Untitled

Kao πto je veÊ spomenuto, osnovna poteπkoÊa umodeliranju energetskih transformatora je nelinearnikarakter induktiviteta æeljezne jezgre transformatora.Ostali parametri transformatora: otpor irasipni induktiviteti primarnog i sekundarnog namotakao i otpor koji reprezentira gubitke u æeljezuuzimaju se konstantnim [12]. Osnovna krivuljamagnetiziranja transformatora dana je na slici 1a.Ova krivulja se moæe kvalitativno aproksimirati sdva pravca, slika 1b, koji predstavljaju tangente unezasiÊenom i zasiÊenom podruËju. Krivulja magnetiziranjaenergetskih transformatora ima jakooπtar prijelaz iz nezasiÊenog u zasiÊeno podruËje.Ovo je posljedica konstruktivne izvedbe visokonaponskihenergetskih transformatora. Naime, sporastom naponske razine, odnosno nazivne snagetransformatora struja praznog hoda se smanjuje iiznosi [13] oko 5 % do10 % nazivne struje transformatoraza transformatore snaga reda 100 kVAi opada sve do vrijednosti oko 0,47 % do 0,59% nazivne struje transformatora za transformatoresnage reda 500 MVA.Pregled standardnih vrijednosti struje magnetiziranjaza energetske transformatore razliËitih nazivnihsnaga dan je tablicom 1. Struja prijelaza u zasiÊenopodruËje i z jednaka je nazivnoj struji pomnoæenojs faktorom ulaska u zasiÊenje k: i z = k·i 0naz ,gdje je za energetske transformatore obiËno1,05 k 1,3. Dakle, koljeno krivulje magnetiziranjaza energetske transformatore velikih snagaje razmjeπteno u veoma uskom podruËju nazivnestruje transformatora (reda 0,5 % do 1 % i naz ).Povrπina, koja je omeappleena realnom krivuljom magnetiziranjai njenom aproksimacijom preko dvapravca, ovdje je reda svega oko 0,001 % ako uzmemoda je 100 % povrπina ispod cijele krivuljemagnetiziranja u p.u. sistemu. LogiËna je posljedicaovako malih nazivnih struja praznog hoda dapredstavljanje krivulje magnetiziranja preko svegadva pravca Ëini gotovo zanemarive pogreπke u usporedbis realnim predstavljanjem krivulje [14].As previously mentioned, the basic difficulty in modelingpower transformers is the nonlinear characterof the inductance of the iron transformer core. Theother transformer parameters, the resistance andleakage inductance of the primary and secondarywindings as well as the resistance that representslosses in iron are assumed to be constant [12]. Thebasic transformer magnetizing curve is presented inFigure 1a. This curve can be qualitatively approximatedwith two straight lines, Figure 1b, that representtangents in the unsaturated and saturatedregions. The power transformer magnetizing curvehas a very sharp transition from the unsaturatedto the saturated regions. This is a consequence ofthe design of high voltage power transformers. Withan increase in the voltage level or rated power ofthe transformer, no-load current is decreased andamounts to approximately 5 % to 10 % of thetransformer rated current [13] for transformers withpower ratings of 100 kVA and decreases to a valueof approximately 0,47 % to 0,59 % of transformerrated current for transformers with power ratingsof 500 MVA.A review of the standard values of power transformermagnetizing currents for various rated powers ispresented in Table 1. The transition current to thesaturated region i z is equal to the rated current multipliedby the saturation factor k: i z = ki 0rated , whereusually for power transformers 1,05 k 1,3.Thus, the bend in the magnetizing curve for ahigh power transformer is in a very narrow regionof the transformer rated current (an order of 0,5 %to 1% i rated ). The surface, which is bounded by thereal magnetizing curve and its approximation bytwo straight lines is of an order here of only approximately0,001 % if it is taken into accountthat 100 % of the surface below the magnetizingcurve is in a p.u. system. A logical consequenceof such low rated no-load currents is that it is possibleto approximate the magnetizing curve usingtwo straight lines with nearly negligible error incomparison to the real curve [14].Tablica 1 − TipiËne vrijednosti struje praznog hoda kao postotak nazivne struje za energetske transformatoreTable 1 − Typical values of no-load current as a percentage of rated current for power transformersS TR (MVA) 0,1 1,0 10 20 40 60i 0 (% i naz/rated ) 5,0 − 8,0 1,75 − 2,32 0,35 − 1,1 0,8 − 1,2 0,65 − 0,94 0,58 − 0,84S TR (MVA) 80 100 150 200 300 500i 0 (% i naz/rated ) 0,54 − 0,77 0,51 − 0,73 0,47 − 0,67 0,51 − 0,64 0,49 − 0,61 0,47 − 0,59587TokiÊ,A., UglešiÊ, I., NumeriËki proraËun niskofrekvencijskih..., Energija, god. 56(2007), br. 5., str. 584-607TokiÊ, A., UglešiÊ, I.,The Numerical Calculation of..., Energija, vol. 56(2007), No. 5, pp. 584-607