Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

Orthogonal packing of identical rectangles within isotropic convex regions

A mixed integer continuous nonlinear model and a solution method for the problem of orthogonally packing identical rectangles within an arbitrary convex region are introduced in the present work. The convex region is assumed to be made of an isotropic material in such a way that arbitrary rotations of the items, preserving the orthogonality constraint, are allowed. The solution method is based on a combination of branch and bound and active-set strategies for bound-constrained minimization of smooth functions. Numerical results show the reliability of the presented approach. (C) 2010 Elsevier Ltd. All rights reserved.

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.

Loss minimization by the predictor-corrector modified barrier approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analysis of the Coupled Stretching-Bending Problem of Stiffened Plates by a BEM Formulation Based on Reissner's Hypothesis

In this work, the plate bending formulation of the boundary element method - BEM, based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.

Open and Standardized Resources for Smart Transducer Networking

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The STATFLUX code: a statistical method for calculation of flow and set of parameters, based on the Multiple-Compartment Biokinetical Model

The code STATFLUX, implementing a new and simple statistical procedure for the calculation of transfer coefficients in radionuclide transport to animals and plants, is proposed. The method is based on the general multiple-compartment model, which uses a system of linear equations involving geometrical volume considerations. Flow parameters were estimated by employing two different least-squares procedures: Derivative and Gauss-Marquardt methods, with the available experimental data of radionuclide concentrations as the input functions of time. The solution of the inverse problem, which relates a given set of flow parameter with the time evolution of concentration functions, is achieved via a Monte Carlo Simulation procedure.Program summaryTitle of program: STATFLUXCatalogue identifier: ADYS_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYS_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputer for which the program is designed and others on which it has been tested: Micro-computer with Intel Pentium III, 3.0 GHzInstallation: Laboratory of Linear Accelerator, Department of Experimental Physics, University of São Paulo, BrazilOperating system: Windows 2000 and Windows XPProgramming language used: Fortran-77 as implemented in Microsoft Fortran 4.0. NOTE: Microsoft Fortran includes non-standard features which are used in this program. Standard Fortran compilers such as, g77, f77, ifort and NAG95, are not able to compile the code and therefore it has not been possible for the CPC Program Library to test the program.Memory, required to execute with typical data: 8 Mbytes of RAM memory and 100 MB of Hard disk memoryNo. of bits in a word: 16No. of lines in distributed program, including test data, etc.: 6912No. of bytes in distributed Program, including test data, etc.: 229 541Distribution format: tar.gzNature of the physical problem: the investigation of transport mechanisms for radioactive substances, through environmental pathways, is very important for radiological protection of populations. One such pathway, associated with the food chain, is the grass-animal-man sequence. The distribution of trace elements in humans and laboratory animals has been intensively studied over the past 60 years [R.C. Pendlenton, C.W. Mays, R.D. Lloyd, A.L. Brooks, Differential accumulation of iodine-131 from local fallout in people and milk, Health Phys. 9 (1963) 1253-1262]. In addition, investigations on the incidence of cancer in humans, and a possible causal relationship to radioactive fallout, have been undertaken [E.S. Weiss, M.L. Rallison, W.T. London, W.T. Carlyle Thompson, Thyroid nodularity in southwestern Utah school children exposed to fallout radiation, Amer. J. Public Health 61 (1971) 241-249; M.L. Rallison, B.M. Dobyns, F.R. Keating, J.E. Rall, F.H. Tyler, Thyroid diseases in children, Amer. J. Med. 56 (1974) 457-463; J.L. Lyon, M.R. Klauber, J.W. Gardner, K.S. Udall, Childhood leukemia associated with fallout from nuclear testing, N. Engl. J. Med. 300 (1979) 397-402]. From the pathways of entry of radionuclides in the human (or animal) body, ingestion is the most important because it is closely related to life-long alimentary (or dietary) habits. Those radionuclides which are able to enter the living cells by either metabolic or other processes give rise to localized doses which can be very high. The evaluation of these internally localized doses is of paramount importance for the assessment of radiobiological risks and radiological protection. The time behavior of trace concentration in organs is the principal input for prediction of internal doses after acute or chronic exposure. The General Multiple-Compartment Model (GMCM) is the powerful and more accepted method for biokinetical studies, which allows the calculation of concentration of trace elements in organs as a function of time, when the flow parameters of the model are known. However, few biokinetics data exist in the literature, and the determination of flow and transfer parameters by statistical fitting for each system is an open problem.Restriction on the complexity of the problem: This version of the code works with the constant volume approximation, which is valid for many situations where the biological half-live of a trace is lower than the volume rise time. Another restriction is related to the central flux model. The model considered in the code assumes that exist one central compartment (e.g., blood), that connect the flow with all compartments, and the flow between other compartments is not included.Typical running time: Depends on the choice for calculations. Using the Derivative Method the time is very short (a few minutes) for any number of compartments considered. When the Gauss-Marquardt iterative method is used the calculation time can be approximately 5-6 hours when similar to 15 compartments are considered. (C) 2006 Elsevier B.V. All rights reserved.

