Effect of Modal Interaction on Transient Behavior in Double-Input SEPIC DC–DC Converters

2020 ◽  
Vol 30 (10) ◽  
pp. 2050145
Author(s):  
Hao Zhang ◽  
Min Jing ◽  
Shuai Dong ◽  
Wei Liu ◽  
Zhaohua Cui
Keyword(s):  
Transient Behavior ◽  
Approximate Solutions ◽  
Underlying Mechanism ◽  
Response Characteristic ◽  
State Variables ◽  
Modal Interaction ◽  
Oscillation Modes ◽  
Dynamic Response Characteristic ◽  
The One ◽  
Averaged Model

In this paper, we exploit an idea of nonlinear modal series method to investigate the effects of modal interaction in the one-cycle controlled (OCC) double-input SEPIC DC–DC converter. Based on the proposed nonlinear averaged model, the analytical approximate solutions are obtained to characterize the dynamic response characteristic of the transient behaviors in the double-input SEPIC converters. The fundamental modal analysis is utilized to identify the dominant oscillation modes and discover the relationship between parameters, fundamental modes and state variables. Furthermore, the second-order interaction indices are proposed to uncover the underlying mechanism of nonlinear interaction behaviors. In particular, the correlation between parameters and modal interaction are derived to optimize the transient process of the double-input SEPIC converters. Finally, numerical simulations are performed to verify the theoretical analysis.

Nonlinear Modal Analysis of Transient Behavior in Cascade DC–DC Boost Converters

2017 ◽  
Vol 27 (09) ◽  
pp. 1750140 ◽  
Author(s):  
Hao Zhang ◽  
Weijie Li ◽  
Honghui Ding ◽  
Pengcheng Luo ◽  
Xiaojin Wan ◽  
...  
Keyword(s):  
Transient Process ◽  
Transient Behavior ◽  
Approximate Solutions ◽  
Second Order ◽  
Series Method ◽  
State Variables ◽  
Modal Interactions ◽  
Balance Principle ◽  
Nonlinear Modal Analysis ◽  
Averaged Model

This paper deals with the transient characteristics of the cascade DC–DC Boost converter under a large disturbance by using nonlinear modal series method. Based on the power balance principle, a nonlinear averaged model is derived to describe the nonlinear dynamics of the cascade converter. And then, the modal series method is described in detail and the second order approximate solutions are derived by this method. Furthermore, the simulation results and the theoretical analysis demonstrate that there are plenty of modal interactions, particularly the stronger second order modal interactions, which can affect the transient behavior significantly in the disturbed transient process. The modified approximate solutions considering the dominant nonlinear interaction modes of some state variables are subsequently obtained. In addition, by selecting appropriate system parameters, we can improve the transient behavior of the system under disturbance so that the amplitude and duration of the oscillation can be effectively reduced to satisfy the requirements of the system tolerance during the transient process. Moreover, the dominant oscillation modes of each state variable are also studied, which will help us improve the understanding of the salient transient behaviors in DC–DC cascade converters with disturbance. Finally, PSpice circuit experiments are performed to verify the above theoretical and numerical results.

Filippov solutions of vector Dirichlet problems

2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů
Keyword(s):  
Differential Equations ◽  
The State ◽  
State Variables ◽  
Dirichlet Problems ◽  
Filippov Solutions ◽  
Natural Notion ◽  
Growth Restrictions ◽  
The One ◽  
The Right ◽  
Effective Growth

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

scholarly journals Semi-Analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian Expansion of Distance Operators W= RC1-nRD1-M, RC1-Nr12-M, R12-Nr13-M

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Gaussian Function ◽  
Approximate Solutions ◽  
Equation System ◽  
Least Square ◽  
Position Vector ◽  
Least Square Fit ◽  
Analytic Expressions ◽  
The One ◽  
Analytical Expressions ◽  
Coulomb Integrals

The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)…rho(rk) W(r1,…,rk) dr1…drk, where the one-electron density, rho(r1), is a linear combination (LC) of Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical expressions are well known, are widely used in the practice of computation chemistry (CC) or physics, and analytical expressions are also known for the cases n,m=0,1,2. The rest of the cases – mainly with any real (integer, non-integer, positive or negative) n and m - needs evaluation. We base this on the Gaussian expansion of |r|^-u, of which only the u=1 is the physical Coulomb potential, but the u≠1 cases are useful for (certain series based) correction for (the different) approximate solutions of Schrödinger equation, for example, in its wave-function corrections or correlation calculations. Solving the related linear equation system (LES), the expansion |r|^-u about equal SUM(k=0toL)SUM(i=1toM) Cik r^2k exp(-Aik r^2) is analyzed for |r| = r12 or RC1 with least square fit (LSF) and modified Taylor expansion. These evaluated analytic expressions for Coulomb integrals (up to Gaussian function integrand and the Gaussian expansion of |r|^-u) are useful for the manipulation with higher moments of inter-electronic distances via W, even for approximating Hamiltonian.

