[pt] A estabilidade de tensão tornou-se nos últimos anos tema de intensa pesquisa, envolvendo principalmente a identificação da natureza do problema e a busca de estratégias mais favoráveis para a operação e planejamento dos sistemas de potência. Este trabalho apresenta um relato da evolução da análise do fenômeno sendo, posteriormente descritos os detalhes de sua abordagem através da teoria das bifurcações em sistemas dinâmicos não-lineares. São caracterizados o limite de transmissão de potência à estabilidade de tensão e a geometria das trajetórias no espaço de estados em pontos de equilíbrio em suas proximidades. O estabelecimento de equivalência entre os modelos dinâmico e estático tornou possível o emprego de métodos baseados nas equações algébricas do fluxo de carga na determinação do limite de estabilidade de tensão e na avaliação do comportamento dinâmico local. Com base no algoritmo de fluxo de carga convencional, foi desenvolvido um programa computacional que emprega o método de continuação parametrizado. Os métodos de continuação permitem a obtenção do conjunto completo das soluções reais, relacionadas por um parâmetro escalar, de um sistema de equações. Mostra-se que a aplicação desses métodos em conjunto com as técnicas de análise modal resulta em uma forma eficiente para a seleção e localização de reforços visando aumentar a capacidade global de transmissão dos sistemas de potência. / [en] In the past few years voltage stabiity has become a subject of intense research involving the identification of the nature of this problem and the seek of suitable strategies for power systems operation and planning. In this work it is presented a report on the evolution in the analysis of this phenomena and it is described the details of its approach through the dynamic nonlinear systems bifurcation theory. The power transmission limit imposed by the voltage stability conditions is addressed and the geometry of the trajectories in state space considering the equilibrium points on the vicinity of this limit is deeply studied. The establishment of the equivalence conditions between the dynamic and static power system models made it possible to employ load-flow algebraic equations based methods on both the determination of the power transmission limit and the evaluation of local dynamic behaviour. A load-flow based computer program which uses the parameterized continuation method was developed. The continuation methods are widely known for providing the determination of whole set of a system s solutions which are related by a scalar parameter. In the closure, it is shown that the application of these methods, in a complementary basis with the modal analysis techniques, results in an efficient procedure to promote the choice and location of devices to improve the power system global tranmission capacity.

This thesis contains a summary of voltage stability issues caused by appliances with constant load output. It also contains models of this appliance and outcomes of simulations done for the purpose of conformation of influence of appliances with constant output on voltage stability.

Voltage stability is a major concern when planning and operating electrical power systems.As demand for electric power increases, power systems are stressed more and more. TheFACTS family of components were introduced to utilize the existing grid to a higherdegree, while still maintaining system stability.This thesis investigates if the addition of another SVC to the Swedish national gridcould increase the power transfer from north to south. Placement of the SVC was basedon two different indices used to indicate weak areas of the grid; the Q-V sensitivity indexand the V CPI index.Simulations were performed with both the added SVC and regular switched shuntcompensation and the results were compared against each other. Studies were alsoperformed to investigate the effect of an SVC installed at the grid connection of a large(1000 MW) wind farm. Simulations were performed where the wind farm was modeledby either doubly fed induction generators (DFIG) or single cage induction generators.This simulation study was performed using PSSTME, based on a detailed model ofthe Nordic power system as it existed in 2007.The studies showed that adding a ±200 MVAr SVC to the Swedish national gridcould increase the power transfer by 150 MW, where an equally rated switched shuntcapacitor/reactor would result in a 100 MW increase. In these studies, the transfercapacity was limited by voltage collapse situations.However, installing the same ±200 MVAr SVC at the connection of a large windfarm showed an increase in power transfer by 1000 MW, while the switched shuntcompensation only resulted in a 500 MW increase. In the simulations that showed thegreatest increase in transfer capacity, the added wind farm was modeled by single-cageinduction generators. In this case the transfer capacity was limited by transient stabilityproblems.

