Year 2040 the goal is to have a 100 % renewable Swedish energy system. Svenska kraftnät (Svk) predicts fully decommissioned nuclear power plants and an increased amount of connected wind power plants, especially offshore, year 2045. These kind of renewable power plants are non-synchronous and do not provide the grid with the same system stability services naturally as synchronous generators, such as nuclear power plants. With the increased number of renewables connected, one future challenge is to maintain the stability of the power grid. Grid stability can be divided into voltage-, frequency- and rotor angle stability.This thesis has investigated how large-scale offshore wind power plants (OWPPs) can contribute with reactive power compensation and in turn voltage stability to a nearby onshore power grid in Sweden. The evaluation has been done from the perspective of the TSO and the OWPP owner interests, with a focus on grid codes, economic incentives and technical capabilities.This project has been made in three parts. First, a comparison of voltage stability control requirements in different European grid codes was made. Secondly, static power flow simulations of a case study of a 1000 MW OWPP have been performed in PowerWorld Simulator, testing the OWPP’s reactive power outputs under different circumstances. Thirdly, a market opportunity analysis has been completed, analyzing reactive power market opportunities for OWPPs as well as for TSOs.The study shows that the reactive power capabilities of the simulated OWPP is considerable higher than the Swedish grid codes requires. Thus, an opportunity is to make the grid codes stricter, in combination with economic incentives. The case study showed that the distance offshore has an impact of the reactive power reaching the grid onshore. Though, the OWPP’s contribution to local voltage stability onshore is considered as good. Finally, with short- and long-term contracts, a reactive power market can be favorable for both the OWPP owner and the TSO.

[pt] O fenômeno de estabilidade de tensão é um problema associado ao fluxo de potência ativa e reativa nas linhas de transmissão. A manifestação mais conhecida do fenômeno é a existência de uma máxima carga que pode ser alimentada pela rede. Outra possibilidade é a existência de uma máxima injeção de potência ativa e reativa fornecida por geradores e compensadores. A curva QV possibilita o cálculo da margem Q, que corresponde à distância entre o caso-base e ponto de fronteira da curva. A margem Q, supostamente, é um índice para avaliação da estabilidade do sistema, determinando uma operação normal quando a inclinação da curva é positiva. O método da matriz D também fornece a relação Q e V de cada barra, avaliando, supostamente, as condições de estabilidade do sistema. Nesta dissertação foi proposta a análise desses dois índices, com o objetivo de explicitar as premissas, similaridades e diferenças das duas maneiras de se calcular a relação VQ. E assim, avaliar e identificar possíveis resultados não coerentes. / [en] The phenomenon of voltage stability is a problem associated with active and reactive power flow in transmission lines. The best-known manifestation of the event is the existence of a maximum load that can be supplied by the grid. Another possibility is the existence of a maximum injection of active and reactive power provided by generators and compensators. The QV curve enables the calculation of the Q margin, which corresponds to the distance between the base case and the curve s inflection point. The Q margin, supposedly, is an index for evaluating the system stability, consisting of normal operation when the slope of the curve is positive. The matrix method D also provides the relation Q and V of each bar evaluating, supposedly, conditions of system stability. In this dissertation, an analysis of these two indices was proposed to clarify the assumptions, similarities, and differences between the two ways of calculating the VQ relation. And so, evaluate and identify possible non-coherent results.

[pt] Cada dia a operação dos sistemas elétricos de energia é mais complexo. Mantiver um correto fornecimento da energia de forma empírica é uma tarefa difícil e pouco confiável, este trabalho se realizou para ajudar a atender com maior confiabilidade este fornecimento de energia. Neste trabalho apresentam-se modelagens de fluxo de carga para obter diferentes pontos de operação. Modelou-se a regulação própria da carga e o controle carga-frequência das unidades geradoras, incluindo regulação primária e secundária. As modelagens são estendidas para a avaliação da estabilidade de tensão, inclusive considerando-se a influência da frequência. A avaliação foi feita em pontos de operação antes e após a atuação do controle carga-frequência. Em cada caso, as variações de carga ou geração das barras em análise (infinitesimais) são absorvidas pelos geradores de diferentes formas: de acordo com os fatores de proporcionalidade na regulação secundária, com as energias de regulação na regulação primária ou com a proporcionalidade das gerações das barras swing no despacho proporcional. De acordo com o apresentado neste trabalho obtêm-se pontos de operação em regime permanente, nestes pontos de operação foi onde se realizo o cálculo da estabilidade de tensão para todas as barras do sistema. Os sistemas testados tiveram 6 e 39 barras. / [en] Each day the operation of electric power system is more complex. Maintain a correct supply of energy empirically is difficult and unreliable task, this work was realized to comply with more reliably this power supply. This dissertation presents the modeling of power flow to get different steady state. The load response to frequency deviation, the primary and the secondary frequency control were models. The models are extended to the evaluation of voltage stability, even considering the frequency influence. The evaluation is done in the state before and after the response of load-frequency control. In each case, the generators units absorb the variation (infinitesimal) in the load or in the generation (bus in analysis) in different ways: according to the proportionality factor in the secondary control, the speed regulations in the primary control or the proportionality of the swing bus generation in the proportional dispatch. According to the presented in this dissertation was obtained a state in permanent regime, in this state was evaluated the voltage stability in all bus of the system. The tested system had 6 and 39 bus.

