Direct methods are an alternative for power system transient stability analysis to avoid the enormous computational efforts of conventional time-domain method. The development of direct methods in last three decades makes it an effective potential approach to both on-line security assessment and off-line analysis tools. Among the direct methods, the Boundary of stability region based Controlling Unstable equilibrium point (BCU) method is the most successful, having a sound theoretical basis and practical application in power systems. It finds the controlling UEP of the original system via a reduced-state system. This thesis investigates the development of direct methods and the related theoretical foundation. Several widely used direct methods are presented and compared. The theoretical foundation and computational issues of BCU methods are discussed. Incorporation of more realistic power system models can be incorporated in BCU methods is introduced. Based on BCU method, some small system cases are tested for a given fault. / text

abstract: The power system is the largest man-made physical network in the world. Performing analysis of a large bulk system is computationally complex, especially when the study involves engineering, economic and environmental considerations. For instance, running a unit-commitment (UC) over a large system involves a huge number of constraints and integer variables. One way to reduce the computational expense is to perform the analysis on a small equivalent (reduced) model instead on the original (full) model. The research reported here focuses on improving the network reduction methods so that the calculated results obtained from the reduced model better approximate the performance of the original model. An optimization-based Ward reduction (OP-Ward) and two new generator placement methods in network reduction are introduced and numerical test results on large systems provide proof of concept. In addition to dc-type reductions (ignoring reactive power, resistance elements in the network, etc.), the new methods applicable to ac domain are introduced. For conventional reduction methods (Ward-type methods, REI-type methods), eliminating external generator buses (PV buses) is a tough problem, because it is difficult to accurately approximate the external reactive support in the reduced model. Recently, the holomorphic embedding (HE) based load-flow method (HELM) was proposed, which theoretically guarantees convergence given that the power flow equations are structure in accordance with Stahl’s theory requirements. In this work, a holomorphic embedding based network reduction (HE reduction) method is proposed which takes advantage of the HELM technique. Test results shows that the HE reduction method can approximate the original system performance very accurately even when the operating condition changes. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2017

abstract: Today, the electric power system faces new challenges from rapid developing technology and the growing concern about environmental problems. The future of the power system under these new challenges needs to be planned and studied. However, due to the high degree of computational complexity of the optimization problem, conducting a system planning study which takes into account the market structure and environmental constraints on a large-scale power system is computationally taxing. To improve the execution time of large system simulations, such as the system planning study, two possible strategies are proposed in this thesis. The first one is to implement a relative new factorization method, known as the multifrontal method, to speed up the solution of the sparse linear matrix equations within the large system simulations. The performance of the multifrontal method implemented by UMFAPACK is compared with traditional LU factorization on a wide range of power-system matrices. The results show that the multifrontal method is superior to traditional LU factorization on relatively denser matrices found in other specialty areas, but has poor performance on the more sparse matrices that occur in power-system applications. This result suggests that multifrontal methods may not be an effective way to improve execution time for large system simulation and power system engineers should evaluate the performance of the multifrontal method before applying it to their applications. The second strategy is to develop a small dc equivalent of the large-scale network with satisfactory accuracy for the large-scale system simulations. In this thesis, a modified Ward equivalent is generated for a large-scale power system, such as the full Electric Reliability Council of Texas (ERCOT) system. In this equivalent, all the generators in the full model are retained integrally. The accuracy of the modified Ward equivalent is validated and the equivalent is used to conduct the optimal generation investment planning study. By using the dc equivalent, the execution time for optimal generation investment planning is greatly reduced. Different scenarios are modeled to study the impact of fuel prices, environmental constraints and incentives for renewable energy on future investment and retirement in generation. / Dissertation/Thesis / M.S. Electrical Engineering 2012

