Solutions to physical problems described by Differential Equationson complex domains are in except for special cases almost impossibleto find. This turns our interest toward numerical approaches. Sincethe size of the numerical models tends to be very large when handlingcomplex problems, the area of model reduction is always a hot topic. Inthis report we look into a model reduction method called ComponentMode Synthesis. This can be described as dividing a large and complexdomain into smaller and more manageable ones. On each of thesesubdomains, we solve an eigenvalue problem and use the eigenvectorsas a reduced basis. Depending on the required accuracy we mightwant to use many or few modes in each subdomain, this opens for anadaptive selection of which subdomains that affects the solution most.We cover two numerical examples where we solve Helmholtz equationin a linear elastic problem. The first example is a truss and the othera gear wheel. In both examples we use an adaptive algorithm to refinethe reduced basis and compare the results with a uniform refinementand with a classic model reduction method called Modal Analysis. Wealso introduce a new approach when computing the coupling modesonly on the adjacent subdomains.

Frequency response analysis (FRA) has emerged as the de-facto industry standard condition-monitoring tool to assess mechanical integrity of transformer windings during its service life. It the prerequisite detection sensitivity and customized portable commercial instruments are also available. Considering its importance and taking cognizance of its hidden potential, international bodies, viz., IEEE, IEC, and CIGRE have published standards/guides on its use and interpretation. In spite of all the progress witnessed over the past two decades, FRA has still not attained the status of a diagnostics tool. Probing the vast literature and research carried out in this points to the fact that lack of a rigorous mathematical basis to explain the underlying complex processes is, perhaps, one of the main reasons for the present predicament of FRA method. How-ever, it must be acknowledged that domain-knowledge is di cult to generalize in this. Having said that, the diagnostic part, which involves, the task of working back-wards starting from the FRA data to interpret a winding damage, locate it, and assess its severity, has so far remained teasingly elusive. As a consequence, FRA continues to remain as a sensitive condition-monitoring tool. Given its inherent potential, this situation seems to be a paradox, and so, calls for investigations. Once a mechanical damage has been detected by FRA, the next task is to locate its position and estimate its severity. An engineer expects FRA to provide these answers, so that corrective action, if needed, can be determined and initiated. In this context, even though FRA has attained global acceptance as a monitoring tool, it has failed as a diagnostic tool. Therefore, e orts that aim to address this issue are desirable. Driven by this motivation, the author's thesis proposes to explore a new school of thought in this direction, viz., to theoretically analyze the problem of localization of an incipient/minor mechanical damage (displacement in particular) and also assess its severity. Such an investigation seems to have not been undertaken previously. So, the goal is to establish a relationship to capture the complex interactions that exist between specific winding damages, winding parameters, and their overall in hence on the natural frequency deviations observable in the FRA data. Hence, exploring this possibility, subject to the constraint that the proposed method shall use inputs that are measurable at the terminals, becomes the primary objective of this research. In this thesis, a generalized analytical framework for handling winding displacements and FRA data has been successfully formulated. The formulation provides a general platform for localization and severity assessment of true radial and axial winding dis-placements occurring in an actual winding. An analytical solution becomes possible mainly due to manipulation of the system matrix, i.e., to consider the harmonic sum of squares of natural frequencies, instead of just the natural frequencies. This manipulation leads to an elegant closed-form expression that connects the displacement location and its severity, to changes in natural frequencies. For its implementation, short circuit natural frequencies and a few other terminal measurements are the only inputs that are necessary. This formulation is initially used in Chapter-3 to demonstrate localization of radial displacement in an isolated, actual, single, air-cored continuous-disk winding. Armed with this success, the supplicant proceeds further to show (in Chapter-4) how a minor manipulation of the formulation renders it suitable for localization of actual axial displacements as well. Extensive experimental verification was done and the results are encouraging. Accuracy of localization of radial/axial displacement is uniformly good for all positions, and so is the estimation of severity. Further details are presented in the thesis.

