be summarized in he following seps: A. Conversion of all volage sources o curren sources. The conversion is done by means of Noron-Thevenin ransformaion. B. Consrucion of seady-sae nework conducance marix. The iniial seady-sae conducance marix Y(jω) is a complex funcion of frequency. C. Consrucion of he seady-sae equaions. The sysem of seady-sae equaions in marix form is Y (jω) E(jω) = J(jω) T A E(jω) = V(jω) () A I(jω ) = where E, V, J, I he node volage, branch volage, node curren sources and branch curren vecors respecively and A he nework incidence marix. The soluion of () is iniially expressed in frequency-domain (phasors). Then he expressions are ransformed ino ime-domain. D. Producion of iniial volage and curren expressions. From he resuls obained from he previous sep, expressions of volages across he conacs o close (for closing cases) or currens hrough he conacs o open (for opening cases) a he same swiching insan and oher currens and volages of ineres as well as he iniial condiions for he nex swiching operaion, are derived. E. Calculaion of Vin or Iin. From he above derived volage or curren expressions, Vin or Iin (for closing and opening cases respecively) is calculaed as described in paragraph II. Vin (or Iin) are ransformed from ime-domain o s-domain via Laplace ransformaion. F. Applicaion of Injecion Mehod. Subsiuion of volage and curren sources of he original nework wih shor- and open-circuis respecively and connecion of a volage source Vin (for closing cases) or a curren source Iin (for opening cases) beween he nework nodes represening he poles of he swich o close or open respecively, as described in paragraph II. G. (For closing cases only) Conversion of all Vin volage sources o curren sources. The conversion is done by means of Noron-Thevenin ransformaion. H. Consrucion of new equivalen nework conducance marix. The conducance marix Ye(s) of he new equivalen nework resuling afer he applicaion of he seps F and G, is a funcion of Laplace variable s.

4 I. Consrucion of he sysem of injecion-sae equaions. The sysem of injecion-sae equaions in marix form is Ye (s) Ee(s) = Je(s) + We(s) T Ae Ee(s) = Ve(s) (3) Ae Ie(s ) = where Ee, Ve, Je, Ie he node volage, branch volage, node curren sources (corresponding o Vin and Iin) and branch curren vecors of he equivalen injecion-sae nework respecively, We a vecor including he iniial condiions and Ae he equivalen injecion-sae nework incidence marix. The soluion of (3) is iniially expressed in s-domain and hen is ransformed ino ime domain. J. Producion of full volage and curren expressions. Full ime-domain expressions of volages and currens of ineres afer his operaion insan are calculaed as a sum of he resuls obained from he previous sep and he respecive resuls obained from sep C (prior o he swiching operaion a his insan). K. If here are more swiching operaions go o sep D, else go o he nex sep. The operaion of each circui-breaker conac is considered as individual swiching operaion. L. Reading user-defined daa. The user deermines specific values or defines he range and he sep of he possible values of each parameer, he effec of which o he conrolled swiching is invesigaed. The same is done for each swiching insan window. Finally, circui-breaker daa (volage wihsand characerisic as a funcion of arge insans, saisical scaers, maximum chopping curren level ec.) are defined by he user. M. Calculaion of he opimum swiching insan windows combinaion. The calculaion is execued arihmeically for each combinaion of he parameers under invesigaion and is based on he minimizaion of he objecive funcion Am among all possible swiching insan windows combinaions, as described in paragraph II. N. Calculaion of he maximum ransien volages and/or currens obained by he algorihm. For each opimum swiching insans windows combinaion resuling in he previous sep, he maximum ransien volages and/or currens of ineres are calculaed. O. Procedure erminaion. The resuls obained by he wo previous seps (opimum swiching insans windows combinaions, maximum obained volages and currens) for each invesigaed parameer values combinaion are sored o be furher processed (e.g. curve ploing). IV. STUDY CASES The energizaion of a shun capacior bank sudied in his paper is a common sudy case for conrolled swiching applicaions due o he subsanial reducion of he ransien overvolages and inrush currens ha can be achieved [3, 4, 7, 8]. An imporan parameer which affecs he opimum swiching insans in hese cases is he degree of he rapped charge in he capacior bank, resuling afer he bank deenergizaion [3]. For his reason, he rapped charge is he variable parameer, he influence of which o he opimum swiching insans is invesigaed in his sudy. The single line diagram of he sudied nework is given in Fig. 4. The frequency of he 15 kv volage source is 5 Hz. The nework series impedance corresponds o a shor-circui power of 5 GVA. The 1 MVAr capacior bank is wyeconneced wih grounded neural. Fig. 4. Single-line diagram considered for he energizaion of a capacior bank. The objecive of conrolled-swiching applicaion o his case is he reducion of he inrush currens (3 funcions, one for each phase) and he ransien phase-o-ground overvolages a he capacior bank side (3 funcions, one for each phase). Execuion of Injecion Mehod gives he following expressions for hese funcions for each phase: V ( ) = e + D cos[ ω A ( ) ( G ( ) { B V cos[ ω ( ) + θ ]} ) + θ D ] + F cos( ω + θ { H V cos[ ω ( ) + θ ]} I( ) = e H (5) + K cos[ ω ( ) + θ K ] + M cos( ω + θ M ) where V he rapped charge, he making insan in he respecive phase, ω he circui naural frequency and A, B, D, F, G, H, K, M coefficiens depending on he nework elemens. Thus, from (1) he following objecive funcion is derived: A( ) = X R VR ( ) + X S VS ( ) + X T VT ( ) (6) + YR I R ( ) + YS I S ( ) + YT I T ( ) The nex imporan sep is he definiion of he coefficiens X R, X S, X T, Y R, Y S, Y T, which is no obvious, as he p.u. values of inrush currens depend on he value of he sysem basic power which has been chosen and hus, hey may be several ens of imes eiher higher or lower han hose of phase-o-ground overvolages. However, he high frequency of he expeced inrush currens (in he order of 1 khz or even higher) and consequenly he relaively low energy which hey conain, makes hem less dangerous han he ransien overvolages. Therefore, a small value for he curren weighing facors Y j is sufficien jus for ensuring he avoidance of exremely high overcurrens. In he presen sudy, he values 1. and.1 are chosen for he volage B F ) (4)

5 weighing facors X i and he curren weighing facors Y j respecively. In every capacior bank energizaion case he range of possible values of he rapped charge is by defaul from (for he case of a fully uncharged bank energizaion) o 1. p.u. (for he energizaion of a bank shorly afer is deenergizaion). In his sudy he above range of values of rapped charge is considered, wih a sep of.1 p.u.. Circui-breaker nominal volage wihsand characerisic is considered sraigh, wih a slope (RDDS) equal o he slope of he phase-o-ground source volage a zero crossing poin, wih a deviaion of ±%. The saisical scaer of he arge insans is considered ±1%. Boh of he above deviaions deermine he possible arge insan windows for each pole o close. Considering ha he insan of ms corresponds o a source-side volage zero of he phase o close firs (in his case R), he range of values of he possible arge insans for he firs phase o close is from o ms, since he waveform of he volage across he respecive opened conacs is he same in every 5 Hz period. In general, closing of he firs pole migh affec he volage waveform across he second pole o close, so in ha case he range of values of he possible arge insans for he second pole would have o be exended, so ha i would include an inerval of ransien volage waveform, which would be differen from he normal seady-sae waveform of he firs period. In he presen case however, where he capacior bank neural is ideally grounded, he volage waveforms across each breaker pole is no affeced by he previous closing of oher poles. Therefore, assuming ha he sequence of he phases o close is R - T - S (which provides he shores possible duraion of he closing operaion), he invesigaed ime inervals is beween and 3.33 ms for he second phase o close and beween and 6.66 ms for he hird one. As ime sep beween each possible arge insan is chosen he value of 1 μs. The resuls of he procedure are lised in Table 1. As opimum ime insan is considered he insan in he middle of he opimum ime insan window for each phase. Table 1 Opimum arge insans for he energizaion of a capacior bank wih grounded neural and maximum phase-o-ground overvolages and inrush currens achieved - Injecion Mehod applicaion V (p.u.),r (ms),s (ms),t (ms) V R (p.u.) V S (p.u.) V T (p.u.) I R (p.u.) I S (p.u.) I T (p.u.) The respecive resuls afer EMTP simulaions are shown in Table. For he modelling of he circui-breaker characerisics he circui-breaker model [9] has been used. As i can be easily seen, he resuls have a sufficien conformiy. Table Opimum arge insans for he energizaion of a capacior bank wih grounded neural and maximum phase-o-ground overvolages and inrush currens achieved - Resuls from EMTP simulaions V (p.u.),r (ms),s (ms),t (ms) V R (p.u.) V S (p.u.) V T (p.u.) I R (p.u.) I S (p.u.) I T (p.u.) From he previous resuls i is obvious ha he ideally grounded neural makes he problem of he opimum arge insans finding in each phase independen from he oher phases. The effec of an ungrounded neural can be found ou wih he repeiion of he procedure, wih he only difference ha he invesigaed ime inervals should become o 4 ms and o 6 ms for he second and hird phase o close respecively. The resuls are shown in he nex Tables.

