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One of the consequences of competitive electricity markets and international commitments to green energy is the fast development and increase in the amount of distributed generation (DG) in distribution grids. These DGs are resulting in a change in the nature of distribution systems from being "passive", containing only loads, to "active", including loads and DGs. This will affect the dynamic behavior of both transmission and distribution systems. There are many technical aspects and challenges of DGs that have to be properly understood and addressed. One of them is the need for adequate static and dynamic models for DG units, particularly under unbalanced conditions, to perform proper studies of distribution systems with DGs (e.g., microgrids). The primary objective of this thesis is the development and implementation of dynamic and static models of various DG technologies for stability analysis. These models allow studying systems with DGs both in the long- and short-term; thus, differential and algebraic equations of various DGs are formulated and discussed in order to integrate these models into existing power system analysis software tools. The presented and discussed models are generally based on dynamic models of different DGs for stability studies considering the dynamics of the primary governor, generators, and their interfaces and controls. A new comprehensive investigation is also presented of the effects of system unbalance on the stability of distribution grids with DG units based on synchronous generator (SG) and doubly-fed induction generator (DFIG) at different loading levels. Detailed steady-state and dynamic analyses of the system are performed. Based on voltage and angle stability studies, it is demonstrated that load unbalance can significantly affect the distribution system dynamic performance. Novel, simple, and effective control strategies based on an Unbalanced Voltage Stabilizer (UVS) are also proposed to improve the system control and the stability of unbalanced distribution systems with SG- and DFIG-based DGs.

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Cette thèse porte sur la dynamique de modèles de leucémie myéloïde chronique (LMC). Les modèles qui nous intéressent décrivent les populations de cellules leucémiques dans la moelle osseuse ou le sang, en compétition avec des populations de cellules saines ou avec le système immunitaire. Dans un premier chapitre, nous proposons une version mathématiquement analysable d'un modèle à équations différentielles ordinaires qui décrit l'interaction du système immunitaire avec les cellules leucémiques. Nous caractérisons l'existence d'équilibres et leur stabilité puis nous fournissons une analyse de bifurcation complète en co-dimension 1. Dans un deuxième chapitre, nous confrontons ce modèle à des données cliniques. Dans un troisième chapitre, nous proposons et analysons une version simplifiée d'un modèle d'équations aux dérivées partielles qui décrit la prolifération et la différenciation des cellules souches leucémiques dans la moelle osseuse et l'effet d'un traitement par ITK sur ces cellules. Nous nous intéressons au comportement à long terme des solutions, et à sa dépendance vis à vis du traitement. Dans un quatrième et dernier chapitre, nous nous intéressons à la stabilité des équations différentielles scalaires et autonomes à deux retards, qui apparaissent naturellement dans la modélisation de nombreux phénomènes biologiques ou physiques, comme la LMC / This thesis deals with the dynamics of models of chronic myeloid leukemia (CML). Models of interest describe leukemic cell populations in the bone marrow or in the blood, in competition with healthy cell populations or with the immune system. In a first chapter, we propose a mathematically tractable version of an ordinary differential equation model that describes the interaction of the immune system with leukemic cells. We characterize the existence of steady states and their stability and then we provide a complete bifurcation analysis in co-dimension 1. In a second chapter, we confront this model with clinical data. In a third chapter we propose and analyze a simplified version of a model of partial differential equations that describes the proliferation and differentiation of leukemic stem cells in the bone marrow and the effect of an TKI treatment on these cells. We are interested in the long-term behavior of the solutions, and its dependence on treatment. In a fourth and final chapter, we are interested in the stability of scalar and autonomous differential equations with two delays, which appear naturally in the modeling of many biological or physical phenomena, such as CML

