Mathematical decomposition technique applied to the probabilistic power flow problem

In this paper a framework based on the decomposition of the first-order optimality conditions is described and applied to solve the Probabilistic Power Flow (PPF) problem in a coordinated but decentralized way in the context of multi-area power systems. The purpose of the decomposition framework is to solve the problem through a process of solving smaller subproblems, associated with each area of the power system, iteratively. This strategy allows the probabilistic analysis of the variables of interest, in a particular area, without explicit knowledge of network data of the other interconnected areas, being only necessary to exchange border information related to the tie-lines between areas. An efficient method for probabilistic analysis, considering uncertainty in n system loads, is applied. The proposal is to use a particular case of the point estimate method, known as Two-Point Estimate Method (TPM), rather than the traditional approach based on Monte Carlo simulation. The main feature of the TPM is that it only requires resolve 2n power flows for to obtain the behavior of any random variable. An iterative coordination algorithm between areas is also presented. This algorithm solves the Multi-Area PPF problem in a decentralized way, ensures the independent operation of each area and integrates the decomposition framework and the TPM appropriately. The IEEE RTS-96 system is used in order to show the operation and effectiveness of the proposed approach and the Monte Carlo simulations are used to validation of the results. © 2011 IEEE.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.

Efficient PGD-based dynamic calculation of non-linear soil behavior

Non-linear behavior of soils during a seismic event has a predominant role in current site response analysis. Soil response analysis consistently indicates that the stress-strain relationship of soils is nonlinear and shows hysteresis. When focusing in forced response simulations, time integrations based on modal analysis are widely considered, however parametric analysis, non-linear behavior and complex damping functions make difficult the online use of standard discretization strategies, e.g. those based on the use of finite element. In this paper we propose a new harmonic analysis formulation, able to address forced response simulation of soils exhibiting their characteristic nonlinear behavior. The solution can be evaluated in real-time from the offline construction of a parametric solution of the associated linearized problem within the Proper Generalized Decomposition framework.

Tail gas catalyzed N2O decomposition over Fe-beta zeolite. On the promoting role of framework connected AlO6 sites in the vicinity of Fe by controlled dealumination during exchange

A novel route to prepare highly active and stable N2O decomposition catalysts is presented, based on Fe-exchanged beta zeolite. The procedure consists of liquid phase Fe(III) exchange at low pH. By varying the pH systematically from 3.5 to 0, using nitric acid during each Fe(III)-exchange procedure, the degree of dealumination was controlled, verified by ICP and NMR. Dealumination changes the presence of neighbouring octahedral Al sites of the Fe sites, improving the performance for this reaction. The so-obtained catalysts exhibit a remarkable enhancement in activity, for an optimal pH of 1. Further optimization by increasing the Fe content is possible. The optimal formulation showed good conversion levels, comparable to a benchmark Fe-ferrierite catalyst. The catalyst stability under tail gas conditions containing NO, O2 and H2O was excellent, without any appreciable activity decay during 70 h time on stream. Based on characterisation and data analysis from ICP, single pulse excitation NMR, MQ MAS NMR, N2 physisorption, TPR(H2) analysis and apparent activation energies, the improved catalytic performance is attributed to an increased concentration of active sites. Temperature programmed reduction experiments reveal significant changes in the Fe(III) reducibility pattern with the presence of two reduction peaks; tentatively attributed to the interaction of the Fe-oxo species with electron withdrawing extraframework AlO6 species, causing a delayed reduction. A low-temperature peak is attributed to Fe-species exchanged on zeolitic AlO4 sites, which are partially charged by the presence of the neighbouring extraframework AlO6 sites. Improved mass transport phenomena due to acid leaching is ruled out. The increased activity is rationalized by an active site model, whose concentration increases by selectively washing out the distorted extraframework AlO6 species under acidic (optimal) conditions, liberating active Fe species.

Autonomic workflow activities: the award framework

Workflows have been successfully applied to express the decomposition of complex scientific applications. This has motivated many initiatives that have been developing scientific workflow tools. However the existing tools still lack adequate support to important aspects namely, decoupling the enactment engine from workflow tasks specification, decentralizing the control of workflow activities, and allowing their tasks to run autonomous in distributed infrastructures, for instance on Clouds. Furthermore many workflow tools only support the execution of Direct Acyclic Graphs (DAG) without the concept of iterations, where activities are executed millions of iterations during long periods of time and supporting dynamic workflow reconfigurations after certain iteration. We present the AWARD (Autonomic Workflow Activities Reconfigurable and Dynamic) model of computation, based on the Process Networks model, where the workflow activities (AWA) are autonomic processes with independent control that can run in parallel on distributed infrastructures, e. g. on Clouds. Each AWA executes a Task developed as a Java class that implements a generic interface allowing end-users to code their applications without concerns for low-level details. The data-driven coordination of AWA interactions is based on a shared tuple space that also enables support to dynamic workflow reconfiguration and monitoring of the execution of workflows. We describe how AWARD supports dynamic reconfiguration and discuss typical workflow reconfiguration scenarios. For evaluation we describe experimental results of AWARD workflow executions in several application scenarios, mapped to a small dedicated cluster and the Amazon (Elastic Computing EC2) Cloud.

Autonomic Activities in the Execution of Scientific Workflows: Evaluation of the AWARD Framework

Workflows have been successfully applied to express the decomposition of complex scientific applications. However the existing tools still lack adequate support to important aspects namely, decoupling the enactment engine from tasks specification, decentralizing the control of workflow activities allowing their tasks to run in distributed infrastructures, and supporting dynamic workflow reconfigurations. We present the AWARD (Autonomic Workflow Activities Reconfigurable and Dynamic) model of computation, based on Process Networks, where the workflow activities (AWA) are autonomic processes with independent control that can run in parallel on distributed infrastructures. Each AWA executes a task developed as a Java class with a generic interface allowing end-users to code their applications without low-level details. The data-driven coordination of AWA interactions is based on a shared tuple space that also enables dynamic workflow reconfiguration. For evaluation we describe experimental results of AWARD workflow executions in several application scenarios, mapped to the Amazon (Elastic Computing EC2) Cloud.

A system’s approach to cache hierarchy-aware decomposition of data-parallel computations

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Towards an algorithmic skeleton framework for programming the Intel R Xeon PhiTM processor

The Intel R Xeon PhiTM is the first processor based on Intel’s MIC (Many Integrated Cores) architecture. It is a co-processor specially tailored for data-parallel computations, whose basic architectural design is similar to the ones of GPUs (Graphics Processing Units), leveraging the use of many integrated low computational cores to perform parallel computations. The main novelty of the MIC architecture, relatively to GPUs, is its compatibility with the Intel x86 architecture. This enables the use of many of the tools commonly available for the parallel programming of x86-based architectures, which may lead to a smaller learning curve. However, programming the Xeon Phi still entails aspects intrinsic to accelerator-based computing, in general, and to the MIC architecture, in particular. In this thesis we advocate the use of algorithmic skeletons for programming the Xeon Phi. Algorithmic skeletons abstract the complexity inherent to parallel programming, hiding details such as resource management, parallel decomposition, inter-execution flow communication, thus removing these concerns from the programmer’s mind. In this context, the goal of the thesis is to lay the foundations for the development of a simple but powerful and efficient skeleton framework for the programming of the Xeon Phi processor. For this purpose we build upon Marrow, an existing framework for the orchestration of OpenCLTM computations in multi-GPU and CPU environments. We extend Marrow to execute both OpenCL and C++ parallel computations on the Xeon Phi. We evaluate the newly developed framework, several well-known benchmarks, like Saxpy and N-Body, will be used to compare, not only its performance to the existing framework when executing on the co-processor, but also to assess the performance on the Xeon Phi versus a multi-GPU environment.

Disentangling water usage in the European Union: A decomposition analysis

The Water Framework Directive (WFD) defines common objectives for water resources throughout the European Union (EU). Given this general approach to water preservation and water policy, the objective of this paper is to analyse whether common patterns of water consumption exist within Europe. In particular, our study uses two methods to reveal the reasons behind sectoral water use in all EU countries. The first method is based on an accounting indicator that calculates the water intensity of an economy as the sum of sectoral water intensities. The second method is a subsystem input‐output model that divides total water use into different income channels within the production system. The application uses data for the years 2005 and 2009 on water consumption in the production system of the 27 countries of the EU. From our analysis it emerges that EU countries are characterized by very different patterns of water consumption. In particular water consumption by the agriculture sector is extremely high in Central/Eastern Europe, relative to the rest of Europe. In most countries, the water used by the fuel, power and water sector is consumed to satisfy domestic final demand. However, our analysis shows that for some countries exports from this sector are an important driver of water consumption. Focusing on the agricultural sector, the decomposition analysis suggests that water usage in Mediterranean countries is mainly driven by final demand for, and exports of, agricultural products. In Central/Eastern Europe domestic final demand is the main driver of water consumption, but in this region the proportion of water use driven by demand for exports is increasing over time. Given these heterogeneous water consumption patterns, our analysis suggests that Mediterranean and Central/Eastern European countries should adopt specific water policies in order to achieve efficient levels of water consumption in the European Union. JEL codes: N5; C67 Keywords: Water use, Subsystem input–output model; Water intensity, European Union.

