The process of quantifying the robustness of a given nonlinear system is not necessarily trivial. If the dynamics of the system in question are not sufficiently involved, then a tight estimate of a bound on system performance may be obtained. As the dynamics of the system concerned become more and more involved, it is often found that using the results existing in the literature provides a very conservative bound on system performance. Therefore, the motivation for this work is to develop a general method to obtain a less conservative estimate of a bound on system performance, compared to the results already available in literature. The scope of this work is limited to two dimensions at present. Note that working in a two dimensional space does not necessarily make the objective easily achievable. This is because quantifying the robustness of a general nonlinear system perturbed by disturbances can very easily become intractable, even on a space with dimension as low as two. The primary contribution of this work is a computational algorithm, the points generated by which are conjectured to lie on the boundary of the smallest robust forward invariant set for a given nonlinear system. A well known path-planning algorithm, available in existing literature, is leveraged to make the algorithm developed computationally efficient. If the system dynamics are not accurately known, then the above computed approximation of an invariant set may cease to be invariant over the given finite time interval for which the computed set is expected to be invariant. Therefore, the secondary contribution of this work is an algorithm monitoring a computed approximation of an invariant set. It is shown that for a certain type of systems, this secondary monitoring algorithm can be used to detect that a computed approximation of an invariant set is about to cease to be invariant, even if the primary algorithm computed the set based on an unsophisticated dynamical model of a system under consideration. The work related to computing approximations of invariant sets is tested mainly with the curve tracking problem in two dimensions. The algorithm monitoring whether a computed approximation of an invariant set is about to cease to be invariant is inspired by work related to detecting Lithium-ion (Li-ion) battery terminal voltage collapse detection.

With the rise of global sustainability energy initiatives,the implementation of renewable energy sources infuture electrical grids is increasing. Many of the renewableenergy sources are however intermittent, meaning they providevarying levels of power. As grids meet the demand of largerloads of intermittent renewable energy sources, small signalinstability arises as result of the power oscillations. Small signalinstability occurs when a system cannot return to steady stateafter being exposed to small disturbances. One method to damppower oscillations in an unstable system is by using a PowerSystem Stabilizer (PSS). The goal of this project is to tunea PSS or PSSs required to successfully damp out the poweroscillations in a system which is small signal unstable without anyPSSs connected. The PSSs are tuned through a trial and errorapproach, and the system is a Kundur two-area four-machineMATLAB Simulink model. Overall, the trial and error methodis successful in tuning PSSs, which damp out the system’s poweroscillations. Other methods of tuning are discussed and comparedin terms of efficiency to damp out power oscillations. / Med en ökning av globala hållbarhetsinitiativförväntas implementeringen av förnybara energikälloröka i elnäten. Förnyelsebara energikällor som sol och vindär intermittenta, vilket innebär att de ger varierande effektnivåer.När nätet belastas med intermittenta energikällor uppstårlågfrekvensfel, vilket skapar oscillationer i spänning. För attdämpa svängningarna i ett instabilt system kan en Power SystemStabilizer (PSS) användas. Målet med projektet är att regulera enPSS som dämpar svängningarna i ett system som har lågfrekvensfel.En metod baserat på trial-and-error används för att regleraPSS:en. Detta görs i en Kundur Two-Area four machine Systemsimuleringsmodell i mjukvaruprogrammen Simulink och Matlab.Trial-and-error-metoden lyckas reglera svängningarna med hjälpav två PSS som dämpar effektsvängningarna i systemet. Irapporten diskuteras även alternativa metoder för att dämpasvängningarna i ett instabilt system. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

Este trabalho apresenta uma estratégia de controle coordenado para potência reativa e tensão terminal de um grupo moto gerador (GMG) para uso em um sistema de geração distribuída (GD). A partir da construção de uma superfície fuzzy, baseada no comportamento do erro e da derivada do erro de uma malha de controle, foi realizada a sintonia de controladores fuzzy PD+I para potências ativa e reativa e tensão terminal. O controlador coordenado fuzzy PD+I ajusta automaticamente a tensão nos terminais da máquina e a potência reativa fornecidas à rede de distribuição. A estratégia coordenada é dada através de um parâmetro que regula a malha de potência reativa a partir do erro de tensão terminal, priorizando o ajuste da tensão e ponderando a malha de controle de potência reativa. Para avaliar o desempenho do sistema de controle, a GD é conectada a uma rede de distribuição e submetida a eventos como entrada e saída de cargas locais. O conjunto de cargas locais é composto por um motor de indução, uma carga RLC e um retificador trifásico não controlado. Sete cenários foram simulados para avaliar a estratégia de controle em diferentes regimes de operação do GMG. Resultados para tensão terminal, fator de potência e fluxo de potências entre o sistema, as cargas e a rede, ilustram a eficiência da estratégia de controle apresentada. A estratégia de controle coordenado para potência reativa e tensão terminal se mostrou capaz de melhorar os índices de fator de potência controlando o fluxo de potência do barramento em que a GD estava conectada, sem prejudicar a tensão terminal do gerador, mantendo a GD em limites seguros de operação. / This work presents a coordinated control strategy to terminal voltage and reactive power for a diesel generation set used as a distributed gerenation system (DG). From desired control actions, a fuzzy surface was designed for fuzzy PD+I controllers. Fuzzy PD+I controllers automatically adjust the terminal voltage and the reactive power delivered to the grid. The coordinated control strategy weighs the control action for the reactive power through a variable parameter, prioritizing the terminal voltage adjustment. To illustrate the system control performance, the DG is connected to a grid dynamic model and the system is subjected to connection and disconnection of loads at the local bus. The local loads set was composed of an induction machine, a RLC load and an uncontrolled three-phase rectifier. Seven scenarios were simulated to evaluate the control strategy in different DG regime of operation. Results for terminal voltage, power factor and reactive power among the DG, the local loads and the grid, illustrates the control strategy efficiency improved the power factor by regulating the reactive power injected at the bus, maintaining the DG terminal voltage in safe operation limits.

Este trabalho apresenta uma estratégia de controle coordenado para potência reativa e tensão terminal de um grupo moto gerador (GMG) para uso em um sistema de geração distribuída (GD). A partir da construção de uma superfície fuzzy, baseada no comportamento do erro e da derivada do erro de uma malha de controle, foi realizada a sintonia de controladores fuzzy PD+I para potências ativa e reativa e tensão terminal. O controlador coordenado fuzzy PD+I ajusta automaticamente a tensão nos terminais da máquina e a potência reativa fornecidas à rede de distribuição. A estratégia coordenada é dada através de um parâmetro que regula a malha de potência reativa a partir do erro de tensão terminal, priorizando o ajuste da tensão e ponderando a malha de controle de potência reativa. Para avaliar o desempenho do sistema de controle, a GD é conectada a uma rede de distribuição e submetida a eventos como entrada e saída de cargas locais. O conjunto de cargas locais é composto por um motor de indução, uma carga RLC e um retificador trifásico não controlado. Sete cenários foram simulados para avaliar a estratégia de controle em diferentes regimes de operação do GMG. Resultados para tensão terminal, fator de potência e fluxo de potências entre o sistema, as cargas e a rede, ilustram a eficiência da estratégia de controle apresentada. A estratégia de controle coordenado para potência reativa e tensão terminal se mostrou capaz de melhorar os índices de fator de potência controlando o fluxo de potência do barramento em que a GD estava conectada, sem prejudicar a tensão terminal do gerador, mantendo a GD em limites seguros de operação. / This work presents a coordinated control strategy to terminal voltage and reactive power for a diesel generation set used as a distributed gerenation system (DG). From desired control actions, a fuzzy surface was designed for fuzzy PD+I controllers. Fuzzy PD+I controllers automatically adjust the terminal voltage and the reactive power delivered to the grid. The coordinated control strategy weighs the control action for the reactive power through a variable parameter, prioritizing the terminal voltage adjustment. To illustrate the system control performance, the DG is connected to a grid dynamic model and the system is subjected to connection and disconnection of loads at the local bus. The local loads set was composed of an induction machine, a RLC load and an uncontrolled three-phase rectifier. Seven scenarios were simulated to evaluate the control strategy in different DG regime of operation. Results for terminal voltage, power factor and reactive power among the DG, the local loads and the grid, illustrates the control strategy efficiency improved the power factor by regulating the reactive power injected at the bus, maintaining the DG terminal voltage in safe operation limits.