Tese de mestrado. Engenharia Electrotécnica e de Computadores (Especialização em Energias Renováveis). Faculdade de Engenharia. Universidade do Porto. 2007

This dissertation presents a new algorithm for optimal power flow in distribution systems. The new algorithm, Discrete Ascent Optimal Programming (DAOP), will converge to the same solution as the Lagrange multiplier approach as demonstrated by example. An intuitive discussion illustrating the path of convergence is presented along with a theorem concerning convergence. Because no partial derivatives, solutions of simultaneous equations, or matrix operations are required, the DAOP algorithm is simple to apply and program. DAOP is especially suited for programming with pointers. Advantages of the new algorithm include its simplicity, ease of incorporating inequality constraints, and the ability to predict the number of steps required to reach a solution. In addition to optimal power flow, the algorithm, heuristic in nature, can be applied to switch placement design, reconfiguration, and economic dispatch. The basic principles of the algorithm have been used to devise a phase balancing routine which has been implemented in the Distribution Engineering Workstation (DEWorkstation) software package sponsored by the Electric Power Research Institute (EPRI). The new algorithm presented in this dissertation works toward a solution by performing a series of calculations within a finite number of steps. At the start of the algorithm, the assumption is made that no power is flowing in the system. Each step adds a discrete unit of load to the system in such a fashion as to minimize loss. As progress toward the solution is made, more and more load is satisfied and the losses in the system continue to increase. The algorithm is terminated when all system load is satisfied. When the algorithm is finished, the sources which should supply each load have been identified along with the amount of power delivered by each source. Discussion will show that the method will converge to a solution that is within the discrete step size of the optimum. The algorithm can be thought of as an ascent method because the cost (losses) continually increases as more and more load is satisfied. Hence, the name Discrete Ascent Optimal Programming (DAOP) has been given to the algorithm. The new algorithm uses the topology of the power system such that the entire system is not considered at each step. Therefore, DAOP is not an exhaustive state enumeration scheme. Only those portions of the system containing loads most closely connected (via least loss paths) to the sources are first considered. As loads become supplied during the course of the solution, other loads are considered and supplied until the system is fully loaded. / Ph. D.

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.

With the deregulation of power industry and the market competition, low cost, reliable power supply, and secured system operations are major concerns of the advanced deregulation markets. It is a natural extension to revise the objectives of the traditional optimal power flow (OPF) to help dispatch the power. Maximizing social welfare to create more values of the market is becoming an interesting topic. In the deregulation environment, a user-friendly mechanism is desirable to form an auction market information framework (AMIF) for power auction and market operation. This thesis proposed a prototype system to combine internet based technology, database system, and the auction market to construct an information framework of power auction market. The Internet technology used Dynamic HTML (DHTML) in WWW website to develop a convenient bidding environment for users. The database based on MS Access used open database connection (ODBC) technology to connect database and internet. The auction market integrates auction functions and re-designed OPF to support the auction mechanism and congestion management. This research could also provide a solid foundation for Taiwan¡¦s power system deregulation in the future. The proposed mechanism and its expansion could guarantee a smooth migration process and successful market/system operation.

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.

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.

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.