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.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-03-21T17:50:55Z No. of bitstreams: 1 thiagoresendedealmeida.pdf: 4974622 bytes, checksum: 0f8c86117d7625e1546498cd6c17f367 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-04-24T02:16:26Z (GMT) No. of bitstreams: 1 thiagoresendedealmeida.pdf: 4974622 bytes, checksum: 0f8c86117d7625e1546498cd6c17f367 (MD5) / Made available in DSpace on 2016-04-24T02:16:26Z (GMT). No. of bitstreams: 1 thiagoresendedealmeida.pdf: 4974622 bytes, checksum: 0f8c86117d7625e1546498cd6c17f367 (MD5) Previous issue date: 2013-10-30 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O principal objetivo deste trabalho é avaliar a influência da variação dos parâmetros da rede elétrica em função da frequência do sistema em estudos relacionados à avaliação da segurança de tensão de Sistemas Elétricos de Potência (SEP). Neste sentido, é proposta uma alteração na formulação denominada Fluxo de Potência com Regulação Primária. Tal formulação representa uma modelagem alternativa do problema de Fluxo de Potência, onde a frequência do sistema pode ser estimada com precisão satisfatória. É importante destacar que a metodologia proposta neste trabalho mantém a formulação full Newton do problema. A partir deste contexto são consideradas as variações dos parâmetros da rede, tais como shunts de barra, shunts de linha e o modelo de Linhas de Transmissão e Transformadores, tornando estes parâmetros dependentes com os desvios de frequência do sistema. É também realizada uma avaliação das cargas tipo motor de indução. Assim como os parâmetros da rede, os parâmetros do motor de indução são modificados de acordo com os desvios de frequência do sistema. Em seguida são desenvolvidos estudos de avaliação da segurança de tensão a partir do desenvolvimento e implementação de um Fluxo de Potência Continuado modificado e de uma formulação alternativa do problema de Fluxo de Potência Ótimo (FPO). A partir dessas ferramentas é possível avaliar a variação da frequência do sistema em função do aumento do seu carregamento. Também são feitas análises a partir dos autovalores da matriz Jacobiana do método proposto. Finalmente são utilizados cinco sistemas de pequeno e médio portes para a validação da metodologia proposta. Além de dois sistemas tutoriais de pequeno porte, é utilizado o sistema 16 Barras, que é um sistema criado a partir de dados reais e condições operativas encontradas no Sistema Interligado Nacional (SIN), os sistemas New England e IEEE-118 Barras, que são sistemas testes normalmente utilizados na literatura. O programa ANATEM, desenvolvido pelo CEPEL, é utilizado de forma a validar os desenvolvimentos realizados neste trabalho. / The main objective of this work is to evaluate the influence of varying the network parameters depending on the system frequency in studies related to the voltage security assessment of Electric Power Systems. In this sense, it is proposed a modification in the formulation of the called Governor Power Flow. Such formulation represents an alternative modeling of the power flow problem, where the system frequency can be estimated with satisfactory accuracy. It is important to highlight that in this work the proposed methodology retains full Newton formulation of the problem. From this context it is considered variations of the network parameters, such as shunt devices (capacitors and reactors) and equivalent models of transmission lines and transformers, making them dependent parameters with frequency system. It is also studied the induction motor modeling. As the network parameters, the parameters of the induction motor are modified according to the deviation of system frequency. Then voltage security assessment studies are carried out through the development and implementation of a Modified Continuation Power Flow and an Optimal Power Flow. Using these tools it is possible to evaluate the system frequency variation due to the increase of the system loading. Analyzes are also made using the eigenvalues of the Jacobian matrix associated with the proposed methodology. Finally six systems of small and medium scale are used in validation process of the proposed methodology. In addition to two tutorials small systems are used a 16 buses test system, which is created from real data and operating conditions found in the Interconnected Brazilian System, the well know New England system and the IEEE-118 buses test systems, which are systems commonly used in the literature. The ANATEM program, developed by CEPEL, is used to validate the developments made in this work.

