Esta tese trata de dar um passo na direção de revisar o problema de estabilidade transitória e a teoria do método PEBS para incluir em seus fundamentos modelos de fontes alternativas e seus limites operacionais. A conceituação do método direto com restrição é estabelecida via teoria de sistemas dinâmicos restritos e do conceito de região de estabilidade restrita. Particularmente, avalia-se a estabilidade de velocidade das principais configurações de aerogeradores equipados com gerador de indução, considerando como requisito operacional a curva de suportabilidade a afundamentos de tensão, ou curva LVRT. Um sistema dinâmico auxiliar aumentado é desenvolvido para representar a curva LVRT, que é um requisito dependente do tempo, por meio de uma restrição invariante no tempo descrita em termos de uma variável de estado auxiliar. Este sistema auxiliar tem sua região de estabilidade irrestrita igual à região de estabilidade restrita do sistema dinâmico restrito. Os modelos são apresentados na forma de equações algébricas e diferenciais. O problema de estabilidade de velocidade e o problema de violação de limites de tensão são investigados via análises da região de estabilidade do ponto de equilíbrio estável do sistema pós-falta e dos tempos críticos de abertura obtidos para várias perturbações. Os resultados mostram que: i) para distintos limites operacionais e para distintos parâmetros da máquina de indução, as regiões de estabilidade para um dado ponto de equilíbrio podem ser significativamente diferentes, ii) na maioria dos casos analisados, os limites de tensão são violados antes dos aerogeradores perderem a estabilidade de velocidade, o que mostra como é importante considerar limites operacionais nas avaliações de estabilidade via método direto para evitar que o sistema elétrico de potência fique vulnerável e iii) as funções energia desenvolvidas, tanto para avaliar o problema de estabilidade de velocidade, como para avaliar o problema de violação de limites de tensão, são em geral capazes de realizar boas estimativas dos tempos críticos de abertura. Os estudos elaborados nesta tese sobre a avaliação da estabilidade de aerogeradores via método direto, contribuem com aplicações inéditas que podem ser utilizadas nas análises de segurança em tempo real de sistemas elétricos de potência que contemplem fontes alternativas e seus limites operacionais. / This thesis gives a step forward in the direction of reviewing the problem of transient stability and the theory of PEBS method to include models of renewable power plants and their operational limits. The formulation of direct methods with constraint is accomplished by exploring the theory of constrained dynamic systems and the concept of constrained stability region. In particular, the speed stability of the main wind turbine configurations equipped with an induction generator is analyzed, considering the low voltage ride-through requirement, or LVRT curve, as a constraint to the model. An augmented auxiliary dynamical system is developed to represent the time-dependent LVRT constraint as an equivalent time invariant constraint written in terms of an auxiliary state variable. This auxiliary system has its unconstrained stability region equals to the constrained stability region of the constrained dynamic system. The models are described in the form of algebraic and differential equations. The problem of speed stability and the problem of disconnection of wind turbines due to voltage limits violation are investigated via analysis of stability region of the post-fault equilibrium point and critical clearing times obtained for several perturbations. The results show that: i) for different operational limits and for different parameters of the induction machine, the stability regions for a given operating point can be significantly different, ii) in most cases, the violation of the LVRT curve occurs before the speed instability, which reveals the importance of include operational limits in transient stability analysis and in the formulation of direct methods and iii) in most cases, the developed energy functions to evaluate the problem of speed stability and the problem of voltage limits violation, are generally capable of making good estimates of critical clearing times. The developed studies about the transient stability assessment of different models of wind turbines via direct method contribute with applications that can be used in real-time security assessments of power systems that contemplate renewable power plants and their operational limits.

The thesis project outlined in this report aims to comprehensively assess and optimize methods for long-term power production estimation of hybrid PV-wind energy systems. Through practical case studies, this approach seeks to exemplify the challenges and opportunities inherent in such systems. The research is conducted within the Wind Technical Team of Akuo Energy, an independent French renewable energy producer, leveraging their extensive expertise in technologies, industry practices, and data processing. The primary objective is to evaluate the relevance of two key parameters used in Akuo’s internal estimation methods, focusing on their impact on long-term production and revenues within the context of hybrid PV-wind energy systems. These parameters include unavailability losses, modeled on an hourly basis using Markovian transition matrices, and interannual variability of resources, statistically modeled by randomly shuffling yearly production profiles of individual wind and solar plants. Python will be employed to generate hybrid production time series, incorporating the models for unavailability losses and interannual variability. This approach facilitates the creation of multiple scenarios for sensitivity analysis, allowing for the variation of parameters to compare the productivity and profitability of different scenarios. The study sheds light on the importance of employing realistic models to account for unavailability losses, revealing that simpler models tend to overestimate revenues from hybrid power plants systematically. Moreover, the research shows the impact of interannual variability of resources on both production and revenues, emphasizing the necessity of generating multiple scenarios to anticipate best and worst-case outcomes. Ultimately, the results of this study aim to assist the company on the necessity and relevance of using such models for calculating long-term production and revenues in future hybrid PV-wind projects, as opposed to current simpler methods. / Det avhandlingsprojekt som beskrivs i denna rapport syftar till att heltäckande utvärdera och optimera metoder för långsiktig kraftproduktionsestimering av hybrid PV-vindenergisystem. Genom praktiska fallstudier söker detta tillvägagångssätt att exemplifiera de utmaningar och möjligheter som är inneboende i sådana system. Forskningen utförs inom vindtekniska teamet på Akuo Energy, en oberoende fransk producent av förnybar energi, där man dra nytta av deras omfattande expertis inom teknik, branschpraxis och datahantering. Det primära målet är att utvärdera relevansen av två viktiga parametrar som används i Akuos interna estimeringsmetoder och fokuserar på deras påverkan på långsiktig produktion och intäkter inom ramen för hybrid PV-vindenergisystem. Dessa parametrar inkluderar otillgänglighetsförluster, modellerade på timbasis med hjälp av Markovska övergångsmatriser, och årlig variabilitet av resurser, statistiskt modellerade genom att slumpmässigt ordna årliga produktionsprofiler för enskilda vind- och solanläggningar. Python kommer att användas för att generera hybridproduktionsserier och inkludera modeller för otillgänglighetsförluster och årlig variabilitet. Detta tillvägagångssätt möjliggör skapandet av flera scenarier för känslighetsanalys, vilket gör det möjligt att variera parametrar för att jämföra produktiviteten och lönsamheten för olika scenarier. Studien belyser vikten av att använda realistiska modeller för att ta hänsyn till otillgänglighetsförluster och visar att enklare modeller tenderar att systematiskt överskatta intäkter från hybridkraftverk. Dessutom visar forskningen påverkan av årlig variabilitet av resurser på både produktion och intäkter och betonar nödvändigheten av att generera flera scenarier för att förutse bästa och sämsta fall. Slutligen syftar resultaten av denna studie till att bistå företaget när det gäller nödvändigheten och relevansen av att använda sådana modeller för att beräkna långsiktig produktion och intäkter i framtida hybrid PV-vindprojekt, jämfört med nuvarande enklare metoder.