Problem Of Oscillations Research Articles

Modeling of Direct Drive Wind Turbine for Wide-band Oscillation Analysis in Large Power Grid

Abstract Aiming at the problem of wide-band oscillation caused by power grid with high proportion of direct drive wind turbine (DDWT), a transient model of DDWT for wide-band oscillation analysis is established in this paper. Firstly, the mechanism and key factors of wide-band oscillation occurred in large power grid with high proportion of DDWT was analyzed. Secondly, the model of DDWT was established by simplifying the full electromagnetic transient model of DDWT while the key factors of wide-band oscillation mode were retained and the secondary factors unrelated or weakly related to wide-band oscillation mode were ignored. Finally, the simulation result shows that the model can improve the convergence and computational efficiency of the simulation analysis and ensure the accuracy of the simulation result at the same time, and can be applied to the simulation analysis of wide-band oscillation occurred in large power grid with high proportion of DDWT.

New family for Runge‐Kutta‐Nyström pairs of orders 6(4) with coefficients trained to address oscillatory problems

In this paper, we consider the integration of the special second‐order initial value problem (IVP) by Runge‐Kutta‐Nyström (RKN) pairs of algebraic orders 6 and 4. For achieving this, we have to solve a certain set of order conditions. The main contribution of the present work is that we introduce a new methodology of solving them that possesses nine free parameters instead of four used by similar pairs until now. This family uses the FSAL (first stage as last) devise. Selecting these extra coefficients properly we may construct methods with better properties. Here, we exploit the free parameters in order to derive a pair with coefficients trained to furnish better results on problems with periodic solutions. Extensive numerical tests justify our approach.

INFLUENCE OF THE PARAMETERS OF THE BOTTOM BOREHOLE ZONE ON THE OWN VIBRATIONS OF THE LIQUID IN THE PUMP COMPRESSOR TUBING

The problem of natural oscillations of a liquid column in a tubing string, arising after a sudden opening or closing of a vertical well (water hammer), is considered. For this, a mathematical model has been built that describes the dynamics of the fluid column in the well and the filtration flow in the bottomhole zone, analytical solutions of the system of equations have been obtained. To determine the frequency, period, coefficient and decrement of damping of oscillations, a characteristic equation is found. The impact of such parameters as the length of the open section, the perforation zones of the well, the length of the tubing string, the permeability coefficient on the dynamic nature of natural pressure fluctuations has been analyzed.

ASSESSMENT OF GROUND SURFACE FLUCTUATIONS DURING SHIELD TUNNELING OF SUBWAY TUNNELS

T The problems of evaluation of ground surface vibrations created by underground vibration sources are quite acute, especially in the conditions of urban development. During the construction of subway tunnels by the shield method there is a dynamic impact during the work of working mechanisms. The oscillations during the excavation of the soil by cutting mechanisms of the shield complex, during the ground bailing and pumping of mortar behind the lining can reach the day surface and cause significant deformations. When designing long underground tunnels built next to existing buildings, it is necessary to estimate the parameters of dynamic impact on the buildings caused by the operation of shielding mechanisms. The paper deals with the estimation of dynamic effects of various devices and mechanisms used in underground works. At this stage, the problems of oscillations of the surface of an elastic half-space from various point sources of waves located at different depths, taking into account the waves reflected from the free surface, are solved. The distribution of stresses and displacements during wave propagation in elastic media is a complex picture. In confined media the picture of wave propagation becomes even more complicated due to reflection of waves from boundaries. The reciprocity theorem is used to estimate the levels of ground surface oscillations created by dynamic effects of various devices and mechanisms during shield tunneling. The dynamic effects of working mechanisms are modeled by: the force directed along the axis of the shield, a pair of forces, two pairs of forces without momentum, a combination of a pair of forces and a longitudinal force, a combination of two pairs without momentum and longitudinal force.

Nonlinear Random Vibrations Using Second-Order Adjoint and Projected Differentiation Methods

Abstract This paper proposes a new computationally efficient methodology for random vibrations of nonlinear vibratory systems using a time-dependent second-order adjoint variable (AV2) method and a second-order projected differentiation (PD2) method. The proposed approach is called AV2–PD2. The vibratory system can be excited by stationary Gaussian or non-Gaussian random processes following the traditional translation process model. A Karhunen–Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. A second-order adjoint approach is used to obtain the required first- and second-order output derivatives accurately by solving as many sets of equations of motion (EOMs) as the number of KL random variables. These derivatives are used to compute the marginal cumulative distribution function (CDF) of the output process with second-order accuracy. Then, a second-order projected differentiation method calculates the autocorrelation function of each output process with second-order accuracy, at an additional cost of solving as many sets of EOMs as the number of outputs of interest, independently of the time horizon (simulation time). The total number of solutions of the EOM scales linearly with the number of input KL random variables and the number of output processes. The efficiency and accuracy of the proposed approach are demonstrated using a nonlinear Duffing oscillator problem under a quadratic random excitation and a nonlinear half-car suspension example.

Estimation of dynamic systems using a method of characteristics filter

This paper deals with the technical formulation and implementation details of an algorithm that provides an estimate of the probability density function of the state of a nonlinear dynamical system from discrete time measurements. In contrast to other state estimation methods that propagate the conditional moments, the proposed filter is shown to propagate and update the full probability density function of the state. Characteristic solutions to the Liouville equation are used to propagate the exact probability density values along the flow of the dynamical system. The reconstruction of the state probability density function is then posed as a convex programming problem. An adaptive regression-tree based region-decomposition approach is used to efficiently compute expectation integrals involved in implementing the Bayes rule associated with posterior density function. Numerical examples capturing the non-Gaussian nature of the uncertainty in the duffing oscillator problem and the two body problem are used to demonstrate the efficacy of the proposed methods.

Microgrid’s multi-VSGs cooperative control method based on distributed communication

Microgrid is a group of interconnected Distributed Generators (DGs) and loads. As an application of renewable energy, microgrid began to enter people’s vision. The technology of Virtual Synchronous Generator (VSG) is becoming a research hotspot owing to it can supply inertia for distributed generation system. For the oscillation problem in microgrid after using VSG technology, this paper theoretically analyzes the variation in output frequency and power of parallel VSGs after system load fluctuation, and proposes a cooperative control method of multi-VSGs. Through distributed communication network, this method improves the output control of each VSG. In the transient process, applied method alleviates the uneven distribution in the active power of the microgrid, while reducing the difference in the output frequency of each VSG, therefore, it can significantly restrain the oscillation and ameliorate the dynamic characteristics of microgrid. A simulation model is established to prove the validity and advantage of this method at the end of this paper.

A method for analyzing bursting oscillations in grid-connected renewable energy generation systems based on a complex network

For analyzing the problem of frequent wideband oscillations in grid-connected renewable energy generation systems, an analysis method based on small-world networks and fast-slow dynamics is proposed. A direct-driven permanent magnet synchronous generator (DPMSG) was chosen as an example to discuss the process of bursting oscillations in a single system with both alternating large-amplitude and micro-amplitude oscillations due to the multi-timescale coupling effect introduced by the disturbance. Meanwhile, a complex network consisting of multiple DPMSGs connected to the grid was selected to investigate the process of bursting oscillations in generation nodes spreading among the system nodes. The results showed that the bursting oscillations created by the power generation nodes in grid-connected renewable energy generation systems can lead to oscillation instability of the entire system. Our simulation verified the feasibility and effectiveness of the method proposed in this paper.

