20.500.12556/RUL-190372 Primerjava modelov za izračun napetosti na stresani reaktanci in aksialne sile v navitjih energetskega transformatorja s cik-cak vezavo Comparison of models for calculating leakage reactance voltage and axial force in the windings of a zigzag-connected power transformer Stresana napetost predstavlja induktivni del kratkostične napetosti transformatorja in je, kot njen večinski delež, pomemben parameter pri projektiranju, saj vpliva na kratkostične tokove ter mehanske in toplotne obremenitve. Pri transformatorjih z vezavo cik-cak je njen izračun še posebej zahteven, saj klasični analitični modeli pogosto ne dajejo dovolj natančnih rezultatov. Namen prve polovice magistrskega dela je primerjati različne metode izračuna stresane napetosti ter ugotoviti, kateri model se najbolj približa meritvam na realnih transformatorjih. V delu so obravnavani analitični in numerični pristopi. Najprej je predstavljena analitična metoda Rogowskega, nato pa več numeričnih modelov, ki temeljijo na metodi končnih elementov v programu FEMM. Preizkušen je bil enostebrni dvodimenzionalni osno simetrični model, trifazni dvodimenzionalni planarni model ter več izpeljanih modelov s popravljenim volumnom, pri katerih je bila magnetna energija preračunana z uporabo različnih reprezentativnih radijev. Modeli so bili preverjeni na več različnih zasnovah transformatorjev, za katere so bile na voljo meritve kratkostične napetosti od tovarniških prevzemnih preizkusov. Rezultati kažejo, da ima analitični model omejeno uporabnost, osnovni planarni model pa nezadostno natančnost. Najboljše ujemanje z meritvami dosega planarni model s popravljenim volumnom, pri katerem je volumen določen s težiščnim radijem magnetne energije. Ta pristop predstavlja dober kompromis med natančnostjo in računsko zahtevnostjo ter je primeren za praktično uporabo pri projektiranju transformatorjev s cik-cak vezavo. Druga polovica magistrskega dela pa obravnava mehanske obremenitve med trifaznim kratkim stikom. Naloga je osredotočena na kumulativno aksialno silo, ki je izračunana na podlagi rezultatov osno simetričnega in planarnega modela. Obravnavane so največja kumulativna aksialna sila, rezultanta kumulativne aksialne sile ter sila na stebrne letve, pri čemer so upoštevani različni trenutki opazovanja ter različni izmiki različnih navitij. Planarni model je bil razdeljen na šest različnih podmodelov, ki so se razlikovali glede na pozicijo mreže. Od planarnih podmodelov se je osno simetričnemu najbolj približal model z mrežo levo od desnega stebra, vendar so bili rezultati planarnih modelov precej razpršeni in pogosto večji od rezultatov osno simetričnega modela. Ugotovljeno je, da je planarni model s popravljenim volumnom primeren za izračun stresane napetosti, medtem ko je zaradi cilindrične geometrije navitij osno simetrični model zanesljivejši pri izračunu aksialnih mehanskih obremenitev. Leakage reactance voltage represents the inductive component of a transformer’s short-circuit voltage. As it constitutes the predominant component, it is an important design parameter because it affects short-circuit currents as well as mechanical and thermal stresses. Its calculation is particularly demanding in transformers with a zig-zag connection, as conventional analytical models often fail to provide sufficiently accurate results. The aim of the first part of this master’s thesis is to compare different methods for calculating leakage reactance voltage and to determine which model most closely matches measurements obtained from actual transformers. Both analytical and numerical approaches are considered. First, Rogowsky’s analytical method is presented, followed by several numerical models based on the finite element method and implemented in FEMM. The examined models include a single-limb two-dimensional axisymmetric model, a three-phase two-dimensional planar model, and several derived models with corrected volumes, in which the magnetic energy is recalculated using different representative radiuses. The models are validated using several different transformer designs for which short-circuit voltage measurements from factory acceptance tests are available. The results show that the analytical model has limited applicability, while the basic planar model provides insufficient accuracy. The best agreement with the measurements is achieved by the corrected-volume planar model, in which the volume is determined using the radius where the center of magnetic energy is located. This approach provides a good compromise between accuracy and computational complexity and is suitable for practical application in designing transformers with zig-zag windings. The second part of the thesis examines mechanical stresses during a three-phase short circuit. The study focuses on the cumulative axial force, calculated using the results of the axisymmetric and planar models. The maximum cumulative axial force, resultant cumulative axial force, and force acting on the flitch plates are considered, taking into account different observation instants and different axial displacements of individual windings. The planar model is divided into six submodels according to the position of the sampling grid. Among the planar submodels, the model with the grid positioned to the left of the middle limb most closely matches the axisymmetric model. Nevertheless, the results obtained using the planar models are widely dispersed and are frequently higher than those obtained using the axisymmetric model. It is concluded that the corrected-volume planar model is suitable for calculating leakage reactance voltage, whereas the axisymmetric model is more reliable for calculating axial mechanical stresses because it better represents the cylindrical geometry of transformer windings. transformator stresana napetost cik-cak vezava metoda končnih elementov kumulativna aksialna sila kratek stik FEMM transformer leakage reactance voltage zig-zag connection finite element method cumulative axial force short circuit FEMM true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-10-27 07:45:06 2026-10-27 07:45:27 2026-10-28 04:08:42 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1970-01-01 63430 Papez_Zan_-_Primerjava_modelov_za_izracun_napetosti_na_stresani_reaktanci_in_aksialne_sile_v_nav.pdf Papez_Zan_-_Primerjava_modelov_za_izracun_napetosti_na_stresani_reaktanci_in_aksialne_sile_v_nav.pdf 1 846E905B3458DEA36C22608A22C3FAF7 ff751b01d28a96cc1d3759ca7433b7efa0065af828aba4115c8c5e9aa235c643 fc0b4933-d1d1-11f1-aea2-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=251650 Fakulteta za elektrotehniko 0 0 0