Using analytical formula to estimate a complex problem of cavity based on a transmission line approach is called the ETL (Equivalent Transmission Line) method . Operating frequency of dominant mode of standard case is several hundreds of megahertz that is lower than frequency of CPU, higher-order mode must be considered . Several papers always discuss a single aperture that does not correspond to practical array of apertures of case .Array of apertures can be estimated using analytical formula and higher-order mode can be considered in this paper .Usually array of apertures is not placed at the center of metallic plate, we can modify the analytical formula to get ETL of shifted array of apertures. To consider industrial design and esthetics, many possible shape of array of apertures are discussed by adapting to the ETL method .The problem of how to improve the shielding effectiveness of array of apertures is treated in the latter half of this thesis. The FDTD (Finite-Difference Time Domain) method is a full-wave analytical algorithm and is not efficient for analyzing cavity. Advantage of ETL is that it is faster than full-wave analytical algorithm .However, traditional ETL can not get accurate level of shielding effectiveness without higher-order modes. Thus improved ways are introduced in the paper to simulate practical array of apertures to reach the result of good agreement and short computing time.

A detailed study of the performance of finite-difference time-domain (FDTD) and adaptive integral method (AIM) based simulators is presented for bioelectromagnetic (BIOEM) analysis in the UHF band. The comparison is complicated because modern simulators based on these methods can routinely perform high-fidelity BIOEM analysis with hundreds of millions of degrees of freedom. In this thesis, an empirical approach is adopted to investigate the accuracy-efficiency tradeoffs of an FDTD and an AIM based simulator. Specifically, comprehensive numerical experiments are performed using several benchmark multi-layered spherical phantoms. Scattering from these phantoms are computed by using increasingly finer resolution meshes and the results are compared to analytical solutions to investigate the accuracy as well as computational costs of the different methods. The results from the benchmark problems show that both FDTD and AIM based simulators achieve similar error levels for staircased voxel meshes but FDTD based simulation is less expensive, especially when the memory requirement and preprocessing cost are considered. The results also show that although both simulators can reduce errors by refining voxel meshes, AIM based simulators can significantly reduce errors by using CAD meshes instead of voxel ones without significant cost increase. / text

Graphene is a single atomic layer of graphite and has many extraordinary properties. Many graphene based applications have been proposed in recent years and the need of a time domain simulation tool for studying graphene based devices emerges. This thesis focuses on developing a simulation framework for graphene based devices using finite-difference time-domain (FDTD) method. Formulation for a perfectly matched layer (PML) for the sub-cell FDTD method for thin dispersive layers has been derived and implemented. Such a PML is useful when thin layers extend to the boundaries of the computational domain. Using the sub-cell PML formulation to model the graphene thin layers significantly reduces the computational cost compared to using the conventional FDTD. The proposed formulation is accompanied by detailed validation and error analysis studies. Several graphene applications are simulated using the new framework and the results show good agreement with the respective analytical models.

Graphene is a single atomic layer of graphite and has many extraordinary properties. Many graphene based applications have been proposed in recent years and the need of a time domain simulation tool for studying graphene based devices emerges. This thesis focuses on developing a simulation framework for graphene based devices using finite-difference time-domain (FDTD) method. Formulation for a perfectly matched layer (PML) for the sub-cell FDTD method for thin dispersive layers has been derived and implemented. Such a PML is useful when thin layers extend to the boundaries of the computational domain. Using the sub-cell PML formulation to model the graphene thin layers significantly reduces the computational cost compared to using the conventional FDTD. The proposed formulation is accompanied by detailed validation and error analysis studies. Several graphene applications are simulated using the new framework and the results show good agreement with the respective analytical models.

