Este trabalho propõe um novo modelo e uma nova abordagem para resolução do problema de fluxo de potência ótimo reativo com variáveis de controle discretas e restrições de atuação de dispositivos de controle de tensão. Matematicamente, esse problema é formulado como um problema de programação não linear com variáveis contínuas e discretas e restrições de complementaridade, cuja abordagem para resolução proposta neste trabalho se baseia na resolução de uma sequência de problemas modificados pelo algoritmo da função Lagrangiana barreira modificada-penalidade-discreto. Nessa abordagem, o problema original é modificado da seguinte forma: 1) as variáveis discretas são tratadas como contínuas por funções senoidais incorporadas na função objetivo do problema original; 2) as restrições de complementaridade são transformadas em restrições de desigualdade equivalentes; e 3) as restrições de desigualdade são transformadas em restrições de igualdade a partir do acréscimo de variáveis de folga não negativas. Para resolver o problema modificado, a condição de não negatividade das variáveis de folga é tratada por uma função barreira modificada com extrapolação quadrática. O problema modificado é transformado em um problema Lagrangiano, cuja solução é determinada a partir da aplicação das condições necessárias de otimalidade. No algoritmo da função Lagrangiana barreira modificada-penalidade-discreto, uma sequência de problemas modificados é resolvida até que todas as variáveis do problema modificado associadas às variáveis discretas do problema original assumam valores discretos. Para demonstrar a eficácia do modelo proposto e a robustez dessa abordagem para resolução de problemas de fluxo de potência ótimo reativo, foram realizados testes com os sistemas elétricos IEEE de 14, 30, 57 e 118 barras e com o sistema equivalente CESP 440 kV de 53 barras. Os resultados mostram que a abordagem para resolução de problemas de programação não linear proposta é eficaz no tratamento de variáveis discretas e restrições de complementaridade. / This work proposes a novel model and a new approach for solving the reactive optimal power flow problem with discrete control variables and voltage-control actuation constraints. Mathematically, such problem is formulated as a nonlinear programming problem with continuous and discrete variables and complementarity constraints, whose proposed resolution approach is based on solving a sequence of modified problems by the discrete penalty-modified barrier Lagrangian function algorithm. In this approach, the original problem is modified in the following way: 1) the discrete variables are treated as continuous by sinusoidal functions incorporated into the objective function of the original problem; 2) the complementarity constraints are transformed into equivalent inequality constraints; and 3) the inequality constraints are transformed into equality constraints by the addition of non-negative slack variables. To solve the modified problem, the non-negativity condition of the slack variables is treated by a modified barrier function with quadratic extrapolation. The modified problem is transformed into a Lagrangian problem, whose solution is determined by the application of the first-order necessary optimality conditions. In the discrete penalty- modified barrier Lagrangian function algorithm, a sequence of modified problems is successively solved until all the variables of the modified problem that are associated with the discrete variables of the original problem assume discrete values. The efectiveness of the proposed model and the robustness of this approach for solving reactive optimal power flow problems were verified with the IEEE 14, 30, 57 and 118-bus test systems and the 440 kV CESP 53-bus equivalent system. The results show that the proposed approach for solving nonlinear programming problems successfully handles discrete variables and complementarity constraints.

Orientador: Júlio Borges de Souza / Resumo: Devido a um conjunto de questões econômicas e ambientais, a geração distribuída baseada em fontes renováveis tem sido incentivada por vários países. No Brasil, a conexão de unidades de geração distribuída fotovoltaica (GDFV) às redes de distribuição de baixa tensão, por meio de unidades residenciais e comerciais, tem apresentado uma rápida expansão. Diante deste cenário, é necessário investigar os possíveis impactos negativos que tal expansão pode resultar sobre os sistemas de distribuição. Neste trabalho, busca-se avaliar o impacto sobre a tensão em regime permanente. Para se alcançar tal objetivo, utiliza-se como modelo do sistema de distribuição a rede de teste IEEE 13 barras. Através do software de acesso livre OpenDss, o qual é devidamente apresentado, o comportamento da tensão ao longo desta rede, antes e depois da inserção da GDFV, é estudado por meio de simulações pontuais e diárias. Também é analisado neste trabalho de que forma o sistema de geração distribuída fotovoltaica, através do uso do controle voltvar, pode atenuar tal impacto. / Abstract: Due to a set of economic and environmental issues, distributed generation based on renewable sources has been encouraged by several countries. In Brazil, the connection of photovoltaic distributed generation units (PVDG) to low voltage distribution networks through residential and commercial units has shown a rapid expansion. Given this scenario, it is necessary to investigate the possible negative impacts that such expansion may result on distribution systems. This work aims to evaluate the impact on the steady state voltage. To achieve this goal, the IEEE 13 bus test network is used as a model of the distribution system. Through the open access software OpenDss, which is properly presented, the behavior of the voltage along this network, before and after the insertion of the PVDG, is studied through punctual and daily simulations. It is also analyzed in this work how the photovoltaic distributed generation system, by voltvar control, can mitigate such impact. / Mestre

