La present tesi proposa una metodología per a la simulació probabilística de la fallada de la matriu en materials compòsits reforçats amb fibres de carboni, basant-se en l'anàlisi de la distribució aleatòria de les fibres. En els primers capítols es revisa l'estat de l'art sobre modelització matemàtica de materials aleatoris, càlcul de propietats efectives i criteris de fallada transversal en materials compòsits.El primer pas en la metodologia proposada és la definició de la determinació del tamany mínim d'un Element de Volum Representatiu Estadístic (SRVE) . Aquesta determinació es du a terme analitzant el volum de fibra, les propietats elàstiques efectives, la condició de Hill, els estadístics de les components de tensió i defromació, la funció de densitat de probabilitat i les funcions estadístiques de distància entre fibres de models d'elements de la microestructura, de diferent tamany. Un cop s'ha determinat aquest tamany mínim, es comparen un model periòdic i un model aleatori, per constatar la magnitud de les diferències que s'hi observen.Es defineix, també, una metodologia per a l'anàlisi estadístic de la distribució de la fibra en el compòsit, a partir d'imatges digitals de la secció transversal. Aquest anàlisi s'aplica a quatre materials diferents.Finalment, es proposa un mètode computacional de dues escales per a simular la fallada transversal de làmines unidireccionals, que permet obtenir funcions de densitat de probabilitat per a les variables mecàniques. Es descriuen algunes aplicacions i possibilitats d'aquest mètode i es comparen els resultats obtinguts de la simulació amb valors experimentals. / This thesis proposes a methodology for the probabilistic simulation of the transverse failure of Carbon Fibre Reinforced Polymers (CFRP) by analyzing the random distribution of the fibres within the composite. First chapters are devoted to the State-of-the-art review on the modelization of random materials, the computation of effective properties and the transverse failure of fibre reinforced polymers.The first step in the proposed methodology is the definition of a Statistical Representative Volume Element (SRVE). This SRVE has to satisfy criteria based on the analysis of the volume fraction, the effective properties, the Hill Condition, the statistics of the stress and strain components, the probability density function of the stress and strain components and the inter-fibre distance statistical distributions. Once this SRVE has been achieved, a comparison between a periodic model and a random model is performed to quantitatively analyze the differences between the results they provide.Also a methodology for the statistical analysis of the distribution of the fibre within the composite from digital images of the transverse section. This analysis is performed for four different materials.Finally, a two-scale computational method for the transverse failure of unidirectional laminae is proposed. This method is able to provide probability density functions of the mechanical variables in the composite. Some applications and possibilities of the method are given and the simulation results are compared with experimental tests.

Made available in DSpace on 2016-08-17T14:52:40Z (GMT). No. of bitstreams: 1 Dissertacao-JoaoEduardoRibeiroBaptista.pdf: 2670437 bytes, checksum: 709f4ff36e9da086fee6d4ce44374bb1 (MD5) Previous issue date: 2016-03-15 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Driven by the high indices of solar irradiation in Brazil, the increasing reduction on the price of the photovoltaic solar panels and the high tariffs charged by the utility companies, the photovoltaic distributed generation (PVDG) shall considerably increase its participation percentage in the Brazilian energy matrix in the next years. Due to this tendency, it is important to know the technical impacts of the connection of PVDG to electric grid. It is known that the insertion of DG affects the short circuit levels. One of the most important power quality disturbances in sensitive loads are the short duration voltage variations (SDVV) caused mainly by short circuits (faults) in the electric network. Thus, the insertion of PVDG has the potential to affect quality indices associated with SDVV. However, the power output of the PVDG depends on the stochastic environmental conditions, i.e., the solar irradiance and the environmental temperature. Due to this, a precise assessment of the impact of PVDG on the indices associated with SDVV must be carried out considering uncertainties related to these environmental conditions. This work assessed the impact of PVDG in the SDVV indices of the secondary distribution system proposed by the CIGRÈ using a probabilistic approach. For this purpose, it was developed a model based on the following techniques: network representation in phase coordinates, admittance