Due to the ever-increasing penetration of distributed generation units connected to the power distribution system, electric power systems, worldwide, are undergoing a paradigm shift with regards to system monitoring, operation and control. We envision that with the emergence of `active' distribution systems consisting of `prosumers' and localized energy markets, decentralized control methods in power systems are gaining a growing attention among power researchers. Traditionally, two main types of control schemes have been implemented in power systems: (a) wide-area monitoring based centralized control, and (b) local measurement based primary (machine) level control. By contrast, decentralized control schemes based on local monitoring and control of strategically-determined subsystems (or `areas') of a large-scale power system are not used. The latter control schemes offer several advantages over the former, which include more flexibility, simplicity, economy and scalability for large-scale systems. In this dissertation, we summarize our research work on hierarchical and decentralized control techniques for the enhancement in a unified manner of voltage and rotor angle stability in large-scale power systems subject to large (e.g., short circuits) and small (e.g., small load changes) disturbances. We study system robustness by calculating local stability margins. We derive decentralized control laws that guaranty global asymptotic stability by applying Lyapunov's second method for interconnected systems. Furthermore, we argue that the current centralized control structure must only play a supervisory control role at a higher (tertiary) hierarchical level by processing the decisions taken by the regional control entities regarding the stability/instability of the system. This ensures system-wide situational awareness while minimizing the communication bandwidth requirements. We also develop a multi-agent based framework for this hierarchical control scheme. Finally, we compare different communication protocols using simulation models and propose an efficient communication network design for decentralized control schemes. This work, in principle, motivates the development of fast stability analysis which, in the future, may also account for the non-linear coupling that exist between machine rotor angles and bus voltages in power system models. As a future work, we propose the use of statistical techniques like random-effects regression and saddlepoint approximation method to reliably estimate the type-I and type-II probability errors in the proposed hierarchical, decentralized control decision process. / Ph. D. / In the present research work, we have proposed a decentralized, hierarchical control scheme for large-scale, interconnected power systems. Using Lyapunov’s second method for interconnected systems, we have derived <i>decentralized</i> control laws for control devices which ensure global asymptotic stability of weakly interconnected power systems. The decentralized control schemes have several advantages over centralized ones. For instance, the former approaches lead to a reduction of dimensionality in terms of both modeling and controlling the state variables of a system. One of the major contributions of this research work is the reduction of the dimensionality of the energy function and of the regression models used to determine the control laws, which results from the non requirement of exchanging information between control areas or of sending all the measurements to a central controller. Hence, the proposed scheme also yields smaller communication requirements than those of completely centralized wide-area controllers, while offering a better situational awareness. Similar decentralized control schemes are commonly used in robotic, transportation and surveillance systems.

Mais que fenômenos exóticos, oscilações de corrente e potencial são bastante comuns em vários sistemas eletroquímicos. Ainda que conhecidos há muito tempo, processos oscilatórios na interface sólido/líquido eletrificada são relativamente pouco investigados sob o ponto de vista teórico. São apresentados nessa Tese dois trabalhos, o primeiro relacionado às instabilidades cinéticas observadas em tais sistemas, por meio de um modelo formado por três equações diferenciais não-lineares ordinárias acopladas, que representam um protótipo mínimo do comportamento complexo observado em reações eletrocatalíticas. Especificamente, este protótipo reproduz as características gerais de osciladores eletroquímicos caracterizados por uma resistência diferencial negativa parcialmente escondida em uma curva de corrente/potencial em forma de N. O modelo foi abordado utilizando as análises convencionais e os diagramas de estabilidade, de Lyapunov e de período. A partir dos diagramas de estabilidade foi possível descrever o comportamento do sistema levando em consideração a condição homoclínica de Shilnikov. Já os diagramas de Lyapunov e período mostraram de forma detalhada o comportamento caótico e periódico do modelo, em que se pode observar a existência de estruturas auto-organizadas nos domínios de periodicidade em um fundo caótico, onde tais estruturas são chamadas de shrimps. A observação de tais estruturas que também são encontradas em outros sistemas reforçando a hipótese da universalidade estrutural para fenômenos de codimensão dois. A segunda parte dessa Tese consiste num estudo do drift observado em séries experimentais aplicando técnicas de análise multivariada a uma série temporal experimental obtida para eletro-oxidação da molécula do metanol em Pt policristalina. O resultado mostrou que podemos descrever a influência do drift no comportamento oscilatório por meio de três variáveis