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In order to optimize limited infrastructure, many power systems are frequently operated close to critical, or bifurcation, points. While operating close to such critical points can be economically advantageous, doing so increases the probability of a blackout. With the continued deployment of Phasor Measurement Units (PMUs), high sample rate data are dramatically increasing the real time observability of the power grids. Prior research has shown that the statistics of these data can provide useful information regarding network stability and associated bifurcation proximity. Currently, it is not common practice for transmission and distribution control centers to leverage the higher order statistical properties of PMU data. If grid operators have the tools to determine when these statistics warrant control action, though, then the otherwise unused statistical data present in PMU streams can be transformed into actionable information. In order to address this problem, we present two methods that aim to gauge and improve system stability using the statistics of PMU data. The first method shows how sensitivity factors associated with the spectral analysis of the reduced power flow Jacobian can be used to weight and filter incoming PMU data. We do so by demonstrating how the derived participation factors directly predict the relative strength of bus voltage variances throughout a system. The second method leverages an analytical solver to determine a range of "critical" bus voltage variances. The monitoring and testing of raw statistical data in a highly observable load pocket of a large system are then used to reveal when control actions are needed to mitigate the risk of voltage collapse. A simple reactive power controller is then implemented that pushes the stability of the system back to a stable operating paradigm. Full order dynamic time domain simulations are used in order to test this method on both the IEEE 39 bus system and the 2383 bus Polish system. We also compare this method to two other, more conventional, controllers. The first relies on voltage magnitude signals, and the second depends only on local control of a reactive power resource. This comparison illustrates how the use of statistical information from PMU measurements can substantially improve the performance of voltage collapse mitigation methods.

[pt] Restrições econômicas e ecológicas têm limitado o investimento em novas usinas e linhas de transmissão de energia elétrica. Com os sistemas de potência trabalhando bastante carregados, o risco da ocorrência da instabilidade de tensão se acentua. Neste trabalho estabeleceram-se as características operacionais do fenômeno do colapso de tensão, e sua similaridade e diferença em relação ao problema da estabilidade angular. Forma desenvolvidos métodos para avaliar um ponto de operação do sistema quanto à proximidade da ocorrência do fenômeno. Os resultados foram comparados. Finalmente, foi abordado o problema da prevenção do colapso / [en] Investiments on new generators and transmission lines for electrical power systems have been limited due to economical and environmental constraints. This dissertation established the operational characteristics of the voltage collapse phenomenon, as well as pointed out similarities and differences in relation to the angular stability problem. Voltage collapse assessment methods were developed and results compared. Finallu, the collapse prevention problem was mentioned.

The basic idea deals with detecting the voltage collapse ahead of time to provide the operators a lead time for remedial actions and for possible prevention of blackouts. To detect cases of voltage collapse, we shall create methods using pattern recognition in conjunction with real time simulation of case studies and shall develop heuristic methods for separating voltage stable cases from voltage unstable cases that result in response to system contingencies and faults. Using Real Time Simulator in Entergy-UNO Power & Energy Research Laboratory, we shall simulate several contingencies on IEEE 39-Bus Test System and compile the results in two categories of stable and unstable voltage cases. The second stage of the proposed work mainly deals with the study of different patterns of voltage using artificial neural networks. The final stage deals with the training of the controllers in order to detect stability of power system in advance.

The purpose of this dissertation is to analyze dynamic behavior of a stressed power system and to correlate the dynamic responses to a near future system voltage abnormality. It is postulated that the dynamic response of a stressed power system in a short period of time-in seconds-contains sufficient information that will allow prediction of voltage abnormality in future time-in minutes. The PSSE dynamics simulator is used to study the dynamics of the IEEE 39 Bus equivalent test system. To correlate dynamic behavior to system voltage abnormality, this research utilizes two different pattern recognition methods one being algorithmic method known as Regularized Least Square Classification (RLSC) pattern recognition and the other being a statistical method known as Classification and Regression Tree (CART). Dynamics of a stressed test system is captured by introducing numerous contingencies, by driving the system to the point of abnormal operation, and by identifying those simulated contingencies that cause system voltage abnormality. Normal and abnormal voltage cases are simulated using the PSSE dynamics tool. The results of simulation from PSSE dynamics will be divided into two sets of training and testing set data. Each of the two sets of data includes both normal and abnormal voltage cases that are used for development and validation of a discriminator. This research uses stressed system simulation results to train two RLSC and CART pattern recognition models using the training set obtained from the dynamic simulation data. After the training phase, the trained pattern recognition algorithm will be validated using the remainder of data obtained from simulation of the stressed system. This process will determine the prominent features and parameters in the process of classification of normal and abnormal voltage cases from dynamic simulation data. Each of the algorithmic or statistical pattern recognition methods have their advantages and disadvantages and it is the intention of this dissertation to use them only to find correlations between the dynamic behavior of a stressed system in response to severe contingencies and the outcome of the system behavior in a few minutes into the future.

