Primal-dual logarithmic barrier and augmented Lagrangian function to the loss minimization in power systems

This article presents a new approach to minimize the losses in electrical power systems. This approach considers the application of the primal-dual logarithmic barrier method to voltage magnitude and tap-changing transformer variables, and the other inequality constraints are treated by augmented Lagrangian method. The Lagrangian function aggregates all the constraints. The first-order necessary conditions are reached by Newton's method, and by updating the dual variables and penalty factors. Test results are presented to show the good performance of this approach.

An adaptation of the dual-affine interior point method for the surface flatness problem

This paper presents an adaptation of the dual-affine interior point method for the surface flatness problem. In order to determine how flat a surface is, one should find two parallel planes so that the surface is between them and they are as close together as possible. This problem is equivalent to the problem of solving inconsistent linear systems in terms of Tchebyshev's norm. An algorithm is proposed and results are presented and compared with others published in the literature. (C) 2006 Elsevier B.V. All rights reserved.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

Integration of a regional GPS network within ITRF using precise point positioning

GPS precise point positioning (PPP) can provide high precision 3-D coordinates. Combined pseudorange and carrier phase observables, precise ephemeris and satellite clock corrections, together with data from dual frequency receivers, are the key factors for providing such levels of precision (few centimeters). In general, results obtained from PPP are referenced to an arbitrary reference frame, realized from a previous free network adjustment, in which satellite state vectors, station coordinates and other biases are estimated together. In order to obtain consistent results, the coordinates have to be transformed to the relevant reference frame and the appropriate daily transformation parameters must be available. Furthermore, the coordinates have to be mapped to a chosen reference epoch. If a velocity field is not available, an appropriated model, such as NNR-NUVEL-IA, has to be used. The quality of the results provided by this approach was evaluated using data from the Brazilian Network for Continuous Monitoring of the Global Positioning System (RBMC), which was processed using GIPSY-OASIS 11 software. The results obtained were compared to SIRGAS 1995.4 and ITRF2000, and reached precision better than 2cm. A description of the fundamentals of the PPP approach and its application in the integration of regional GPS networks with ITRF is the main purpose of this paper.

Interior point method for long-term generation scheduling of large-scale hydrothermal systems

This paper presents an interior point method for the long-term generation scheduling of large-scale hydrothermal systems. The problem is formulated as a nonlinear programming one due to the nonlinear representation of hydropower production and thermal fuel cost functions. Sparsity exploitation techniques and an heuristic procedure for computing the interior point method search directions have been developed. Numerical tests in case studies with systems of different dimensions and inflow scenarios have been carried out in order to evaluate the proposed method. Three systems were tested, with the largest being the Brazilian hydropower system with 74 hydro plants distributed in several cascades. Results show that the proposed method is an efficient and robust tool for solving the long-term generation scheduling problem.

Investigação e aplicação de métodos primal - dual pontos interiores em problemas de despacho econômico e ambiental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Método primal-dual de pontos interiores aplicado ao problema de despacho econômico e ambiental

Este artigo traz os resultados obtidos através do estudo e da aplicação do Método Primal-Dual Previsor-Corretor de Pontos Interiores para Problema de Programação Quadr´atica convexa a um Problema de Despacho Econômico (PDE) e a um Problema Multiobjetivo de Despacho Econômico e Ambiental (DEA). O primeiro problema busca determinar a solução ótima aproximada, minimizando os custos dos combustíveis empregados na geração termoelétrica de energia e satisfazendo as restrições operacionais. Já o segundo é solucionado através do Método da Soma Ponderada, que apresenta um balanceamento entre o problema de otimização dos custos e o problema de emissão de poluentes. Ao final do artigo, um algoritmo para cada problema é proposto e implementado computacionalmente utilizando o software Borland C++ Builder 6.0. Os testes foram realizados utilizando um PDE de 13 geradores e um DEA de 06 geradores e os resultados obtidos demonstram a eficiˆencia dos m´etodos quando comparados a outros encontrados na literatura.