Cette thèse traite de la commande hiérarchique de réseaux à courant continu multi-terminaux à haute tension (MT-HVDC) intégrant des sources d'énergie renouvelables à grande échelle. Le schéma de contrôle proposé est composé de quatre ‘couches’ : le contrôle local où se trouvent les convertisseurs de puissance, avec une échelle de temps de l’ordre de la milliseconde ; le contrôle primaire qui est décentralisé et appliqué à plusieurs terminaux avec une échelle du temps de l’ordre de la seconde ; un niveau de commande où la communication est prise en compte et où l’approche de Modèle du Commande Prédictive (MPC) assure la planification de la tension et de la puissance à leur état d'équilibre, pour l'ensemble du système; enfin, le contrôleur de niveau supérieur, qui est principalement basé sur les techniques d'optimisation, où les aspects économiques sont pris en compte (il s’agit du réglage dit tertiaire).Au niveau des convertisseurs, un accent particulier est mis sur les convertisseurs bidirectionnels DC/DC. Dans cette thèse, trois topologies différentes sont étudiées en profondeur: deux phases Dual Active Bridge (DAB), trois phases DAB, et l’utilisation de la technologie Modular Multilevel converter (MMC) comme convertisseur DC/DC. Pour chaque topologie, une commande non-linéaire spécifique est discutée. D’autre part une nouvelle fonction pour le convertisseur DC/DC est étudiée. Il s’agit de son utilisation comme disjoncteur à courant continu (DC-CB). En ce qui concerne le contrôle primaire, qui permet de maintenir le niveau de tension continue dans le réseau, nous avons étudié trois philosophies de contrôle: celle de maître/esclave, celui du contrôle « voltage margin control » et celle de la commande du statisme (droop control). Enfin, nous avons choisi d'utiliser le droop control, entre autres, parce que la communication entre les nœuds n’est pas nécessaire. Concernant la commande secondaire, son principal objectif est de planifier le transfert de puissance entre les nœuds du réseau, qui fournissent la tension et la puissance de référence aux contrôleurs locaux et primaires, même lorsque des perturbations apparaissent. Dans cette partie, nous avons proposé une nouvelle approche pour résoudre les problèmes de flux de puissance (équations non-linéaires) basée sur le théorème du point fixe de l’application contractive. Ceci permet d'utiliser plus d'un slack bus, contrairement à l’approche classique basée sur la méthode de Newton-Raphson. Par ailleurs, le réglage secondaire joue un rôle très important dans les applications pratiques, en particulier lorsque les sources d'énergie renouvelables (variables dans le temps). Dans de tels cas, il est intéressant de considérer des dispositifs de stockage afin d'améliorer la stabilité de tout le système. Il est également possible d'envisager différents types de prévisions (météo, charge, ..) basées sur la gestion des réserves de stockage. Toutes ces caractéristiques ont suggéré l'utilisation d'une approche MPC. Dans ce contexte, plusieurs critères d'optimisation ont été considérés, en particulier la minimisation des pertes de transmission ou des congestions dans le réseau.La tâche principale de réglage tertiaire est de d'atteindre l'optimisation économique de l'ensemble du réseau. Dans cette thèse, nous avons pu maximiser le profit économique du système en agissant sur le marché réel, et en optimisant l'utilisation des périphériques de stockage. Dans le but de mettre en œuvre la philosophie de contrôle hiérarchique présentée dans cette thèse, nous avons construit un banc d'essai expérimental. Cette plate-forme dispose de quatre terminaux reliés entre eux par l'intermédiaire d'un réseau à courant continu, et connectés au réseau principal de courant alternatif. Ce réseau DC peut fonctionner à un maximum de 400 V, et avec une courant maximal de 15 A. / This thesis focuses on the hierarchical control for a multi-terminal high voltage direct current (MT-HVDC) grid suitable for the integration of large scale renewable energy sources. The proposed control scheme is composed of 4 layers, from the low local control at the power converters in the time scale of units of ms; through distributed droop control (primary control) applied in several terminals in the scale of unit of seconds; and then to communication based Model Predictive Control (MPC) that assures the load flow and the steady state voltage/power plan for the whole system, manage large scale storage and include weather forecast (secondary control); finally reaching the higher level controller that is mostly based on optimization techniques, where economic aspects are considered in the same time as longer timespan weather forecast (tertiary control).Concerning the converters' level, special emphasis is placed on DC/DC bidirectional converters. In this thesis, three different topologies are studied in depth: two phases dual active bridge (DAB), the three phases DAB, and the use of the Modular Multilevel Converter (MMC) technology as DC/DC converter. For each topology a specific non-linear control is presented and discussed. In addition, the DC/DC converter can provide other important services as its use as a direct current circuit breaker (DC-CB). Several operation strategies are studied for these topologies used as DC-CB.With respect to primary control, which is the responsible to maintain the DC voltage control of the grid, we have studied several control philosophies: master/slave, voltage margin control and droop control. Finally we have chosen to use droop control, among other reasons, because the communication between nodes is not required. Relative to the secondary control, its main goal is to schedule power transfer between the network nodes providing voltage and power references to local and primary controllers, providing steady state response to disturbances and managing power reserves. In this part we have proposed a new approach to solve the power flow problem (non-linear equations) based on the contraction mapping theorem, which gives the possibility to use more than one bus for the power balance (slack bus) instead of the classic approach based on the Newton-Raphson method. Secondary control plays a very important role in practical applications, in particular when including time varying power sources, as renewable ones. In such cases, it is interesting to consider storage devices in order