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NUMERIČNI MODEL PORAZDELITVE TOKA V VARISTORSKI MIKROSTRUKTURI ZA OPTIMIZACIJO PRENAPETOSTNIH ZAŠČITNIH NAPRAV
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TOPČAGIĆ, ZUMRET
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Križaj, Dejan
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Abstract
Vzporedno z razvojem, naraščajočo kompleksnostjo in predvsem občutljivostjo nizkonapetostnih omrežij, je potrebno slednja ustrezno opremiti s čim bolj zanesljivo zaščito pred prenapetostnimi pojavi. V te namene se uporabljajo standardizirane naprave za prenapetostno zaščito (ang. Surge Protective Devices (SPDs)), ki so sestavljene iz vsaj enega nelinearnega elementa (metal-oksidnega varistorja (MOV), iskrišča (ang. Spark Gap (SG)) ali plinskega odvodnika (ang. Gas Discharge Tube (GDT))) in termičnega odklopnika [1{4]. Dandanes veliko komercialno dostopnih SPD naprav temelji na uporabi ZnO varistorjev kot nelinearnih elementov [5{7]. Temelji ZnO varistorske tehnologije so bili razviti leta 1968 in kasneje predstavljeni v prispevku Matsuoke [8], v katerem avtor opisuje detaljne lastnosti ZnO varistorjev, kot so proizvodni procesi, nelinearne značilnosti, temperaturne odvisnosti in podobno. Zaradi mikrostrukturne zgradbe varistorske keramike ter porazdelitve aditivov in proizvodnega procesa, je nehomogenost izrazita značilnost vsakega varistorja. Eno od prvih raziskav nehomogenosti varistorjev je naredil Mizukoshi et al. [9]. Po njihovih rezultatih je kasneje K. Eda [10] analiziral preboj varistorja zaradi lokalizacije toka, povzročene z varistorsko nehomogenostjo. Dokazal je, da nehomogenost varistorske strukture predstavlja ključni faktor pri lokalizaciji električnega toka v varistorju. Greuter et al. [11] so eksperimentalno dokazali lokalizacijo električnega toka na mikronivoju z uporabo elektroluminiscence [12]. Dejstvo, da "električna" nehomogenost ZnO varistorja ni povzročena samo z nehomogenostjo mikrostrukture, je dokazal Tao et al. [13]. Avtorji so eksperimentalno dokazali, da vsak posamezni mikro-spoj predstavlja svojo lastno električno karakteristiko. Sledi, da je porazdelitev električnega toka v ZnO varistorju določena s strukturno nehomoxiii genostjo, distribucijo električnih parametrov posameznih mikro-spojev in, kot je prikazano v [9, 14], od priključene napetosti. Prvi model pojava lokalizacije toka v varistorski keramiki je predstavil Vojta et al. v [15]. Predstavljen model temelji na razumevanju varistorske mikrostrukture kot mreže prostorsko enakomerno porazdeljenih nelinearnih uporov. Za natančnejšo predstavitev nehomogenosti varistorske keramike je Bartkowiak et al. [16] predlagal uporabo Voronoi mreže kot modela varistorske keramike [6, 8, 17, 18]. Primerjava Voronoi mreže, prikazane v [16], in SEM (ang. Scanning Electron Microscope) posnetkov ZnO varistorja, kot je na primer prikazano v [17, 18] in na sliki 1.3, jasno nakazuje ustreznost takšnega pristopa za modeliranje naključne mikrostrukture varistorja. V [16] so avtorji uporabili Voronoi mrežo kot osnovo za generacijo neenakomerno povezane mreže nelinearnih uporov, kar (kot prikazano v [15]) rezultira v reševanju sistema tokovnih enačb z uporabo analize vezij. S pripisovanjem različnih (porazdeljenih) kolenskih napetostih in nelinearnih koe- cientov uporom v Voronoi generirani mreži so avtorji v [16] uspeli združiti strukturno in "električno" nehomogenost varistorske keramike. Po delu Bartkowiaka je bilo objavljenih več prispevkov [14, 18{20], ki opisujejo rabo numeričnih modelov temelječih na Voronoi mreži za analiziranje ZnO varistorski karakteristik. He et al. v [14] predstavlja modeliranje nehomogene porazdelitve toka v ZnO varistorjih z rabo Voronoi mreže in podaja odvisnost lokalizacije toka v odvisnosti od priključene napetosti. Rezultati nakazujejo, da lokalizacija toka doseže maksimum v tako imenovanem TOV (ang: temporary overvoltage) področju. TOV napetosti so napetosti velikosti, ki presegajo vrednost kolenske napetosti varistorja in so hkrati manjše od amplitud udarnih napetosti po "IEC 61643-11:2011 - Low voltage surge protective devices" standardu [21]. Modeliranje ZnO varistorjev na osnovi FEM (ang. Finite Element Method) analiz je predstavil Lengauer et al. [22]. Avtorji so izvedli FEM analizo mehanskih obremenitev v ZnO diskih, kjer je varistorska keramika predstavljena kot homogen cilinder. Avtorji v [23] predstavljajo FEM model za izračun toplotnih izgub v varistorju, kjer v modelu varistorsko keramiko predpostavijo kot homogen disk (enako kot v [22]). Bavelis et al. [24] so predlagali 3D FEM model za analizo porazdelitve toka v ZnO varistorju, v katerem je model mikrostrukture predstavljen z uporabo 3D Voronoi mreže. Velika pomanjkljivost predlaganega modela je, da je FEM model uporabljen le pri izračunu matrike prevodnosti posameznih ZnO zrn, ki je potem uporabljena v 3D mreži nelinearnih uporov. Model, predstavljen v [24], torej rezultira v reševanju vezij brez popolnega reševanja električnega in tokovnega polja v modelirani geometriji.
Language:
Slovenian
Keywords:
Metal-Oksidni Varistor
,
mikrostruktura
,
prenapetostne obremenitve
,
naprave za prenapetostno zaščito
,
energijske zmogljivosti varistorjev
,
varistor
,
metoda končnih elementov (FEM)
,
Voronoi mreža
,
lokalizacija toka
Work type:
Doctoral dissertation
Organization:
FE - Faculty of Electrical Engineering
Year:
2019
PID:
20.500.12556/RUL-113237
Publication date in RUL:
16.12.2019
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1347
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259
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Secondary language
Language:
English
Title:
NUMERICAL MODEL OF CURRENT DISTRIBUTION IN VARISTOR'S MICROSTRUCTURE FOR OPTIMIZATION OF SURGE PROTECTIVE DEVICES
Abstract:
Nonuniform current distribution inside varistor ceramics is a key factor in uencing its performance and failures. Therefore understanding, modeling and predicting of current distribution in varistor ceramics is of crucial signicance. Moreover, the electrothermal processes occurring within varistors microstructure decidedly in uence their energy absorption capability, as a vital parameter for the eective surge protection. In the rst part of doctoral thesis, a 2D numerical model for the simulation of nonuniform electric current distribution inside Zinc-(Metal)-Oxide Varistors is discused. A numerical model is based on physical modeling of the varistor's grain-structured geometry presented by Voronoi network using Finite Element Method (FEM) simulation. The presented method is solving complete electric eld inside the modeled geometry and therefore provides a more physically accurate approach for better understanding and predicting nonuniform current distribution in the varistor. In order to properly establish the FEM model a novel approach in dening grain boundary characteristic is proposed. Thus, a macroscopic model of the varistor microstructure has been developed and the grain micro-junction boundary characteristic has been derived. The simulation results of nonuniform current distribution in a varistor agree well with the measurement results for a typical ZnO varistor. In the second part of thesis, a 3D numerical model for the simulation of the electrothermal phenomenons occurring in the metal-oxide varistors is proposed. The model is based on a 3D representation of the varistor's polycrystalline microstructure and, as in the case of the 2D model, on the FEM analysis. With the aid of the proposed model, the interdependence of the varistor's energy absorption capability, nonuniform current conduction, and the thermal behavior is investigated. Results are in good alignment with experimental data and discussed in the context of electrothermal properties of the varistor's microstructure. An unambiguous dependency of the varistor's energy handling capability on the applied overvoltage is shown to exist. A quantitative evaluation of the eective volume decrease due to the severe current localization at temporary overvoltages is demonstrated. In the third part, the varistors current conduction under temporary overvoltages has been analyzed providing the means for extension of the varistors IV characteristics into the time domain so as to accurately predict their dynamic electrothermal behavior. The introduced dynamic (IV t) model of the varistors characteristics may have signicant implications in energy absorption requirements and design principles for the eective surge protection of the modern power systems. Implementation of the time domain extension of the varistors' IV characteristics in Spice library was performed and presented. The presented 2D and 3D models enable investigation of in uences of varistor geometry (shapes, sizes) and material properties on the current distribution, energy absorption capabilities and other electrothermal properties. The advantage of the presented models is an ability to have all of the microstructure parameters (grain sizes, thermal properties of grains, grain boundary breakdown voltages, nonlinearities, and etc.) xed while the effects of the specic one, are investigated. This is hardly achievable in the experimental processes since the interconnections of the material properties are comprehensive hence demanding large experimental data in order to evaluate the effect of the single parameter i.e. microstructure feature.
Keywords:
Metal-Oxide Varistors
,
Microstructure
,
Overload behavior
,
Temporaryovervoltages (TOVs)
,
Surge Protective Devices (SPDs)
,
Energy Absorption Capability(EAC)
,
Varistor
,
Finite Element Method (FEM)
,
Voronoi network
,
Current distribution
,
Non-uniformity
,
Current localization factor
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