Non-convergence Problem Research Articles

Dual-loop iteration algorithm for steady-state determination of current-programmed dc/dc switching converters

The methodology starts with separating the gate signal from the feedback circuit to the power stage in order to convert a closed-loop configuration into an open-loop one. The first iteration loop applies the Newton's method together with a time-domain simulation technique to find the steady-state state variables when the transformed configuration is operating at a constant duty cycle. The second iteration loop is to find the steady-state duty cycle using the secant method. The algorithm includes all of the advantages of a previously developed time-domain simulation technique and solves the nonconvergence problem in the single-loop iteration method, due to the amplifying effect of poor guess values of the state variables on the duty cycle in the feedback path during the iteration. A current-programmed boost converter is illustrated. The performances of the single-loop and the proposed methods are compared. The theoretical results are verified with the experimental measurements.

Solution of a 3-D complex finite element model of skewed rotor induction motors using an iterative method

One of the difficulties of the three-dimensional (3-D) eddy current finite element methods is to solve large finite element equations economically. In this paper, a 3-D eddy-current finite element model using a four component formulation of complex variables to study skewed rotor induction motors is described. An iterative process among the four specific components during the solution of large algebraic equations is presented. The proposed method overcomes the nonconvergence problems when the ICCG method or the shifting ICCG method is used directly. The algorithm also requires much less computer storage compared with the Gaussian elimination method.

Steady-state analysis of PWM DC/DC switching regulators using iterative cycle time-domain simulation

A new iterative technique for the steady-state analysis of pulsewidth modulated (PWM) DC/DC switching regulators is presented. The methodology is based on transforming the closed-loop regulator into an open-loop configuration. The steady-state solution is solved by two iteration loops. The first loop is to find the steady-state state variables when the power converter is at a fixed duty cycle. The circuit waveforms are obtained by a stepwise time-domain simulation method, which is based on using stepwise quadratic formulation of the circuit state variables with progressive analysis of the switches' states. The second iteration loop is to determine the steady-state duty cycle of the PWM modulator output, using an explicit fictitious ramp offset value as the error index. This two-loop iteration approach lessens the occurrence of the nonconvergence problem that is sometimes found in the single-loop iteration method. Furthermore, the advantages of this method include the following: (1) substantial improvement in speeding up the convergence to steady-state solution; (2) simplicity in requiring simple algebraic manipulations; (3) generality in determining valid topology without prior knowledge of the regulator operation; and (4) directness in determining the switching instants. Several examples illustrating the computational efficiency and the accuracy are presented and are verified with the available literature.

Computational analysis of spinodal decomposition dynamics in polymer solutions

AbstractIn this work a model, composed of the nonlinear Cahn‐Hilliard and Flory‐Huggins theories, is used to numerically simulate the phase separation and pattern formation phenomena of oligomer and polymer solutions when quenched into the unstable region of their binary phase diagrams. This model takes into account the initial thermal concentration fluctuations. In addition, zero mass flux and natural nonperiodic boundary conditions are enforced to better reflect experimental conditions. The model output is used to characterize the evolution and morphology of the phase separation process. The sensitivity of the time and length scales to processing conditions (initial condition c) and properties (dimensionless diffusion coefficient D) is elucidated. The results replicate frequently reported experimental observations on the morphology of spinodal decomposition (SD) in binary solutions: (1) critical quenches yield interconnected structures, and (2) off‐critical quenches yield a droplet‐type morphology. As D increases, the dominant dimensionless wave number k increases as well, but the dimensionless transition time t from the early stage to the intermediate stage decreases. In addition, t is shortest when c is at the critical concentration, but increases to infinity when c is at one of the two spinodal concentrations. These results are found when the solute degree of polymerization N2 is in the range 1 ≤ N2 ≤ 100. When N2 > 100, however, a problem of numerical nonconvergence due to diverging relaxation rates occurs because of the very unsymmetric nature of the phase diagram. A novel scaling procedure is introduced to explain the phase separation phenomena due to SD for any value of N2 during the time range explored in this study.

Confirmatory tetrad analysis in SAS

Bollen and Ting (1993) proposed confirmatory tetrad analysis (CTA) as a method for testing structural equation models. CTA holds promise as a complementary method to the conventional model testing methodology. It applies to some underidentified models and nonnested models that cannot be tested in the conventional approach, and it is a noniterative estimator that does not have nonconvergence problems. This article illustrates an SAS macro, named CTA‐SAS, that implements the CTA testing methodology. Essential elements of the test and the syntax of the program are discussed, and an example is used to illustrate the application of the program.

Stability of the molecular anions ClO 4−, HCO − and O 3− from the self-interaction corrected multiple-scattering Xα method

Non-convergence problems normally occur when molecular anions are calculated using the local-density-functional method because of the incomplete cancellation of the self-interaction in the Coulomb integral by that in the statistical exchange integral. This problem is overcome by introducing the self-interaction correction into the multiple-scattering xα method. Calculation of the electronic structures of the molecular anions ClO 4 −, HCO −, and O 3 −1 shows that the self-interaction correction avoids the non-convergence problem, improves the results significantly, and gives one-electron eigenvalues comparable to the negative of the experimental ionization potentials much more accurately than transition state calculations.

