Modelo matemático para o controle ótimo de Volt/VAr em sistemas de distribuição de energia elétrica trifásicos

Pós-graduação em Engenharia Elétrica - FEIS

Comparing lock-in ranges and transient responses of second- and third-order phase-locked loops in master-slave clock distribution networks

The distribution of clock signals throughout the nodes of a network is essential for several applications. in control and communication with the phase-locked loop (PLL) being the component for electronic synchronization process. In systems with master-slave (MS) strategies, the PLLs are the slave nodes responsible for providing reliable clocks in all nodes of the network. As PLLs have nonlinear phase detection, double-frequency terms appear and filtering becomes necessary. Imperfections in filtering process cause oscillations around the synchronous state worsening the performance of the clock distribution process. The behavior of one-way master-slave (OWMS) clock distribution networks is studied and performances of first- and second-order filter processes are compared, concerning lock-in ranges and responses to perturbations of the synchronous state. (c) 2007 Elsevier GmbH. All rights reserved.

Ecuaciones diferenciales estocásticas con condición final y soluciones de viscosidad de EDPS semilineales de segundo orden

El objetivo de este documento es recopilar algunos resultados clasicos sobre existencia y unicidad ´ de soluciones de ecuaciones diferenciales estocasticas (EDEs) con condici ´ on final (en ingl ´ es´ Backward stochastic differential equations) con particular enfasis en el caso de coeficientes mon ´ otonos, y su cone- ´ xion con soluciones de viscosidad de sistemas de ecuaciones diferenciales parciales (EDPs) parab ´ olicas ´ y el´ıpticas semilineales de segundo orden.

No evidence of UV cone input to mono- and biphasic horizontal cells in the goldfish retina

Many animal species make use of ultraviolet (UV) light in a number of behaviors, such as feeding and mating. The goldfish (Carassius auratus) is among those with a UV photoreceptor and pronounced UV sensitivity. Little is known, however, about the retinal processing of this input. We addressed this issue by recording intracellularly from second-order neurons in the adult goldfish retina. In order to test whether cone-driven horizontal cells (HCs) receive UV cone inputs, we performed chromatic adaptation experiments with mono- and biphasic HCs. We found no functional evidence of a projection from the UV-sensitive cones to these neurons in adult animals. This suggests that goldfish UV receptors may contact preferentially triphasic HCs, which is at odds with the hypothesis that all cones contact all cone-driven HC types. However, we did find evidence of direct M-cone input to monophasic HCs, favoring the idea that cone-HC contacts are more promiscuous than originally proposed. Together, our results suggest that either UV cones have a more restricted set of post-synaptic partners than the other three cone types, or that the UV input to mono- and biphasic HCs is not very pronounced in adult animals.

Horizontal cells reveal cone type-specific adaptation in primate retina

The human cone visual system maintains contrast sensitivity over a wide range of ambient illumination, a property known as light adaptation. The first stage in light adaptation is believed to take place at the first neural step in vision, within the long, middle, and short wavelength sensitive cone photoreceptors. To determine the properties of adaptation in primate outer retina, we measured cone signals in second-order interneurons, the horizontal cells, of the macaque monkey. Horizontal cells provide a unique site for studying early adaptational mechanisms; they are but one synapse away from the photoreceptors, and each horizontal cell receives excitatory inputs from many cones. Light adaptation occurred over the entire range of light levels evaluated, a luminance range of 15–1,850 trolands. Adaptation was demonstrated to be independent in each cone type and to be spatially restricted. Thus, in primates, a major source of sensitivity regulation occurs before summation of cone signals in the horizontal cell.

Liquid polymorphism, order-disorder transitions and anomalous behavior: A Monte Carlo study of the Bell-Lavis model for water

The Bell-Lavis model for liquid water is investigated through numerical simulations. The lattice-gas model on a triangular lattice presents orientational states and is known to present a highly bonded low density phase and a loosely bonded high density phase. We show that the model liquid-liquid transition is continuous, in contradiction with mean-field results on the Husimi cactus and from the cluster variational method. We define an order parameter which allows interpretation of the transition as an order-disorder transition of the bond network. Our results indicate that the order-disorder transition is in the Ising universality class. Previous proposal of an Ehrenfest second order transition is discarded. A detailed investigation of anomalous properties has also been undertaken. The line of density maxima in the HDL phase is stabilized by fluctuations, absent in the mean-field solution. (C) 2009 American Institute of Physics. [doi:10.1063/1.3253297]

Design constraints for third-order PLL nodes in master-slave clock distribution networks

Clock signal distribution in telecommunication commercial systems usually adopts a master-slave architecture, with a precise time basis generator as a master and phase-locked loops (PLLs) as slaves. In the majority of the networks, second-order PLLs are adopted due to their simplicity and stability. Nevertheless, in some applications better transient responses are necessary and, consequently, greater order PLLs need to be used, in spite of the possibility of bifurcations and chaotic attractors. Here a master-slave network with third-order PLLs is analyzed and conditions for the stability of the synchronous state are derived, providing design constraints for the node parameters, in order to guarantee stability and reachability of the synchronous state for the whole network. Numerical simulations are carried out in order to confirm the analytical results. (C) 2009 Elsevier B.V. All rights reserved.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

GNSS signal detection based on first-order absolute statistics

Aquest projecte es centra principalment en el detector no coherent d’un GPS. Per tal de caracteritzar el procés de detecció d’un receptor, es necessita conèixer l’estadística implicada. Pel cas dels detectors no coherents convencionals, l’estadística de segon ordre intervé plenament. Les prestacions que ens dóna l’estadística de segon ordre, plasmada en la ROC, són prou bons tot i que en diferents situacions poden no ser els millors. Aquest projecte intenta reproduir el procés de detecció mitjançant l’estadística de primer ordre com a alternativa a la ja coneguda i implementada estadística de segon ordre. Per tal d’aconseguir-ho, s’usen expressions basades en el Teorema Central del Límit i de les sèries Edgeworth com a bones aproximacions. Finalment, tant l’estadística convencional com l’estadística proposada són comparades, en termes de la ROC, per tal de determinar quin detector no coherent ofereix millor prestacions en cada situació.

A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

Support Vector Machines: Training and Applications

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.