This work presents an alternative approach to power system computations, Graph Trace Analysis (GTA), and applies GTA to the power flow problem. A novel power flow algorithm is presented, where GTA traces are used to implement a modified Gauss-Seidel algorithm coupled with a continuation method. GTA is derived from the Generic Programming Paradigm of computer science. It uses topology iterators to move through components in a model and perform calculations. Two advantages that GTA brings are the separation of system equations from component equations and the ability to distribute calculations across processors. The implementation of KVL and KCL in GTA is described. The GTA based power flow algorithm is shown to solve IEEE standard transmission models, IEEE standard distribution models, and integrated transmission and distribution models (hybrid models) constructed from modifying IEEE standard models. The GTA power flow is shown to solve a set of robustness testing circuits, and solutions are compared with other power flow algorithms. This comparison illustrates convergence characteristics of different power flow algorithms in the presence of voltage stability concerns. It is also demonstrated that the GTA power flow solves integrated transmission and distribution system models. Advantages that GTA power flow bring are the ability to solve realistic, complex circuit models that pose problems to many traditional algorithms; the ability to solve circuits that are operating far from nominal conditions; and the ability to solve transmission and distribution networks together in the same model. / PHD

Interconnection of DERs into the transmission lines is starting to take a substantial share of the total power capacity. Although the largest share of power generation attributes to coal and gas power plants, renewable energy is gradually increasing. However, in the past, the size of DERs was relatively smaller, and rooftop PV was the dominant renewable energy source. As a result, the studies for interconnection focused on those rooftop PVs on the distribution side. Since the scenario is slowly changing as more utilities increase the share of clean energy by building large-scale solar farms and wind farms, it is necessary to study the effect of those DERs in the transmission system. Among the various issues, this work focuses on the impact on a transmission system's voltage stability. When the voltage stability at a point in the system is compromised, it can affect the entire power system's overall security, quality, and reliability. Therefore, this work aims to assess the system's stress due to increased loading conditions and increased growth of DERs integration. A steady-state voltage stability index is used to generate a heat-map that identifies the areas where the system can go unstable in events like the loss of the renewable generation under a bus. The steady-state simulation is performed on the IEEE 14 bus system in Distributed Engineering Workstation (DEW) to find the system's weak links using the stability heat-map. DERs are added to the corresponding weak buses, and the improvement in the stability margin for various penetration levels are studied. The results obtained from the steady-state analysis are also verified using the dynamic simulation of the model using OpenModelica. / Master of Science / Transmission networks are going through some of the fundamental changes in how they are planned and operated as more and more renewable energy sources are connected to the grid. Unlike the traditional setup where the transmission line transfers bulk power from a large generator to the load center at a different location, the advent of renewable energy resources enables the power to be generated in distributed form. It allows electrical power to be generated closer to the demand. In the long run, the transmission system's stress reduces as a significant portion of demand is supplied locally. Thus, the distributed energy resources (DERs) in the power grid have the potential for substantial economic and environmental benefits. However, it can also bring about a range of challenges to the power system. Among the various issues, this work focuses on the effects on a transmission system's voltage stability. When the voltage stability at a point in the system is compromised, it can affect the entire power system. Therefore, this work aims to assess the stress on the system due to increased loading conditions and increased growth of DERs integration, utilizing a voltage stability index to identify the areas where the system can go unstable in events like the loss of renewable generation under a bus. The steady-state simulation is performed on the IEEE 14 bus system to find the weak links in the system where DERs can improve the system's stability. The results obtained from the steady-state analysis are verified using the dynamic simulation of the model.

