The increasing penetration of proactive agents in distribution systems (DS) has opened new possibilities to make the grid more resilient and to increase participation of responsive loads (RL) and non-conventional generation resources. On the resiliency side, plug-in hybrid electric vehicles (PHEV), energy storage systems (ESS), microgrids (MG), and distributed energy resources (DER), can be leveraged to restore critical load in the system when the utility system is not available for extended periods of time. Critical load restoration is a key factor to achieve a resilient distribution system. On the other hand, existing DERs and responsive loads can be coordinated in a market environment to contribute to efficiency of electricity consumption and fair electricity tariffs, incentivizing proactive agents' participation in the distribution system. Resiliency and market applications for distribution systems are highly complex decision-making problems that can be addressed using modern optimization techniques. Complexities of these problems arise from non-linear relations, integer decision variables, scalability, and asynchronous information. On the resiliency side, existing models include optimization approaches that consider system's available information and neglect asynchrony of data arrival. As a consequence, these models can lead to underutilization of critical resources during system restoration. They can also become computationally intractable for large-scale systems. In the market design problem, existing approaches are based on centralized or computational distributed approaches that are not only limited by hardware requirements but also restrictive for active participation of the market agents. In this context, the work of this dissertation results in major contributions regarding new optimization algorithms for market design and resiliency improvement in distribution systems. In the DS market side, two novel contribution are presented: 1) A computational distributed coordination framework based on bilateral transactions where social welfare is maximized, and 2) A fully decentralized transactive framework where power suppliers, in a simultaneous auction environment, strategically bid using a Markowitz portfolio optimization approach. On the resiliency side, this research proposed a system restoration approach, taking into account uncertain devices and associated asynchronous information, by means of a two-module optimization models based on binary programming and three phase unbalanced optimal power flow. Furthermore, a Reinforcement Learning (RL) method along with a Monte Carlo tree search algorithm has been proposed to solve the scalability problem for resiliency enhancement. / Doctor of Philosophy / Distribution systems (DS) are evolving from traditional centralized and fossil fuel generation resources to networks with large scale deployment of responsive loads and distributed energy resources. Optimization-based decision-making methods to improve resiliency and coordinate DS participants are required. Prohibitive costs due to extended power outages require efficient mechanisms to avoid interruption of service to critical load during catastrophic power outages. Coordination mechanisms for various generation resources and proactive loads are in great need. Existing optimization-based approaches either neglect the asynchronous nature of the information arrival or are computationally intractable for large scale system. The work of this dissertation results in major contributions regarding new optimization methods for market design, coordination of DS participants, and improvement of DS resiliency. Four contributions toward the application of optimization approaches for DS are made: 1) A distributed optimization algorithm based on decomposition and best approximation techniques to maximize social welfare in a market environment, 2) A simultaneous auction mechanism and portfolio optimization method in a fully decentralized market framework, 3) Binary programming and nonlinear unbalanced power flow, considering asynchronous information, to enhance resiliency in a DS, and 4) A reinforcement learning method together with an efficient search algorithm to support large scale resiliency improvement models incorporating asynchronous information.

A typical problem in traffic control is the steering over a network of vehicles with different origins and destinations. In this report this scenario is formulated as a multi-commodity network flow problem, a linear programming problem whose objective is to transport, with minimum cost, different commodities from their respective sources to their sinks through a network, while respecting the capacity constraints of the roads. The dynamic network flow formulation of the problem is also presented, extending the network over time to incorporate the temporal dimension. Different algorithms for solving the multi-commodity network flow problem are examined. First, the simplex method, more precisely its revised version, is considered, and then the Dantzig-Wolfe decomposition is illustrated, an optimization algorithm which exploits specific block structures in the constraints. These methods are applied using state-of-the-art linear programming solvers and evaluated with a simulation based on the road network in central Stockholm. The results show that both methods allow for solving the traffic flow problem, with limitations given by the specifics of the solvers and by the space and time discretization of the problem. In particular, the revised simplex algorithm results the faster method.