to improve the stability and the efficiency of the whole system. Due to the sample time of secondary control is on the order of minutes, it is also possible to consider different kinds of forecast (weather, load,..) and to achieve additional control objectives, based on managing storage reserves. All these characteristics encourage the use of a model predictive control (MPC) approach to design this task. In this context, several possibilities of optimization objective were considered, like to minimize transmission losses or to avoid power network congestions.The main task of tertiary control is to manage the load flow of the whole HVDC grid in order to achieve economical optimization. This control level provides power references to the secondary controller. In this thesis we were able to maximize the economic profit of the system by acting on the spot market, and by optimizing the use of storage devices. In this level it is again used the MPC approach.With the aim of implementing the hierarchical control philosophy explained in this thesis, we have built an experimental test bench. This platform has 4 terminals interconnected via a DC grid, and connected to the main AC grid through VSC power converters. This DC grid can work at a maximum of 400 V, and with a maximum allowed current of 15 A.

An Equivalent Current Injection¡]ECI¡^based Preventive Security- Constrained Optimal Power Flow¡]PSCOPF¡^is presented in this paper and a particle swarm optimization (PSO) algorithm is developed for solving non-convex Optimal Power Flow (OPF) problems. This thesis integrated Simulated Annealing Particle Swarm Optimization¡]SAPSO¡^ and Multiple Particle Swarm Optimization¡]MPSO¡^, enabling a fast algorithm to find the global optimum. Optimal power flow is solved based on Equivalent- Current Injection¡]ECIOPF¡^algorithm. This OPF deals with both continuous and discrete control variables and is a mixed-integer optimal power flow¡]MIOPF¡^. The continuous control variables modeled are the active power output and generator-bus voltage magnitudes, while the discrete ones are the shunt capacitor devices. The feasibility of the proposed method is exhibited for a standard IEEE 30 bus system, and it is compared with other stochastic methods for the solution quality. Security Analysis is also conducted. Ranking method is used to highlight the most severe event caused by a specific fault. A preventive algorithm will make use of the contingency information, and keep the system secure to avoid violations when fault occurs. Generators will be used to adjust the line flow to the point that the trip of the most severe line would not cause a major problem.

Electric power systems continue to increase in complexity because of the deployment of market mechanisms, the integration of renewable generation and distributed energy resources (DER) (e.g., wind and solar), the penetration of electric vehicles and other price sensitive loads. These revolutionary changes and the consequent increase in uncertainty and dynamicity call for significant modifications to power system operation models including unit commitment (UC), economic load dispatch (ELD) and optimal power flow (OPF). Planning and operation of these ???smart??? electric grids are expected to be impacted significantly, because of the intermittent nature of various supply and demand resources that have penetrated into the system with the recent advances. The main focus of this thesis is on the application of the Affine Arithmetic (AA) method to power system operational problems. The AA method is a very efficient and accurate tool to incorporate uncertainties, as it takes into account all the information amongst dependent variables, by considering their correlations, and hence provides less conservative bounds compared to the Interval Arithmetic (IA) method. Moreover, the AA method does not require assumptions to approximate the probability distribution function (pdf) of random variables. In order to take advantage of the AA method in power flow analysis problems, first a novel formulation of the power flow problem within an optimization framework that includes complementarity constraints is proposed. The power flow problem is formulated as a mixed complementarity problem (MCP), which can take advantage of robust and efficient state-of-the-art nonlinear programming (NLP) and complementarity problems solvers. Based on the proposed MCP formulation, it is formally demonstrated that the Newton-Raphson (NR) solution of the power flow problem is essentially a step of the traditional General Reduced Gradient (GRG) algorithm. The solution of the proposed MCP model is compared with the commonly used NR method using a variety of small-, medium-, and large-sized systems in order to examine the flexibility and robustness of this approach. The MCP-based approach is then used in a power flow problem under uncertainties, in order to obtain the operational ranges for the variables based on the AA method considering active and reactive power demand uncertainties. The proposed approach does not rely on the pdf of the uncertain variables and is therefore shown to be more efficient than the traditional solution methodologies, such as Monte Carlo Simulation (MCS). Also, because of the characteristics of the MCP-based method, the resulting bounds take into consideration the limits of real and reactive power generation. The thesis furthermore proposes a novel AA-based method to solve the OPF problem with uncertain generation sources and hence determine the operating margins of the thermal generators in systems under these conditions. In the AA-based OPF problem, all the state and control variables are treated in affine form, comprising a center value and the corresponding noise magnitudes, to represent forecast, model error, and other sources of uncertainty without the need to assume a pdf. The AA-based approach is benchmarked against the MCS-based intervals, and is shown to obtain bounds close to the ones obtained using the MCS method, although they are slightly more conservative. Furthermore, the proposed algorithm to solve the AA-based OPF problem is shown to be efficient as it does not need the pdf approximations of the random variables and does not rely on iterations to converge to a solution. The applicability of the suggested approach is tested on a large real European power system.