La simulation des processus complexes dans des réseaux de transport d'électricité de grande taille nécessite la réduction de la dimension du problème. Comment réduire la complexité spatiale d'un réseau de grande dimension en gardant un bon niveau de précision ? Pour répondre à cette question nous avons divisé ce travail en trois grandes étapes : 1) la réduction par agrégation du nombre de nœuds; 2) la modélisation des liaisons entre ces clusters de nœuds et 3) le calcul des capacités des lignes équivalentes.L'agrégation des nœuds dans un cluster implique que celui-ci sera traité comme une plaque de cuivre par le modèle de marché. En conséquence, pour l'agrégation des nœuds, les congestions récurrentes dans le réseau sont identifiées et placées idéalement aux frontières des clusters. Après la réduction, la même répartition des flux dans le réseau complet et dans le modèle réduit du réseau doit être trouvée. Pour ce fait une méthodologie d'estimation d'une matrice PTDF a été développée. Pour les études économiques la limite thermique des lignes est un paramètre clé. Pour résoudre ce problème, nous proposons une méthodologie qui estime les capacités équivalentes à partir des points de fonctionnement historiques du système complet. Les approches présentées dans ce travail ont été appliquées sur un modèle du réseau continental européen et ont permis d'obtenir un modèle simplifié qui minimise la perte d'information. / The simulation of complex processes in large scale power systems needs the reduction of the problem. How to reduce the spatial complexity of a large scale power network while minimizing information loss? To answer this question we have divided this work in three main steps: 1) network buses aggregation; 2) modelling of the clusters' links; 3) defining the equivalent branches maximum exchange capacity.The bus aggregations in a cluster implies that it will be treated as a coppper-plate by the market model. Therefore, the most frequent network congestions must be identified ideally placed at the clusters frontiers. After the reduction, the same power flow repartition must be found in both reduced and complete model. To do that, a methodology to define a PTDF matrix was developed. For economic purpose studies, the branches maximum capacity is a key parameter, to define this value, a methodology is proposed that estimates the equivalent transmission capacities using historical system operating set points.These approaches were applied to the European transmission network and allowed to define a reduced model that minimises the information loss.

O objetivo principal deste trabalho é o desenvolvimento de algoritmos para análise de estabilidade transitória com esforço computacional reduzido. Com este propósito é desenvolvido uma metodologia para o equivalente dinâmico, a qual é um resultado da eliminação das barras de cargas providas com diferentes modelagens: PQ como constante, PQ como função de tensão e PQ como função de tensão e frequência. O sistema elétrico de potência é reduzido à barras geradoras internas através do método clássico de determinação de equivalentes desenvolvidos por Ward. Uma versão melhorada do equivalente de Ward atualiza a injeção de corrente equivalente nas barras geradoras internas através da utilização das Unidades Medidoras de fasores (PMU\'s) que fornecem os desvios angulares de potência das unidades geradoras e ele uma matriz ele sensibilidade W. A atualização da injeção ele corrente equivalente nas barras geradoras internas é efetuada através da matriz de sensibilidade W para cada novo ponto ele operação. A técnica utilizada para o desenvolvimento da matriz de sensibilidade W foi feita atráves da linearização da equação do fluxo de carga não linear e considerando diferentes modelagens das cargas. Programas que levam em consideração os aspectos acima foram desenvolvidos onde as diferentes modelagens de cargas são incorporadas. Para isto, o sistema AEP de 14 barras foi utilizado como teste para este projeto. / The development of algorithms for analysis of transient stability with reduced computational effort is the main objective of this work. With that purpose a methodology to build reduced equivalents of a power system in a dynamic way is developed. The expression for the injected equivalent currents at the generator buses, is a result of load buses elimination corresponding to different load models, that is: constant PQ loads, PQ as voltage dependency model,as well as PQ as voltage and frequency dependency models. The electric power system is reduced to the generator buses only, using the classic methodology for equivalents developed by Ward. An improved version for the Ward equivalent updates the injected equivalent currents at the generator buses through the use of the phasor measurement units (PMU\'s) and a sensitivity matrix W; those units give the power angle deviation of the generators when some perturbation is applied to the system. In the process of correcting the injected equivalent currents the sensitivity matrix W is updated every time the operating point changes significatively. The technique used in developing the sensitivity matrix W was made through linearization of the load flow equations applied to the different load models. Computer programs taking the considerations above mentioned were developed. The AEP-14 bus power system was used to test the models proposed on this work.

In this dissertation, we introduce three techniques for network sciences. The first of these techniques is a series of new models for describing network growth. These models, called network specialization models, are built with the idea that networks grow by specializing the function of subnetworks. Using these models we create theoretical networks which exhibit well-known properties of real networks. We also demonstrate how the spectral properties are preserved as the models grow. The second technique we describe is a method for decomposing networks that contain automorphisms in a way that preserves the spectrum of the original graph. This method for graph (or equivalently matrix) decomposition is called an equitable decomposition. Previously this method could only be used for particular classes of automorphisms, but in this dissertation we have extended this theory to work for every automorphism. Further we explain a number of applications which use equitable decompositions. The third technique we describe is a generalization of network symmetry, called latent symmetry. We give numerous examples of networks which contain latent symmetries and also prove some properties about them

abstract: Due to great challenges from aggressive environmental regulations, increased demand due to new technologies and the integration of renewable energy sources, the energy industry may radically change the way the power system is operated and designed. With the motivation of studying and planning the future power system under these new challenges, the development of the new tools is required. A network equivalent that can be used in such planning tools needs to be generated based on an accurate power flow model and an equivalencing procedure that preserves the key characteristics of the original system. Considering the pervasive use of the dc power flow models, their accuracy is of great concern. The industry seems to be sanguine about the performance of dc power flow models, but recent research has shown that the performance of different formulations is highly variable. In this thesis, several dc power-flow models are analyzed theoretically and evaluated numerically in IEEE 118-bus system and Eastern Interconnection 62,000-bus system. As shown in the numerical example, the alpha-matching dc power flow model performs best in matching the original ac power flow solution. Also, the possibility of applying these dc models in the various applications has been explored and demonstrated. Furthermore, a novel hot-start optimal dc power-flow model based on ac power transfer distribution factors (PTDFs) is proposed, implemented and tested. This optimal-reactance-only dc model not only matches the original ac PF solution well, but also preserves the congestion pattern obtain from the OPF results of the original ac model. Three improved strategies were proposed for applying the bus-aggregation technique to the large-scale systems, like EI and ERCOT, to improve the execution time, and memory requirements when building a reduced equivalent model. Speed improvements of up to a factor of 200 were observed. / Dissertation/Thesis / M.S. Engineering 2013

O objetivo principal deste trabalho é o desenvolvimento de algoritmos para análise de estabilidade transitória com esforço computacional reduzido. Com este propósito é desenvolvido uma metodologia para o equivalente dinâmico, a qual é um resultado da eliminação das barras de cargas providas com diferentes modelagens: PQ como constante, PQ como função de tensão e PQ como função de tensão e frequência. O sistema elétrico de potência é reduzido à barras geradoras internas através do método clássico de determinação de equivalentes desenvolvidos por Ward. Uma versão melhorada do equivalente de Ward atualiza a injeção de corrente equivalente nas barras geradoras internas através da utilização das Unidades Medidoras de fasores (PMU\'s) que fornecem os desvios angulares de potência das unidades geradoras e ele uma matriz ele sensibilidade W. A atualização da injeção ele corrente equivalente nas barras geradoras internas é efetuada através da matriz de sensibilidade W para cada novo ponto ele operação. A técnica utilizada para o desenvolvimento da matriz de sensibilidade W foi feita atráves da linearização da equação do fluxo de carga não linear e considerando diferentes modelagens das cargas. Programas que levam em consideração os aspectos acima foram desenvolvidos onde as diferentes modelagens de cargas são incorporadas. Para isto, o sistema AEP de 14 barras foi utilizado como teste para este projeto. / The development of algorithms for analysis of transient stability with reduced computational effort is the main objective of this work. With that purpose a methodology to build reduced equivalents of a power system in a dynamic way is developed. The expression for the injected equivalent currents at the generator buses, is a result of load buses elimination corresponding to different load models, that is: constant PQ loads, PQ as voltage dependency model,as well as PQ as voltage and frequency dependency models. The electric power system is reduced to the generator buses only, using the classic methodology for equivalents developed by Ward. An improved version for the Ward equivalent updates the injected equivalent currents at the generator buses through the use of the phasor measurement units (PMU\'s) and a sensitivity matrix W; those units give the power angle deviation of the generators when some perturbation is applied to the system. In the process of correcting the injected equivalent currents the sensitivity matrix W is updated every time the operating point changes significatively. The technique used in developing the sensitivity matrix W was made through linearization of the load flow equations applied to the different load models. Computer programs taking the considerations above mentioned were developed. The AEP-14 bus power system was used to test the models proposed on this work.

Beginning the study with a regional network map with an intent to perform a detailed harmonic study for a certain location, the first question that comes up is how far out in the system should detailed modeling of individual devices (transmission lines, loads, transformers, capacitor banks, etc) be done. The reason why this is extremely important is because system components that will affect the frequency response characteristics in the specific location should not be missed or poorly modeled. Frequency scan is the simplest and most commonly used simulation technique used to characterize the response of a power system network as a function of frequency. Unfortunately, there are two major problems using frequency scan techniques when real harmonic studies are considered: 1) the size of the admittance matrices (this calculation is repeated using discrete frequency steps throughout the range of interest) may be so large that an exact mathematical model of the system is not realistic and 2) the complexity of a rigorous and complete mathematical model of the system does not necessarily explain the extent to which system components affect the frequency response characteristics in a specified location. It is seldom clear how much of the system must be represented in order to get accurate results in a harmonic study. Realistic procedures to identify whether to include a particular element in a detailed model or to lump the element into a simplifying equivalent are yet to be developed in the industry. It is safe to say that practicing engineers are using tools and techniques of questionable validity. Two new computer-oriented methods that use eigen analysis techniques to identify easily and accurately the boundary between system areas to be modeled in detail and those represented by equivalents are proposed in this dissertation. The key here is to recognize that not all elements present in the ?external? system will participate in the resonant harmonic modes and could therefore be lumped into a simplified short-circuit equivalent. Achieving these objectives from either one of the two methods can be economically attractive. In short, the work described in this dissertation is a fundamentally sound alternative for the purposes of network equivalencing and model reduction.

abstract: Electric power systems are facing great challenges from environmental regulations, changes in demand due to new technologies like electric vehicle, as well as the integration of various renewable energy sources. These factors taken together require the development of new tools to help make policy and investment decisions for the future power grid. The requirements of a network equivalent to be used in such planning tools are very different from those assumed in the development of traditional equivalencing procedures. This dissertation is focused on the development, implementation and verification of two network equivalencing approaches on large power systems, such as the Eastern Interconnection. Traditional Ward-type equivalences are a class of equivalencing approaches but this class has some significant drawbacks. It is well known that Ward-type equivalents "smear" the injections of external generators over a large number of boundary buses. For newer long-term investment applications that take into account such things as greenhouse gas (GHG) regulations and generator availability, it is computationally impractical to model fractions of generators located at many buses. A modified-Ward equivalent is proposed to address this limitation such that the external generators are moved wholesale to some internal buses based on electrical distance. This proposed equivalencing procedure is designed so that the retained-line power flows in the equivalent match those in the unreduced (full) model exactly. During the reduction process, accommodations for special system elements are addressed, including static VAr compensators (SVCs), high voltage dc (HVDC) transmission lines, and phase angle regulators. Another network equivalencing approach based on the dc power flow assumptions and the power transfer distribution factors (PTDFs) is proposed. This method, rather than eliminate buses via Gauss-reduction, aggregates buses on a zonal basis. The bus aggregation approach proposed here is superior to the existing bus aggregation methods in that a) under the base case, the equivalent-system inter-zonal power flows exactly match those calculated using the full-network-model b) as the operating conditions change, errors in line flows are reduced using the proposed bus clustering algorithm c) this method is computationally more efficient than other bus aggregation methods proposed heretofore. A critical step in achieving accuracy with a bus aggregation approach is selecting which buses to cluster together and how many clusters are needed. Clustering in this context refers to the process of partitioning a network into subsets of buses. An efficient network clustering method is proposed based on the PTDFs and the data mining techniques. This method is applied to the EI topology using the "Saguaro" supercomputer at ASU, a resource with sufficient memory and computational capability for handling this 60,000-bus and 80,000-branch system. The network equivalents generated by the proposed approaches are verified and tested for different operating conditions and promising results have been observed. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012