[pt] Atualmente, o fenômeno de instabilidade de tensão representa uma das principais barreiras à operação estável das redes de energia elétrica, que tendem a crescer e a se tornarem cada vez mais interconectadas. A dificuldade de manter um perfil de tensão aceitável aumenta substancialmente e a estabilidade de tensão na operação dos sistemas elétricos deve ser preservada ao máximo, a fim de evitar os graves efeitos que a sua perda acarreta ao sistema. Esta dissertação atua na operação do sistema de energia elétrica, mais especificamente na área de operação em tempo real, onde é importante se conhecer a proximidade da condição operativa atual do sistema daquela que corresponde ao ponto crítico de estabilidade. Tal conhecimento permite que ações preventivas sejam realizadas no sentido de se evitar a instabilidade. O objetivo do trabalho é, a partir da comparação entre a margem sistêmica e a margem nodal, calculadas respectivamente pelo Fluxo de Potência Continuado e pelo método da Matriz D, determinar um critério para a margem de capacidade de carga, do ponto de vista de estabilidade de tensão, para a operação segura. No evento de cada contingência, calcula-se o maior crescimento de carga (margem), a partir do caso base, onde os índices nodais ainda são positivos. Define-se como margem mínima a menor dessas margens. A abordagem proposta foi avaliada através dos resultados obtidos com uma versão modificada do chamado sistema Nordic32. / [en] Currently, the phenomenon of voltage instability represents one of the main barriers to the stable operation of electric power networks, which tend to grow and become increasingly interconnected. The difficulty of maintaining an acceptable voltage profile increases substantially and the voltage stability in the operation of the electrical systems must be preserved to the maximum extent in order to avoid the serious effects that its loss entails on the system. This dissertation works in the operation of the electrical system, more specific in the area of operation in real time, where it is important to know the proximity of the operational condition of the current system that corresponds to the critical point of stability. Such knowledge allows preventive actions to be taken in order to avoid instability. The determination of appropriate margins for the various activities carried out in the electric power systems is not a trivial task, motivating the development of this dissertation. The objective of the work is from the comparison between a systemic margin and the nodal margin, calculated respectively by the Continued Power Flow and by the Matrix D method, to determine a criterion for the load capacity margin from the voltage stability point of view, for safe operation. In the event of each contingency, the largest growth (margin) is calculated from the base case, where the nodal indices are still positive. The smallest margin is defined as the minimum margin. The proposed approach was evaluated through the results obtained with a modified version of the so-called Nordic32 test system.

[pt] Com os sistemas elétricos cada vez mais sobrecarregados em virtude do aumento do consumo de energia elétrica e das restrições ambientais e econômicas, a avaliação das condições de estabilidade de tensão é cada vez mais necessária para os estudos de planejamento e na operação. Nesse contexto, os métodos para a avaliação do carregamento da rede auxiliam na compreensão do funcionamento dos sistemas em condições anormais. Para os diferentes tipos de rede, foram deduzidos os índices de avaliação da estabilidade de tensão para carregamentos selecionados, que indicam a região de operação nas curvas (Fator de Potência) constante no plano SV, para cada barra do sistema. Este trabalho tem por objetivo comparar e analisar os resultados obtidos para determinar o ponto de máximo carregamento entre o método do Fluxo de Potência Continuado e o método da Matriz D para diferentes tipos de sistemas teste. / [en] As electrical systems increasingly overloaded due to increased electricity consumption and environmental and economic constraints, the assessment of voltage stability conditions is increasingly needed for planning and operation studies. In this context, the methods for evaluating the load of the network help to understand the system operations under abnormal conditions. For different types of network, the evaluation indices of voltage stability for selected loads were deduced. These indices indicate the operating region in the curves constant in SV plane for each system bar. This study aims to compare and analyze the results obtained to determine the maximum load point between the Continuous Power Flow method and the Matrix D method for different types of test systems.

