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.

It is expected that the grid of the future differs from the current system by the increased integration of distributed generation, distributed storage, demand response, power electronics, and communications and sensing technologies. The consequence is that the physical structure of the system becomes significantly more distributed. The existing centralized control structure is not suitable any more to operate such a highly distributed system. This thesis is dedicated to providing a promising solution to a class of energy management problems in power systems with a high penetration of distributed resources. This class includes optimal dispatch problems such as optimal power flow, security constrained optimal dispatch, optimal power flow control and coordinated plug-in electric vehicles charging. Our fully distributed algorithm not only handles the computational complexity of the problem, but also provides a more practical solution for these problems in the emerging smart grid environment. This distributed framework is based on iteratively solving in a distributed fashion the first order optimality conditions associated with the optimization formulations. A multi-agent viewpoint of the power system is adopted, in which at each iteration, every network agent updates a few local variables through simple computations, and exchanges information with neighboring agents. Our proposed distributed solution is based on the consensus+innovations framework, in which the consensus term enforces agreement among agents while the innovations updates ensure that local constraints are satisfied.

Power flow (PF) control can increase the utilization of the transmission system and connect lower cost generation with load. While PF controllers have demonstrated the ability to realize dynamic PF control for more than 25 years, PF control has been sparsely implemented. This research re-examines PF control in light of the recent development of fractionally-rated PF controllers and the incremental power flow (IPF) control concept. IPF control is the transfer of an incremental quantity of power from a specified source bus to specified destination bus along a specified path without influencing power flows on circuits outside of the path. The objectives of the research are to develop power system operation and planning methods compatible with IPF control, test the technical viability of IPF control, develop transmission planning frameworks leveraging PF and IPF control, develop power system operation and planning tools compatible with PF control, and quantify the impacts of PF and IPF control on multi-decade transmission planning. The results suggest that planning and operation of the power system are feasible with PF controllers and may lead to cost savings. The proposed planning frameworks may incent transmission investment and be compatible with the existing transmission planning process. If the results of the planning tool demonstration scale to the national level, the annual savings in electricity expenditures would be $13 billion per year (2010$). The proposed incremental packetized energy concept may facilitate a reduction in the environmental impact of energy consumption and lead to additional cost savings.

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.

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.

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 Patrícia Cerveira (pcerveira1@gmail.com) on 2017-06-13T15:56:56Z No. of bitstreams: 1 Rene_Cruz_Freire.pdf: 5170376 bytes, checksum: 8c6b6dd8986d23b53ae99ba90dd69ef5 (MD5) / Approved for entry into archive by Biblioteca da Escola de Engenharia (bee@ndc.uff.br) on 2017-06-29T16:38:47Z (GMT) No. of bitstreams: 1 Rene_Cruz_Freire.pdf: 5170376 bytes, checksum: 8c6b6dd8986d23b53ae99ba90dd69ef5 (MD5) / Made available in DSpace on 2017-06-29T16:38:47Z (GMT). No. of bitstreams: 1 Rene_Cruz_Freire.pdf: 5170376 bytes, checksum: 8c6b6dd8986d23b53ae99ba90dd69ef5 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Um dos temas de alta relevância para a sociedade atual é a qualidade do suprimento de energia elétrica, que deve ser ininterrupto, seguro e econômico. Para tal, é primordial que o sistema de potência esteja preparado para um possível defeito de algum equipamento da rede, mantendo a operação dentro dos patamares seguros, evitando os blecautes e todas as suas consequências para a sociedade. Isso pode ser feito através do redespacho das unidades geradoras, de modo a encontrar um ponto de operação que concilie segurança e economicidade, dois objetivos conflitantes, enquanto busca se afastar o mínimo possível do ponto de operação previamente estabelecido, via planejamento eletroenergético, para o sistema de potência em questão. Trata-se de uma abordagem multiobjetiva do Fluxo de Potência Ótimo com Restrições de Segurança (FPORS) que pode ser solucionada com uma abordagem de Computação Evolucionária (CE) com viés multiobjetivo. Neste trabalho, foram implementadas e comparadas duas meta-heurísticas evolutivas multiobjetivo: Nondominated Sorting Genetic Algorithm II (NSGA-II) e o Multi-objective Evolutionary Particle Swarm Optimization (MOEPSO). Os resultados dessas heurísticas também foram comparados com a abordagem mono-objetivo do mesmo problema. Os algoritmos foram implementados no MATLAB® e testados em um sistema-teste que simula as condições do Sistema Interligado Nacional (SIN). As heurísticas multiobjetivo foram comparadas através da metodologia de análise da Fronteira de Pareto (FP), onde é analisado qual método concilia melhor os objetivos de economia e segurança. Na primeira análise o NSGA-II saiu-se melhor, entretanto após a implementação de melhorias no algoritmo, o MOEPSO mostrou desempenho superior na segunda análise. Nas duas análises, o viés multiobjetivo mostrou-se superior ao mono-objetivo, na comparação através do critério de agregação de objetivos. Em relação ao tempo de simulação de cada método, o MOEPSO foi superior na primeira análise, já na segunda análise foi implementado um refinamento baseado no Fluxo de Potência Linearizado no FPORS, que baixou o tempo de simulação das duas heurísticas multiobjetivas em comparação com a primeira análise, e o MOEPSO teve o menor tempo de simulação. Na comparação com o viés mono-objetivo, apenas o NSGA-II teve tempo médio de simulação maior que o método mono-objetivo na primeira análise. Na segunda análise, todas as heurísticas multiobjetivo possuíam tempo de simulação menores que o método mono-objetivo. / One of the topics of high relevance to the today’s society is the quality of electric power supply, which must be uninterrupted, safe and economical. To this end, it is essential that the power system be prepared for a possible defect of some equipment from the network while maintaining operation within safe levels, avoiding blackouts and all its consequences for society. This can be done by redispatch of generating units, in order to find an operation point which conciliate security and economy, two conflicting objectives, while seeking to depart as little as possible of the operation point previously established in the energy planning for the power system in question. This is a multi-objective approach to Security Constrained Optimal Power Flow (SCOPF) that can be solved with an approach of Evolutionary Computation with multi-objective bias. In this work we were implemented and compared two multi-objective evolutionary meta-heuristics: Nondominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Evolutionary Particle Swarm Optimization (MOEPSO). The results of these heuristics were also compared with mono-objective approach to the same problem. The algorithms were implemented in MATLAB® and tested in a test-case that simulates the conditions of the Brazilian Sistema Interligado Nacional (National Interconnected System). The multi-objective heuristics were compared using the analysis methodology of the Pareto Frontier, where is analyzed which method is better to conciliate the economy and security objectives. In the first analysis the NSGA-II fared better, but after the implementation of improvements in the algorithm, the MOEPSO showed superior performance in the second analisys. In both analyzes, the multi-objective bias was superior to the mono-objective bias, in the comparison through objectives aggregation criteria. Concerning the simulation time of each method, the MOEPSO was superior in the first analysis, but in the second analysis was implemented a refinement based on DC Load Flow, which lowered the simulation time of the two multi-objective heuristics compared with the first analysis, and the MOEPSO had the shortest time simulation. Compared to the mono-objective bias, only the NSGA-II had an average time simulation greater than the mono-objective method in the first analysis. In the second analysis, all multi-objectives heuristics had simulation time smaller than the mono-objective method.

[pt] Esta dissertação está estruturada como uma coleção de cinco artigos formatados em capítulos. Os quatro primeiros artigos apresentam contribuições em modelagem e metodológicas para problemas de operação ou investimento em sistemas de potência usando arcabouço de otimização robusta adaptativa e modificações no algoritmo de geração de linhas e colunas (CCGA). O primeiro artigo aborda a programação de curto prazo com restrição de segurança, onde a resposta automática de geradores é considerada. Um modelo robusto de dois estágios é adotado, resultando em complexas instâncias de programação inteira mista, que apresentam variáveis binárias associadas às decisões de primeiro e segundo estágios. Um novo CCGA que explora a estrutura do problema é desenvolvido. O segundo artigo usa redes neurais profundas para aprender o mapeamento das demandas nodais aos pontos de ajuste dos geradores para o problema do primeiro artigo. O CCGA é usados para garantir a viabilidade da solução. Este método resulta em importantes ganhos computacionais em relação ao primeiro artigo. O terceiro artigo propõe uma abordagem adaptativa em dois estágios para um modelo robusto de programação diária no qual o conjunto de incerteza poliedral é caracterizado diretamente a partir dos dados de geração não despachável observados. O problema resultante é afeito ao CCGA. O quarto artigo propõe um modelo de dois estágios adaptativo, robusto em distribuição para expansão de transmissão, incorporando incertezas a longo e curto prazo. Um novo CCGA é desenvolvido para lidar com os subproblemas. Finalmente, sob uma perspectiva diferente e generalista, o quinto artigo investiga a adequação de prêmios de incentivo para promover inovações em aspectos teóricos e computacionais para os desafios de sistemas de potência modernos. / [en] This dissertation is structured as a collection of five papers formatted as chapters. The first four papers provide modeling and methodological contributions in scheduling or investment problems in power systems using the adaptive robust optimization framework and modifications to the column-and-constraint-generation algorithm (CCGA). The first paper addresses the security-constrained short-term scheduling problem where automatic primary response is considered. A two-stage robust model is adopted, resulting in complex mixed-integer linear instances featuring binary variables associated with first- and second-stage decisions. A new tailored CCGA which explores the structure of the problem is devised. The second paper uses deep neural networks for learning the mapping of nodal demands onto generators set point for the first paper s model. Robust-based modeling approaches and the CCGA are used to enforce feasibility for the solution. This method results in important computational gains as compared to results of the first paper. The third paper proposes an adaptive data-driven approach for a two-stage robust unit commitment model, where the polyhedral uncertainty set is characterized directly from data, through the convex hull of a set of previously observed non-dispatchable generation profiles. The resulting problem is suitable for the exact CCGA. The fourth paper proposes an adaptive two-stage distributionally robust transmission expansion model incorporating long- and short-term uncertainties. A novel extended CCGA is devised to tackle distributionally robust subproblems. Finally, under a different and higher-level perspective, the fifth paper investigates the adequacy of systematic inducement prizes for fostering innovations in theoretical and computational aspects for various modern power systems challenges.