summation method, failure rate model based on loading condition, state enumeration method and data clustering. Uncertainties in the fault scenario (for example, fault location, type and resistance) and in the output power variation of the PVDG due to random variations of the solar irradiance and the environmental temperature were considered. The fault scenario uncertainties were modeled according to their known probability distributions, while the one related to the input parameters of the PVDG were modeled using data clustering techniques. The state enumeration method based on fault position was chosen to perform the probabilistic prediction of the SDVV indices after a careful comparison between this method and the Monte Carlo simulation method considering both precision and computational effort. The admittance summation method was used to obtain the pre-fault and the post-fault states of the network. It was proposed an improvement of this method in order to reduce the CPU time of the short-circuit states evaluation. It was also proposed a model to obtain the failure rate of a feeder section according to the loading condition of its conductors. This model intended to investigate the variation on SDVV indices due to changing in the reliability data of the feeders caused by the variation on their loading which is caused by the insertion of PVDG in the system. Tests carried on the CIGRÈ low voltage system showed that the insertion of PVDG has little direct effect in the SDVV indices, but it can significantly reduce the indices by the indirect effect of the failure rate reduction caused by the decrease in the distribution network loading. / Impulsionada pelos altos índices de irradiação solar no Brasil, pela crescente redução do preço dos painéis fotovoltaicos e pelas altas tarifas praticadas pelas concessionárias, a geração distribuída fotovoltaica (GDFV) deve aumentar consideravelmente seu percentual de participação na matriz energética brasileira dos próximos anos. Devido a esta tendência, é importante que se conheçam os impactos técnicos da conexão da GDFV à rede elétrica. Sabe-se que a inserção de GD afeta os níveis de curto-circuito. Um dos distúrbios de qualidade de energia mais impactantes em cargas sensíveis são as variações de tensão de curta-duração (VTCD), cuja principal causa são os curtos-circuitos (faltas) na rede elétrica. Desta forma, a inserção de GDFV tem potencial para afetar índices de qualidade associados com as VTCD. No entanto, a potência de saída da GDFV depende de fatores ambientais estocásticos, i.e., a irradiância solar e a temperatura ambiente. Devido a isto, uma determinação precisa do impacto da GDFV nos índices associados com VTCD deve ser realizada considerando as incertezas relacionadas a tais fatores ambientais. Este trabalho avaliou o impacto da GDFV nos índices de VTCD do sistema de distribuição secundário proposto pelo CIGRÈ a partir de um enfoque probabilístico. Para tanto, desenvolveu-se um modelo baseado nas técnicas: representação da rede em coordenadas de fase, método de soma de admitâncias, modelo de taxa de falha baseado na condição de carregamento, método de enumeração de estados e agrupamentos de dados. Foram consideras as incertezas nos cenários de falta (por exemplo, local, tipo e resistência de falta) e na potência de saída da GDFV devido às variações estocásticas na irradiância solar e na temperatura ambiente. As incertezas do cenário de faltas foram modeladas de acordo com suas distribuições de probabilidade conhecidas, enquanto as relacionadas aos parâmetros de entrada da GDFV foram modeladas utilizando-se técnicas de agrupamentos de dados. O método de enumeração de estados baseado nas posições de falta foi escolhido para efetuar a predição probabilística dos índices de VTCD, após criteriosa comparação deste com o método de simulação Monte Carlo em termos de precisão e esforço computacional. O método de soma de admitâncias foi utilizado para obtenção dos estados pré-falta e pós-falta da rede. Foi proposto um aprimoramento desse método, de forma a reduzir o tempo de execução da avaliação dos estados de curto-circuito. Também foi proposto um modelo de obtenção da taxa de falha de uma seção de alimentador de acordo com a condição de carregamento dos seus condutores. Este modelo buscou investigar a variação nos índices de VTCD resultante da alteração dos dados de confiabilidade dos alimentadores provocada pela variação no carregamento dos mesmos, causada, por sua vez, pela inserção de GDFV no sistema. Os resultados dos testes no sistema de baixa tensão do CIGRÈ mostraram que a inserção de GDFV pouco afeta os índices de VTCD de forma direta, mas pode reduzir os índices significativamente de forma indireta devido à redução das taxas de falha anuais dos alimentadores causada pela diminuição no carregamento da rede de distribuição.

Many researchers have pointed out that the accumulation of strain energy in the Penninsular Indian Shield region may lead to earthquakes of significant magnitude(Srinivasan and Sreenivas, 1977; Valdiya, 1998; Purnachandra Rao, 1999; Seeber et al., 1999; Ramalingeswara Rao, 2000; Gangrade and Arora, 2000). However very few studies have been carried out to quantify the seismic hazard of the entire Pennisular Indian region. In the present study the seismic hazard evaluation of South Indian region (8.0° N - 20° N; 72° E - 88° E) was done using the deterministic and probabilistic seismic hazard approaches. Effects of two of the important geotechnical aspects of seismic hazard, site response and liquefaction, have also been evaluated and the results are presented in this work. The peak ground acceleration (PGA) at ground surface level was evaluated by considering the local site effects. The liquefaction potential index (LPI) and factor of safety against liquefaction wee evaluated based on performance based liquefaction potential evaluation method. The first step in the seismic hazard analysis is to compile the earthquake catalogue. Since a comprehensive catalogue was not available for the region, it was complied by collecting data from different national (Guaribidanur Array, Indian Meterorological Department (IMD), National Geophysical Research Institute (NGRI) Hyderabad and Indira Gandhi Centre for Atomic Research (IGCAR) Kalpakkam etc.) and international agencies (Incorporated Research Institutions for Seismology (IRIS), International Seismological Centre (ISC), United States Geological Survey (USGS) etc.). The collected data was in different magnitude scales and hence they were converted to a single magnitude scale. The magnitude scale which is chosen in this study is the moment magnitude scale, since it the most widely used and the most advanced scientific magnitude scale. The declustering of earthquake catalogue was due to remove the related events and the completeness of the catalogue was analysed using the method suggested by Stepp (1972). Based on the complete part of the catalogue the seismicity parameters were evaluated for the study area. Another important step in the seismic hazard analysis is the identification of vulnerable seismic sources. The different types of seismic sources considered are (i) linear sources (ii) point sources (ii) areal sources. The linear seismic sources were identified based on the seismotectonic atlas published by geological survey of India (SEISAT, 2000). The required pages of SEISAT (2000) were scanned and georeferenced. The declustered earthquake data was superimposed on this and the sources which were associated with earthquake magnitude of 4 and above were selected for further analysis. The point sources were selected using a method similar to the one adopted by Costa et.al. (1993) and Panza et al. (1999) and the areal sources were identified based on the method proposed by Frankel et al. (1995). In order to map the attenuation properties of the region more precisely, three attenuation relations, viz. Toto et al. (1997), Atkinson and Boore (2006) and Raghu Kanth and Iyengar (2007) were used in this study. The two types of uncertainties encountered in seismic hazard analysis are aleatory and epistemic. The uncertainty of the data is the cause of aleatory variability and it accounts for the randomness associated with the results given by a particular model. The incomplete knowledge in the predictive models causes the epistemic uncertainty (modeling uncertainty). The aleatory variability of the attenuation relations are taken into account in the probabilistic seismic hazard analysis by considering the standard deviation of the model error. The epistemic uncertainty is considered by multiple models for the evaluation of seismic hazard and combining them using a logic tree. Two different methodologies were used in the evaluation of seismic hazard, based on deterministic and probabilistic analysis. For the evaluation of peak horizontal acceleration (PHA) and spectral acceleration (Sa) values, a new set of programs were developed in MATLAB and the entire analysis was done using these programs. In the deterministic seismic hazard analysis (DSHA) two types of seismic sources, viz. linear and point sources, were considered and three attenuation relations were used. The study area was divided into small grids of size 0.1° x 0.1° (about 12000 grid points) and the PHA and Sa values were evaluated for the mean and 84th percentile values at the centre of each of the grid points. A logic tree approach, using two types of sources and three attenuation relations, was adopted for the evaluation of PHA and Sa values. Logic tree permits the use of alternative models in the hazard evaluation and appropriate weightages can be assigned to each model. By evaluating the 84th percentile values, the uncertainty in spectral acceleration values can also be considered (Krinitzky, 2002). The spatial variations of PHA and Sa values for entire South India are presented in this work. The DSHA method will not consider the uncertainties involved in the earthquake recurrence process, hypocentral distance and the attenuation properties. Hence the seismic hazard analysis was done based on the probabilistic seismic hazard analysis (PSHA), and the evaluation of PHA and Sa values were done by considering the uncertainties involved in the earthquake occurrence process. The uncertainties in earthquake recurrence rate, hypocentral location and attenuation characteristic were considered in this study. For evaluating the seismicity parameters and the maximum expected earthquake magnitude (mmax) the study area was divided into different source zones. The division of study area was done based on the spatial variation of the seismicity parameters ‘a’ and ‘b’ and the mmax values were evaluated for each of these zones and these values were used in the analysis. Logic tree approach was adopted in the analysis and this permits the use of multiple models. Twelve different models (2 sources x 2 zones x 3 attenuation) were used in the analysis and based on the weightage for each of them; the final PHA and Sa values at bed rock level were evaluated. These values were evaluated for a grid size of 0.1° x 0.1° and the spatial variation of these values for return periods of 475 and 2500 years (10% and 2% probability of exceedance in 50 years) are presented in this work. Both the deterministic and probabilistic analyses highlighted that the seismic hazard is high at Koyna region. The PHA values obtained for Koyna, Bangalore and Ongole regions are higher than the values given by BIS-1893(2002). The values obtained for south western part of the study area, especially for parts of kerala are showing the PHA values less than what is provided in BIS-1893(2002). The 84th percentile values given DSHA can be taken as the upper bound PHA and Sa values for South India. The main geotechnical aspects of earthquake hazard are site response and seismic soil liquefaction. When the seismic waves travel from the bed rock through the overlying soil to the ground surface the PHA and Sa values will get changed. This amplification or de-amplification of the seismic waves depends on the type of the overlying soil. The assessment of site class can be done based on different site classification schemes. In the present work, the surface level peak ground acceleration (PGA) values were evaluated based on four different site classes suggested by NEHRP (BSSC, 2003) and the PGA values were developed for all the four site classes based on non-linear site amplification technique. Based on the geotechnical site investigation data, the site class can be determined and then the appropriate PGA and Sa values can be taken from the respective PGA maps. Response spectra were developed for the entire study area and the results obtained for three major cities are discussed here. Different methods are suggested by various codes to Smooth the response spectra. The smoothed design response spectra were developed for these cities based on the smoothing techniques given by NEHRP (BSSC, 2003), IS code (BIS-1893,2002) and Eurocode-8 (2003). A Comparison of the results obtained from these studies is also presented in this work. If the site class at any location in the study area is known, then the peak ground acceleration (PGA) values can be obtained from the respective map. This provides a simplified methodology for evaluating the PGA values for a vast area like South India. Since the surface level PGA values were evaluated for different site classes, the effects of surface topography and basin effects were not taken into account. The analysis of response spectra clearly indicates the variation of peak spectral acceleration values for different site classes and the variation of period of oscillation corresponding to maximum Sa values. The comparison of the smoothed design response spectra obtained using different codal provisions suggest the use of NEHRP(BSSC, 2003) provisions. The conventional liquefaction analysis method takes into account only one earthquake magnitude and ground acceleration values. In order to overcome this shortfall, a performance based probabilistic approach (Kramer and Mayfield, 2007) was adopted for the liquefaction potential evaluation in the present work. Based on this method, the factor of safety against liquefaction and the SPT values required to prevent liquefaction for return periods of 475 and 2500 years were evaluated for Bangalore city. This analysis was done based on the SPT data obtained from 450 boreholes across Bangalore. A new method to evaluate the liquefaction return period based on CPT values is proposed in this work. To validate the new method, an analysis was done for Bangalore by converting the SPT values to CPT values and then the results obtained were compared with the results obtained using SPT values. The factor of safety against liquefaction at different depths were integrated using liquefaction potential index (LPI) method for Bangalore. This was done by calculating the factor of safety values at different depths based on a performance based method and then the LPI values were evaluated. The entire liquefaction potential analysis and the evaluation of LPI values were done using a set of newly developed programs in MATLAB. Based on the above approaches it is possible to evaluate the SPT and CPT values required to prevent liquefaction for any given return period. An analysis was done to evaluate the SPT and CPT values required to prevent liquefaction for entire South India for return periods of 475 and 2500 years. The spatial variations of these values are presented in this work. The liquefaction potential analysis of Bangalore clearly indicates that majority of the area is safe against liquefaction. The liquefaction potential map developed for South India, based on both SPT and CPT values, will help hazard mitigation authorities to identify the liquefaction vulnerable area. This in turn will help in reducing the liquefaction hazard.

En chimiotaxie, le modèle parabolique-parabolique classique de Keller-Segel en dimension d décrit l’évolution en temps de la densité d'une population de cellules et de la concentration d'un attracteur chimique. Cette thèse porte sur l’étude des équations de Keller-Segel parabolique-parabolique par des méthodes probabilistes. Dans ce but, nous construisons une équation différentielle stochastique non linéaire au sens de McKean-Vlasov dont le coefficient dont le coefficient de dérive dépend, de manière singulière, de tout le passé des lois marginales en temps du processus. Ces lois marginales couplées avec une transformation judicieuse permettent d’interpréter les équations de Keller-Segel de manière probabiliste. En ce qui concerne l'approximation particulaire il faut surmonter une difficulté intéressante et, nous semble-t-il, originale et difficile chaque particule interagit avec le passé de toutes les autres par l’intermédiaire d'un noyau espace-temps fortement singulier. En dimension 1, quelles que soient les valeurs des paramètres de modèle, nous prouvons que les équations de Keller-Segel sont bien posées dans tout l'espace et qu'il en est de même pour l’équation différentielle stochastique de McKean-Vlasov correspondante. Ensuite, nous prouvons caractère bien posé du système associé des particules en interaction non markovien et singulière. Nous établissons aussi la propagation du chaos vers une unique limite champ moyen dont les lois marginales en temps résolvent le système Keller-Segel parabolique-parabolique. En dimension 2, des paramètres de modèle trop grands peuvent conduire à une explosion en temps fini de la solution aux équations du Keller-Segel. De fait, nous montrons le caractère bien posé du processus non-linéaire au sens de McKean-Vlasov en imposant des contraintes sur les paramètres et données initiales. Pour obtenir ce résultat, nous combinons des techniques d'analyse d’équations aux dérivées partielles et d'analyse stochastique. Finalement, nous proposons une méthode numérique totalement probabiliste pour approcher les solutions du système Keller-Segel bi-dimensionnel et nous présentons les principaux résultats de nos expérimentations numériques. / The standard d-dimensional parabolic--parabolic Keller--Segel model for chemotaxis describes the time evolution of the density of a cell population and of the concentration of a chemical attractant. This thesis is devoted to the study of the parabolic--parabolic Keller-Segel equations using probabilistic methods. To this aim, we give rise to a non linear stochastic differential equation of McKean-Vlasov type whose drift involves all the past of one dimensional time marginal distributions of the process in a singular way. These marginal distributions coupled with a suitable transformation of them are our probabilistic interpretation of a solution to the Keller Segel model. In terms of approximations by particle systems, an interesting and, to the best of our knowledge, new and challenging difficulty arises: each particle interacts with all the past of the other ones by means of a highly singular space-time kernel. In the one-dimensional case, we prove that the parabolic-parabolic Keller-Segel system in the whole Euclidean space and the corresponding McKean-Vlasov stochastic differential equation are well-posed in well chosen space of solutions for any values of the parameters of the model. Then, we prove the well-posedness of the corresponding singularly interacting and non-Markovian stochastic particle system. Furthermore, we establish its propagation of chaos towards a unique mean-field limit whose time marginal distributions solve the one-dimensional parabolic-parabolic Keller-Segel model. In the two-dimensional case there exists a possibility of a blow-up in finite time for the Keller-Segel system if some parameters of the model are large. Indeed, we prove the well-posedness of the mean field limit under some constraints on the parameters and initial datum. Under these constraints, we prove the well-posedness of the Keller-Segel model in the plane. To obtain this result, we combine PDE analysis and stochastic analysis techniques. Finally, we propose a fully probabilistic numerical method for approximating the two-dimensional Keller-Segel model and survey our main numerical results.