[pt] O surgimento do fenômeno de estabilidade de tensão na operação dos sistemas elétricos motivou centenas de pesquisadores a desenvolverem métodos que permitam detectar a proximidade à instabilidade de tensão, com eficiência computacional, e tomar medidas acertadas para garantir a operação confiável e segura. Neste trabalho são analisados diferentes métodos que permitem transformar sistemas de grande porte em circuitos simples: o circuito equivalente entre geradores e cargas, baseado no cálculo de correntes de curto-circuito, na técnica de redução de rede pela eliminação de barras intermediárias e no equivalente de Thévenin. É analisada a utilização destes equivalentes na avaliação das condições de estabilidade de tensão com sistemas-testes de 3 e 4 barras. Através de diferentes testes verificou-se que o circuito equivalente entre geradores e cargas e a técnica de redução de rede não podem ser usados para o cálculo de índices de avaliação das condições de estabilidade de tensão, enquanto que, usando circuito equivalente de Thévenin encontrou-se um método que funciona corretamente para barra de carga terminal, barra não-terminal e barra de tensão controlada por gerador. / [en] The emergence of voltage stability phenomenon in the operation of power systems has motivated hundreds of researchers to develop methods to detect the proximity to voltage instability, with computational efficiency and to take all necessary and appropriate measures to ensure reliable and safe operation. In this work, different methods that allow transforming large systems into simple circuits were analyzed, such as the equivalent circuit between generators and loads, based on the calculation of short-circuit currents; the network reduction technique for eliminating intermediate buses; and the Thévenin equivalent. The application of these equivalents on voltage stability assessment of 3 and 4 bus testing systems were extensively tested. At the end, it was verified that that the equivalent circuit between the generator and load, and the network reduction technique, cannot be used for calculating the voltage stability conditions evaluation indexes. However, using Thévenin equivalent circuit, it was found a proper method, which works correctly for terminal buses, transit buses and voltage-controlled buses.

In a power system it is important to keep voltages at specific levels at network buses. Deviations from that can lead to reduced efficiency of transferred power or, in more severe cases, widespread power outages affecting large parts of society. There exists a variety of power system devices that have the ability to regulate the voltage levels. These devices have maximum and minimum control capacities and may have additional operational constraints. It is desired to keep the control capacity of these actuators close to neutral operation so that they have the ability to respond to future disturbances. Due to the nature of such a control problem, a suitable tool is Model Predictive Control. In this thesis, a centralised model predictive control is designed for long-term voltage stability control of a power system. The system model employed is a two-area power system model, where each area includes a network of generators and loads. The model predictive control regulates the tap position of a tap-changing transformer and the reactive power compensation provided by two capacitor banks. In this thesis, it is shown that a centralised model predictive controller successfully maintains voltages within the desired range for a 3.5 % longer duration compared to a decentralised control approach when facing a voltage collapse scenario. Additionally, thanks to its predictive capabilities, it efficiently dampened oscillations in the post-transient steadystate scenario, leading to a 6.6 % shorter settling time than that observed with the decentralised control approach. / I ett kraftsystem är det viktigt att hålla spänningen på specifika nivåer vid nätverksbussarna. Avvikelser från detta kan leda till nedsatt effektöverföringseffektivitet eller, i allvarligare fall, omfattande strömavbrott som påverkar stora delar av samhället. Det finns en mängd olika kraftsystemsenheter som har förmågan att reglera spänningsnivåerna. Dessa enheter har maximala och minimala kontrollkapaciteter och kan ha ytterligare driftbegränsningar. Det är önskvärt att hålla kontrollkapaciteten hos dessa enheter nära neutral drift så att de har förmågan att svara på framtida störningar. På grund av arten av ett sådant kontrollproblem är ett lämpligt verktyg Model Predictive Control. I den här avhandlingen är en centraliserad modellprediktiv reglering utformad för långsiktig spänningsstabilitetskontroll av ett kraftsystem. Systemmodellen som används är en två-area kraftsystemmodell, där varje område inkluderar ett nätverk av generatorer och belastningar. Kontrollen reglerar varvtalet hos en lindningskopplare och den reaktiva effektkompensationen som tillhandahålls av två kondensatorbanker. I denna avhandling visas det att en centraliserad modell-prediktiv reglering framgångsrikt kan upprätthålla spänningar inom det önskade intervallet under en 3.5 % längre varaktighet jämfört med en decentraliserad styrmetod under ett spänningskollapsscenario. Dessutom, tack vare dess prediktiva kapacitet, dämpade den effektivt svängningar i det post-transienta steady-state-scenariot, vilket ledde till en 6.6 % kortare insvängningstid än den som observerades med den decentraliserade styrmetoden.