6 Table 3 Opimum arge insans for he energizaion of a capacior bank wih ungrounded neural and maximum phase-o-ground overvolages and inrush currens achieved - Injecion Mehod applicaion (The value of,r has been chosen randomly, as i has no influence) V (p.u.),r (ms),s (ms),t (ms) V R (p.u.) V S (p.u.) V T (p.u.) I R (p.u.) I S (p.u.) I T (p.u.) Table 4 Opimum arge insans for he energizaion of a capacior bank wih ungrounded neural and maximum phase-o-ground overvolages and inrush currens achieved - Resuls from EMTP simulaions V (p.u.),r (ms),s (ms),t (ms) V R (p.u.) V S (p.u.) V T (p.u.) I R (p.u.) I S (p.u.) I T (p.u.) V. CONCLUSIONS As a general conclusion derived by he previous ables, he small differences beween he resuls obained using Injecion Mehod and hose obained via EMTP show he reliabiliy of he proposed mehodology. As far as he sudy cases concerned, i can be easily seen ha he higher values of he capacior bank rapped charge, he higher ime delay o he opimum arge insans is caused. Furhermore, he higher values of rapped charge and consequenly he lower iniial volages across circui-breaker poles, conribue o he appearing of lower ransien overvolages and inrush currens VI. REFERENCES [1] B.C. Papadias, Power Sysem Analysis, Vol. II, Texbook, Naional Technical Universiy of Ahens (NTUA), 1985 (In Greek). [] J. Panek, Tes Procedures, IEEE Tuorial Course Applicaion of Power Circui-Breakers, Course Tex 75CHO975-3-PWR, [3] CIGRE WG13.7, Conrolled Swiching of HVAC Circui-Breakers - Guide for Applicaion Lines, Reacors, Capaciors, Transformers, 1s Par, Elecra No 183, April nd Par, Elecra No 185, Augus [4] CIGRE WG13.4, Shun Capacior Bank Swiching - Sresses and Tes Mehods, 1s Par, Elecra No 18, February nd Par, Elecra No 183, April [5] CIGRE WG13., Inerrupion of Small Inducive Currens, Chaper 1 and, Elecra No 7, Ocober Chaper 3 Par A, Elecra No 75, March Chaper 3 Par B, Elecra No 95, July Chaper 4 Par A, Elecra No 11, July Chaper 4 Par B, Elecra No 113, July [6] W.M.C. van den Heuvel, B.C. Papadias, Ineracion Beween Phases in Three-Phase Reacor Swiching, 1s Par, Elecra No 91, December nd Par, Elecra No 11, June [7] A. Holm, R. Alvinsson, U. Akesson, O. Karlen, Developmen of Conrolled Swiching of Reacors, Capaciors, Transformers and Lines, 33rd CIGRE Session, paper 13-1, Paris, 199. [8] A.C. Carvalho, W. Hofbauer, P. Högg, K. Fröhlich, Conrolled Swiching as a Reliable Mean o Reduce Sresses Imposed o he Circui-Breaker and o he Nework, Colloquium of CIGRE SC 13 in Florianópolis, Repor 1.1, Sepember [9] R. Rocha, J.L. Tavora, EMTP Model for Conrolled Swiching by Means of a TACS Rouine, Proceedings of he 1997 Inernaional Conference on Power Sysems Transiens, Seale, USA, pp , June 1997.