[pt] Com o uso extremo das linhas de transmissão surgiram os problemas de estabilidade, ou mais apropriadamente, de segurança de tensão. A avaliação das condições de segurança de tensão é realizada pelo programa computacional ESTABTEN. Como os índices calculados são baseados em um ponto de operação do sistema e em um modelo linearizado das equações de fluxo de carga, assim como a função Fluxo de Carga do pacote computacional ANAREDE também o é, é importante que os modelos matemáticos do sistema, de equipamentos, de controles e de limites sejam compatíveis nos dois programas. Assim como o programa de fluxo de carga é continuamente estendido, o programa ESTABTEN deve continuar a ter sua capacidade estendida para atender as necessidades dos estudos.Estuda-se neste trabalho a modelagem em regime permanente de alguns equipamentos especiais da rede de transmissão e sua incorporação à função de avaliação da segurança de tensão. Os equipamentos contemplados foram: elos de corrente contínua (elo CC), compensadores estáticos de potência reativa (CER), esquemas de HVDC/CCC e linhas com compensação série controlada a tiristores (CSC). São mostrados exemplos numéricos que ilustram a necessidade de uma modelagem realista, na medida do possível. / [en] With the extreme use of the transmission lines, the voltage stability problem, or more properly, the voltage security problem has appeared. The voltage security condition assessment is achieved using the computational program ESTABTEN. The calculated indexes are based on a system operation point and on a linear model of load flow equations, likewise the ANAREDE load flow function. It is important that the mathematical models of systems, equipments, control devices and limits are compatible in both programs. As the load flow program is continually extended, the ESTABTEN program is to have its capability enhanced in order to attend the study requirements. This work is concerned with the steady-state modelling of some special equipments of the transmission network and its incorporation to the voltage security assessment function. The equipments considered were: direct current link (DC link), static VAR compensators (SVC), HVDC/CCC and lines with series controlled compensation (TSSC).Numerical examples are presented to illustrate the necessity of realistic modelling.

[pt] Após a incidência de inúmeros colapsos ocorridos nos sistemas de transmissão de energia devido ao uso extremo das linhas de transmissão, a estabilidade, ou mais adequadamente, a segurança de tensão tornou-se um assunto importante ao longo dos últimos anos. Este trabalho foi desenvolvido com o intuito de complementar um método de reforço das condições de estabilidade de tensão. O método consta de ações de controle para diminuir o fluxo de potência ativa no ramo crítico do caminho de transmissão mais carregado associado a uma barra crítica, conceitos estes apresentados nesta dissertação. Para o propósito citado, e considerando que o problema de estabilidade de tensão causa restrições nos fluxos de potência na rede de transmissão, são estudados métodos que analisam o congestionamento dessas redes. Se destacam algoritmos que, a partir dos fluxos de potência ativa e reativa que deixam um gerador, ou que chegam a uma carga, determinam a distribuição nos ramos de um sistema de transmissão, e o algoritmo que avalia os impactos no sistema de transmissão devido a uma determinada transação, entre barras geradoras e/ou de cargas. São mostrados exemplos numéricos que ilustram a possibilidade ou não da adequação destes métodos para o problema do reforço das condições de segurança de tensão. / [en] After a number of collapses due to the extreme use of the transmission lines, the voltage stability, or voltage security, became an important issue. This work was developed in order to contribute to a voltage security reinforcement method. The method calculates control actions to decrease the power flowing through the critical branch of the most loaded transmission path associated with the critical bus (concepts present in this dissertation). For this propose, and considering that the power flow in a transmission network may be restricted by voltage stability limits, transmission congestion analysis methods were study. Two of them deal with the contribution of real and reactive outflows of individual generator buses, and real and reactive inflows of individual load buses, in all network branches. Another method assess the impact of a given power transaction on the network. Numerical examples are presented to illustrate whether it is the possible or not to employ the studied methods in the voltage security reinforcement problem.

This thesis investigates an important power system phenomenon, voltage stability, by using continuation power flow method. Voltage collapse scenario is presented which can be a serious result of voltage instability and the parameters that affect voltage collapse are discussed. In analyzing power system voltage stability, continuation power flow method is utilized which consists of successive load flows. This method is applied to a sample test system and Turkish Power System and load-voltage curves for several buses are obtained.