A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition

Transient neural assemblies mediated by synchrony in particular frequency ranges are thought to underlie cognition. We propose a new approach to their detection, using empirical mode decomposition (EMD), a data-driven approach removing the need for arbitrary bandpass filter cut-offs. Phase locking is sought between modes. We explore the features of EMD, including making a quantitative assessment of its ability to preserve phase content of signals, and proceed to develop a statistical framework with which to assess synchrony episodes. Furthermore, we propose a new approach to ensure signal decomposition using EMD. We adapt the Hilbert spectrum to a time-frequency representation of phase locking and are able to locate synchrony successfully in time and frequency between synthetic signals reminiscent of EEG. We compare our approach, which we call EMD phase locking analysis (EMDPL) with existing methods and show it to offer improved time-frequency localisation of synchrony.

Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

Effect of cationic micelles on the decomposition of alpha-aminophenyl cephalosporins

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

Thermal decomposition of crystalline Ni-II-Cr-III layered double hydroxide: A structural study of the segregation process

A structural study of the thermal evolution of Ni0.69Cr0.31(OH)(2)(CO3)(0.155)(.)nH(2)O into NiO and tetragonal NiCr2O4 is reported. The characteristic structural parameters of the two coexisting crystalline phases, as well as their relative abundance, were determined by Rietveld refinement of powder x-ray diffraction (PXRD) patterns. The results of the simulations allowed us to elucidate the mechanism of the demixing process of the oxides. It is demonstrated that nucleation of a metastable nickel chromite within the common oxygen framework of the parent Cr-III-doped bunsenite is the initial step of the cationic redistribution. The role that trivalent cations play in the segregation of crystalline spinels is also discussed.

Harmonic, reactive and unbalance compensation by means of CPT framework

This paper presents possible selective current compensation strategies based on the Conservative Power Theory (CPT). This recently proposed theory, introduces the concept of complex power conservation under non-sinusoidal conditions. Moreover, the related current decompositions results in several current terms, which are associated with a specific physical phenomena (power absorption P, energy storage Q, voltage and current distortion D). Such current components are used in this work for the definition of different current compensators, which can be selective in terms of minimizing particular disturbing effects. The choice of one or other current component for compensation directly affects the sizing and cost of active and/or passive devices and it will be demonstrated that it can be done to attend predefined limits for harmonic distortion, unbalances and/or power factor. Single and three-phase compensation strategies will be discussed by means of the CPT Framework. Simulation and experimental results will be demonstrated in order to validate their performance. © 2009 IEEE.

Decomposition and reformulation of integer linear programming problems

This thesis deals with an investigation of Decomposition and Reformulation to solve Integer Linear Programming Problems. This method is often a very successful approach computationally, producing high-quality solutions for well-structured combinatorial optimization problems like vehicle routing, cutting stock, p-median and generalized assignment . However, until now the method has always been tailored to the specific problem under investigation. The principal innovation of this thesis is to develop a new framework able to apply this concept to a generic MIP problem. The new approach is thus capable of auto-decomposition and autoreformulation of the input problem applicable as a resolving black box algorithm and works as a complement and alternative to the normal resolving techniques. The idea of Decomposing and Reformulating (usually called in literature Dantzig and Wolfe Decomposition DWD) is, given a MIP, to convexify one (or more) subset(s) of constraints (slaves) and working on the partially convexified polyhedron(s) obtained. For a given MIP several decompositions can be defined depending from what sets of constraints we want to convexify. In this thesis we mainly reformulate MIPs using two sets of variables: the original variables and the extended variables (representing the exponential extreme points). The master constraints consist of the original constraints not included in any slaves plus the convexity constraint(s) and the linking constraints(ensuring that each original variable can be viewed as linear combination of extreme points of the slaves). The solution procedure consists of iteratively solving the reformulated MIP (master) and checking (pricing) if a variable of reduced costs exists, and in which case adding it to the master and solving it again (columns generation), or otherwise stopping the procedure. The advantage of using DWD is that the reformulated relaxation gives bounds stronger than the original LP relaxation, in addition it can be incorporated in a Branch and bound scheme (Branch and Price) in order to solve the problem to optimality. If the computational time for the pricing problem is reasonable this leads in practice to a stronger speed up in the solution time, specially when the convex hull of the slaves is easy to compute, usually because of its special structure.