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Este trabalho apresenta um novo formalismo bi-dimensional em diferenças finitas no domínio do tempo (2D-FDTD) para a simulação de estruturas baseadas em metamateriais. A natureza dispersiva destes meios é levada em consideração de forma precisa pela inclusão dos modelos materiais de Drude para os tensores permissividade elétrica e permeabilidade magnética. Todos os elementos dos tensores são considerados neste formalismo, o que o torna muito atraente para a modelagem de uma classe geral de estruturas eletromagnéticas. Dois efeitos de enorme impacto são analisados em detalhes, sendo eles a cobertura de invisibilidade e o rotacionamento de campo. Ambos os efeitos requerem a utilização de técnicas de transformação de coordenadas a qual deve ser aplicada apenas na região onde os campos eletromagnéticos precisam ser manipulados, tirando vantagem da invariância das equações de Maxwell quanto a estas operações. Esta técnica redefine localmente os parâmetros de permissividade e permeabilidade do meio transformado. O formalismo implementado apresentou grande estabilidade e precisão, uma conseqüência direta da natureza dispersiva dos modelos materiais de Drude, o que o caracteriza como uma boa contribuição para uma completa compreensão da fenomenologia por trás destes efeitos fascinantes. Os resultados numéricos apresentaram boa concordância com os disponíveis na literatura. Foi também observado que ambas estruturas são muito sensíveis a variações de freqüência do campo de excitação. / This work introduces an extended two-dimensional finite difference time domain method (2D-FDTD) for the simulation of metamaterial based structures. The dispersive nature of these media is accurately taken into account through the inclusion of the Drude material models for the permittivity and permeability tensors. All tensor elements are properly accounted for, making the formalism quite attractive for the modeling of a general class of electromagnetic structures. Two striking effects are investigated with the proposed model, namely, the invisibility cloaking and the field rotation effects. Both effects require the utilization of a coordinate transformation technique which must be applied only in the region where the electromagnetic field needs to be manipulated, taking advantage of the invariance of Maxwell\'s equations with respect to these operations. This technique locally redefines the permittivity and permeability parameters of the transformed media. The implemented formalism has proved to be quite stable and accurate, a direct consequence of the dispersive nature of the Drude material model, which characterizes it as a good contribution to fully understand the phenomenology behind these fascinating effects. The numerical results are in good agreement with those available in the literature. It was also verified that both structures are very sensitive to frequency variations of the excitation field.

Σκοπός της παρούσας διπλωματικής είναι η εξέταση των προτεινόμενων συστημάτων γείωσης για ανεμογεννήτριες σύμφωνα με την IEC και η προσομοίωση με Matlab της συμπεριφοράς τους σε πλήγμα κεραυνού στην κατασκευή μέσω της μεθόδου FDTD. Στο πρώτο κεφάλαιο αναπτύσσεται σύντομα το φαινόμενο του κεραυνού και οι ανανεώσιμες πηγές ενέργειας. Στη συνέχεια δίνονται στοιχεία για την αιολική ενέργεια και την εκμετάλλευσή της στον κόσμο και στην Ελλάδα. Επίσης αναλύονται τα βασικά μέρη και η λειτουργία μιας ανεμογεννήτριας. Στο δεύτερο κεφάλαιο αναλύεται η αντικεραυνική προστασία ανεμογεννητριών όπως προτείνεται στο διεθνές πρότυπο IEC-61024 και η διαδικασία αξιολόγησης της επικινδυνότητας μιας τέτοιας κατασκευής. Δίνονται οι βασικοί ορισμοί για συστήματα γείωσης. Διεξοδικότερα εξετάζονται οι δύο τύποι συστημάτων γείωσης για ανεμογεννήτριες, σύμφωνα πάντα με την IEC. Στο τρίτο κεφάλαιο αναλύεται η μέθοδος FDTD (Finite Difference Time Domain ) και ο αλγόριθμος του Yee. Η καινοτομία του αλγορίθμου αυτού ήταν η γεωμετρική απεικόνιση για τη δειγματοληψία των τιμών του ηλεκτρικού και του ηλεκτρομαγνητικού πεδίου η οποία αντιπροσωπεύει τις ολοκληρωτικές και τις διαφορικές μορφές των εξισώσεων του Maxwell. Για την προσομοίωση χρησιμοποιήθηκε επίσης η μέθοδος λεπτού αγωγού (thin wire) η οποία επιτρέπει την ακριβή μοντελοποίηση ενός λεπτού αγωγού(όπου λεπτός αγωγός ορίζεται ως αγώγιμο καλώδιο η ακτίνα του οποίου είναι μικρότερη από το μέγεθος του κελιού που χρησιμοποιεί η FDTD) και περιγράφεται στη συνέχεια του κεφαλαίου. Στο τέταρτο κεφάλαιο εξετάζουμε δυο προτεινόμενες διατάξεις γείωσης σύμφωνα με το πρότυπο της IEC. Εξηγείται αναλυτικά πως υλοποιήθηκε ο αλγόριθμος FDTD στο Matlab και αναφέρονται οι παραδοχές που έγιναν για τη σύγκλιση της μεθόδου .Παρουσιάζεται με γραφική απεικόνιση από το MAtlab η μοντελοποίηση του χώρου για τις 2 διατάξεις. Μελετάμε την αύξηση δυναμικού ,την βηματική τάση και την μεταβατική αντίσταση για τη διάταξη τύπου Α με ένα κάθετο ηλεκτρόδιο . Εξετάζουμε πως επηρεάζει τα παραπάνω μεγέθη η μεταβολή του βάθους του ηλεκτροδίου και πως μεταβάλλονται σε διαφορετικούς τύπους εδαφών. Ακόμα εξετάζουμε την συμπεριφορά ενός συστήματος γείωσης για τη διάταξη τύπου Β με ένα οριζόντιο δακτύλιο και τέσσερα κάθετα ηλεκτρόδια συγκριτικά με τη διάταξη Α. Στο τελευταίο κεφάλαιο σχολιάζονται τα αποτελέσματα των προσομοιώσεων και γίνεται σύγκριση των δύο προτεινόμενων διατάξεων γείωσης από την IEC. Συνοψίζονται τα πλεονεκτήματα και τα μειονεκτήματα της μεθόδου FDTD για προσομοίωση συμπεριφοράς συστημάτων γείωσης σε πλήγμα κεραυνού. Επίσης προτείνονται διαφορετικές προσεγγίσεις στην υλοποίηση της μεθόδου για την αντιμετώπιση των μειονεκτημάτων. / The subject of this essay is the analysis of the suggested by IEC grounding systems for wind turbines and the simulation of these systems using the FDTD method .The software used for the simulations was MATLAB. First chapter is a brief but essential theoretical approach on the lightning phenomenon. Moreover facts and figures are given for renewable energy and particularly wind power in Greece and worldwide. Furthermore the components and the function of a wind turbine are analyzed. The second chapter is a thorough study of the lightning protection systems for wind turbines as suggested by the international standard IEC-61204.The standard defines the risk assessment process of a wind turbine. The components of grounding systems are introduced and the two types of grounding systems for wind turbines according to IEC are analyzed. FDTD (Finite Difference Time Domain) method is analyzed in the third chapter along with Yee’s algorithm. The novelty of this method is the geometrical representation of the electrical and magnetic fields and the equations of Maxwell. The thin wire method was also used for the simulation in order to model precisely the conductors (as thin wire we define a wire with radius smaller than the cell used in the FDTD) and is described in this chapter. Along with writing this essay various grounding systems were simulated with MATLAB. In the forth chapter some brief comments about the development of the simulation are stated along with the description of the FTDT algorithm implementation. We study the potential rise, the step voltage and the transient resistance for the two types of grounding systems suggested by IEC and we observe how the depth of the rods and the resistivity of the soil affect them. In addition to that we also examine some variations of the two types of grounding systems in order to conclude to the optimal grounding system for a wind turbine. In the last chapter results are examined and conclusion are extracted and presented. The suggested by the IEC grounding systems are compared. Further optimizations of the simulation process are discussed leading to possible, future improvement. The advantages and disadvantages of the FTDT method for simulation of grounding systems after a lightning are presented.