Made available in DSpace on 2014-06-11T19:22:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-25Bitstream added on 2014-06-13T18:49:30Z : No. of bitstreams: 1 lopezquizhpi_jc_me_ilha.pdf: 769238 bytes, checksum: 591b6116b31bf1d4b2d4b7817c38a698 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Neste trabalho apresenta-se uma metodologia para resolver o problema de planejamento ótimo de reativos em sistemas de potência interconectados multi-áreas, utilizando a técnica de decomposição de Dantzig-Wolfe. O problema original multi-área é separado em subproblemas (um para cada área) e um problema mestre (coordenador). A solução do problema decomposto é baseada na aplicação de programação linear sucessiva para a resolução dos subproblemas de planejamento de reativos de cada área, e o esquema de coordenação é baseado nos custos marginais de potência reativa nas barras de fronteiras. Desta forma, o problema de planejamento do sistema é resolvido usando a estratégia descentralizada por regiões ou por áreas, onde os operadores dos sistemas podem planejar a opera- ção e a expansão de seus sistemas, independentemente das outras áreas, obtendo uma solução ótima coordenada, porém descentralizada de cada área. O objetivo do modelo é proporcionar mecanismos para realizar o planejamento preservando a autonomia e confidencialidade para cada área, garantindo a economia global do sistema multi-área completo. Utilizando-se o modelo matemático e a imple- mentação computacional da metodologia proposta, apresentam-se resultados, análises e discussões de testes efetuados em 3 sistemas de 3 áreas, onde cada uma das áreas é composta por 3 sistemas iguais formados pelos sistemas IEEE30, IEEE118 e IEEE300 / In this thesis presents a methodology for solving the optimal reactive power planning problem in inter- conected multi-area electric power systems, using the Dantzig-Wolfe technique. The original multi- area problem is separated into subproblems (one for each area) and a master problem (coordinator). The solution of the decomposed problem is based on the application of sucessive linear programming for solving the reactive planning subproblems in each area, and the coordination scheme is based on the reactive power marginal costs in the border bus. Thus the planning problem system is solved using a descentralized approach by regions or areas, where de transmission system operator in each area can planning the operation and expansion of its system regardless of the other areas, obtaining a optimal solution coordinated by descentralized in each area. The purpose of the mathematical model is to provide mechanism for develope the planning preserving the autonomy and confidentiality for each area, ensuring the economy of the overal multi-area full system. Using the mathematical model and computational implementation of the methodology proposed results are presented analisys and discussion of testes performed on three systems in three areas where each area is composed of three equal systems formed by IEEE30, IEEE118, and IEEE300 bus system

There are many real cases where a company needs to determine the price of its products so as to maximise its revenue or profit.<p>To do so, the company must consider customers' reactions to these prices, as they may refuse to buy a given product or service if its price is too high. This is commonly known in literature as a pricing problem.<p>This class of problems, which is typically bilevel, was first studied in the 1990s and is NP-hard, although polynomial algorithms do exist for some particular cases. Many questions are still open on this subject.<p><p>The aim of this thesis is to investigate mathematical properties of pricing problems, in order to find structural properties, formulations and solution methods that are as efficient as possible. In particular, we focus our attention on pricing problems over a network. In this framework, an authority owns a subset of arcs and imposes tolls on them, in an attempt to maximise his/her revenue, while users travel on the network, seeking for their minimum cost path.<p><p>First, we provide a detailed review of the state of the art on bilevel pricing problems. <p>Then, we consider a particular case where the authority is using an unit toll scheme on his/her subset of arcs, imposing either the same toll on all of them, or a toll proportional to a given parameter particular to each arc (for instance a per kilometre toll). We show that if tolls are all equal then the complexity of the problem is polynomial, whereas in case of proportional tolls it is pseudo-polynomial.<p>We then address a robust approach taking into account uncertainty on parameters. We solve some polynomial cases of the pricing problem where uncertainty is considered using an interval representation.<p><p>Finally, we focus on another particular case where toll arcs are connected such that they constitute a path, as occurs on highways. We develop a Dantzig-Wolfe reformulation and present a Branch-and-Cut-and-Price algorithm to solve it. Several improvements are proposed, both for the column generation algorithm used to solve the linear relaxation and for the branching part used to find integer solutions. Numerical results are also presented to highlight the efficiency of the proposed strategies. This problem is proved to be APX-hard and a theoretical comparison between our model and another one from the literature is carried out. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished