Methodology for Dynamic Stability and Robustness Analysis of Commercial-Power-Module-Based DC-Distributed Systems

El propósito de esta tesis es presentar una metodología para realizar análisis de la dinámica en pequeña señal y el comportamiento de sistemas de alimentación distribuidos de corriente continua (CC), formados por módulos comerciales. Para ello se hace uso de un método sencillo que indica los márgenes de estabilidad menos conservadores posibles mediante un solo número. Este índice es calculado en cada una de las interfaces que componen el sistema y puede usarse para obtener un índice global que indica la estabilidad del sistema global. De esta manera se posibilita la comparación de sistemas de alimentación distribuidos en términos de robustez. La interconexión de convertidores CC-CC entre ellos y con los filtros EMI necesarios puede originar interacciones no deseadas que dan lugar a la degradación del comportamiento de los convertidores, haciendo el sistema más propenso a inestabilidades. Esta diferencia en el comportamiento se debe a interacciones entre las impedancias de los diversos elementos del sistema. En la mayoría de los casos, los sistemas de alimentación distribuida están formados por módulos comerciales cuya estructura interna es desconocida. Por ello los análisis presentados en esta tesis se basan en medidas de la respuesta en frecuencia del convertidor que pueden realizarse desde los terminales de entrada y salida del mismo. Utilizando las medidas de las impedancias de entrada y salida de los elementos del sistema, se puede construir una función de sensibilidad que proporciona los márgenes de estabilidad de las diferentes interfaces. En esta tesis se utiliza el concepto del valor máximo de la función de sensibilidad (MPC por sus siglas en inglés) para indicar los márgenes de estabilidad como un único número. Una vez que la estabilidad de todas las interfaces del sistema se han evaluado individualmente, los índices obtenidos pueden combinarse para obtener un único número con el que comparar la estabilidad de diferentes sistemas. Igualmente se han analizado las posibles interacciones en la entrada y la salida de los convertidores CC-CC, obteniéndose expresiones analíticas con las que describir en detalle los acoplamientos generados en el sistema. Los estudios analíticos realizados se han validado experimentalmente a lo largo de la tesis. El análisis presentado en esta tesis se culmina con la obtención de un índice que condensa los márgenes de estabilidad menos conservativos. También se demuestra que la robustez del sistema está asegurada si las impedancias utilizadas en la función de sensibilidad se obtienen justamente en la entrada o la salida del subsistema que está siendo analizado. Por otra parte, la tesis presenta un conjunto de parámetros internos asimilados a impedancias, junto con sus expresiones analíticas, que permiten una explicación detallada de las interacciones en el sistema. Dichas expresiones analíticas pueden obtenerse bien mediante las funciones de transferencia analíticas si se conoce la estructura interna, o utilizando medidas en frecuencia o identificación de las mismas a través de la respuesta temporal del convertidor. De acuerdo a las metodologías presentadas en esta tesis se puede predecir la estabilidad y el comportamiento de sistemas compuestos básicamente por convertidores CC-CC y filtros, cuya estructura interna es desconocida. La predicción se basa en un índice que condensa la información de los márgenes de estabilidad y que permite la obtención de un indicador de la estabilidad global de todo el sistema, permitiendo la comparación de la estabilidad de diferentes arquitecturas de sistemas de alimentación distribuidos. ABSTRACT The purpose of this thesis is to present dynamic small-signal stability and performance analysis methodology for dc-distributed systems consisting of commercial power modules. Furthermore, the objective is to introduce simple method to state the least conservative margins for robust stability as a single number. In addition, an index characterizing the overall system stability is obtained, based on which different dc-distributed systems can be compared in terms of robustness. The interconnected systems are prone to impedance-based interactions which might lead to transient-performance degradation or even instability. These systems typically are constructed using commercial converters with unknown internal structure. Therefore, the analysis presented throughout this thesis is based on frequency responses measurable from the input and output terminals. The stability margins are stated utilizing a concept of maximum peak criteria, derived from the behavior of impedance-based sensitivity function that provides a single number to state robust stability. Using this concept, the stability information at every system interface is combined to a meaningful number to state the average robustness of the system. In addition, theoretical formulas are extracted to assess source and load side interactions in order to describe detailed couplings within the system. The presented theoretical analysis methodologies are experimentally validated throughout the thesis. In this thesis, according to the presented analysis, the least conservative stability margins are provided as a single number guaranteeing robustness. It is also shown that within the interconnected system the robust stability is ensured only if the impedance-based minor-loop gain is determined at the very input or output of each subsystem. Moreover, a complete set of impedance-type internal parameters as well as the formulas according to which the interaction sensitivity can be fully explained and analyzed, is provided. The given formulation can be utilized equally either based on measured frequency responses, time-domain identified internal parameters or extracted analytic transfer functions. Based on the analysis methodologies presented in this thesis, the stability and performance of interconnected systems consisting of converters with unknown internal structure, can be predicted. Moreover, the provided concept to assess the least conservative stability margins enables to obtain an index to state the overall robust stability of distributed power architecture and thus to compare different systems in terms of stability.

Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation

The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

Design Parameter Analysis of Point Absorber WEC via an Evolutionary-Algorithm-Based Dimensioning Tool

Wave energy conversion has an essential difference from other renewable energies since the dependence between the devices design and the energy resource is stronger. Dimensioning is therefore considered a key stage when a design project of Wave Energy Converters (WEC) is undertaken. Location, WEC concept, Power Take-Off (PTO) type, control strategy and hydrodynamic resonance considerations are some of the critical aspects to take into account to achieve a good performance. The paper proposes an automatic dimensioning methodology to be accomplished at the initial design project stages and the following elements are described to carry out the study: an optimization design algorithm, its objective functions and restrictions, a PTO model, as well as a procedure to evaluate the WEC energy production. After that, a parametric analysis is included considering different combinations of the key parameters previously introduced. A variety of study cases are analysed from the point of view of energy production for different design-parameters and all of them are compared with a reference case. Finally, a discussion is presented based on the results obtained, and some recommendations to face the WEC design stage are given.