The growth of electricity markets around the world has introduced new challenges in which one of the challenges is the uncertainty that has become a structural element in this new environment. Market players have to deal with it to guarantee the appropriate power system planning and operation as well as its own economical liquidity. Under an open access environment in a deregulated power system, transmission management holds a vital role in supporting transactions between suppliers and customers. Nevertheless, a transmission network has some constraints that should be addressed in order to ensure sufficient control to maintain the security level of a power system while maximizing market efficiency. The most obvious drawback of transmission constraints is a congestion problem that becomes an obstacle of perfect competition among the market participants since it can influence spot market pricing. The system becomes congested when the supplier and customer agree to produce and consume a particular amount of electric power, but this can cause the transmission network to exceed its thermal limits. Congestion can cause the market players to exercise market power that can result in price volatility beyond the marginal costs. Thus, it is important to manage congestion efficiently in the design of a power market. One mechanism that has direct correlation with transmission management is market clearing price (MCP). Under an open access environment, energy prices throughout the network will be different and measured based on transmission constraint and network losses. When network losses are ignored and there is no congestion on the transmission lines, the power price will be the same at all nodes. This is known as uniform marginal pricing (UMP). However, as the power flow violates transmission constraints, redispatching generating units is required and this will cause the price at every node to vary. This phenomenon is defined as locational marginal pricing (LMP). Therefore, the market clearing price has a strong relationship with transmission management, which is needed to be assessed in order to obtain an efficient and transparent price but satisfying all market participants. This project investigates an alternative solution to the dispatch mechanism, and then formulates a new Locational Marginal Price scheme using optimization technique that may well control congestion as the main issue. The model will vary and be improved, to be distilled into energy price, congestion revenue, cost of losses, as well as transmission usage tariff. The objective of the project is to support developing standard market design (SMD) in managing transmission systems which promotes economic efficiency, lowers delivered energy costs, maintains power system reliability and mitigates exercising market power.

Abstract: This work is concerned with the development and the implementation of a global optimization method for solving nonlinear nonconvex problems with continuous or mixed integer variables, related to power systems analysis. The proposed method relaxes the problem under study into a linear outer approximation problem by using the concept of special ordered sets. The obtained problem is then successively refined by a branch-and-bound strategy. In this way, the convergence to a global optimum is guaranteed, provided the discrete variables or those appearing nonlinearly in the original problem are bounded. Our method, conceived to solve a specific kind of problem, has been developed in a general framework in such a way that it can be easily extended to solve a large class of problems. We first derive the method theoretically and next present numerical results, fixing some choices inherent to the method to make it as optimal as possible. / Résumé: Ce travail a pour objet la conception et l'implémentation d'une méthode d'optimisation globale pour la résolution de problèmes non linéaires et non convexes, continus ou avec variables mixtes (entières et continues), issus de l'analyse des réseaux électriques. La méthode proposée relâche le problème traité en un problème d'approximation externe linéaire en se basant sur le concept d ensembles spécialement ordonnés. Le problème obtenu est alors successivement raffiné grâce à une stratégie de branch-and-bound. La convergence vers un optimum global est ainsi assurée, pour autant que les variables discrètes ou apparaissant non linéairement dans le problème de départ soient bornées. Notre méthode, mise au point pour résoudre un type de problème bien particulier, a été conçue dans un cadre général permettant une extension aisée à la résolution d'une grande variété de problèmes. Nous développons tout d'abord la méthode théoriquement et présentons ensuite des résultats numériques dont le but est de fixer certains choix inhérents à la méthode afin de la rendre la plus optimale possible.