Power distribution systems continue to evolve to accommodate the advancements in the field of microgrids and renewable energy resources. The future grids will be highly connected and will require increased reliability of the network. To this effect, low-voltage distribution systems with meshed or networked topology can be utilized. Currently, the use of low-voltage heavily-meshed distribution systems is restricted to urban areas with high load density that require increased reliability of power. A reason for this is the high cost of construction of such systems and complex topology which creates additional challenges. The direction of power flow in such systems is not unidirectional, which makes the power flow analysis difficult. Complicated network analysis techniques are required to determine the fault currents and protection settings in the network. Due to the aforementioned reasons, there is limited work analyzing the effectiveness of existing power flow algorithms to solve complex meshed systems. In this thesis, the robustness of two power flow algorithms is compared using an index called static stability breakdown margin parameter of circuit elements. For this study, a low-voltage heavily-meshed distribution test system is also proposed. Additionally, a study is conducted to show how reliable the meshed test system is against any fault in the system. The steady-state voltage stability of the test system is observed during the event of a fault. The stability margin parameter is then used to determine the vulnerable components in the system which need to be strengthened to increase the stability and voltage profile of the system. / Master of Science / Distribution systems carry electricity from the transmission system and deliver it to the customers. Distribution systems mainly operate using two topologies for their feeders: Radial and Meshed. The majority of customers are served using radial distribution systems, as in the radial feeders power flows in one direction (i.e. from substation to the end-user). They are simple in design and operation and are constructed at a moderate cost. However, if there is a fault along the main feeder, there will be an interruption of power to the end-use customer. On the other hand, meshed distribution systems involve multiple paths of power flow between all the points in the network. If a fault occurs along the feeder, the power flow is rerouted to the other available paths. Thus, Heavily Due to their complex topology, meshed systems are expensive to construct and deploy. The power flow analysis of these systems poses many challenges. Because of these reasons, their use is mainly restricted to urban areas with high load density which require very high reliability. The future grid is becoming increasingly complex and evolving to a meshed distribution topology has its own advantages. However, as presently the use of meshed systems is sparse, the work done on evaluating the stability of these systems is minimal. As a result of which, this thesis focuses on determining the optimal power flow solvers for these complex systems, analyzing their stability under abnormal operating conditions, and suggesting methods to reinforce the vulnerabilities in the system.

Yes / Voltage instability problems in power system is an important issue that should be taken into consideration during the planning and operation stages of modern power system networks. The system operators always need to know when and where the voltage stability problem can occur in order to apply suitable action to avoid unexpected results. In this paper, a study has been conducted to identify the weakest bus in the power system based on multi-variable control, modal analysis, and Singular Value Decomposition (SVD) techniques for both static and dynamic voltage stability analysis. A typical IEEE 3-machine, 9-bus test power system is used to validate these techniques, for which the test results are presented and discussed.

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.