relacionados aos processos superficiais. / More than just an exotic phenomenon, oscillations of potential and current are often found in several electrochemical systems. Although oscillatory processes at solid/liquid electrified interfaces have been reported a long time ago, just few theoretical studies have been done so far. This Thesis comprises two parts: the first one analyzes kinetic instabilities observed in electrochemical systems by using a model consisting of three non-linear coupled ordinary differential equations that represent a prototype of the complex behavior observed in electrocatalytic systems. Specifically, this prototype captures the general characteristics of electrochemical oscillators that display a negative differential resistance partially hidden for an N-shaped current/potential curve. The model was studied using conventional analyses and stability diagrams, Lyapunov exponents and the evaluation of the period of oscillations. From the stability diagrams it was possible to describe the behavior of the system taking into consideration the homoclinic Shilnikov condition. The Lyapunov and period analyses showed in a very detailed manner the chaotic and periodic behavior of the model, where it is observed the existence of self-organized structures in the domains of periodicity on a chaotic background. Those structures are known as shrimps. The observation of such structures that are also found in other systems reinforces the idea of structural universality for codimension two phenomena. The second part of the Thesis deals with the analysis of the oscillatory drift by using multivariate analysis techniques to an experimental time series obtained for the electroxidation of methanol on polycrystalline Pt. The results showed that it is possible to describe the influence of the drift during the oscillatory behavior by means of three variables that act on the surface of the electrode.

Mais que fenômenos exóticos, oscilações de corrente e potencial são bastante comuns em vários sistemas eletroquímicos. Ainda que conhecidos há muito tempo, processos oscilatórios na interface sólido/líquido eletrificada são relativamente pouco investigados sob o ponto de vista teórico. São apresentados nessa Tese dois trabalhos, o primeiro relacionado às instabilidades cinéticas observadas em tais sistemas, por meio de um modelo formado por três equações diferenciais não-lineares ordinárias acopladas, que representam um protótipo mínimo do comportamento complexo observado em reações eletrocatalíticas. Especificamente, este protótipo reproduz as características gerais de osciladores eletroquímicos caracterizados por uma resistência diferencial negativa parcialmente escondida em uma curva de corrente/potencial em forma de N. O modelo foi abordado utilizando as análises convencionais e os diagramas de estabilidade, de Lyapunov e de período. A partir dos diagramas de estabilidade foi possível descrever o comportamento do sistema levando em consideração a condição homoclínica de Shilnikov. Já os diagramas de Lyapunov e período mostraram de forma detalhada o comportamento caótico e periódico do modelo, em que se pode observar a existência de estruturas auto-organizadas nos domínios de periodicidade em um fundo caótico, onde tais estruturas são chamadas de shrimps. A observação de tais estruturas que também são encontradas em outros sistemas reforçando a hipótese da universalidade estrutural para fenômenos de codimensão dois. A segunda parte dessa Tese consiste num estudo do drift observado em séries experimentais aplicando técnicas de análise multivariada a uma série temporal experimental obtida para eletro-oxidação da molécula do metanol em Pt policristalina. O resultado mostrou que podemos descrever a influência do drift no comportamento oscilatório por meio de três variáveis relacionados aos processos superficiais. / More than just an exotic phenomenon, oscillations of potential and current are often found in several electrochemical systems. Although oscillatory processes at solid/liquid electrified interfaces have been reported a long time ago, just few theoretical studies have been done so far. This Thesis comprises two parts: the first one analyzes kinetic instabilities observed in electrochemical systems by using a model consisting of three non-linear coupled ordinary differential equations that represent a prototype of the complex behavior observed in electrocatalytic systems. Specifically, this prototype captures the general characteristics of electrochemical oscillators that display a negative differential resistance partially hidden for an N-shaped current/potential curve. The model was studied using conventional analyses and stability diagrams, Lyapunov exponents and the evaluation of the period of oscillations. From the stability diagrams it was possible to describe the behavior of the system taking into consideration the homoclinic Shilnikov condition. The Lyapunov and period analyses showed in a very detailed manner the chaotic and periodic behavior of the model, where it is observed the existence of self-organized structures in the domains of periodicity on a chaotic background. Those structures are known as shrimps. The observation of such structures that are also found in other systems reinforces the idea of structural universality for codimension two phenomena. The second part of the Thesis deals with the analysis of the oscillatory drift by using multivariate analysis techniques to an experimental time series obtained for the electroxidation of methanol on polycrystalline Pt. The results showed that it is possible to describe the influence of the drift during the oscillatory behavior by means of three variables that act on the surface of the electrode.