Im Beitrag wird zunächst die konventionelle auf Signalflüssen basierte Modellbildung mit modernen leistungsflussbasierten Methoden, die auf dem Prinzip von Aktion und Reaktion aufbauen, verglichen. BG (Bond Graph), POG (Power Oriented Graph) und EMR (Energetic Macroscopic representation) sind solche modernen Methoden die den Leistungsaustausch zwischen Teilsystemen als Grundlage für den Modellbildungsansatz nutzen. Diese Werkzeuge erhalten die physikalische Struktur, erlauben es in das dynamische System hineinzuschauen und unterstützen das Verständnis des Leistungsflusses. Unterschiede werden anhand verschiedener Eigenschaften in einer Tabelle angegeben. Nach Erläuterung der Grundlagen zu POG und BG erfolgt die Vorstellung einer Freeware Zusatzbibliothek zur Simulation von Bondgraphen. Spezielle Eigenschaften werden kurz umrissen. Diese Blockbibliothek läuft unter Simulink, besteht aus nur 9 mittels Menü konfigurierbaren Blöcken und realisiert bidirektionale Verbindungen. Die Beispiele Gleichstrommotor, Pulssteller und elastische Welle demonstrieren die Vorteile der leistungsflussorientierten Modellbildung. Zustandsregelung, Energieeffizienz und Simulink LTI Analysewerkzeuge führen in die Anwendung der vorgestellten Simulink Zusatzbibliothek für Bondgraphen ein. / The paper starts with a comparison of the conventional modelling method based on signal flow and modern power flow oriented modelling methods based on the principle of action and reaction. BG (Bond Graph), POG (Power Oriented Graph) and EMR (Energetic Macroscopic representation) are such modern methods based on the power exchange between partial systems as a key element for the basic modelling approach. These tools preserve the physical structure, enable a view inside dynamical systems and support understanding the power flow. Relationships between these graphical representations will be given. After the explanation of basics for POG and BG an overview and special features of a freeware add-on library for simulation of BGs will be outlined. The block library runs under Simulink, consists of nine menu-driven customised blocks only and realises bidirectional connections. Examples DC motor, chopper and elastic shaft demonstrate the advantages of power flow oriented modelling. State space control, energy efficiency and Simulink LTI analysis tools exemplify the application of the presented Simulink add-on BG library.

High penetration of wind energy requires innovations in different areas of power engineering. Methods for improving wind energy and power system interconnection, control, and operation are proposed in this dissertation. A feed-forward transient compensation control scheme is proposed to enhance the low-voltage ride-through capability of wind turbines equipped with doubly fed induction generators. Stator-voltage transient compensation terms are introduced to suppress rotor-current overshoots and torque ripples during grid faults. A dynamic stochastic optimal power flow control scheme is proposed to optimally reroute real-time active and reactive power flow in the presence of high variability and uncertainty. The performance of the proposed power flow control scheme is demonstrated in test power systems with large wind plants. A combined energy-and-reserve wind market scheme is proposed to reduce wind production uncertainty. Variable wind reserve products are created to absorb part of the wind production variation. These fast wind reserve products can then be used to regulate system frequency and improve system security.

As tools for dynamic system modelling both conventional methods such as transfer function or state space representation and modern power flow based methods are available. The latter methods do not depend on energy domain, are able to preserve physical system structures, visualize power conversion or coupling or split, identify power losses or storage, run on conventional software and emphasize the relevance of energy as basic principle of known physical domains. Nevertheless common control structures as well as analysis and design tools may still be applied. Furthermore the generalization of power flow methods as pseudo-power flow provides with a universal tool for any dynamic modelling. The phenomenon of power flow constitutes an up to date education methodology. Thus the paper summarizes fundamentals of selected power flow oriented modelling methods, presents a Bond Graph block library for teaching power oriented modelling as compact menu-driven freeware, introduces selected examples and discusses special features.

For planning issues, it is useful to know the upper limit for photovoltaics (PV) in the electrical grid with current design and operation (defined as hosting capacity) and how this limit can be increased. Future costs for grid reinforcement can be avoided if measures are taken to implement smart grid technology in the distribution grid. The aim of this project is to identify challenges in Swedish electricity distribution grids with a high penetration of local generation of electricity from PV. The aim is also to help Swedish Distribution System Operators (DSOs) to better understand hosting capacity issues, and to see which room for PV integration there is before there is need for actions to maintain power quality. Three distribution grids are modelled and simulated in Matlab: Rural area, Residential area and City (Stockholm Royal Seaport). Since the project is a cooperation between Uppsala University and Fortum, three different representative grids from Fortum’s grid software ”Power Grid” have been used as input to a flexible simulation program developed at Uppsala University. The simulation includes Newton-Raphson power-flow computing but has also been improved with a model of the temperature dependency of the resistance. The results show that there is room for a lot of PV systems in the Swedish grids. When using voltage rise above 1.1 p.u. voltage as limitation, the hosting capacity 60% PV electricity generation as a fraction of the yearly load were determined for the rural grid and the suburban grid. For the city grid, which is very robust, the hosting capacity 325% was determined. When using overload as limitation, the hosting capacities 70%, 20% and 25%, were determined for the same grids.

