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.

Neste trabalho abordamos o equipamento UPFC, pertencente à família FACTS, adequado ao estudo do regime permanente de sistemas de potência, sendo descritos modelos com diferentes níveis de detalhamento, assim como sua associação com a rede elétrica. Uma proposição alternativa para o modelamento do UPFC foi apresentada, sendo discutidos seus aspectos e particularidades por meio da análise nodal modificada (ANM), cujo tratamento permite obter a corrente nos conversores série de maneira direta. Desenvolvemos um programa de otimização de fluxo de potência, utilizando o método dos pontos interiores, sendo também elaborado um programa de otimização baseado no método Quase-Newton, permitindo uma análise comparativa de métodos e de modelos. Várias condições operativas de uma rede de pequeno porte, com apenas quatro barras e de uma rede de médio porte, com 39 barras, foram estudadas do ponto de vista de otimização e de limites de tensões e fluxos, observando-se a influência do UPFC no controle de variáveis da rede elétrica. / In this work we deal with the UPFC device which belongs to the FACTS family and is suitable to study the steady state of power systems. We describe models with different levels of detail, as well as their association with the electric network. One alternative proposition to the model of the UPFC is shown. The aspects and particularities are discussed by means of modified nodal analysis (ANM), which treatment allows us to get directly the current in series converters. We developed an optimization program of load flow, using the interior points method, and also worked out an optimization program based on the Quasi-Newton method, allowing a comparative analysis of methods and models. Several operating conditions of a small size network, with only 4 bars and of a medium size network, with 39 bars, were studied from the point of view of the optimization and of the voltage and of the flow limits, observing the influence of the UPFC on control of variables of the electric network.

Neste trabalho abordamos o equipamento UPFC, pertencente à família FACTS, adequado ao estudo do regime permanente de sistemas de potência, sendo descritos modelos com diferentes níveis de detalhamento, assim como sua associação com a rede elétrica. Uma proposição alternativa para o modelamento do UPFC foi apresentada, sendo discutidos seus aspectos e particularidades por meio da análise nodal modificada (ANM), cujo tratamento permite obter a corrente nos conversores série de maneira direta. Desenvolvemos um programa de otimização de fluxo de potência, utilizando o método dos pontos interiores, sendo também elaborado um programa de otimização baseado no método Quase-Newton, permitindo uma análise comparativa de métodos e de modelos. Várias condições operativas de uma rede de pequeno porte, com apenas quatro barras e de uma rede de médio porte, com 39 barras, foram estudadas do ponto de vista de otimização e de limites de tensões e fluxos, observando-se a influência do UPFC no controle de variáveis da rede elétrica. / In this work we deal with the UPFC device which belongs to the FACTS family and is suitable to study the steady state of power systems. We describe models with different levels of detail, as well as their association with the electric network. One alternative proposition to the model of the UPFC is shown. The aspects and particularities are discussed by means of modified nodal analysis (ANM), which treatment allows us to get directly the current in series converters. We developed an optimization program of load flow, using the interior points method, and also worked out an optimization program based on the Quasi-Newton method, allowing a comparative analysis of methods and models. Several operating conditions of a small size network, with only 4 bars and of a medium size network, with 39 bars, were studied from the point of view of the optimization and of the voltage and of the flow limits, observing the influence of the UPFC on control of variables of the electric network.

As novas tecnologias FACTS aplicadas ao sistema de transmissão, com base em eletrônica de potência, podem também ser úteis à distribuição. Para tal é preciso conduzir um procedimento de consolidação da utilização e do desempenho destas, para sua aplicação sem riscos. Neste trabalho, dois aspectos serão contemplados. O primeiro se refere à aplicação do dispositivo FACTS atuando como um capacitor série. Em se tendo controle de módulo e da fase da tensão inserida em série com a linha pode-se fazê-la comportar-se como uma queda em uma reatância série capacitiva ou indutiva. O controle dessa reatância série (aumentando/diminuindo) permitirá a aplicação do conceito de compensação série em qualquer ponto do sistema de distribuição, provendo benefícios de um controle contínuo da tensão e também do controle do fluxo de carga no sistema independente da corrente. O segundo aspecto refere-se ao uso dos dispositivos na conexão de alimentadores controlando a potência ativa entre eles. Para esta operação outro dispositivo UPFC, com conceito similar ao descrito acima, entretanto atuando na fase da tensão entre 2 barras, comporta-se como um transformador defasador com variação contínua de ?taps?, podendo controlar a potência ativa entre os alimentadores. A aplicação destas tecnologias propiciarão vários benefícios para a expansão da distribuição tais como, flexibilização do uso da rede, interligação de alimentadores permitindo manobras de blocos de energia sem ?pisca?, ajuste contínuo do suporte de reativos durante a operação, controle dinâmico do fluxo de potência. O objetivo deste trabalho é estudar a aplicabilidade da tecnologia FACTS e estender este conceito para aplicação em sistemas de distribuição e conduzir simulações digitais em redes de distribuição (15kV) identificando o desempenho e os benefícios atingidos. O programa de simulação utilizado é o ATP (Alternative Transients Program). / The new FACTS technologies applied to the transmission system, based on power electronics, can also be useful to the distribution. For that, it is necessary to drive a procedure to consolidate the use and the performance for their application without risks. In this work two aspects will be approached. The first refers to the application of a FACTS device acting as series compensator. This device will be able to control the voltage in module and phase in order to act as a voltage drop in a serie reactance with capacitive or inductive features. The control of this series reactance (increasing/ decreasing) will allow the application of series compensation concept to any point of the distribution system, providing the benefits of continuous control of the voltage added to the load flow control in the system independent of the current. The second aspect refers to its use in the connection of two feeders controlling the active power between them. For this operation other device, UPFC, with similar concept as described previously, acts mainly in the phase of the injected voltage in the line, performing as a phase-shift with continuous taps variation and is able to control the active power flow between feeders. The application of this technology will provide several benefits for the distribution expansion, such as, a greater flexibility in the use of the network, connection of feeders without load flow interruption, continuous adjust of reactive power during the operation and dynamic control of power flow. The purpose of this work is to study the applicability of the FACTS technology, to extend this concept for the application in the distribution system by using digital simulations in distribution network up to 15kV identifying the performance and the reached benefits.