Este trabalho apresenta um novo formalismo bi-dimensional em diferenças finitas no domínio do tempo (2D-FDTD) para a simulação de estruturas baseadas em metamateriais. A natureza dispersiva destes meios é levada em consideração de forma precisa pela inclusão dos modelos materiais de Drude para os tensores permissividade elétrica e permeabilidade magnética. Todos os elementos dos tensores são considerados neste formalismo, o que o torna muito atraente para a modelagem de uma classe geral de estruturas eletromagnéticas. Dois efeitos de enorme impacto são analisados em detalhes, sendo eles a cobertura de invisibilidade e o rotacionamento de campo. Ambos os efeitos requerem a utilização de técnicas de transformação de coordenadas a qual deve ser aplicada apenas na região onde os campos eletromagnéticos precisam ser manipulados, tirando vantagem da invariância das equações de Maxwell quanto a estas operações. Esta técnica redefine localmente os parâmetros de permissividade e permeabilidade do meio transformado. O formalismo implementado apresentou grande estabilidade e precisão, uma conseqüência direta da natureza dispersiva dos modelos materiais de Drude, o que o caracteriza como uma boa contribuição para uma completa compreensão da fenomenologia por trás destes efeitos fascinantes. Os resultados numéricos apresentaram boa concordância com os disponíveis na literatura. Foi também observado que ambas estruturas são muito sensíveis a variações de freqüência do campo de excitação. / This work introduces an extended two-dimensional finite difference time domain method (2D-FDTD) for the simulation of metamaterial based structures. The dispersive nature of these media is accurately taken into account through the inclusion of the Drude material models for the permittivity and permeability tensors. All tensor elements are properly accounted for, making the formalism quite attractive for the modeling of a general class of electromagnetic structures. Two striking effects are investigated with the proposed model, namely, the invisibility cloaking and the field rotation effects. Both effects require the utilization of a coordinate transformation technique which must be applied only in the region where the electromagnetic field needs to be manipulated, taking advantage of the invariance of Maxwell\'s equations with respect to these operations. This technique locally redefines the permittivity and permeability parameters of the transformed media. The implemented formalism has proved to be quite stable and accurate, a direct consequence of the dispersive nature of the Drude material model, which characterizes it as a good contribution to fully understand the phenomenology behind these fascinating effects. The numerical results are in good agreement with those available in the literature. It was also verified that both structures are very sensitive to frequency variations of the excitation field.