A framework for building distributed social network websites

Las redes son la esencia de comunidades y sociedades humanas; constituyen el entramado en el que nos relacionamos y determinan cómo lo hacemos, cómo se disemina la información o incluso cómo las cosas se llevan a cabo. Pero el protagonismo de las redes va más allá del que adquiere en las redes sociales. Se encuentran en el seno de múltiples estructuras que conocemos, desde las interaciones entre las proteínas dentro de una célula hasta la interconexión de los routers de internet. Las redes sociales están presentes en internet desde sus principios, en el correo electrónico por tomar un ejemplo. Dentro de cada cliente de correo se manejan listas contactos que agregadas constituyen una red social. Sin embargo, ha sido con la aparición de los sitios web de redes sociales cuando este tipo de aplicaciones web han llegado a la conciencia general. Las redes sociales se han situado entre los sitios más populares y con más tráfico de la web. Páginas como Facebook o Twitter manejan cifras asombrosas en cuanto a número de usuarios activos, de tráfico o de tiempo invertido en el sitio. Pero las funcionalidades de red social no están restringidas a las redes sociales orientadas a contactos, aquellas enfocadas a construir tu lista de contactos e interactuar con ellos. Existen otros ejemplos de sitios que aprovechan las redes sociales para aumentar la actividad de los usuarios y su involucración alrededor de algún tipo de contenido. Estos ejemplos van desde una de las redes sociales más antiguas, Flickr, orientada al intercambio de fotografías, hasta Github, la red social de código libre más popular hoy en día. No es una casualidad que la popularidad de estos sitios web venga de la mano de sus funcionalidades de red social. El escenario es más rico aún, ya que los sitios de redes sociales interaccionan entre ellos, compartiendo y exportando listas de contactos, servicios de autenticación y proporcionando un valioso canal para publicitar la actividad de los usuarios en otros sitios web. Esta funcionalidad es reciente y aún les queda un paso hasta que las redes sociales superen su condición de bunkers y lleguen a un estado de verdadera interoperabilidad entre ellas, tal como funcionan hoy en día el correo electrónico o la mensajería instantánea. Este trabajo muestra una tecnología que permite construir sitios web con características de red social distribuída. En primer lugar, se presenta una tecnología para la construcción de un componente intermedio que permite proporcionar cualquier característica de gestión de contenidos al popular marco de desarrollo web modelo-vista-controlador (MVC) Ruby on Rails. Esta técnica constituye una herramienta para desarrolladores que les permita abstraerse de las complejidades de la gestión de contenidos y enfocarse en las particularidades de los propios contenidos. Esta técnica se usará también para proporcionar las características de red social. Se describe una nueva métrica de reusabilidad de código para demostrar la validez del componente intermedio en marcos MVC. En segundo lugar, se analizan las características de los sitios web de redes sociales más populares, con el objetivo de encontrar los patrones comunes que aparecen en ellos. Este análisis servirá como base para definir los requisitos que debe cumplir un marco para construir redes sociales. A continuación se propone una arquitectura de referencia que proporcione este tipo de características. Dicha arquitectura ha sido implementada en un componente, Social Stream, y probada en varias redes sociales, tanto orientadas a contactos como a contenido, en el contexto de una asociación vecinal tanto como en proyectos de investigación financiados por la UE. Ha sido la base de varios proyectos fin de carrera. Además, ha sido publicado como código libre, obteniendo una comunidad creciente y está siendo usado más allá del ámbito de este trabajo. Dicha arquitectura ha permitido la definición de un nuevo modelo de control de acceso social que supera varias limitaciones presentes en los modelos de control de acceso para redes sociales. Más aún, se han analizado casos de estudio de sitios de red social distribuídos, reuniendo un conjunto de caraterísticas que debe cumplir un marco para construir redes sociales distribuídas. Por último, se ha extendido la arquitectura del marco para dar cabida a las características de redes sociales distribuídas. Su implementación ha sido validada en proyectos de investigación financiados por la UE. Abstract Networks are the substance of human communities and societies; they constitute the structural framework on which we relate to each other and determine the way we do it, the way information is diseminated or even the way people get things done. But network prominence goes beyond the importance it acquires in social networks. Networks are found within numerous known structures, from protein interactions inside a cell to router connections on the internet. Social networks are present on the internet since its beginnings, in emails for example. Inside every email client, there are contact lists that added together constitute a social network. However, it has been with the emergence of social network sites (SNS) when these kinds of web applications have reached general awareness. SNS are now among the most popular sites in the web and with the higher traffic. Sites such as Facebook and Twitter hold astonishing figures of active users, traffic and time invested into the sites. Nevertheless, SNS functionalities are not restricted to contact-oriented social networks, those that are focused on building your own list of contacts and interacting with them. There are other examples of sites that leverage social networking to foster user activity and engagement around other types of content. Examples go from early SNS such as Flickr, the photography related networking site, to Github, the most popular social network repository nowadays. It is not an accident that the popularity of these websites comes hand-in-hand with their social network capabilities The scenario is even richer, due to the fact that SNS interact with each other, sharing and exporting contact lists and authentication as well as providing a valuable channel to publize user activity in other sites. These interactions are very recent and they are still finding their way to the point where SNS overcome their condition of data silos to a stage of full interoperability between sites, in the same way email and instant messaging networks work today. This work introduces a technology that allows to rapidly build any kind of distributed social network website. It first introduces a new technique to create middleware that can provide any kind of content management feature to a popular model-view-controller (MVC) web development framework, Ruby on Rails. It provides developers with tools that allow them to abstract from the complexities related with content management and focus on the development of specific content. This same technique is also used to provide the framework with social network features. Additionally, it describes a new metric of code reuse to assert the validity of the kind of middleware that is emerging in MVC frameworks. Secondly, the characteristics of top popular SNS are analysed in order to find the common patterns shown in them. This analysis is the ground for defining the requirements of a framework for building social network websites. Next, a reference architecture for supporting the features found in the analysis is proposed. This architecture has been implemented in a software component, called Social Stream, and tested in several social networks, both contact- and content-oriented, in local neighbourhood associations and EU-founded research projects. It has also been the ground for several Master’s theses. It has been released as a free and open source software that has obtained a growing community and that is now being used beyond the scope of this work. The social architecture has enabled the definition of a new social-based access control model that overcomes some of the limitations currenly present in access control models for social networks. Furthermore, paradigms and case studies in distributed SNS have been analysed, gathering a set of features for distributed social networking. Finally the architecture of the framework has been extended to support distributed SNS capabilities. Its implementation has also been validated in EU-founded research projects.