Nonlinear transformer model for circuit simulation

A transformer model which consists of a nonlinear core with hysteresis and multiple windings is described as implemented in DSPICE. In contrast to previous implementations, the nonlinear behavior of the new model is described by continuous piecewise-hyperbolic functions characterized by three parameters. These parameters are the same as parameters previously published in the literature. A loop-traversing algorithm has been implemented which avoids discontinuities and eliminates both nonconvergence problems and the occurrence of erroneous voltage spikes during time-domain simulation. In the large-signal time-domain analysis the frequency-dependent eddy current losses in the core and wire losses are modeled. Additional effects, such as wire skin effect and temperature dependence, are also included. In the small-signal AC analysis the transformer is modeled as frequency-dependent lossy mutual inductors. For both analyses, the air gap and the elated fringe field effect are modeled by extending the magnetic path length of the core appropriately. >

An Investigation of Procedures for Computerized Adaptive Testing Using Partial Credit Scoring

The purposes of our investigation were to manipulate systematically various aspects of the computerized adaptive testing (CAT) procedure for partial credit scoring and to determine the effects of the manipulations on the operational characteristics of the CAT. We examined the effects of item-pool size, item-pool information, and stepsizes used along the trait continuum until maximum likelihood estimates could be calculated. We found that item banks consisting of as few as 30 items could be used successfully for partial-credit adaptive testing. The use of a variable stepsize method for trait estimation prior to maximum-likelihood estimation and the use of information functions to select items virtually eliminated the problem of nonconvergence of trait estimation. The implications of these findings for educational applications are also discussed.

Computer-aided kinematic analysis of basic spatial mechanisms

Using the spherical coordinate system in conjunction with the principle of algebraic correspondence between the displacement equations of the plane, spherical and spatial four-bar mechanisms and the plane and spatial slider-crank mechanisms, an efficacious procedure has been developed to carry out kinematic analysis for the coupler and output link of the mechanisms. The iteration-free nature of the procedure precludes any non-convergence problem and the inherent complexity of the 3-dimensional analysis is mitigated substantially.

Matrix interpretation of the spectral iteration technique (electromagnetic scattering)

A matrix interpretation of the spectral iteration technique is presented to illustrate improvements in accuracy and convergence for both transverse magnetic and transverse electric waves incident on two-dimensional homogeneous scatterers producing solutions identical to a method of moments scheme. In this scheme, it is possible to improve the convergence rate of the technique by the use of nonphysical Green's function terms in the extended matrix. These terms result in the generation of a nonphysical field outside the scatterer, while still maintaining the correct solution of the current. Although the problem of nonconvergence has not been entirely overcome, a particular taper method used in the examples provided shows an improvement over their nontapered counterparts.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An Evaluation of the Effects of Variable Sampling On Component, Image, and Factor Analysis

An attribution of a latent variable procedure, such as factor analysis, that is sometimes cited is superior generalization from the variables sampled to the population of variables. Principal component analysis, image component analysis, and maximum likelihood factor analysis were compared to assess the effects of variable sampling. Three other independent variables were manipulated: (a) the size of the loadings or saturation, (b) the average number of variables per factor, and (c) the number of variables sampled. Five different correlation matrices were generated for each condition. Ten different variable samples were randomly selected. The sample pattern was then compared to the appropriate population pattern. The effects of method of analysis were relatively minor and very complex. The results with respect to degree of saturation and average number of variables per factor were clear and dramatic. Differential effects on boundary cases and nonconvergence problems were also found.

Some aspects of an adaptive digital notch filter with constrained poles and zeros

The paper derives the range of filter parameters which can be used for monitoring purposes in adaptive notch filtering applications. The nonconvergence problem associated with the stochastic Gauss-Newton algorithm is illustrated, and the paper proposes the use of a less efficient recursive estimation algorithm-the appropriate maximum likelihood method-to overcome this problem. Results from simulations are presented for demonstration purposes.

A general fitting program for resolution of complex profiles

An interactive, conversational, general purpose program to fit experimental profiles to a set of distribution functions is reported. The non-convergence problem is discussed, and routines constituting a new procedure to solve it are explained and listed.

Reactive Switching Simulation in Security Analysis At Florida Power and Light System Control Center

This paper describes a method for simulating the switching of reactive devices in the Security Analysis function at Florida Power and Light Company System Control Center. The method closely simulates the automatic switching of reactive devices in the field, resolves problems of non-convergence of some highly critical contingencies, provides tools for a better VAR management and reactive device control, and thus relieves the system operator from the guesswork in interpreting Security Analysis results. Real time results are also presented to show the effectiveness of the method.

On the nonconvergence problem in computing the capacity of strange attractors

The convergence of box-counting algorithm for computing the capacity of strange attractors is affected by the discretization procedure, because the period of the difference equations differs from that of the original ODE's and, in addition, a damping factor appears.

ON THE NONCONVERGENCE PROBLEM IN COMPUTING THE CAPACITY OF STRANGE ATTRACTORS

The convergence of box-counting algorithm for computing the capacity of strange attrac-tors is affected by the discretization procedure, because the period of the difference equations differs from that of the original ODE'S and, in addition, a damping factor appears. Simply decreasing the time-steps in the integration scheme not only costs more computer time, but also may deprive the convergence at all. The nonconvergence problem can be overcome by choosing at first a correct sampling interval. We give numerical evidence for what said above on the example of the periodically forced Brusselator.

Application of a Time-Dependent Approach to Burnup Calculations for Pressurized Water Reactor Cores

The feasibility and relative merits of a quasi-time-dependent approach to burnup calculations is investigated. This method, which is shown to be practically equivalent to a true time-dependent approach, uses one iterative level less than the conventional method and is less liable to nonconvergence problems. The method has been formulated using the finite difference form of the neutron diffusion equation and is implemented in a computer code named TDB. Several one- and two-dimensional pressurized water reactor cores were analyzed using both proposed and conventional methods. The calculations show that the proposed method is about twice as fast as the conventional one with a relative accuracy of less than or equal to0.5% in material power fractions and critical boron value.