[pt] O problema da estabilidade de tensão está associado à máxima injeção de potência em barras da rede e à possibilidade do controle de tensão ter o efeito oposto ao esperado. Alguns casos reais de blecaute, caracterizados por afundamento de tensão, sugerem que os procedimentos normais para o controle de tensão do sistema podem agravar ainda mais o problema. Isso ocorreria porque, em determinadas situações especiais, caracterizadas pela relação inversa entre as variáveis de controle dos equipamentos, as ações de controle teriam o efeito oposto ao esperado da sua lógica de projeto. Esta afirmação é baseada no critério de estabilidade de tensão a pequenas perturbações que diz: Dada uma condição de operação para cada barra no sistema, o sistema é estável caso o módulo da tensão na barra aumente à medida que a injeção de potência reativa nessa mesma barra é aumentada. Um sistema é instável se, para pelo menos uma barra no sistema, o módulo de tensão da barra diminui conforme a injeção de potência reativa nessa barra é aumentada. Adicionalmente, o critério da curva 𝑉𝑄 diz: Uma vez que todos os dispositivos de controle de potência reativa são projetados para funcionar satisfatoriamente quando um aumento em 𝑄 é acompanhado por um aumento em 𝑉, a operação do lado direito das curvas 𝑉𝑄 é estável e do lado esquerdo é instável. Além disso, a parte inferior da curva 𝑉𝑄 representa o limite de estabilidade e define o valor de potência reativa mínimo para uma operação estável. Esse efeito não esperado do controle poderia causar tensões excessivamente baixas (ou altas) para a operação normal do sistema e provocar consequências indesejáveis. Visto isso, esse trabalho tem como principal objetivo investigar, no domínio do tempo, o efeito das ações de controle de tensão em pontos onde as variáveis de controle dos equipamentos apresentam relação inversa e, assim, validar (ou não) os resultados estimados pelos métodos baseados em análise estática como, por exemplo, os critérios de estabilidade de tensão a pequenas perturbações e da curva 𝑉𝑄. As simulações dinâmicas mostram que a análise estática não pode ser aplicada a todos os tipos de equipamentos que controlam a tensão. Outra possível causa do problema da estabilidade de tensão está relacionada à atuação de limitadores de sobre-excitação de máquinas síncronas e, por esta razão, é proposto um método para identificar as máquinas propensas a atingir o limite de sobre-excitação em estudos de regime permanente. No entanto, a atuação desses limitadores, na grande maioria das vezes, não apresenta efeito prejudicial na estabilidade do sistema e, por isto, também é proposto um critério que aponta a iminente perda da estabilidade devido à atuação dos limitadores. Este critério pode ser útil na concepção de esquemas automáticos de rejeição de carga, a fim de impedir a perda de estabilidade, e ele também pode ser utilizado em avaliações de segurança online para alertar sobre possíveis riscos de instabilidade e, consequentemente, para indicar ações preventivas. / [en] The voltage stability problem is associated with the maximum power injection in the network and the possibility of the voltage control having the opposite effect. Some real cases of blackouts characterized by voltage decays suggest that normal procedures for automatic voltage control can adversely affect the voltage level in the system. This may have been because in special situations, characterized by an inverse relationship between the controls variables in the devices used to control the system voltage, the automatic voltage control can have the opposite effect to that expected based on the design logic. This statement is based on the criterion for small-disturbance voltage stability: At a given operating condition for every bus in the system, a system is voltage-stable if the bus voltage magnitude increases as the reactive power injection at the same bus is increased. A system is voltage-unstable if, for at least one bus in the system, the bus voltage magnitude decreases as the reactive power injection at the same bus is increased. In addition, it is based on the 𝑉𝑄 curve criterion: Since all reactive power control devices are designed to operate satisfactorily when an increase in 𝑄 is accompanied by an increase in 𝑉, operation on the right side of the 𝑉𝑄 is stable and on the left side is unstable. Besides, the bottom of the 𝑉𝑄 curve represents the stability limit and defines the minimum reactive power requirement for stable operation. The unexpected control effect could produce excessively low (or high) voltages for normal system operation and cause undesirable consequences. In light of this, the present work seeks to analyze in the time domain the effects of device control actions starting from points where the control variables are inversely related and validated (or not) the results estimated by methods based on static analysis, for example, the criterion for small-disturbance voltage stability and 𝑉𝑄 curve. Dynamic simulations show that static analysis cannot be applied to all types of devices used to control the voltage. Another possible cause of the voltage stability problem is the action of overexcitation limiters. For this reason, it is proposed a way for identifying the machines that have a chance to hit the overexcitation limit in static analysis studies. However, in most cases, the action of these limiters has no detrimental effect on system stability and, therefore, it is also proposed a criterion that identifies the imminent loss of stability due to these limiters. This criterion may be useful in design of load shedding schemes, in order to prevent loss of stability, and can be used for online security assessment, warning for instability and indicating preventive actions.

