Real-Time State Estimation and Voltage Stability Assessment of Power Grids: From Theoretical Foundations to Practical Applications

The operators of power distribution systems strive to lower their operational costs and improve the quality of the power service provided to their customers. Furthermore, they are faced with the challenge of accommodating large numbers of Distributed Energy Resources (DERs) into their grids. It is expected that these problems will be tackled with a large-scale deployment of automation technology, which will enable the real-time monitoring and control of power distribution systems (i.e., similar to power transmission systems). For this purpose, real-time situation awareness w.r.t. the state and the stability of the system is needed. In view of the deployment of such automation functions into power distribution grids, there are two binding requirements. Firstly, the system models have to account for the inherent unbalances of power distribution systems (i.e., w.r.t. the components of the grid and the loads). Secondly, the analysis methods have to be real-time capable when deployed into low-cost embedded systems platforms, which are the cornerstones of automation. In other words, the analysis methods need to be computationally efficient. This thesis focuses on the modeling of unbalanced polyphase power systems, as well as the development, validation, and deployment of real-time methods for State Estimation (SE) and Voltage Stability Assessment (VSA) of such systems. More precisely, the following theoretical and practical contributions are made to the field of power system engineering. 1. Fundamental properties of the compound admittance matrix of polyphase power grids are identified. Specifically, theorems w.r.t. the rank of the compound admittance matrix, the feasibility of Kron Reduction (KR), and the existence of compound hybrid matrices are stated and formally proven. These theorems hold for generic polyphase power grids (i.e., which may be unbalanced, and have an arbitrary number of phases). 2. A Voltage Stability Index (VSI) for real-time VSA of polyphase power systems is proposed. The proposed VSI is a generalization of the well-known L-index, which is achieved by integrating more generic models of the power system components. More precisely, the grid is represented by a compound hybrid matrix, slack nodes by Thévenin equivalents, and resource nodes by polynomial load models. In this regard, the theorems mentioned under item 1 substantiate the applicability of the proposed VSI. 3. A Field-Programmable Gate Array (FPGA) implementation for real-time SE of polyphase power systems is presented. This state estimator is based on a Sequential Kalman Filter (SKF), which - in contrast to the standard Kalman Filter (KF) - is suitable for implementation in such dedicated hardware. In this respect, it is formally proven that the SKF and the standard KF are equivalent if the measurement noise variables are uncorrelated. To achieve high computational performance, the grid model is reduced through KR, and the SKF calculations on the FPGA are parallelized and pipelined. 4. The methods stated under items 1-3 are deployed into an industrial real-time controller, which is used to control a real-scale microgrid. This microgrid is equipped with a metering system composed of Phasor Measurement Units (PMUs) coupled with a Phasor Data Concentrator (PDC). The real-time capability of the developed methods is validated experimentally by measuring the latencies of the PDC-SE-VSA processing chain w.r.t. the PMU timestamps

Métodos de redução de sistemas de distribuição e contribuições aos estudos do limite de estabilidade de tensão e das múltiplas soluções do fluxo de potência

It is proposed in this thesis the following methods and tools for application on Distribution Systems (DS): (i) reduction methods; (ii) a tool for analyzing the voltage stability limit and the reactive power margin; (iii) method for initializing the neutral voltage; (iv) formulation to demonstrate the existence of multiple operationally-stable solutions in DS. Firstly, it is presented the mathematical development of reduction methods of DS for the purpose of representation in analysis tools, seeking to reduce the overall computational processing time. When applying the proposed methods, the reduced system solution aims to be mathematically equivalent to the original one, for all loading levels or with a small numerical error. The developed proposals are validated in several studies, considering different characteristics of DS. Secondly, the use of the multiphase continuation power flow is expanded, establishing a new algorithm and the formulation to obtain the QV curves in threephase four-wire DS. The development of such a tool allows the evaluation of the voltage stability limit and the reactive power margin in DS. Following, it is developed a procedure for initializing the neutral voltage when solving DS, which has also allowed an improvement in the convergence of iterative power flow solution tools. Lastly, a study is carried out where the nonlinear equations of a generic two-bus DS are deduced and used to verify the existence of multiple maximum loading points in DS. It is used the Bertini tool to solve such equations under a parametric variation on the power factor of the load, grounding impedance, loading level, and unbalance level of the load, proving the existence of multiple solutions that present operationally stable values. It must be highlighted that all the developed methods, tools, and studies may assist researchers and utilities in the decision-making on several aspects related to DS.Nesta tese são propostos os seguintes métodos e ferramentas para aplicação em Sistemas de Distribuição (SDs): (i) métodos de redução; (ii) ferramenta para análise do limite de estabilidade de tensão e da margem de potência reativa; (iii) método de inicialização da tensão de neutro; (iv) formulação para comprovação da possibilidade de existência de múltiplas soluções operacionalmente estáveis em SDs. Primeiramente, apresenta-se o desenvolvimento matemático de métodos de redução dos SDs para fins de representação em ferramentas de análise, buscando a redução do tempo computacional. Ao aplicar os métodos propostos, a solução do sistema reduzido busca ser matematicamente equivalente à solução do sistema original, para todo nível de carregamento, ou com um pequeno erro numérico. As propostas desenvolvidas são validadas em diversos estudos, considerando diferentes características dos SDs. Num segundo momento, amplia-se o uso do fluxo de potência continuado multifásico, estabelecendo um novo algoritmo e a formulação para obtenção de curvas QV em SDs trifásicos a quatro fios. A concepção de tal ferramenta permite avaliar a margem de potência reativa e o limite de estabilidade de tensão de tais sistemas. Em seguida, é desenvolvido um procedimento para a inicialização da tensão de neutro na solução de SDs, permitindo a melhora da convergência de ferramentas iterativas de solução do fluxo de potência. Por fim, é realizado um estudo onde são deduzidas as equações não lineares de um SD genérico de duas barras, as quais são utilizadas para verificar a existência de múltiplos pontos de máximo carregamento no SD. Utiliza-se a ferramenta Bertini para solucionar tais equações sob a variação paramétrica do fator de potência da carga, impedância de aterramento, nível de carregamento e nível de desequilíbrio da carga, e comprova-se a existência de múltiplas soluções que apresentam valores operacionalmente factíveis. Destaca-se que os métodos, ferramentas e estudos desenvolvidos poderão auxiliar os pesquisadores e concessionárias nas tomadas de decisões em diversos aspectos referentes aos SD

SIRM 2017

This volume contains selected papers presented at the 12th International Conference on vibrations in rotating machines, SIRM, which took place February 15-17, 2017 at the campus of the Graz University of Technology. By all meaningful measures, SIRM was a great success, attracting about 120 participants (ranging from senior colleagues to graduate students) from 14 countries. Latest trends in theoretical research, development, design and machine maintenance have been discussed between machine manufacturers, machine operators and scientific representatives in the field of rotor dynamics. SIRM 2017 included thematic sessions on the following topics: Rotordynamics, Stability, Friction, Monitoring, Electrical Machines, Torsional Vibrations, Blade Vibrations, Balancing, Parametric Excitation, and Bearings. The papers struck an admirable balance between theory, analysis, computation and experiment, thus contributing a richly diverse set of perspectives and methods to the audience of the conference