Orientador: Dilson Amancio Alves / Banca: Percival Bueno de Araujo / Banca: Carlos Roberto Minussi / Banca: Geraldo Roberto Martins da Costa / Banca: Luiz Carlos Pereira da Silva / Resumo: Este trabalho apresenta dois métodos para a análise estática de contingências em Sistemas Elétricos de Potência utilizando o Método da Continuação. No primeiro método a margem de carregamento pós-contingência é obtida a partir do ponto de máximo carregamento do caso base. A magnitude de tensão de uma barra qualquer é usada como parâmetro na etapa de parametrização do fluxo de carga continuado. O ramo selecionado para avaliação da contingência é parametrizado por um fator de escalonamento que possibilita a remoção gradual do ramo e assegura a convergência nos casos em que o método diverge para a retirada total da linha de transmissão. Em geral, para a maioria das contingências analisadas são necessárias poucas iterações para a determinação do ponto de máximo carregamento pós-contingência. Mostra-se que o método pode ser usado como uma técnica alternativa para a averiguação e até mesmo para a obtenção da lista de contingências críticas fornecida pela função de análise de segurança de sistemas elétricos. No outro método, o qual obtém o ponto de máximo carregamento de pós-contingência a partir do caso base, as variáveis ângulo de fase e magnitude de tensão de uma barra k qualquer, e a perda total de potência ativa, são propostas como parâmetros para a etapa de parametrização do fluxo de carga continuado utilizado na averiguação da lista de contingências críticas fornecida pela função de análise de segurança de sistemas elétricos. Nos casos em que há divergência do fluxo de carga, o método proposto possibilita confirmar se esta ocorre devido à deficiência numérica do método em si ou a inexistência de um ponto de operação factível de pós-contingência. O uso da perda total de potência ativa como parâmetro traz como vantagem a possibilidade da determinação de pontos além do ponto de singularidade sem a necessidade...(Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This work presents two methods for static contingency analysis of electric power systems by using Continuation Methods. In the first the post-contingency loading margin is obtained from the base case maximum loading point. The voltage magnitude of any bus can be used as a parameter in the parameterization step of the proposed continuation power flow. The branch selected for contingency evaluation is parameterized by a scaling factor which allows its the gradual removal and assures the continuation power flow convergence for the cases where the method would diverge for the complete transmission line removal. In general, for most of the analyzed contingencies little iterations are necessary for the determination of the post-contingency maximum loading point. It is shown that the method can be used as an alternative technique to verify and even to obtain the list of critical contingencies supplied by the electric power systems security analysis function. In the other method, which obtains the maximum loading point from the base case, new parameters, namely the voltage magnitudes, phase angles and the total power losses, for evaluating the effects of branch outages. The approach can be used as a verification tool after a list of critical contingencies had been ranked according to their severities by the contingency selection functions. It is then possible to find whether the non-convergence of a power flow is due to a numerical problem or to an infeasible operating situation. The mains advantage of using the total real power losses as a parameter is that it is not necessary to change parameters during the solutions tracing until beyond the simple limit point, where the original Jacobian is singular. The proposed methods facilitate the development and the implementation of continuation methods for contingencies analysis / Doutor

Determining the maximum power system loadability, as well as preventing the system from being operated close to the stability limits is very important in power systems planning and operation. The application of optimization techniques to power systems security and electricity markets is a rather relevant research area in power engineering. The study of optimization models to determine critical operating conditions of a power system to obtain secure power dispatches in an electricity market has gained particular attention. This thesis studies and develops optimization models and techniques to detect or avoid voltage instability points in a power system in the context of a competitive electricity market. A thorough analysis of an optimization model to determine the maximum power loadability points is first presented, demonstrating that a solution of this model corresponds to either Saddle-node Bifurcation (SNB) or Limit-induced Bifurcation (LIB) points of a power flow model. The analysis consists of showing that the transversality conditions that characterize these bifurcations can be derived from the optimality conditions at the solution of the optimization model. The study also includes a numerical comparison between the optimization and a continuation power flow method to show that these techniques converge to the same maximum loading point. It is shown that the optimization method is a very versatile technique to determine the maximum loading point, since it can be readily implemented and solved. Furthermore, this model is very flexible, as it can be reformulated to optimize different system parameters so that the loading margin is maximized. The Optimal Power Flow (OPF) problem with voltage stability (VS) constraints is a highly nonlinear optimization problem which demands robust and efficient solution techniques. Furthermore, the proper formulation of the VS constraints plays a significant role not only from the practical point of view, but also from the market/system perspective. Thus, a novel and practical OPF-based auction model is proposed that includes a VS constraint based on the singular value decomposition (SVD) of the power flow Jacobian. The newly developed model is tested using realistic systems of up to 1211 buses to demonstrate its practical application. The results show that the proposed model better represents power system security in the OPF and yields better market signals. Furthermore, the corresponding solution technique outperforms previous approaches for the same problem. Other solution techniques for this OPF problem are also investigated. One makes use of a cutting planes (CP) technique to handle the VS constraint using a primal-dual Interior-point Method (IPM) scheme. Another tries to reformulate the OPF and VS constraint as a semidefinite programming (SDP) problem, since SDP has proven to work well for certain power system optimization problems; however, it is demonstrated that this technique cannot be used to solve this particular optimization problem.