Résumé: Le comportement des turbomachines (pompes, compresseurs) fonctionnant à des conditions hors conception, et particulièrement aux débits partiels, est sujet à des phénomènes d'instabilité qui pourraient affecter leur performance et peuvent être dramatiques pour les machines ou leur environnement. Cette étude se concentre sur la décrochage tournant dans un diffuseur lisse radial. L'objectif est proposer un modèle théorique pour prédire rapidement les caractéristiques de décrochage tournant. Une étude expérimentale est effectuée en premier pour obtenir les caractéristiques de décrochage tournant dans un transparent diffuseur lisse d’une roué radiale. L'effet de décrochage tournant sur la performance du diffuseur est discuté basé sur les mesures de pression statique. Le résultat montre que décrochage tournant amélioré la récupération de la diffuseur pression, et les raisons sont proposes. Basé sur la configuration expérimentale, une analyse de stabilité linéaire qui est construit par l'équation de continuité, l'équation de la quantité de mouvement et les équations de vorticité, est propose. Les caractéristiques expérimentales de décrochage tournant: le nombre et la vitesse de propagation des cellules de décrochage tournant, sont calculés théoriquement. Le taux de croissance dans le modèle linéaire, est proposé pour déterminer la critique condition de décrochage tournant, et le dominant mode de décrochage tournant lorsque différents modes existent par intermittence. La théorique vitesse et pression fluctuations sont tracées pour décrire le débit du diffuseur à l'état de décrochage. Les capacités et les limites de la linéaire stabilité analyse sont conclues par la comparaison entre les résultats théoriques et expérimentaux. Ensuit, une non linéaire stabilité analyse est étendue pour considérer les non linéaires combinaisons qui sont négligées dans le modèle linéaire. L'objectif est donner des corrections (par termes non linéaires) aux résultats linéaires, les conclusions et les discussions sont faites à la fin. / Abstract:The behavior of work-absorbing turbomachines (pumps, compressors) operating at off design conditions, and especially at partial flow rates, is subject to instability phenomena that could affect their performance and can be dramatic for the machines or their environment. This study is focused on the rotating stall in the vaneless diffuser, the objective is to propose a theoretical model to fast predict the characteristics of such an instability. An experimental study is performed first to obtain those characteristics of rotating stall in a transparent vaneless diffuser of a radial impeller. The effect of rotating stall on the diffuser performance is discussed based on the static pressure measurements. The result shows rotating stall improved the diffuser pressure recovery, and the reasons are proposed. Based on the experimental setup, a linear stability analysis which is constructed by the continuity equation, momentum equation and vorticity equations, is proposed. The experimental characteristics of rotating stall: number and propagation velocity of stall cells, are theoretical calculated. The growth rate in the linear model, is proposed to determine the critical stall condition, and the dominant stall mode when different stall modes exist intermittently. The theoretical velocity and pressure fluctuations are also plotted to show the diffuser flow at stall condition. The abilities and limits of the linear stability analysis are concluded through the comparisons between theoretical and experimental results. Based on the linear model, a nonlinear stability analysis is extended to consider the nonlinear combinations which are neglected in the linear model, the aim is to give corrections (from nonlinear terms) to the linear results of rotating stall, the conclusions and discussions are made at the end.

This thesis details potential design improvements by exploiting a new general grid model utilizing multiple wind and solar energy plants. A single renewable energy plant which relies on wind speed or solar insolation is unreliable because of the stochastic nature of weather patterns. To allow such a plant to match the requirements of a variable load some form of energy storage must be incorporated. To ensure a low loss of load expectation (LOLE) the size of this energy storage must be large to cope with the strong fluctuations in energy production. It is theorized that by using multiple renewable energy plants in separate areas of a region, the different weather conditions might approach a probabilistically independent relationship. The probability of energy generated from combined plants will then approach a Gaussian distribution by the central limit theorem. While maintaining the same LOLE as a single renewable plant this geographic separation model theoretically stabilizes the energy production and reduces the system variables: energy storage size, energy storage efficiency, and cumulative plant capacity. New generic weather models that incorporate levels of independence are created for wind speeds and solar insolations at different locations to support the geographic separation model. As the number of geographically separated plants increases and the weather approaches independence the system variables are reduced.