scholarly journals Dynamic Modeling of Mechanical Draft Counter-Flow Wet Cooling Tower With Modelica

2010 ◽  
Author(s):  
Xiao Li ◽  
Yaoyu Li ◽  
John E. Seem
Keyword(s):  
Dynamic Modeling ◽  
Cooling Tower ◽  
Transient Behavior ◽  
Counter Flow ◽  
Inlet Conditions ◽  
The One ◽  
Control Volumes ◽  
Air Conditioning Systems ◽  
Volume Method ◽  
Energy Balances

Cooling towers are important equipments for the heating, ventilation and air conditioning systems in commercial buildings, rejecting the process heat generation to the atmosphere. Dynamic modeling of cooling tower is beneficial for control design and fault detection and diagnostics of the chilled-water systems. This paper proposes a simple and yet effective dynamic model for a typical mechanical draft counter-flow cooling tower. The finite volume method is applied to the one-dimensional heat and mass transfer analysis. With control volumes defined separately for the water and air sides, the dynamic equations are constructed with the mass and energy balances. The steady-state performance of the proposed model is evaluated with the experimental data from literature. The transient behavior is simulated under the changes of tower inlet conditions, with the performance to be evaluated in the future with field test data.

Design-Oriented Analysis of Slow-Scale Bifurcations in Single Phase DC–AC Inverters via Autonomous Transformation Approach

2017 ◽  
Vol 27 (06) ◽  
pp. 1750086 ◽  
Author(s):  
Hao Zhang ◽  
Honghui Ding ◽  
Chuanzhi Yi
Keyword(s):  
Theoretical Analysis ◽  
Circuit Design ◽  
Single Phase ◽  
Underlying Mechanism ◽  
System Stability ◽  
Equivalent Model ◽  
Eigenvalue Sensitivity ◽  
Physical Experiments ◽  
Averaged Model ◽  
Theoretical Results

This paper deals with the design-oriented analysis of slow-scale bifurcations in single phase DC–AC inverters. Since DC–AC inverter belongs to a class of nonautonomous piecewise systems with periodic equilibrium orbits, the original averaged model has to be translated into an equivalent autonomous one via a virtual rotating coordinate transformation in order to simplify the theoretical analysis. Based on the virtual equivalent model, eigenvalue sensitivity is used to estimate the effect of the important parameters on the system stability. Furthermore, theoretical analysis is performed to identify slow-scale bifurcation behaviors by judging in what way the eigenvalue loci of the Jacobian matrix move under the variation of some important parameters. In particular, the underlying mechanism of the slow-scale unstable phenomenon is uncovered and discussed thoroughly. In addition, some behavior boundaries are given in the parameter space, which are suitable for optimizing the circuit design. Finally, physical experiments are performed to verify the above theoretical results.

scholarly journals A perturbed algorithm for strongly nonlinear variational-like inclusions

2000 ◽  
Vol 62 (3) ◽  
pp. 417-426 ◽  
Author(s):  
C.-H. Lee ◽  
Q. H. Ansari ◽  
J.-C. Yao
Keyword(s):  
Exact Solution ◽  
General Setting ◽  
Approximate Solutions ◽  
Strongly Nonlinear ◽  
Special Cases ◽  
The One

In this paper, we define the concept of η- subdifferential in a more general setting than the one used by Yang and Craven in 1991. By using η-subdifferentiability, we suggest a perturbed algorithm for finding the approximate solutions of strongly nonlinear variational-like inclusions and prove that these approximate solutions converge to the exact solution. Several special cases are also discussed.