Utilization of power electronics based controllable systems (or devices) in transmission systems has opened new opportunities for the power industry to optimize utilization of the existing transmission systems, and at the same time to keep high system reliability and security. As a member of these controllable systems, Voltage Source Converters-based High Voltage direct current (VSC-HVdc) systems have the ability to rapidly control the transmitted active power, and also to independently exchange reactive power with transmissions systems. Therefore, VSC-HVdcs with a suitable control scheme can offer an alternative means to enhance transient stability, to improve power oscillations damping, and to provide voltage support. An interesting application of this system is the analysis of a power system when a VSC-HVdc is connected in parallel with ac transmission lines. This thesis presents the derivation of control strategies to damp power oscillations, to enhance the transient stability and to provide voltage support for a VSC-HVdc. The thesis also formulates a multichoice control strategy and its application when the VSC-HVdc is connected in a synchronous system. The control strategy for enhancing transient stability is based on the theory of Control Lyapunov Function. The control strategy for increasing the damping is based on Linear Analysis. A very effective well known way to increase damping in the system is modulating the active power through the HVdc. However, besides the control of active power, the thesis explores an alternative way to mitigate power oscillations by controlling the reactive power. This condition might be very useful when the dc link in the VSC-HVdc system is out of service, but the converter stations are in operating conditions. A simple model of VSC-HVdc is considered in order to test the control strategy. The model represents the VSC-HVdc as an element in the power system that provides adequate interaction with other systems elements. The model is intended for analysis of power flows and electromechanical transients. It is then sufficient to consider the power frequency components of voltages and currents represented by phasors that vary with time during transients. The model is valid for symmetrical conditions, i.e. positive sequence phasors are used for the representation of the electrical state. / QC 20101117

In order to identify the weakest bus in a power system so that the Unified Power Flow Controller could be connected, an investigation of static and dynamic voltage stability is presented. Two stability indices, static and dynamic, have been proposed in the thesis. Multi-Input Multi-Output (MIMO) analysis has been used for the dynamic stability analysis. Results based on the Western System Coordinate Council (WSCC) 3-machine, 9-bus test system and IEEE 14 bus Reliability Test System (RTS) shows that these indices detect with the degree of accuracy the weakest bus, the weakest line and the voltage stability margin in the test system before suffering from voltage collapse. Recently, Flexible Alternating Current Transmission systems (FACTs) have become significant due to the need to strengthen existing power systems. The UPFC has been identified in literature as the most comprehensive and complex FACTs equipment that has emerged for the control and optimization of power flow in AC transmission systems. Significant research has been done on the UPFC. However, the extent of UPFC capability, connected to the weakest bus in maintaining the power flows under fault conditions, not only in the line where it is installed, but also in adjacent parallel lines, remains to be studied. In the literature, it has normally been assumed the UPFC is disconnected during a fault period. In this investigation it has been shown that fault conditions can affect the UPFC significantly, even if it occurred on far buses of the power system. This forms the main contribution presented in this thesis. The impact of UPFC in minimizing the disturbances in voltages, currents and power flows under fault conditions are investigated. The WSCC 3-machine, 9-bus test system is used to investigate the effect of an unsymmetrical fault type and position on the operation of UPFC controller in accordance to the G59 protection, stability and regulation. Results show that it is necessary to disconnect the UPFC controller from the power system during unsymmetrical fault conditions.