Modern day power systems present an open access environment, inspiring participation from small scale and large power suppliers. With multiple players in the system driven by the market, proper monitoring and control of system becomes a major concern. This transformation is accompanied by dynamic consumption patterns and rising power demands. The expanding network encompassing EHV/AC network, HVDC and FACTS devices, along with increased penetration of renewable sources, viz. solar and wind energy at medium and low voltage levels, adds to the problem. Independent System Operators (ISO) are entrusted with ensuring smooth operation, and employing proper preventive measures to eliminate a possible cascade tripping leading to a partial or large-scale blackout. To aid the operator in the process of ensuring secure operation of the grid, there are many tools that provide required information and guidance. Power flow tracing is one such tool that aids the operator in congestion management, transmission pricing, transaction evaluation, loss allocation and reactive power optimization. In this thesis, a novel active power flow tracing approach is proposed that takes into account, the real-time operating conditions and network topology. It provides the decomposition of active power flow in a line into respective components injected by various generators in the system. It also provides the contribution of the generators to various loads in the system. The approach is simple and computationally fast, making it an ideal tool to aid preventive control decisions. Based on the proposed active power flow tracing, a congestion management approach is developed. The approach indicates the least number of generators that need to be coordinated for generation rescheduling, so as to alleviate overloading in affected transmission lines and transformers. The approach also takes into consideration the operating constraints on the system, while computing the optimal rescheduling amongst selected generators using LP technique. The thesis also presents a real power loss allocation approach based on the proposed power flow tracing. Loss allocation is an important part of tariff design as the cost associated with losses amounts to a sizable fraction of total revenue collected from the loads. The approach provides information as to how losses are distributed among loads and how much each generator is providing for the loss share of each load. The approaches developed in the thesis are illustrated on a sample 10-bus equivalent system, IEEE 30-bus, and IEEE 39-bus systems. Results for typical case studies are presented for practical systems of 72-bus equivalent and 203-bus equivalent of Indian Southern grid.

Orientador: Edméa Cássia Baptista / Resumo: O problema de maximização da margem de carregamento operacional tem por finalidade determinar a maior demanda de carga em um sistema elétrico de potência que satisfaça todas as restrições operacionais do sistema e de equipamentos. Em linhas gerais, conhecer com precisão a máxima demanda de potência ativa e reativa suportada pelo sistema elétrico de potência para que o mesmo opere em condições satisfatórias é uma informação importante para a operação e planejamento do sistema. Muitos trabalhos, da literatura, formulam o problema de máximo carregamento através de um modelo de otimização contínuo, e mais recentemente, alguns trabalhos apresentam modelos que também passaram a levar em consideração o fator de potência da demanda das barras de carga. Neste trabalho propõe-se um modelo para o problema de máximo carregamento baseado no fator de potência de demanda ajustável e levando em consideração restrições de segurança. O problema de maximização da margem de carregamento operacional será formulado como um problema de programação não linear, não convexo de grande porte com variáveis contínuas e visa maximizar o somatório de potências ativas demandadas pelas barras de carga, respeitando um fator de potência mínimo pré-estabelecidos e restrições de segurança pós-contingência. Destaca-se que uma contribuição do trabalho é que o modelo encontre para o sistema um ponto de operação factível na presença de contingências pré-definidas, além disso, respeita os limites físicos e operacionai... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The problem of maximizing the operating load margin aims to determine the highest load demand in an electrical power system that satisfies all operational constraints of the system and equipment. In general, knowing precisely the maximum demand for active and reactive power supported by the electrical power system, in order that it operates in satisfactory conditions, is an important information for the operation and planning of the system. Many works in the literature formulate the problem of maximum loading through a continuous optimization model, and more recently, some works present models that also started to take into account the power factor of the load bars demand. This work proposes a model for the maximum load problem based on the adjustable demand power factor, taking into account security constraints. The problem of maximizing the operating load margin will be formulated as a non-linear, non-convex large programming problem with continuous variables and aims to maximize the sum of active powers demanded by the load bars, respecting an established minimum power factor and post-contingency security constraints. It is important to highlight that the model also ensures that the system finds a feasible operating point, even in the presence of predefined contingencies, besides; it respects the physical and operational limits provided for in the traditional Optimal Power Flow. The proposed model was tested for the IEEE 14, 30, 118 bus systems, simulated on the GAMS platf... (Complete abstract click electronic access below) / Doutor