[pt] O problema de estabilidade de tensão está intimamente ligado à falta de recursos e questões ambientais que limitam a expansão do sistema de transmissão. Esta realidade em conjunto com o crescimento da carga submete os sistemas elétricos a carregamentos pesados, podendo levar a situações de colapso de tensão. O desenvolvimento de métodos para avaliação do carregamento da rede de transmissão tornou-se necessário e imprescindível para que se possa entender o funcionamento do sistema nestas condições e possibilitar a sua operação de modo correto. Em relatório de força-tarefa internacional está explicitada a necessidade de uma ferramenta computacional capaz de verificar a eficácia das ações de controle de tensão na operação do sistema elétrico em tempo-real. Com esse objetivo, foi desenvolvida uma ferramenta computacional com base no sistema linearizado das equações de fluxo de carga, e de todas as outras equações de controles e limites, julgadas pertinentes, para avaliação do efeito das ações de controle de tensão. Determinase uma matriz de sensibilidade [VCS], voltage control sensitivity matrix, através da qual se pode estabelecer a relação existente entre as tensões controladas e as grandezas controladoras. Os elementos diagonais relacionam a grandeza controladora de cada equipamento com a respectiva tensão controlada. A análise do sinal desses elementos estabelece se uma determinada ação de controle será adequada ou não, isto é, se terá efeito esperado ou oposto. Os elementos fora da diagonal representam a interdependência existente entre os equipamentos controladores de tensão. A matriz de sensibilidade também permite que ações de controle de tensão sejam calculadas com o objetivo de mover um ponto de operação inadequado, ou que esteja suscetível à inadequacidade do controle de tensão, colocando-os em um ponto de operação seguro, onde ações operativas de controle de tensão tenham o efeito esperado. Os resultados da avaliação do método desenvolvido e aplicado a sistemas-teste e reais foram qualitativamente coerentes com aqueles obtidos pela resolução (analítica, iterativa por Newton ou iterativa continuada) das equações de fluxo de carga, validando a proposta. A dimensão da matriz [VCS] é proporcional ao número de barras com tensão controlada em análise. Esta matriz não é esparsa e então, quando utilizada para representar o controle de tensão realizado por um número elevado de equipamentos controladores, sua análise direta pode se tornar complexa. Portanto, uma análise baseada nos autovalores e autovetores associados à matriz [VCS] é aplicada objetivando identificar barras de tensão controlada com efeito reverso, ocorrendo de modo contrário ao esperado, e a existência de controles conflitantes. Buscam-se autovalores negativos, nulos ou próximos de zero. A localização das barras com problemas se dá através do exame dos autovetores e fatores de participação associados a esses autovalores. O cálculo e a análise da matriz de sensibilidade dos controles de tensão são executados de forma extremamente rápida e, portanto, o esforço computacional não impede que a ferramenta desenvolvida possa ser usada durante a operação em tempo-real. / [en] The voltage stability problem has been associated with environment questions and lack of financial resources for transmission system expansion. This reality together with the load growth makes the electrical system to be subject of heavy loadings, what can lead to situations of voltage collapse. The development of methods for evaluation of transmission network loading became necessary and indispensable in order to correct operation of the system under heavy loading conditions. In an international force-task report it is stated the need for analytical tools capable of verifying the voltage control action adequacy in the real-time operation. This work reports the development of a computation tool able to evaluate the effect of voltage control actions on the voltage itself. It is based the linearized load flow equations, including control and limit equations judged pertinent. The tool establishes a sensitive matrix, named [VCS] for voltage control sensitivity matrix, that relates the controlling variables and the controlled voltages. Through the analysis of the sign of each diagonal element, it is possible to know whether a specific control action is adequate or not. Moreover, the off-diagonal elements represent the interdependence among the voltage controller devices of the power system under analysis. The sensitivity matrix also allows the calculation of control actions necessary to move the operating point from an unstable area, or near by, to a secure operating region where all voltage control actions would have the expected effect. The results obtained with the voltage control sensitivity matrix applied on real and test-systems was qualitatively coherent with those calculated by analytical, iteractive by Newton-Raphson and/or continuationiteractive solution of power flow equations, validating the proposed method. The [VCS] dimension is proportional to the number of buses with controlled voltage in the system area under analysis. The matrix is not sparse and when there are a large number of voltage control equipments, its immediate analysis may be complex. Therefore, an analysis based on eigenvalues and eigenvectors associated with [VCS] matrix is used in order to identify voltage control action with opposite effect. In this case, the analysis is focused on negative eigenvalues. The identification of conflicting controls existence of any system area under analysis is a by-product. The voltage control sensitivity matrix computation and analysis are performed extremely fast. Therefore, the computational effort does not constrain its use in real-time operation.