Transmission loss allocation based on optimal power flow and sensitivity analysis

This paper presents a new approach to the transmission loss allocation problem in a deregulated system. This approach belongs to the set of incremental methods. It treats all the constraints of the network, i.e. control, state and functional constraints. The approach is based on the perturbation of optimum theorem. From a given optimal operating point obtained by the optimal power flow the loads are perturbed and a new optimal operating point that satisfies the constraints is determined by the sensibility analysis. This solution is used to obtain the allocation coefficients of the losses for the generators and loads of the network. Numerical results show the proposed approach in comparison to other methods obtained with well-known transmission networks, IEEE 14-bus. Other test emphasizes the importance of considering the operational constraints of the network. And finally the approach is applied to an actual Brazilian equivalent network composed of 787 buses, and it is compared with the technique used nowadays by the Brazilian Control Center. (c) 2007 Elsevier Ltd. All rights reserved.

Distributed Estimation Over an Adaptive Incremental Network Based on the Affine Projection Algorithm

We study the problem of distributed estimation based on the affine projection algorithm (APA), which is developed from Newton`s method for minimizing a cost function. The proposed solution is formulated to ameliorate the limited convergence properties of least-mean-square (LMS) type distributed adaptive filters with colored inputs. The analysis of transient and steady-state performances at each individual node within the network is developed by using a weighted spatial-temporal energy conservation relation and confirmed by computer simulations. The simulation results also verify that the proposed algorithm provides not only a faster convergence rate but also an improved steady-state performance as compared to an LMS-based scheme. In addition, the new approach attains an acceptable misadjustment performance with lower computational and memory cost, provided the number of regressor vectors and filter length parameters are appropriately chosen, as compared to a distributed recursive-least-squares (RLS) based method.

Restless bandits, linear programming relaxations and a primal-dual index heuristic

We develop a mathematical programming approach for the classicalPSPACE - hard restless bandit problem in stochastic optimization.We introduce a hierarchy of n (where n is the number of bandits)increasingly stronger linear programming relaxations, the lastof which is exact and corresponds to the (exponential size)formulation of the problem as a Markov decision chain, while theother relaxations provide bounds and are efficiently computed. Wealso propose a priority-index heuristic scheduling policy fromthe solution to the first-order relaxation, where the indices aredefined in terms of optimal dual variables. In this way wepropose a policy and a suboptimality guarantee. We report resultsof computational experiments that suggest that the proposedheuristic policy is nearly optimal. Moreover, the second-orderrelaxation is found to provide strong bounds on the optimalvalue.

Implementation of an interior point source in the ultra weak variational formulation through source extraction

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftz-type basis functions incorporates the known wave-like behaviour of the solution in the discrete space, allowing large reductions in the required number of degrees of freedom for a given accuracy, when compared to standard finite element methods. However, the UWVF is not well disposed to the accurate approximation of singular sources in the interior of the computational domain. We propose an adjustment to the UWVF for seismic imaging applications, which we call the Source Extraction UWVF. Differing fields are solved for in subdomains around the source, and matched on the inter-domain boundaries. Numerical results are presented for a domain of constant wavenumber and for a domain of varying sound speed in a model used for seismic imaging.

Um método primal-dual aplicado na resolução do problema de fluxo de potência ótimo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method

We present a novel approach to the reconstruction of depth from light field data. Our method uses dictionary representations and group sparsity constraints to derive a convex formulation. Although our solution results in an increase of the problem dimensionality, we keep numerical complexity at bay by restricting the space of solutions and by exploiting an efficient Primal-Dual formulation. Comparisons with state of the art techniques, on both synthetic and real data, show promising performances.

Using interior point algorithms for the solution of linear programs with special structural features

Linear Programming (LP) is a powerful decision making tool extensively used in various economic and engineering activities. In the early stages the success of LP was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is reported here. The preconditional conjugate gradient method is one of the most powerful tools for the solution of the least square problem, present in every iteration of all interior point methods. The effect of using different preconditioners on a range of problems with various condition numbers is presented. Decomposition algorithms has been one of the main fields of research in linear programming over the last few years. After reviewing the latest decomposition techniques, three promising methods were chosen the implemented. Sparsity is again a consideration and suggestions have been included to allow improvements when solving problems with these methods. Finally, experimental results on randomly generated data are reported and compared with an interior point method. The efficient implementation of the decomposition methods considered in this study requires the solution of quadratic subproblems. A review of recent work on algorithms for convex quadratic was performed. The most promising algorithms are discussed and implemented taking sparsity into account. The related performance of these algorithms on randomly generated separable and non-separable problems is also reported.