Esta dissertação apresenta um modelo aproximado de rede desenvolvido para análise de sistemas de distribuição em regime permanente. O modelo é detalhado do ponto de vista matemático e teórico considerando a representação dos elementos em derivação da rede (cargas e geradores) e dos limites operacionais empregando aproximações lineares. A modelagem linear permite determinar de forma simples os valores das tensões e correntes do sistema, podendo ser empregada em problemas de otimização relacionados ao planejamento e expansão de sistemas de distribuição. A representação da carga considera a influência da variação da tensão, fator determinante nas redes de distribuição. Também é considerada a inclusão de geração distribuída (GD) sendo implementada para diferentes modos de operação, permitindo ainda a minimização das perdas para a barra onde a GD está alocada. Para validar a abordagem proposta, os resultados do modelo apresentado foram comparados em termos de tensões, correntes e perdas com resultados obtidos com o modelo convencional de fluxo de carga, solucionado pelo algoritmo de varredura. Os testes foram realizados em dois sistemas de distribuição conhecidos, um de 70 barras e um de 135 barras. Para o sistema de 70 barras foi avaliado o uso de diferentes modos de operação da GD. Finalmente, para o sistema de 135 barras foram comparados os resultados do modelo proposto com o fluxo de carga convencional caracterizando a GD como uma barra de tensão controlada (PV) para diversos valores de injeção ativa na barra selecionada. As conclusões confirmam a validade e as vantagens que o modelo desenvolvido neste trabalho proporciona. / This work presents an approximate model developed to the analysis of electrical distribution systems at steady state. Both mathematical and theoretical details are given considering the representation of the shunt elements (loads and generators) and the operating limits of the network, using linear approximations. The linear modeling adopted resulted in a simple way to determine the values of the voltages and currents of the system; further the model can be applied to optimization problems related to optimal operation and expansion planning of distribution systems. The load representation considers the influence of voltage variations, which play an important role in the distribution networks. This work also considers the inclusion of distributed generation (DG), which is assessed under several modes of operation, including one mode which allows to minimize the losses at the node where the DG is located. To validate the proposed approach, the results for two example networks, given in terms of voltages, currents and losses, were compared with corresponding results obtained with conventional load flow model, solved by the backward-forward sweep method. The examples networks used to test and validate the model are known distribution systems, one having 70 and the other 135 nodes. Regarding the system with 70 nodes, the inclusion of DG was studied for several operational modes. Finally, the system of 135 nodes were used to compare the results of the proposed model with the results of the conventional load flow; in this case, the GD was characterized as a controlled-voltage bar (PV) for various levels of active power injection into the bar where the GD is located. The conclusions show the validity and advantages of the proposed model.

Esta dissertação apresenta um modelo aproximado de rede desenvolvido para análise de sistemas de distribuição em regime permanente. O modelo é detalhado do ponto de vista matemático e teórico considerando a representação dos elementos em derivação da rede (cargas e geradores) e dos limites operacionais empregando aproximações lineares. A modelagem linear permite determinar de forma simples os valores das tensões e correntes do sistema, podendo ser empregada em problemas de otimização relacionados ao planejamento e expansão de sistemas de distribuição. A representação da carga considera a influência da variação da tensão, fator determinante nas redes de distribuição. Também é considerada a inclusão de geração distribuída (GD) sendo implementada para diferentes modos de operação, permitindo ainda a minimização das perdas para a barra onde a GD está alocada. Para validar a abordagem proposta, os resultados do modelo apresentado foram comparados em termos de tensões, correntes e perdas com resultados obtidos com o modelo convencional de fluxo de carga, solucionado pelo algoritmo de varredura. Os testes foram realizados em dois sistemas de distribuição conhecidos, um de 70 barras e um de 135 barras. Para o sistema de 70 barras foi avaliado o uso de diferentes modos de operação da GD. Finalmente, para o sistema de 135 barras foram comparados os resultados do modelo proposto com o fluxo de carga convencional caracterizando a GD como uma barra de tensão controlada (PV) para diversos valores de injeção ativa na barra selecionada. As conclusões confirmam a validade e as vantagens que o modelo desenvolvido neste trabalho proporciona. / This work presents an approximate model developed to the analysis of electrical distribution systems at steady state. Both mathematical and theoretical details are given considering the representation of the shunt elements (loads and generators) and the operating limits of the network, using linear approximations. The linear modeling adopted resulted in a simple way to determine the values of the voltages and currents of the system; further the model can be applied to optimization problems related to optimal operation and expansion planning of distribution systems. The load representation considers the influence of voltage variations, which play an important role in the distribution networks. This work also considers the inclusion of distributed generation (DG), which is assessed under several modes of operation, including one mode which allows to minimize the losses at the node where the DG is located. To validate the proposed approach, the results for two example networks, given in terms of voltages, currents and losses, were compared with corresponding results obtained with conventional load flow model, solved by the backward-forward sweep method. The examples networks used to test and validate the model are known distribution systems, one having 70 and the other 135 nodes. Regarding the system with 70 nodes, the inclusion of DG was studied for several operational modes. Finally, the system of 135 nodes were used to compare the results of the proposed model with the results of the conventional load flow; in this case, the GD was characterized as a controlled-voltage bar (PV) for various levels of active power injection into the bar where the GD is located. The conclusions show the validity and advantages of the proposed model.

Esta dissertação apresenta um modelo aproximado de rede desenvolvido para análise de sistemas de distribuição em regime permanente. O modelo é detalhado do ponto de vista matemático e teórico considerando a representação dos elementos em derivação da rede (cargas e geradores) e dos limites operacionais empregando aproximações lineares. A modelagem linear permite determinar de forma simples os valores das tensões e correntes do sistema, podendo ser empregada em problemas de otimização relacionados ao planejamento e expansão de sistemas de distribuição. A representação da carga considera a influência da variação da tensão, fator determinante nas redes de distribuição. Também é considerada a inclusão de geração distribuída (GD) sendo implementada para diferentes modos de operação, permitindo ainda a minimização das perdas para a barra onde a GD está alocada. Para validar a abordagem proposta, os resultados do modelo apresentado foram comparados em termos de tensões, correntes e perdas com resultados obtidos com o modelo convencional de fluxo de carga, solucionado pelo algoritmo de varredura. Os testes foram realizados em dois sistemas de distribuição conhecidos, um de 70 barras e um de 135 barras. Para o sistema de 70 barras foi avaliado o uso de diferentes modos de operação da GD. Finalmente, para o sistema de 135 barras foram comparados os resultados do modelo proposto com o fluxo de carga convencional caracterizando a GD como uma barra de tensão controlada (PV) para diversos valores de injeção ativa na barra selecionada. As conclusões confirmam a validade e as vantagens que o modelo desenvolvido neste trabalho proporciona. / This work presents an approximate model developed to the analysis of electrical distribution systems at steady state. Both mathematical and theoretical details are given considering the representation of the shunt elements (loads and generators) and the operating limits of the network, using linear approximations. The linear modeling adopted resulted in a simple way to determine the values of the voltages and currents of the system; further the model can be applied to optimization problems related to optimal operation and expansion planning of distribution systems. The load representation considers the influence of voltage variations, which play an important role in the distribution networks. This work also considers the inclusion of distributed generation (DG), which is assessed under several modes of operation, including one mode which allows to minimize the losses at the node where the DG is located. To validate the proposed approach, the results for two example networks, given in terms of voltages, currents and losses, were compared with corresponding results obtained with conventional load flow model, solved by the backward-forward sweep method. The examples networks used to test and validate the model are known distribution systems, one having 70 and the other 135 nodes. Regarding the system with 70 nodes, the inclusion of DG was studied for several operational modes. Finally, the system of 135 nodes were used to compare the results of the proposed model with the results of the conventional load flow; in this case, the GD was characterized as a controlled-voltage bar (PV) for various levels of active power injection into the bar where the GD is located. The conclusions show the validity and advantages of the proposed model.

Parciální diferenciální rovnice hrají důležitou v inženýrských aplikacích. Často je možné tyto rovnice řešit pouze přibližně, tj. numericky. Z toho důvodu vzniklo množství diskretizačních metod pro řešení těchto rovnic. Uvedená nespojitá Galerkinova metoda se zdá jako velmi obecná metoda pro řešení těchto rovnic, především pak pro hyperbolické systémy. Naším cílem je řešit úlohy aeroakustiky, přičemž šíření akustických vln je popsáno pomocí linearizovaných Eulerových rovnic. A jelikož se jedná o hyperbolický systém, byla vybrána právě nespojitá Galerkinova metoda. Mezi nejdůležitější aspekty této metody patří schopnost pracovat s geometricky složitými oblastmi, možnost dosáhnout metody vysokého řádu a dále lokální charakter toho schématu umožnuje efektivní paralelizaci výpočtu. Nejprve uvedeme nespojitou Galerkinovu metodu v obecném pojetí pro jedno- a dvoudimenzionalní úlohy. Algoritmus následně otestujeme pro řešení rovnice advekce, která byla zvolena jako modelový případ hyperbolické rovnice. Metoda nakonec bude testována na řadě verifikačních úloh, které byly formulovány pro testování metod pro výpočetní aeroakustiku, včetně oveření okrajových podmínek, které, stejně jako v případě teorie proudění tekutin, jsou nedílnou součástí výpočetní aeroakustiky.

The first part of the thesis focuses on developing a numerical methodology to simulate the acoustic properties of a hybrid liner consisting of a perforated plate, a porous layer and a Helmholtz cavity. Liners are always a standard way to reduce noise in today’s aeroengines, e.g. the fan noise can be reduced effectively through the installation of acoustic liners as wall treatments in the ducts. In order to optimize a liner in the design phase, an accurate and efficient prediction tool is of interests. Hence, a unified Linearized Navier-Stokes equations(LNSE) approach has been implemented in the thesis, combining the LNSE in frequency domain with the fluid equivalent model. The LNSE is applied in the vicinity of the perforated plate to simulate sound propagation including viscous damping effect, and the fluid equivalent model is used to model the sound propagation in the porous material including absorption. The second part of the thesis focuses on the prediction of thermoacoustic instabilities. Thermoacoustic instabilities arise when positive coupling occurs between the flame and the acoustics in the feedback loop, i.e. the flame acts as an amplifier of the disturbances (acoustic or fluid) at a natural frequency of the combustion system. Once the thermoacoustic instabilities occur, it will lead to extremely high noise levels within a relatively narrow frequency range, resulting in a huge damage to the structure of the combustors. Hence, a solution must be found, which breaks the link between the combustion process and the structural acoustics. The numerical prediction of thermoacoustic instabilities in the thesis is performed by two different numerical methodologies. One solves the Helmholtz equation in combination of the flame n − tau model with the low Mach number assumptions, and the other solves the Linearized Navier-Stokes equations in frequency domain with mean flow. The result show that the mean flow has a significant effect on the thermoacoustic instabilities, which is non-negligible when the Mach number reaches to 0.15. / <p>QC 20151221</p> / TANGO

<p> Working within the framework of the linearized Boltzmann equation for the conduction electrons the existing theoretical treatments of ultrasonic attenuation in metals are extended to include realistic descriptions of the electronic structure and electron-lattice interaction. A variational solution of the Boltzmann equation which allows the inclusion of phonon drag effects is derived. An anisotropic scattering time solution is also presented. Both of these solutions are applied to calculation of the attenuation coefficient in pure metals and dilute alloys. </p> <p> The theory of the effects of electron-electron collisions on the ultrasonic attenuation in metals is also examined. </p> / Thesis / Doctor of Philosophy (PhD)

