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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. 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.

V pričujočem diplomskem delu sem se posvetil energetskemu varistorju, ki je največkrat vgrajen v prenapetostni zaščiti, in delovanju pod specifičnimi pogoji pri povišani temperaturi in vlagi. Takšni pogoji so prej izjema, kot pravilo, vendar standard pogojuje delovanje v opisanih pogojih. Diplomska naloga je sestavljena iz opisa varistorja in opreme, uporabljene pri preizkusih. Za preizkuse sem izbral dva različna izolacijska materiala in referenčni varistor brez izolacije. Izolacijski material je epoksi, ki je najbolj razširjen pri varistorjih in drugih elektronskih komponentah, ter poliuretanska zalivka, katera omogoča zalivanje v ohišju in je čedalje bolj uporabljena pri ščitenju elektronskih sestavov. Vmesne rezultate sem spremljal s pomočjo namenske naprave AMTTV V1, ki omogoča spremljanje poteka prepustnega toka. Končne meritve so bile izvedene na merilniku Keithley 2410, ki se uporablja za merjenje nazivne napetosti. Najprej sem varistorje testiral le pri povišani temperaturi, ki je pri proizvajalcih varistorjev deklarirana, kot maksimalna obratovalna temperatura. Rezultati so bili glede na standard IEC 61051-2 pozitivni. V drugem preizkusu sem se nanašal na standard EN 50539-11 (točka 7.6.1). Preizkus je potekal pri relativni vlagi 93 % in temperaturi 40 °C. Referenčni varistorji in tisti z epoksi zaščito so med preizkusom kazali stabilen potek. Mnogo slabše so se izkazali vzorci s poliuretansko zalivko. Kljub na videz zaskrbljujočim rezultatom so na koncu vsi izdelki prestali preizkus, saj standard veleva, da morajo biti preizkušanci po testu pomerjeni, nazivna napetost pa ne sme biti višja od začetne vrednosti za več kot 10 %. Preizkusi so mi dali smernice za nadaljnje raziskovalno delo in preizkušanje različnih izolacijskih materialov. In this thesis I was focused on the energy varistor, which is mostly integrated in surge protection devices, and its functioning exposed to higher temperature and humidity. Such conditions are more an exception rather than a common environment, but the standard declares such conditions. The thesis consists of the description of the varistor and equipment used in the tests. For the tests I chose two different types of insulation and a reference varistor, without insulation. Insulation material is epoxy, the most widespread insulation among varistors and other electronic components and polyurethane potting, which allows encapsulation in the housing and is increasingly used in electronic assemblies. I monitored intermediate results with the help of special custom designed device AMTTV V1, which allows monitoring of the leakage current. Final measurements were carried out on the Keithley 2410, which is used to measure the nominal voltage. First I tested varistors only at elevated temperatures, which is declared by producer of varistors, as the maximum operating temperature. The results according to standard IEC 61051-2 were positive. In experiment 2, I refered to the standard EN 50539-11 (paragraph 7.6.1). The experiment was conducted at a relative humidity of 93 % and a temperature of 40 °C. Reference varistors and those with epoxy coating showed a stable leakage current through the whole period of test. Much worse behaved varistors with polyurethane potting. Despite the apparently alarming results, all products passed the test. Standard requires that the varistors need to be measured after the test and nominal voltage must not raise for more than 10 %. Tests gave me directions for further research and testing of different insulation materials.

Varistor je pasivna elektronska komponenta z izrazito nelinearno karakteristiko U-I. V družbi Keko - Varicon ga izdelujemo na osnovi cinkovega oksida s tehnologijo suhega stiskanja in tehnologijo nalivanja. Rezultat tehnologije suhega stiskanja je disk varistor, ki ga poleg ožičevanja vgrajujemo (inkapsuliramo) v plastično SMD-ohišje. Družino teh varistorjev imenujemo PV-serija. Tok puščanja Idc je eden izmed ključnih parametrov, ki vpliva na življenjsko dobo varistorja in izgube v vezju. Po vgradnji s t. i. reflow spajkanjem se še poveča. Ena izmed možnosti odprave tega fenomena je pasiviranje robov varistorja s stekleno frito. Rešitev je zahtevala izdelavo stroja, ki omogoča nanos, pasiviranje robov, iskanje pravega profila žganja frite in vpeljavo tehnologije v proizvodnjo. Varistor is a passive electronic component with highly nonlinear U - I characteristics. Keko - Varicons' product is ceramic varistor based on zinc oxide by dry pressing technology and the technology of casting and printing. The result of dry pressing technology is disc varistor (singlelayer). Disk varistors can be wired (trough hole component) or encapsulated in a plastic SMD housing. Family of incapsulated varistors are called PV series. Leakage current IDC is varistors one of the key parameter, which affects the lifetime of the varistor and losses in the circuit. After reflow soldering leakage current is even higher. One of the possible solutions for eliminate this phenomena is glass pasivation. The solution required facility development, finding the right temperature profile and implementation in to the production line.