Submitted by Maria Aparecida (cidazen@gmail.com) on 2017-04-17T13:14:17Z No. of bitstreams: 1 Elson Moreira.pdf: 7883984 bytes, checksum: cf59b3b0b24a249a7fd9e2390b7f16de (MD5) / Made available in DSpace on 2017-04-17T13:14:17Z (GMT). No. of bitstreams: 1 Elson Moreira.pdf: 7883984 bytes, checksum: cf59b3b0b24a249a7fd9e2390b7f16de (MD5) Previous issue date: 2017-02-10 / CNPQ / A problem of electric power quality that always affects the consumers of the distribution network are the harmonic distortions. Harmonic distortions arise from the presence of socalled harmonic sources, which are nonlinear equipment, i.e., equipment in which the voltage waveform differs from the current. Such equipment injects harmonic currents in the network generating distortions in the voltage waveform. Nowadays, the number of these equipment in the electrical network has increased considerably. However, the increasing use of such equipment over the network makes systems more vulnerable and prone to quality problems in the supply of electricity to consumers. In addition, it is important to note that in the current scenario, the generation of electricity from renewable sources, connected in the secondary distribution network, is increasing rapidly. This is mainly due to shortage and high costs of fossil fuels. In this context, the Photovoltaic Distributed Generation (PVDG), that uses the sun as a primary source for electric energy generation, is the main technology of renewable generation installed in distribution network. However, the PVDG is a potential source of harmonics, because the interface of the PVDG with the CA network is carried out by a CC/CA inverter, that is a highly nonlinear equipment. Thus, the electrical power quality problems associated with harmonic distortion in distribution networks tend to increase and be very frequent. One of the main indicators of harmonic distortion is the total harmonic distortion of voltage ( ) used by distribution utilities to limit the levels of harmonic distortion present in the electrical network. In the literature there are several deterministic techniques to estimate . These techniques have the disadvantage of not considering the uncertainties present in the electric network, such as: change in the network configuration, load variation, intermittence of the power injected by renewable distributed generation. Therefore, in order to provide a more accurate assessment of the harmonic distortions, this dissertation has as main objective to develop a probabilistic methodology to estimate the level of in secondary distribution networks considering the uncertainties present in the network and PVDG connected along the network. The methodology proposed in this dissertation is based on the combination of the following techniques: three-phase harmonic power flow in phase coordinate via method sum of admittance, point estimate method and series expansion of Gram-Charlier. The validation of the methodology was performed using the Monte Carlo Simulation. The methodology was tested in European secondary distribution network with 906 nodes of 416 V. The results were obtained by performing two case studies: without the presence of PVDG and with the PVDG connection. For the case studies, the following statistics for nodal were estimated: mean value, standard deviation and the 95% percentile. The results showed that the probabilistic estimation of is more complete, since it shows the variation of due to the uncertainties associated with harmonic sources and electric network. In addition, they show that the connection of PV-DG in the electric network significantly affects the levels of of the electric network. / Um problema de qualidade de energia elétrica que afeta os consumidores da rede de distribuição secundária são as distorções harmônicas. As distorções harmônicas são provenientes da presença das chamadas fontes de harmônicas que são equipamentos de características não-lineares, ou seja, equipamentos em que a forma de onda da tensão difere da de corrente. Tais equipamentos injetam correntes harmônicas na rede produzindo, portanto distorções na forma de onda da tensão. Nos dias atuais, a quantidade desses equipamentos na rede elétrica tem aumentado consideravelmente. Porém, o uso crescente desse tipo de equipamento ao longo da rede torna os sistemas mais vulneráveis e propensos a apresentarem problemas de qualidade no fornecimento de energia elétrica aos consumidores. Além disso, é importante destacar que no cenário atual, a geração de energia elétrica a partir de fontes renováveis, conectada na rede de distribuição secundária, está aumentando rapidamente. Isso se deve principalmente devido a escassez e altos custos dos combustíveis fosseis. Neste contexto, a Geração Distribuída Fotovoltaica (GDFV), que utiliza o sol