Force impact suppression of contact transition state in robot grinding and polishing of industrial blades

When using robots to carry out grinding and polishing processing of industrial blades, due to factors such as non-zero approach speed and discontinuous dynamic characteristics, the robot grinding and polishing processing has contact force impact and oscillation problems during the contact transition process, which seriously affects the quality of the blade surface processing, contour accuracy, and control system stability. In order to solve the problem of large impact of contact force in robot grinding and polishing, this paper proposes an optimization method for impact suppression in the transition state of robot grinding and polishing. Taking the robot abrasive belt grinding and polishing as the research object, the adaptive weighted particle swarm algorithm is used to optimize the input shaper and realize the parameter self-tuning of the input shaping technology. The experimental results show that the stabilization time is shortened by about 86.5%, and the maximum overshoot of contact force is reduced by about 88.5% during contact transition. The method proposed in this paper can realize the smooth transition of the blade grinding and polishing process, does not need system modeling, effectively shorten the system stabilization time, reduce the maximum overshoot, and accelerate the system response speed, and it has strong stability and flexibility.

Numerical Solution of Stiff and Oscillatory Problems using Third Derivative Trigonometrically Fitted Block Method

This paper considered the formulation of continuous third derivative trigonometrically fitted method for the solution of oscillatory first order initial value problems using the technique of interpolation and collocation of the approximate solution by combining polynomial and trigonometric functions. Solving for the unknown parameters and substituting the results into the approximate solution yielded a continuous linear multistep method, which was evaluated at some selected grid points where two cases were considered at equal intervals to give the discrete schemes which are implemented in block form. The blocks are convergent and stable. Numerical experiments show that the methods compete favorably with existing method.This paper considered the formulation of continuous third derivative trigonometrically fitted block method for the solution of stiff and oscillatory problems. The development of the technique involved the interpolation and collocation of the approximate solution which is the combination of polynomial and trigonometric functions. Solving for the unknown parameters and substituting the results into the approximate solution yielded a continuous linear multistep method, which is evaluated at some selected grid points where two cases were considered at equal intervals to give the discrete schemes which are implemented in block form. The blocks are convergent and stable. Numerical experiments show that the methods compete favorably with existing method and efficient for the solution of stiff and oscillatory problems.

Infinitely many solutions and asymptotics for resonant oscillatory problems

For a class of oscillatory resonant problems, involving Dirichlet problems for semilinear PDE's on balls and rectangles in \(\mathbb{R}^n\), we show the existence of infinitely many solutions, and study the global solution set. The first harmonic of the right hand side is not required to be zero, or small. We also derive asymptotic formulas in terms of the first harmonic of solutions, and illustrate their accuracy by numerical computations. The numerical method is explained in detail. Ffor more information see https://ejde.math.txstate.edu/special/01/k1/abstr.html

The anisotropic Dunkl oscillator problem on the two-dimensional curved spaces

In this paper, we study the two-dimensional (2D) Euclidean anisotropic Dunkl oscillator model in an integrable generalization to curved ones of the 2D sphere [Formula: see text] and the hyperbolic plane [Formula: see text]. This generalized model depends on the deformation parameter [Formula: see text] of underlying space and involves reflection operators [Formula: see text] in such a way that all the results are simultaneously valid for [Formula: see text], [Formula: see text] and [Formula: see text]. It turns out that this system is superintegrable based on the special cases of parameter [Formula: see text], which constant measures the asymmetry of the two frequencies in the 2D Dunkl model. Therefore, the Hamiltonian [Formula: see text] can be interpreted as an anisotropic generalization of the curved Higgs–Dunkl oscillator in the limit [Formula: see text]. When [Formula: see text], the system turns out to be the well-known superintegrable 1:2 Dunkl oscillator on [Formula: see text] and [Formula: see text]. In this way, the integrals of the motion arising from the anisotropic Dunkl oscillator are quadratic in the Dunkl derivatives for the special cases of [Formula: see text]. Moreover, these symmetries obtain by the Jordan–Schwinger representation in the family of the Cayley–Klein orthogonal algebras using the creation and annihilation operators of the dynamical [Formula: see text] algebra of the 1D Dunkl oscillator. The resulting algebra is a deformation of [Formula: see text] with reflections, which is named the Jordan–Schwinger–Dunkl algebra [Formula: see text]. The spectrum of this system is determined by the separation of variables in geodesic polar coordinates, and the resulting eigenfunctions are algebraically given in terms of Jacobi polynomials.