Optimization plays a central role in the control and operation of electricity power networks. In this thesis we focus on two very important optimization problems in power systems. The first is the optimal power flow problem (OPF). This is an old and well-known nonconvex optimization problem in power system. The existence of local solutions of OPF has been a question of interest for decades. Both local and global solution techniques have been put forward to solve OPF problem but without any documented cases of local solutions. We have produced test cases of power networks with local solutions and have collected these test cases in a publicly available online archive (http://www.maths.ed.ac.uk/optenergy/LocalOpt/), which can be used now by researchers and practitioners to test the robustness of their solution techniques. Also a new nonlinear relaxation of OPF is presented and it is shown that this relaxation in practice gives tight lower bounds of the global solution of OPF. The second problem considered is how to split a network into islands so as to prevent cascading blackouts over wide areas. A mixed integer linear programming (MILP) model for islanding of power system is presented. In recent years, islanding of power networks is attracting attention, because of the increasing occurrence and risk of blackouts. Our proposed approach is quite flexible and incorporates line switching and load shedding. We also give the motivation behind the islanding operation and test our model on variety of test cases. The islanding model uses DC model of power flow equations. We give some of the shortcomings of this model and later improve this model by using piecewise linear approximation of nonlinear terms. The improved model yields good feasible results very quickly and numerical results on large networks show the promising performance of this model.

The aim of this research is to demonstrate some more efficient approaches to solve the n-1 security constrained optimal power flow (SCOPF) problems by using structure-exploiting primal-dual interior point methods (IPM). Firstly, we consider a DC-SCOPF model, which is a linearized version of AC-SCOPF. One new reformulation of the DC-SCOPF model is suggested, in which most matrices that need to be factorized are constant. Consequently, most numerical factorizations and a large number of back-solve operations only need to be performed once throughout the entire IPM process. In the framework of the structure-exploiting IPM implementation, one of the major computational efforts consists of forming the Schur complement matrix, which is very computationally expensive if no further measure is applied. One remedy is to apply a preconditioned iterative method to solve the corresponding linear systems which appear in assembling the Schur complement matrix. We suggest two main schemes to pick a good and robust preconditioner for SCOPF problems based on combining different “active” contingency scenarios. The numerical results show that our new approaches are much faster than the default structure-exploiting method in OOPS, and also that it requires less memory. The second part of this thesis goes to the standard AC-SCOPF problem, which is a nonlinear and nonconvex optimization problem. We present a new contingency generation algorithm: it starts with solving the basic OPF problem, which is a much smaller problem of the same structure, and then generates contingency scenarios dynamically when needed. Some theoretical analysis of this algorithm is shown for the linear case, while the numerical results are exciting, as this new algorithm works for both AC and DC cases. It can find all the active scenarios and significantly reduce the number of scenarios one needs to contain in the model. As a result, it speeds up the solving process and may require less IPM iterations. Also, some heuristic algorithms are designed and presented to predict the active contingencies for the standard AC-SCOPF, based on the use of AC-OPF or DC-SCOPF. We test our heuristic algorithms on the modified IEEE 24-bus system, and also present their corresponding numerical results in the thesis.

With Power System being restructured in the vision of Smart Grid, it is important now more than ever to find suitable locations to place Distributed Generators (DG). Distributed generators, which may be renewable, are not limited to specific locations as in the case of conventional generators. Several papers have been published that make suggestions on where the optimal location of DG should be in a system. Objectives ranging from loss minimization to total cost minimization have been the factor for such studies. In this study, a new method is introduced that hopes to improve a current system in three ways by maximizing load, minimizing the locational marginal price and improving line contingency scenarios. The proposed methodology is simulated using MATPOWER’s Optimal Power Flow on the IEEE 14 bus test system.