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Applications of distributed-power systems are on the rise. They are already used in telecommunication power supplies, aircraft and shipboard power-distribution systems, motor drives, plasma applications, and they are being considered for numerous other applications. The successful operation of these multi-converter systems relies heavily on a stable design. Conventional analyses of power converters are based on averaged models, which ignore the fast-scale instability and analyze the stability on a reduced-order manifold. As such, validity of the averaged models varies with the switching frequency even for the same topological structure. The prevalent procedure for analyzing the stability of switching converters is based on linearized smooth averaged (small-signal) models. Yet there are systems (in active use) that yield a non-smooth averaged model. Even for systems for which smooth averaged models are realizable, small-signal analyses of the nominal solution/orbit do not provide anything about three important characteristics: region of attraction of the nominal solution, dependence of the converter dynamics on the initial conditions of the states, and the post-instability dynamics. As such, converters designed based on small-signal analyses may be conservative. In addition, linear controllers based on such analysis may not be robust and optimal. Clearly, there is a need to analyze the stability of power converters from a different perspective and design nonlinear controllers for such hybrid systems. In this Dissertation, using bifurcation analysis and Lyapunov's method, we analyze the stability and dynamics of some of the building blocks of distributed-power systems, namely standalone, integrated, and parallel converters. Using analytical and experimental results, we show some of the differences between the conventional and new approaches for stability analyses of switching converters and demonstrate the shortcomings of some of the existing results. Furthermore, using nonlinear analyses we attempt to answer three fundamental questions: when does an instability occur, what is the mechanism of the instability, and what happens after the instability? Subsequently, we develop nonlinear controllers to stabilize parallel dc-dc and parallel multi-phase converters. The proposed controllers for parallel dc-dc converters combine the concepts of multiple-sliding-surface and integral-variable-structure control. They are easy to design, robust, and have good transient and steady-state performances. Furthermore, they achieve a constant switching frequency within the boundary layer and hence can be operated in interleaving or synchronicity modes. The controllers developed for parallel multi-phase converters retain many of the above features. In addition, they do not require any communication between the modules; as such, they have high redundancy. One of these control schemes combines space-vector modulation and variable-structure control. It achieves constant switching frequency within the boundary layer and a good compromise between the transient and steady-state performances. / Ph. D.

Dans cette thèse nous adressons le problème de commande des véhicules marins sous-actionnés. La motivation clé de ce sujet de recherche vient du fait qui les systèmes sous-actionnés posent des défis aussi bien théoriques et pratiques pour l'ingénieur automaticien. En fait, ces systèmes ne peuvent pas être stabilisés par des commandes lisses invariantes dans le temps. De plus, en dépit du nombre de méthodes disponibles pour la commande des systèmes mécaniques sous-actionnés, peu ont adressé des points pratiques importantes tels que l'inclusion explicite de dynamique dans la formulation de problème de commande et le besoin de faire face aux perturbations environnementales résultants des courants des vagues, par exemple. Cette thèse attaque certains de ces problèmes, formule et résout les problèmes de commande de positionnement dynamique, de la poursuite de trajectoire et du suivie de chemin des véhicules marins sous-actionnés. La première partie de cette thèse (Chapitres 3 et 4) constituent les éléments théoriques fondamentaux pour l'analyse du modèle et la synthèse des commandes pour les véhicules marins sous-actionnés. Particulièrement, nous montrons au chapitre 3 que le modèle de véhicule marin sous-actionné ne satisfait pas la condition de nécessaire Brockett pour la stabilisation des systèmes nonlinéaires par actions continues et invariantes dans le temps. Cependant, Il sera montré qu'il est possible d'atteindre la stabilisation en utilisant une commande discontinue ou variable dans le temps. Le chapitre 4 consiste à appliquer des résultats récents sur les systèmes cascades nonlinéaires pour résoudre le problème de déterminer des lois de commande qui stabilisent à l'origine la position et l'orientation d vaisseau sous-actionnés. Deux transformations sont introduites pour représenter le système dans une forme de cascade. Par quelques propriétés du modèle, nous montrons en premier que la stabilisation globale et asymptotique du système se réduit a stabiliser une forme en chaîne de troisième ordre. Une approche discontinue par backstepping est ensuite employée pour la stabilisation du système de forme en chaîne via un retour d'état partiel. Nous montrons que la loi de commande proposée stabilise exponentiellement le modèle réduit dans un ensemble défini, assurant le stabilisation asymptotique, local et uniforme du modèle de vaisseau marin sous-actionné. Pour assurer la stabilité uniforme globale cependant, un backstepping et le temps combinés variant l'approche de contrôle est donc employée. Prochain, nous exploitons la structure de cascade pour construire une trajectoire convenable produite par les équations dynamiques d'un véritable sous-actionnés bateau. Nous montrons ensuite que la stabilisation globale peut être assurée par une par une combinaison de la commande par backstepping et une commande variable dans le temps. Ensuite nous abordons le problème de poursuite de trajectoire. Dans lequel la trajectoire de référence est générée par un navire sous-actionné virtuel. Nous montrons ensuite qu'il existe une commande qui force exponentiellement le navire à la poursuite de la trajectoire partant d'une condition initiale quelconque. Utilisant une approche des Systems cascades, nous montrons que la dynamique de l'erreur de poursuite peut être vue comme une cascade d'un système linéaire et d'un système en chaine de deuxième ordre. La deuxième partie de cette thèse (Chapitre 5, 6 et 7) est consacrée au problème de la manoeuvre du vaisseau sous-actionné le long d'un chemin désiré avec une dynamique prescrite. La conception de la loi de commande est abordée par deux approches. La première vient d'une observation qu'il est plausible en pratique de manoeuvrer le véhicule tel qu'il soit sur son chemin de référence est que sa vitesse totale soit tangente au chemin. Il sera aussi supposé que le véhicule voyage le long du chemin avec une vitesse directe constante. La seconde approche ne conditionne pas la vitesse directe pour être constante. Dans le Chapitre 5, nous exploitons l'approche abordée pour le suivi de chemin pour résoudre le problème de coordinations d'un groupe de véhicules marins. Il est objet de manoeuvrer le mouvement de chaque véhicule tel que le mouvement du groupe est prescrit par un comportement désiré. Ainsi, le mouvement indépendant est coordonné comme une formation selon le comportement désirée. Dans ce chapitre nous considérerons le problème de formation ou plusieurs véhicules sont synchronisés de manière qu'ils soient commandés comme une formation de structure virtuelle. Le chapitre 6, est dévouée au problème général de la commande par retour de sortie pour la stabilisation globale des véhicules marins sous-actionnés. Une application de tel observateur est ensuite faite au problème de la poursuite de trajectoire d'un vaisseau sous-actionné.