Nowadays, power systems are dealing with some new challenges raisedby the major changes that have been taken place since 80’s, e.g., deregu-lation in electricity markets, significant increase of electricity demands andmore recently large-scale integration of renewable energy resources such aswind power. Therefore, system operators must make some adjustments toaccommodate these changes into the future of power systems.One of the main challenges is maintaining the system stability since theextra stress caused by the above changes reduces the stability margin, andmay lead to rise of many undesirable phenomena. The other important chal-lenge is to cope with uncertainty and variability of renewable energy sourceswhich make power systems to become more stochastic in nature, and lesscontrollable.Flexible AC Transmission Systems (FACTS) have emerged as a solutionto help power systems with these new challenges. This thesis aims to ap-propriately utilize such devices in order to increase the transmission capacityand flexibility, improve the dynamic behavior of power systems and integratemore renewable energy into the system. To this end, the most appropriatelocations and settings of these controllable devices need to be determined.This thesis mainly looks at (i) rotor angle stability, i.e., small signal andtransient stability (ii) system operation under wind uncertainty. In the firstpart of this thesis, trajectory sensitivity analysis is used to determine themost suitable placement of FACTS devices for improving rotor angle sta-bility, while in the second part, optimal settings of such devices are foundto maximize the level of wind power integration. As a general conclusion,it was demonstrated that FACTS devices, installed in proper locations andtuned appropriately, are effective means to enhance the system stability andto handle wind uncertainty.The last objective of this thesis work is to propose an efficient solutionapproach based on Benders’ decomposition to solve a network-constrained acunit commitment problem in a wind-integrated power system. The numericalresults show validity, accuracy and efficiency of the proposed approach. / <p>The Doctoral Degrees issued upon completion of the programme are issued by Comillas Pontifical University, Delft University of Technology and KTH Royal Institute of Technology. The invested degrees are official in Spain, the Netherlands and Sweden, respectively.QC 20141028</p>

The growth of electricity markets around the world has introduced new challenges in which one of the challenges is the uncertainty that has become a structural element in this new environment. Market players have to deal with it to guarantee the appropriate power system planning and operation as well as its own economical liquidity. Under an open access environment in a deregulated power system, transmission management holds a vital role in supporting transactions between suppliers and customers. Nevertheless, a transmission network has some constraints that should be addressed in order to ensure sufficient control to maintain the security level of a power system while maximizing market efficiency. The most obvious drawback of transmission constraints is a congestion problem that becomes an obstacle of perfect competition among the market participants since it can influence spot market pricing. The system becomes congested when the supplier and customer agree to produce and consume a particular amount of electric power, but this can cause the transmission network to exceed its thermal limits. Congestion can cause the market players to exercise market power that can result in price volatility beyond the marginal costs. Thus, it is important to manage congestion efficiently in the design of a power market. One mechanism that has direct correlation with transmission management is market clearing price (MCP). Under an open access environment, energy prices throughout the network will be different and measured based on transmission constraint and network losses. When network losses are ignored and there is no congestion on the transmission lines, the power price will be the same at all nodes. This is known as uniform marginal pricing (UMP). However, as the power flow violates transmission constraints, redispatching generating units is required and this will cause the price at every node to vary. This phenomenon is defined as locational marginal pricing (LMP). Therefore, the market clearing price has a strong relationship with transmission management, which is needed to be assessed in order to obtain an efficient and transparent price but satisfying all market participants. This project investigates an alternative solution to the dispatch mechanism, and then formulates a new Locational Marginal Price scheme using optimization technique that may well control congestion as the main issue. The model will vary and be improved, to be distilled into energy price, congestion revenue, cost of losses, as well as transmission usage tariff. The objective of the project is to support developing standard market design (SMD) in managing transmission systems which promotes economic efficiency, lowers delivered energy costs, maintains power system reliability and mitigates exercising market power.