Reformulation of variational inequalities on a simplex and compactification of complementarity problems

Many variational inequality problems (VIPs) can be reduced, by a compactification procedure, to a VIP on the canonical simplex. Reformulations of this problem are studied, including smooth reformulations with simple constraints and unconstrained reformulations based on the penalized Fischer-Burmeister function. It is proved that bounded level set results hold for these reformulations under quite general assumptions on the operator. Therefore, it can be guaranteed that minimization algorithms generate bounded sequences and, under monotonicity conditions, these algorithms necessarily nd solutions of the original problem. Some numerical experiments are presented.

Optimal Contract Pricing of Distributed Generation in Distribution Networks

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Network reconfiguration and loss allocation in a deregulated environment of distribution systems

Low flexibility and reliability in the operation of radial distribution networks make those systems be constructed with extra equipment as sectionalising switches in order to reconfigure the network, so the operation quality of the network can be improved. Thus, sectionalising switches are used for fault isolation and for configuration management (reconfiguration). Moreover, distribution systems are being impacted by the increasing insertion of distributed generators. Hence, distributed generation became one of the relevant parameters in the evaluation of systems reconfiguration. Distributed generation may affect distribution networks operation in various ways, causing noticeable impacts depending on its location. Thus, the loss allocation problem becomes more important considering the possibility of open access to the distribution networks. In this work, a graphic simulator for distribution networks with reconfiguration and loss allocation functions, is presented. Reconfiguration problem is solved through a heuristic methodology, using a robust power flow algorithm based on the current summation backward-forward technique, considering distributed generation. Four different loss allocation methods (Zbus, Direct Loss Coefficient, Substitution and Marginal Loss Coefficient) are implemented and compared. Results for a 32-bus medium voltage distribution network, are presented and discussed.

A nonlinear model for the long-term hydro-thermal generation scheduling problem over multiple areas with transmission constraints

This paper presents a nonlinear model with individual representation of plants for the centralized long-term hydrothermal scheduling problem over multiple areas. In addition to common aspects of long-term scheduling, this model takes transmission constraints into account. The ability to optimize hydropower exchange among multiple areas is important because it enables further minimization of complementary thermal generation costs. Also, by considering transmission constraints for long-term scheduling, a more precise coupling with shorter horizon schedules can be expected. This is an important characteristic from both operational and economic viewpoints. The proposed model is solved by a sequential quadratic programming approach in the form of a prototype system for different case studies. An analysis of the benefits provided by the model is also presented. ©2009 IEEE.

Optimal contract pricing of distributed generation under a competitive framework

A bilevel programming approach for the optimal contract pricing of distributed generation (DG) in distribution networks is presented. The outer optimization problem corresponds to the owner of the DG who must decide the contract price that would maximize his profits. The inner optimization problem corresponds to the distribution company (DisCo), which procures the minimization of the payments incurred in attending the expected demand while satisfying network constraints. The meet the expected demand the DisCo can purchase energy either form the transmission network through the substations or form the DG units within its network. The inner optimization problem is substituted by its Karush- Kuhn-Tucker optimality conditions, turning the bilevel programming problem into an equivalent single-level nonlinear programming problem which is solved using commercially available software. © 2010 IEEE.

Open regionalism in Asia Pacific and Latin America: a survey of the literature

Includes bibliography

Science and technology policies in open economies: the case of Latin America and the Caribbean

Includes bibliography

Optimal allocation of distributed generators providing reactive power support ancillary service

Problems as voltage increase at the end of a feeder, demand supply unbalance in a fault condition, power quality decline, increase of power losses, and reduction of reliability levels may occur if Distributed Generators (DGs) are not properly allocated. For this reason, researchers have been employed several solution techniques to solve the problem of optimal allocation of DGs. This work is focused on the ancillary service of reactive power support provided by DGs. The main objective is to price this service by determining the costs in which a DG incurs when it loses sales opportunity of active power, i.e, by determining the Loss of Opportunity Costs (LOC). The LOC will be determined for different allocation alternatives of DGs as a result of a multi-objective optimization process, aiming the minimization of losses in the lines of the system and costs of active power generation from DGs, and the maximization of the static voltage stability margin of the system. The effectiveness of the proposed methodology in improving the goals outlined was demonstrated using the IEEE 34 bus distribution test feeder with two DGs cosidered to be allocated. © 2011 IEEE.