V diplomskem delu je opisan postopek uporabe Weibullove verjetnostne porazdelitve na primeru določevanja življenjske dobe varistorja. Podane so potrebne informacije o nelinearnih elementih, ki se uporabljajo na področju zaščite elementov elektroenergetskega sistema. Dalje je v splošnem opisan varistor, natančneje pa so podani podatki o tipu varistorja podjetja Varsi, ki smo ga uporabili pri meritvah. Opisan je postopek določevanja standarda meritev in sam potek izvajanja meritev. Za interpretacijo rezultatov smo si izbrali dvoparametrično Weibullovo porazdelitev ter iskali parametra α in β. Pri tem življenjske dobe nismo merili glede na čas, ampak glede na število udarov, ki jih varistor prenese pri različnih obremenitvah z udarnim generatorjem. Obdelava podatkov je potekala na tri načine: z grafično metodo, metodo linearne regresije najmanjših kvadratov in z na svetovnem spletu prosto dostopnim programom EasyFit. Kot rezultat smo dobili enačbo, na podlagi katere lahko informativno sklepamo, pri katerem udaru bo pri določeni obremenitvi varistor odpovedal. The thesis is based on the process of Weibull probability distribution to determine a lifetime expectancy of a varistor. Necessary information about nonlinear elements which are used in the field of surge protection is provided. Further we also have a description of a varistor and a more detailed overview of the type of varistor manufactured by the company Varsi, which was used for our measurements. It describes the procedure on how we determined the standard for the measurements and the whole process of measurements. Results were interpreted using two-parameter Weibull distribution and we were looking for parameters α and β. Lifetime expectancy wasn't measured in full product lifetime, but considering the number of strikes that varistor can take when exposed to different current loads, which we produced with a strike generator. Data was processed in three ways: with grapf method, linear regression – least squares estimation and with use of the program EasyFit, which is available as a free program on the internet. As a result we got an equasion, based on which we can informatively assume after how many strikes will varistor degrade when exposed to a particular current load.

V tem magistrskem delu je predstavljen eden izmed načinov določanja življenjske dobe varistorja pri normalnih delovnih pogojih. Pri nekaterih napravah in komponentah je nemogoče testirati življenjsko dobo pri normalnih obratovalnih pogojih, ker bi samo testiranje trajalo predolgo (na primer več kot 1 leto). Ta problem nastopi tudi pri testiranju varistorja. Za rešitev tega problema lahko na primer uporabimo tako imenovano pospešeno testiranje. Varistor lahko odpove na več načinov. Zato se lahko tudi testiranje v tem primeru izvaja na več načinov. Sredstva, ki so bila na voljo, so omogočala testiranje v komori pri povišani temperaturi pri delovni napetosti varistorja. Spremljani so bili časi do odpovedi varistorja pri različnih temperaturah. Za izračun življenjske dobe varistorja pri povišanih temperaturah so bili uporabljeni modeli za analizo preživetja. Iz rezultatov pri povišanih temperaturah je dobljena ocena koeficienta aktivacijske energije, ki je nato uporabljena za ekstrapolacijo življenjske dobe varistorja pri 85 °C. Ob tem je predpostavljeno, da je koeficient aktivacijske energije konstanten za dano keramiko. Preverjali smo tudi povezanost med začetnimi električnimi parametri in časi do odpovedi. This thesis addresses one of the possible ways of calculating lifetime of a varistor at normal operating conditions. For some of the devices or components life test at normal operating conditions would take too much time (e.g. more than one year). This problem also arises with life test for a varistor. To solve this problem, we can use accelerated testing. There are several different reasons for a failure of a varistor, therefore accelerated tests are also done in different ways. The available equipment allowed us to make accelerated testing in climatic chamber under operating voltage load. Varistor failure times were recorded at different temperature exposures. Later survival analysis models were used to determine lifetime of a varistor under increased temperature. From results provided by survival analysis, activation energy was calculated, and then using extrapolation it was possible to estimate lifetime of a varistor at 85 °C. It was assumed that activation energy coefficient is constant for the given ceramic. After mean time to failure was estimated it was tested whether starting varistor characteristics are related to varistor failure times or not.

V pričujočem delu je predstavljena posodobitev merilnega mesta in programiranje aplikacije za avtomatizacijo meritev U-I karakteristike varistorja. Posodobljeno merilno mesto vključuje osebni računalnik in inštrument, ki je povezan nanj, ter nadomešča stari, analogni inštrument, kateri ni imel možnosti povezave z računalnikom. Projekt se je začel zaradi zahtev kupcev po bolj točnih in računalniško obdelanih meritvah in merilnih rezultatih ter zaradi boljše sledljivosti in analize preteklih rezultatov. Za programiranje aplikacije sem uporabil programsko opremo National Instruments Labview, za izvedbo meritev pa inštrument Keithley 2410 SourceMeter, ki je priključen na osebni računalnik in v celoti voden preko napisane aplikacije. V delu je opisan varistor, opis obstoječega merilnega sistema, predstavljen je novi merilni sistem, na kratko je opisana primerjava podatkovnega vodila po standardu RS-232 in IEEE-488 vodila (GPIB, General Purpose Interface Bus), načrtovanje programa, zahteve, programiranje in opis programa, potek izvedbe meritve, rešitve problemov in zaključek z možnimi posodobitvami. V poglavju o varistorju je opisana osnovna naloga varistorjev, različne izvedbe le teh in karakteristike. Poglavje o obstoječem merilnem sistemu vsebuje stari merilni postopek in razloge za zamenjavo z novejšim sistemom. Omenjene so tudi druge možnosti glede implementacije merilnega mesta in obrazloženo je, zakaj je izbrana rešitev najbolj optimalna izbira. Opis novega sistema je samostojno poglavje, v katerem je opisan merilni postopek, podatkovne povezave med računalnikom in inštrumentom in razlogi za izbiro le teh. Opis delovanja programa nam pove, kako je program sestavljen ter kakšni ukazi so potrebni za komunikacijo z inštrumentom. Načrtovanje, potek in zahteve za program so opisane v poglavju Potek načrtovanja in programiranja. Opisani so tudi primeri neuresničenih zahtev in obrazloženo je, zakaj je temu tako. V poglavju o programiranju teče beseda o programskem okolju Labview, komponentah in dodatnih programskih paketih, ki sem jih uporabil pri programiranju. V opisu programa je razloženo, kakšne metode so uporabljene za najboljši prikaz merilnih rezultatov, ter kakšna je struktura programskega projekta. Potek testiranja elementa zahteva svoje poglavje in opisuje vse številke in kode, ki se prenesejo iz podatkovne baze, ki so potrebne za izvedbo meritve in za obdelavo rezultatov. Opisani so stresni testi za varistorje, primerjava karakteristik in izračuni koeficientov. Pri programiranju sem naletel na težave. Rešitve težav so opisane v poglavju rešitve problemov. V poglavju, kjer je opisano izvajanje programa, je diagram poteka in opis celotnega postopka ter slikovni prikaz zaslonskih slik po korakih. Zaključek je namenjen pregledu celotnega stanja in pogledu v prihodnost ter morebitne možne posodobitve programa. In the following work an update of the measurment site and programming of the aplication for measurement automatization of UI varistor characteristics is presented. The updated measuring site includes a personal computer and the high voltage testing instrument and replaces the old analog instrument, which did not have the possibility for connecting to a computer. The project started because of the demands of customers for a more accurate and computer aided measurements and also to achieve better traceability and analysis of measured data. For aplication programming the software Labview (by National Instruments) and 2410 SourceMeter (by Keithley) were used. The sourceMeter is fully managed by the computer. In the thesis I have described the varistor element, current measuring system, the new measuring system, short description of RS-232 and IEEE-488 (GPIB, General Purpose Interface Bus) data buses, program planning, customer demands, program code writting and code description, problem solving and cocnlusion with possible fututre upgrades. Chapter about the varistor element containes a description of its basic operation, various versions of varistors and their charateristics. The chapter on the current measuring system contains the old measurement procedure and the reasons for replacement with a new system. There are other options regarding the implementation of the measuring point and I have explained why the chosen solution is the most optimal. Description of the new system is an independent chapter, which describes the measurement procedure, the data connection between the computer and the instrument and the reasons for choosing these. Description of the program tells us what the program consists of and commands needed to communicate with the instrument. The design, development course and requirements for the program are described in this chapter. It also describes examples of unfulfilled requirements and explains the reasons for them. In the chapter on programming, Labview programming environment is discussed and also components and additional software packages which I used in programming. In the description of the program I have explained methods used to present the measurement results and the structure of the software project. Testing procedure for individual elements under test requires a seperate chapter in which I have described all of the needed numbers and codes that are transferred from the database and are essential for performing the measurement and processing of the results. Stress tests for varistors are also described as well as their U-I characteristics comparison and coeffcient calulations. During the programming, I have encountered some problems. Troubleshooting of them is described in the chapter about problem solving. The next chapter contains the program flow chart and the description of measuring procedure and step by step graphical screenshots. Conclusion chapter is dedicated for review of overall project status and future plans to find any possbile updates for the program.