<p>Frequency response analysis (FRA) is a method which is used to detect mechanical faults in transformers. The FRA response of a transformer is determined by its geometry and material properties, and it can be considered as the transformer’s fingerprint. If there are any mechanical changes in the transformer, for example if the windings are moved or distorted, its fingerprint will also be changed so, theoretically, mechanical changes in the transformer can be detected with FRA.</p><p>The purpose of this thesis is to partly create a simple model for the ferromagnetic material in the transformer core, and partly to investigate the high frequency part of the FRA response of the transformer winding. To be able to realize these goals, two different models are developed separately from each other. The first one is a time- and frequency domain complex permeability model for the ferromagnetic core material, and the second one is a time- and frequency domain winding model based on lumped circuits, in which the discretization is made finer and finer in three steps. Capacitances and inductances in the circuit are calculated with use of analytical expressions derived from approximated geometrical parameters.</p><p>The developed core material model and winding model are then implemented in MATLAB separately, using state space analysis for the winding model, to simulate the time- and frequency response.</p><p>The simulations are then compared to measurements to verify the correctness of the models. Measurements were performed on a magnetic material and on a winding, and were compared with obtained results from the models. It was found that the model developed for the core material predicts the behavior of the magnetic field for frequencies higher than 100 Hz, and that the model for the winding predicts the FRA response of the winding for frequencies up to 20 MHz.</p>

No novo contexto do setor elétrico brasileiro, as concessionárias passam a ter uma nova postura quanto à gestão. A energia elétrica, como produto, como negócio, deve levar lucro às empresas concessionárias. Começam a dar mais importância aos custos, entendendo que vários aspectos técnicos devem ser analisados, visando reduzir perdas substanciais. Assim sendo, o transformador de potência assume uma posição destacada, considerando sua posição estratégica no sistema elétrico, fundamental no processo de transporte e entrega de energia elétrica. Por este motivo vem despertando o interesse no desenvolvimento de estudos e pesquisas no sentido de aumentar sua vida útil. O método de Análise da Resposta em Frequência da impedância do transformador permite obter a “assinatura” do mesmo, a fim de verificar futuras degradações. Este método é adotado por várias empresas em todo o mundo, há mais de três décadas. Embora sua ampla aplicação entre muitas técnicas utilizadas na monitoração e análise de falhas em equipamentos, até agora não houve consenso na interpretação dos resultados obtidos por este método. A dificuldade de correlacionar parâmetros com prováveis falhas tem suscitado pesquisas para obtenção de resultados confiáveis e de interpretação fácil. Este trabalho objetiva determinar um modelo elétrico que represente a característica da resposta em frequência para fins de armazenamento de dados e simulações. A partir de dados reais do teste de resposta em frequência da impedância inseridos no modelo proposto, através de um programa computacional, foi verificada a confiabilidade nas respostas obtidas, comparadas com as reais. Os resultados obtidos asseguram que o modelo proposto é viável de ser aplicado. / In the new context of the Brazilian electric industry, the electric power provider companies have adopted a new administration posture. The electric power, as a product and business, should make the companies profitable. They have been paying more attention to the costs, .learning that many technical aspects should be analyzed in order to reduce substantial losses. Therefore, the power transformer takes an outstanding position, considering its strategic position in the electric system and being essential in the process of transport and delivery of the electric power. For this reason, there has been an interest in the development of studies and research in order to increase its useful life. The method of Frequency Response Analysis of impedance of the power transformer permits to obtain reference parameters of this one, in order to verify future degradations. This method has been adopted by many companies throughout the world for over three decades. Despite its wide application among several techniques used in the supervision and analysis of faults of equipments, there has been no consensus in the interpretation of the results obtained by this method so far. The difficulty of correlating the parameters with probable faults have increased research in order to obtain reliable results and of easy interpretation. This study aims to determine an electric model that represents the characteristic of the frequency response in order to store data and simulations. Starting from the real data of the FRA test inserted in the proposed model through a computer program, the reliability of the obtained responses were verified and compared with the real data. The obtained results assure that the proposed model is viable and can be applied.

Natural lightning strikes induce impulsive overvoltages on transmission lines and its terminal equipment. These overvoltages may cause failures in insulation mechanisms of electrical devices in the power system. It is important to test the insulation strength of a device against these impulsive overvoltages. Usually, Marx generators are used to generate impulse waveforms for testing purposes. A novel approach is proposed to obtain resistor settings of a Marx generator for impulse testing of power transformers. This approach enables us to overcome most of the major challenges in the commonly used trial-and-error method, including excessive time consumption and potential damage to the transformer. The proposed approach uses the frequency response of the transformer to synthesize a circuit model. Then, a genetic algorithm based optimization-enabled electromagnetic transient simulation approach is used to obtain the resistor settings. The proposed approach is validated by a real impulse test conducted on a three phase power transformer.

No novo contexto do setor elétrico brasileiro, as concessionárias passam a ter uma nova postura quanto à gestão. A energia elétrica, como produto, como negócio, deve levar lucro às empresas concessionárias. Começam a dar mais importância aos custos, entendendo que vários aspectos técnicos devem ser analisados, visando reduzir perdas substanciais. Assim sendo, o transformador de potência assume uma posição destacada, considerando sua posição estratégica no sistema elétrico, fundamental no processo de transporte e entrega de energia elétrica. Por este motivo vem despertando o interesse no desenvolvimento de estudos e pesquisas no sentido de aumentar sua vida útil. O método de Análise da Resposta em Frequência da impedância do transformador permite obter a “assinatura” do mesmo, a fim de verificar futuras degradações. Este método é adotado por várias empresas em todo o mundo, há mais de três décadas. Embora sua ampla aplicação entre muitas técnicas utilizadas na monitoração e análise de falhas em equipamentos, até agora não houve consenso na interpretação dos resultados obtidos por este método. A dificuldade de correlacionar parâmetros com prováveis falhas tem suscitado pesquisas para obtenção de resultados confiáveis e de interpretação fácil. Este trabalho objetiva determinar um modelo elétrico que represente a característica da resposta em frequência para fins de armazenamento de dados e simulações. A partir de dados reais do teste de resposta em frequência da impedância inseridos no modelo proposto, através de um programa computacional, foi verificada a confiabilidade nas respostas obtidas, comparadas com as reais. Os resultados obtidos asseguram que o modelo proposto é viável de ser aplicado. / In the new context of the Brazilian electric industry, the electric power provider companies have adopted a new administration posture. The electric power, as a product and business, should make the companies profitable. They have been paying more attention to the costs, .learning that many technical aspects should be analyzed in order to reduce substantial losses. Therefore, the power transformer takes an outstanding position, considering its strategic position in the electric system and being essential in the process of transport and delivery of the electric power. For this reason, there has been an interest in the development of studies and research in order to increase its useful life. The method of Frequency Response Analysis of impedance of the power transformer permits to obtain reference parameters of this one, in order to verify future degradations. This method has been adopted by many companies throughout the world for over three decades. Despite its wide application among several techniques used in the supervision and analysis of faults of equipments, there has been no consensus in the interpretation of the results obtained by this method so far. The difficulty of correlating the parameters with probable faults have increased research in order to obtain reliable results and of easy interpretation. This study aims to determine an electric model that represents the characteristic of the frequency response in order to store data and simulations. Starting from the real data of the FRA test inserted in the proposed model through a computer program, the reliability of the obtained responses were verified and compared with the real data. The obtained results assure that the proposed model is viable and can be applied.

No novo contexto do setor elétrico brasileiro, as concessionárias passam a ter uma nova postura quanto à gestão. A energia elétrica, como produto, como negócio, deve levar lucro às empresas concessionárias. Começam a dar mais importância aos custos, entendendo que vários aspectos técnicos devem ser analisados, visando reduzir perdas substanciais. Assim sendo, o transformador de potência assume uma posição destacada, considerando sua posição estratégica no sistema elétrico, fundamental no processo de transporte e entrega de energia elétrica. Por este motivo vem despertando o interesse no desenvolvimento de estudos e pesquisas no sentido de aumentar sua vida útil. O método de Análise da Resposta em Frequência da impedância do transformador permite obter a “assinatura” do mesmo, a fim de verificar futuras degradações. Este método é adotado por várias empresas em todo o mundo, há mais de três décadas. Embora sua ampla aplicação entre muitas técnicas utilizadas na monitoração e análise de falhas em equipamentos, até agora não houve consenso na interpretação dos resultados obtidos por este método. A dificuldade de correlacionar parâmetros com prováveis falhas tem suscitado pesquisas para obtenção de resultados confiáveis e de interpretação fácil. Este trabalho objetiva determinar um modelo elétrico que represente a característica da resposta em frequência para fins de armazenamento de dados e simulações. A partir de dados reais do teste de resposta em frequência da impedância inseridos no modelo proposto, através de um programa computacional, foi verificada a confiabilidade nas respostas obtidas, comparadas com as reais. Os resultados obtidos asseguram que o modelo proposto é viável de ser aplicado. / In the new context of the Brazilian electric industry, the electric power provider companies have adopted a new administration posture. The electric power, as a product and business, should make the companies profitable. They have been paying more attention to the costs, .learning that many technical aspects should be analyzed in order to reduce substantial losses. Therefore, the power transformer takes an outstanding position, considering its strategic position in the electric system and being essential in the process of transport and delivery of the electric power. For this reason, there has been an interest in the development of studies and research in order to increase its useful life. The method of Frequency Response Analysis of impedance of the power transformer permits to obtain reference parameters of this one, in order to verify future degradations. This method has been adopted by many companies throughout the world for over three decades. Despite its wide application among several techniques used in the supervision and analysis of faults of equipments, there has been no consensus in the interpretation of the results obtained by this method so far. The difficulty of correlating the parameters with probable faults have increased research in order to obtain reliable results and of easy interpretation. This study aims to determine an electric model that represents the characteristic of the frequency response in order to store data and simulations. Starting from the real data of the FRA test inserted in the proposed model through a computer program, the reliability of the obtained responses were verified and compared with the real data. The obtained results assure that the proposed model is viable and can be applied.

This master thesis has been executed at Scania CV AB in Södertälje, Sweden. Scania is a manufacturer of heavy transport solutions, an industry which is changing rapidly in order to meet stricter regulations, ensuring a sustainable future. Continuous product improvements and new technologies are required to increase performance and to meet markets requirements. By implementing design optimization in the design process it enables the potential of supporting design exploration, which is beneficial when products with high performance are developed. The purpose was to show the potential of design optimization supported by simulation driven design as a tool in the development process. To examine an alternative way of working for design engineers, elaborating more competitive products in terms of economical and performance aspects. Furthermore, to minimize time and iterations between divisions by developing better initial concept proposals. The alternative working method was developed iteratively in parallel with a case study. The case study was a suction strainer and were used for method improvements and validation, as well as decision basis for the included sub-steps. The working method for implementing design optimization and simulation driven design ended up with a procedure consisted of three main phases, concept generation, detail design and verification. In the concept generation phase topology optimization was used, which turned out to be a beneficial method to find optimized solutions with few inputs. The detail design phase consisted of a parameterized CAD model of the concept which then was shape optimized. The shape optimization enabled design exploration of the concept which generated valuable findings to the product development. Lastly the optimized design was verified with more thorough methods, in this case verification with FE-experts. The working method was tested and verified on the case study component, this resulted in valuable knowledge for future designs for similar components. The optimized component resulted in a performance increase where the weight was decrease by 54% compared with a reference product.

Frequency response analysis (FRA) is a frequency-domain method which is used to detect mechanical faults in transformers. The frequency response of a transformer is determined by its geometry and material properties, and it can be considered as the transformer’s fingerprint. If there are any mechanical changes in the transformer, for example if the windings are moved or distorted, its fingerprint will also be changed so, theoretically, mechanical changes in the transformer can be detected with FRA. A problem with FRA is the fact that there is no general agreement about how to interpret the measurement results for detection of winding damages. For instance, the interpretation of measurement results has still not been standardized.The overall goal of this thesis is to try to enhance the understanding of the information contained in FRA measurements. This has been done in two ways: (1) by examining the FRA method for (much) higher frequencies than what is usual, and (2) by developing a new method in which FRA is combined with the ideas of Time Domain Reflectometry (TDR). As tools for carrying out the above mentioned steps, models for the magnetic core and the winding have been developed and verified by comparison to measurements.The usual upper frequency limit for FRA is around 2 MHz, which in this thesis has been extended by an order of magnitude in order to detect and interpret new phenomena that emerge at high frequencies and to investigate the potential of this high-frequency region for detection of winding deteriorations.Further, in the above-mentioned new method developed in this thesis, FRA and TDR are combined as a step towards an easier and more intuitive detection and localization of faults in transformer windings, where frequency response measurements are visualized in the time domain in order to facilitate their interpretation. / QC 20111122

Frequency response analysis (FRA) of transformers is universally accepted as a highly sensitive tool to detect deformations in its windings. This is evident from the fact that customized commercial equipment (popularly called FRA or SFRA instruments) are used and recently the IEEE has issued a draft trial-use guide. Nevertheless, use of FRA is still limited to only detection and there is little progress towards its use for localization of winding deformation. Toward this end, a possible approach would be to compare the healthy and deformed systems in a suitable domain, e.g., their respective models could be compared. In this context, the mutually-coupled ladder network is ideally suited because not only does it map the length of the winding to sections of the ladder network, but, also inherently captures all subtle intricacies of winding behaviour under lightning impulse excitations insofar as the terminal response, internal oscillations and voltage distributions are concerned. The task of constructing a ladder network from frequency response is not trivial, and so exploration of newer methods is imperative. A system can comprehensively be characterized by its frequency response. With this as the starting point, many approaches exist to construct the corresponding rational function (in s-domain). But, the subsequent step of converting this rational function into a physically-realizable mutually-coupled ladder network has, as yet, remained elusive. A critical analysis of the circuit synthesis literature reveals that there exists no analytical procedure to achieve this task, a fact unequivocally stated by Guillemin in his seminal book "Synthesis of Passive Networks". In recent years, use of iterative methods to synthesize such ladder networks has also been attempted with some degree of success. However, there exists a lot of scope for improvement. Based on this summary, the objectives of this thesis are as follows- _ Development of an analytical procedure, if possible, to synthesize a mutually-coupled ladder network starting from the s-domain representation of the frequency response _ Construction of a nearly-unique, mutually-coupled ladder network employing constrained optimization technique and using frequency response as input, with time-efficiency, physical realizability and repeatability as its features In Chapter 2, analytical solution is presented to convert a given driving-point impedance function (in s-domain) into a physically-realizable ladder network with inductive couplings (between any two sections) and losses considered. The number of sections in the ladder network can vary, but, its topology is assumed fixed. A study of the coefficients of the numerator and denominator polynomials of the driving-point impedance function of the ladder network, for increasing number of sections, led to the identification of certain coefficients, which exhibit very special properties. Generalized expressions for these specific coefficients have also been derived. Exploiting their properties, it is demonstrated that the synthesis method essentially turns out to be an exercise of solving a set of linear, simultaneous, algebraic equations, whose solution directly yields the ladder network elements. The proposed solution is novel, simple, and guarantees a unique network. Presently, the formulation can synthesize a unique ladder network up to 6-sections. Although it is an analytical solution, there are issues which prevent its implementation with actual FRA data. Keeping the above aspect in mind, the second part of the thesis presents results of employing an artificial bee colony search algorithm for synthesizing a mutuallycoupled lumped-parameter ladder network representation of a transformer winding, starting from its measured magnitude frequency response. The bee colony algorithm is modified by defining constraints and bounds to restrict the search-space and thus ensure synthesis of a nearly-unique ladder network, corresponding to each frequency response. Ensuring near-uniqueness while constructing the reference circuit (i.e., a uniform healthy winding) is the objective. The proposed method is easy to implement, time-efficient, ensures physical realizability and problem associated with supply of initial guess in existing methods is circumvented. Experiments were performed on two types of actual, single, isolated transformer windings (continuous-disc and interleaveddisc) and the results are encouraging. Further details are presented in the thesis.