A General Time Dependent Constitutive Model: Part I— Theoretical Developments1

2000 ◽  
Vol 123 (1) ◽  
pp. 51-64 ◽  
Author(s):  
A. F. Saleeb ◽  
S. M. Arnold
Keyword(s):  
Response Characteristic ◽  
Structure Type ◽  
Internal Variable ◽  
Integral Representations ◽  
State Variables ◽  
Qualitative Response ◽  
Response Range ◽  
Starting Point ◽  
Potential Structure ◽  
Hereditary Integral

Using an internal-variable formalism as a starting point, we describe the viscoelastic complement of a previously-developed viscoplasticity formulation of the complete potential structure type. It is mainly motivated by experimental evidence for the presence of rate/time effects in the so-called quasilinear, reversible, material response range. Several possible generalizations are described, in the general format of hereditary-integral representations for nonequilibrium, stress-type, state variables, both for isotropic as well as anisotropic materials. In particular, thorough discussions are given on the important issues of thermodynamic admissibility requirements for such general descriptions, resulting in a set of explicit mathematical constraints on the associated kernel (relaxation and creep compliance) functions. In addition, a number of explicit, integrated forms are derived, under stress and strain control to facilitate the parametric and qualitative response characteristic studies reported here, as well as to help identify critical factors in the actual experimental characterizations from test data that will be reported in Part II.

Inverse Static Analysis of a Planar System With Spiral Springs

2000 ◽  
Author(s):  
Marco Carricato ◽  
Joseph Duffy ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Static Analysis ◽  
External Load ◽  
Degrees Of Freedom ◽  
The Other ◽  
Linear Functions ◽  
State Variables ◽  
Planar System ◽  
Equilibrium Configurations ◽  
Solving Equations ◽  
The One

Abstract In this article the inverse static analysis of a two degrees of freedom planar mechanism equipped with spiral springs is presented. Such analysis aims to detect the entire set of equilibrium configurations of the mechanism once the external load is assigned. While on the one hand the presence of flexural pivots represents a novelty, on the other it extremely complicates the problem, since it brings the two state variables in the solving equations to appear as arguments of both trigonometric and linear functions. The proposed procedure eliminates one variable and leads to write two equations in one unknown only. The union of the root sets of such equations constitutes the global set of solutions of the problem. Particular attention has been reserved to the analysis of the “reliability” of the final equations: it has been sought the existence of critical situations, in which the solving equations hide solutions or yield false ones. A numerical example is provided. Also, in Appendix it is shown a particular design of the mechanism that offers computational advantages.

scholarly journals What Can Machine Learning Tell Us About Intraday Price Patterns in a Frontier Stock Market?

2020 ◽  
Vol 11 (5) ◽  
pp. 205
Author(s):  
Dan Gabriel Anghel
Keyword(s):  
Stock Market ◽  
Spillover Effects ◽  
International Markets ◽  
Investor Behavior ◽  
State Variables ◽  
Different Types ◽  
Market State ◽  
Price Patterns ◽  
The One ◽  
Intraday Patterns

Quite a lot. On the one hand, it enables us to classify intraday patterns into 6 unique classes and to show how each class is related to several important market state variables. On the other hand, it enables us to identify the relevant set of variables and define a better model of the drivers of intraday patterns in a frontier stock market. Overall, our results show that intraday patterns in returns in the frontier stock market of Romania are mostly the result of risk, information flows, and spillover effects from more developed international markets. However, we find that low market efficiency and investor behavior also have a significant contribution. Among others, we identify signs of overreaction to information, irrational exuberance and “making the close” practices by different types of investors.

Reply to "A remark on Moore's new method of obtaining approximate solutions of the Dirac equation"

1981 ◽  
Vol 59 (11) ◽  
pp. 1614-1619 ◽  
Author(s):  
R. A. Moore ◽  
Sam Lee
Keyword(s):  
Dirac Equation ◽  
Structure Constant ◽  
Approximate Solutions ◽  
Wave Functions ◽  
Fine Structure Constant ◽  
Energy Calculation ◽  
Calculation Error ◽  
First Order ◽  
The One ◽  
The Individual

This work was written to clarify the use of a recently developed procedure to obtain approximate solutions of the one-particle Dirac equation directly and in response to a recent critique on its application to lowest order. The critique emphasized the fact that when the wave functions are determined only to zero order then a first order energy calculation contains significant errors of the order of α4, α being the fine structure constant, and a matrix element calculation error of order α2. Tomishima re-affirms that higher order solutions are required to obtain accuracy of these orders. In this work the hierarchy of equations occurring in the procedure is extended to first order and it is shown that exact solutions exist for hydrogen-like atoms. It is also shown that the energy in second order contains all of the contributions of order α4. In addition, we illustrate, in detail, that the procedure can be aplied in such a way as to isolate the individual components of the wave functions and energies as power series of α2. This analysis lays the basis for the determination of suitable numerical methods and hence for application to physical systems.

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