como fonte primária para geração de energia elétrica, é a principal tecnologia de geração renovável instalada na rede de distribuição no Brasil. Contudo, a GDFV é uma potencial fonte de harmônica, pois a interface da GDFV com a rede CA é realizada por um inversor CC/CA, que é um equipamento altamente não-linear. Desde modo, os problemas de qualidade de energia elétrica associados à distorção harmônica nas redes de distribuição tendem a aumentar e a serem bem frequentes nos consumidores da rede de distribuição secundárias. Um dos principais indicadores de distorção harmônica é a distorção harmônica total de tensão ( do inglês “Total Harmonic Distortion of Voltage”) utilizada pelas concessionárias de energia elétrica para quantificar os níveis de distorção harmônica presentes na rede elétrica. Na literatura técnica existem várias técnicas determinísticas para estimar a . Essas técnicas possuem a desvantagem de não considerar as incertezas presentes na rede elétrica, tais como: mudança na configuração da rede, variação de carga e intermitência da potência injetada pela geração distribuída renovável. Portanto, a fim de fornecer uma avaliação mais precisa das distorções harmônicas, este trabalho tem como principal objetivo desenvolver uma metodologia probabilística para estimar o nível de em redes de distribuição secundária considerando as incertezas presentes na rede e na GDFV conectada ao longo da rede. A metodologia proposta nesta dissertação se baseia na combinação das seguintes técnicas: fluxo de potência harmônico trifásico em coordenadas de fase via método de soma de admitância, método de estimação por pontos e expansão em série de Gram-Charlier. Além disso, a validação da metodologia foi realizada utilizando a Simulação Monte Carlo. A metodologia desenvolvida foi testada na rede de distribuição secundária europeia com 906 nós de 416 V. Os resultados foram obtidos realizando dois casos de estudos: sem a presença de GDFV e com a conexão de GDFV. Para ambos os casos de estudo as seguintes estatísticas do nodal foram estimadas: valor médio, desvio padrão e o percentil de 95%. Os resultados demonstraram que a estimação probabilística da é mais completa, pois mostra a variação da devido às incertezas associadas com as fontes de harmônicas e as da rede elétrica. Os resultados também mostram que a conexão da GDFV afeta significativamente os níveis de da rede elétrica

<p> Efficiency is an essential metric for assessing turbine performance. Modern turbines rely heavily on numerical computational fluid dynamic (CFD) tools for design improvement. With more compact turbines leading to lower aspect ratio airfoils, the influence of secondary flows is significant on performance. Secondary flows and detached flows, in general, remain a challenge for commercial CFD solvers; hence, there is a need for high fidelity experimental data to tune these solvers used by turbine designers. Efficiency measurements in engine-representative test rigs are challenging for multiple reasons; an inherent problem to any experiment is to remove the effects specific to the turbine rig. This problem is compounded by the narrow uncertainty band required, ideally less than 0.5% uncertainty, to detect the incremental improvements achieved by turbine designers.  Efficiency measurements carried out in engine-representative turbine rigs have traditionally relied upon strong assumptions, such as neglecting heat transfer effects. Furthermore, prior to this research there was no framework to compute uncertainty propagation that combines both inputs from experiments and computational tools. </p> <p>This dissertation presents a comprehensive methodology to obtain high-fidelity adiabatic efficiency data in engine-representative turbine facilities. This dissertation presents probabilistic sampling techniques to allow for uncertainty propagation. The effect of rig-specific effects such as heat transfer and gas properties, on efficiency is demonstrated. Sources of uncertainty are identified, and a framework is presented which divides the sources into bias and stochastic. The framework allows the combination of experimental and numerical uncertainty. The accuracy of temperature and aerodynamic pressure probes, used for efficiency determination, is quantified. Corrections for those effects are presented that rely on hybrid numerical and experimental methods. Uncertainty is propagated through these methods using numerical sampling. </p> <p>Finally, two test cases are presented, a stator vane in an annular cascade and a two-stage turbine in a rotating rig. The performance is analyzed using the methods and corrections developed. The uncertainty on the measured efficiency is similar to literature but the uncertainty framework allows an uncertainty estimate on the adiabatic efficiency. </p>