When multiple autonomous vehicles drive closelytogether behind each other, it is called a platoon. Platooningprovides several benefits, such as decreased congestion andreduced fuel consumption. In order for more vehicles to takeadvantage of these benefits, the platoon should be able to openup a space for other vehicles to merge into. Thus, our goal withthe project was to develop a system that can split a platoon.To achieve this, we are using model predictive control (MPC) tocontrol the system because it can handle constraints and controlsystems with multiple variables. To test the implemented system,we created a simulation environment in Python. We createdseveral plots to analyze and show the results of the simulations.To make the simulation more realistic, we introduced air drag tothe system. To counteract this effect, we added linearized air dragto the MPC. We showed that the constructed system could splitbetween any two adjacent vehicles in a platoon up to 50 meters.Another significant result was that the MPC could compensatefor the air drag without adding linearized air drag to the MPC. / När flera autonoma fordon kör nära varandra kallas det för en platoon. Det finns flera fördelar med platooning som minskad trafik samt minskad bränsleförbrukning. För att fler fordon ska kunna dra nytta av dessa fördelar bör nya fordon kunna sammansluta till en platoon och på grund av detta bör fordonen i platoonen kunna öppna ett utrymme för det nya fordonet. Därför är vårt mål med detta projekt att utveckla ett system som kan styra och dela på en platoon. För att åstadkomma detta använder vi model prediktiv reglering (MPC) eftersom den är bra på att hanterar bivilkor och styra system med många variabler. Vi implementerade systemet i Python, där en simuleringsmiljö skapades. För att se och analysera resultaten av simuleringen skapades grafer som visade hur fordonen hade färdats under simuleringen. Vi lade till luftmotstånd i simuleringen för att göra den mer realistisk. För att motverka luftmotståndet lade vi även till ett linjäriserat luftmotstånd till i MPC:n. I slutet av projektet kunde systemet dela platoonen mellan två fordon med ett avstånd upp till 50 meter. Vi observerade att MPC:n kunde kompensera motståndet utan implementationen av det linjäriserade luftmotståndet. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

Due to increasing penetration of solar power generation, distribution grids are facing a number of challenges. Frequent reverse active power flows can result in rapid fluctuations in voltage magnitudes. However, with the revised IEEE 1547 standard, smart inverters can actively control their reactive power injection to minimize voltage deviations and power losses in the grid. Reactive power control and globally optimal inverter coordination in real-time is computationally and communication-wise demanding, whereas the local Volt-VAR or Watt-VAR control rules are subpar for enhanced grid services. This thesis uses machine learning tools and poses reactive power control as a kernel-based regression task to learn policies and evaluate the reactive power injections in real-time. This novel approach performs inverter coordination through non-linear control policies centrally designed by the operator on a slower timescale using anticipated scenarios for load and generation. In real-time, the inverters feed locally and/or globally collected grid data to the customized control rules. The developed models are highly adjustable to the available computation and communication resources. The developed control scheme is tested on the IEEE 123-bus system and is seen to efficiently minimize losses and regulate voltage within the permissible limits. / Master of Science

<p>The continuous trend in gas turbine design towards lighter, more powerful and more reliable engines on one side and use of alternative fuels on the other side renders flutter problems as one of the paramount challenges in engine design. Flutter denotes a self-excited and self-sustained aeroelastic instability phenomenon that can lead to material fatigue and eventually damage of structure in a short period of time unless properly damped. The design for flutter safety involves the prediction of unsteady aerodynamics as well as structural dynamics that is mostly based on in-house developed numerical tools. While high confidence has been gained on the structural side unanticipated flutter occurrences during engine design, testing and operation evidence a need for enhanced validation of aerodynamic models despite the degree of sophistication attained. The continuous development of these models can only be based on the deepened understanding of underlying physical mechanisms from test data.</p><p>As a matter of fact most flutter test cases treat the turbomachine flow in two-dimensional manner indicating that the problem is solved as plane representation at a certain radius rather than representing the complex annular geometry of a real engine. Such considerations do consequently not capture effects that are due to variations in the third dimension, i.e. in radial direction. In this light the present thesis has been formulated to study three-dimensional effects during flutter in the annular environment of a low-pressure turbine blade row and to describe the importance on prediction of flutter stability. The work has been conceived as compound experimental and computational work employing a new annular sector cascade test facility. The aeroelastic response phenomenon is studied in the influence coefficient domain having one blade oscillating in various three-dimensional rigid-body modes and measuring the unsteady response on several blades and at various radial positions. On the computational side a state-of-the-art industrial numerical prediction tool has been used that allowed for two-dimensional and three-dimensional linearized unsteady Euler analyses.</p><p>The results suggest that considerable three-dimensional effects are present, which are harming prediction accuracy for flutter stability when employing a two-dimensional plane model. These effects are mainly apparent as radial gradient in unsteady response magnitude from tip to hub indicating that the sections closer to the hub experience higher aeroelastic response than their equivalent plane representatives. Other effects are due to turbomachinery-typical three-dimensional flow features such as hub endwall and tip leakage vortices, which considerably affect aeroelastic prediction accuracy. Both effects are of the same order of magnitude as effects of design parameters such as reduced frequency, flow velocity level and incidence. Although the overall behavior is captured fairly well when using two-dimensional simulations notable improvement has been demonstrated when modeling fully three-dimensional and including tip clearance.</p>

Esta tese trata o escoamento ao redor de um cilindro logo após a sua primeira instabilidade, dentro do seu regime bidimensional periódico. A abordagem é principalmente teórica, passa por experimentos e culmina em uma importante parte numérica que complementa a teoria com evidências e ilustrações. As principais contribuições são a análise sobre a composição modal da solução dentro do regime periódico e o método desenvolvido para identificar autovetores de uma linearização da equação de Navier-Stokes presentes em uma dada solução. As bases compostas pelos autovetores identificados servem para a projeção da equação de Navier-Stokes e dão a essência dos modelos reduzidos deste estudo. A aplicação numérica apresentada para Re = 60 traz duas iterações do processo, com duas bases de autovetores de dimensões 12 e 24. Os modelos reduzidos são numericamente estáveis e a sua integração apresenta custo várias ordens mais baixo que o da simulação numérica completa. As séries temporais das coordenadas e as bases de autovetores possibilitam a recomposição do escoamento e a sua comparação com a simulação numérica de referência. A análise de aderência foi baseada nas médias temporais, nos valores de Strouhal e na estrutura dos harmônicos. Ambos modelos reduzidos têm correspondência próxima com o comportamento assintótico do escoamento e a tendência convergente das iterações é clara. As simetrias espaciais e temporais dos harmônicos são facilmente identificadas na estrutura dos modelos, de forma que as bases construídas podem ser entendidas como conjuntos de estruturas coerentes do fenômeno. / This thesis concerns the flow past a cylinder just after its first bifurcation, within its two-dimensional periodic regime. The approach is mainly theoretical, goes through experiments and is concluded by an important numerical part which complements the theory with evidences and illustrations. The main contributions are the analysis concerning the modal composition of the solution within the periodic regime and a method to identify eigenvectors of some linearizaton of the Navier-Stokes equation participating on a given solution. The bases spanned by the identified eigenvectors are employed in the projection of the Navier-Stokes equation and are central to the reduced models of this study. The numerical results for Re = 60 present two iterations of the process, with two bases of dimensions 12 e 24. The reduced models are numerically stable and their integration is many orders less costly than that of the full simulation. The time series of the modal coordinates and the eigenvectors bases allow the recomposition of the flow and its comparison with the full simulation results. The convergence analysis was based on the time averages, the Strouhal number values and the harmonic structure. Both reduced models have close correspondence with the asymptotic behavior of the flow and the convergent trend of the iterations is clear. The space and time symmetries of the harmonics have a simple representation within the structure of the models, therefore the identified bases can be understood as sets of coherent structures of the phenomenon.