Low-frequency oscillation suppression strategy considering dynamic power characteristics of energy storage system

Aiming at the problem of low-frequency oscillation in the weak power grid, a low-frequency oscillation suppression strategy considering the dynamic power characteristics of the energy storage system (ESS) is proposed in this paper. Firstly, the principle of low-frequency oscillation in the power system is analyzed by using a single machine infinite bus system. Secondly, considering the dynamic characteristics of the ESS output active power, a controller for the ESS to suppress low-frequency oscillation is designed, which can provide positive damping for frequency oscillation of the power grid. Finally, the simulation analysis and experimental results of an actual weak grid are carried out to verify the effectiveness and feasibility of the proposed method. The results show that the suppression effect of the low-frequency oscillations is related to the ESS location in the weak power grid.

Path stability in partially deployed secure BGP routing

Border Gateway Protocol (BGP), as the current de-facto routing protocol connecting various cooperating domains on the Internet, did not consider security when it was originally designed. With the expansion of the Internet, security is increasingly valued and many BGP enhancement mechanisms are proposed and experimented. Some of them like BGPsec have been standardized and promoted by the IETF. However, the deployment of these inter-domain secure routing mechanisms is subject to many economic and political restrictions. Consequently, there will be a long period of partial deployment, during which instability of BGP can be observed. Specifically, when some networks start deploying secure BGP mechanisms, they may be involved in some temporary or persistent route oscillations. In this paper, we systematically study the stability problem induced by partially deployed secure BGP mechanisms. We analyze the characteristics of topology and routing strategies when BGP oscillations will be introduced. In particular, we propose dispute chain, a derived structure of dispute wheel proposed in Griffin et al. (2002), to formally analyze this problem. Based on dispute chain, we analyze how different security adoption strategies can cause BGP oscillations under the general Gao–Rexford model. Our analysis shows that, even in a situation when there is no dispute wheel, dispute chains may widely appear, indicating that BGP oscillation problems will be introduced when security mechanisms are casually deployed, affecting the security and quality of inter-domain communications. To avoid possible oscillations, we also propose some deployment guidelines from different perspectives of the operator and the Internet, so that a wider deployment of security mechanisms will not blindly disrupt the Internet.

Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants

In this paper, we consider a class of stochastic midpoint and trapezoidal Lawson schemes for the numerical discretization of highly oscillatory stochastic differential equations. These Lawson schemes incorporate both the linear drift and diffusion terms in the exponential operator. We prove that the midpoint Lawson schemes preserve quadratic invariants and discuss this property as well for the trapezoidal Lawson scheme. Numerical experiments demonstrate that the integration error for highly oscillatory problems is smaller than that of some standard methods.

Fast Computation of Highly Oscillatory ODE Problems: Applications in High-Frequency Communication Circuits

The paper demonstrates symmetric integral operator and interpolation based numerical approximations for linear and nonlinear ordinary differential equations (ODEs) with oscillatory factor x′=ψ(x)+χω(t), where the function χω(t) is an oscillatory forcing term. These equations appear in a variety of computational problems occurring in Fourier analysis, computational harmonic analysis, fluid dynamics, electromagnetics, and quantum mechanics. Classical methods such as Runge–Kutta methods etc. fail to approximate the oscillatory ODEs due the existence of oscillatory term χω(t). Two types of methods are presented to approximate highly oscillatory ODEs. The first method uses radial basis function interpolation, and then quadrature rules are used to evaluate the integral part of the solution equation. The second approach is more generic and can approximate highly oscillatory and nonoscillatory initial value problems. Accordingly, the first-order initial value problem with oscillatory forcing term is transformed into highly oscillatory integral equation. The transformed symmetric oscillatory integral equation is then evaluated numerically by the Levin collocation method. Finally, the nonlinear form of the initial value problems with an oscillatory forcing term is converted into a linear form using Bernoulli’s transformation. The resulting linear oscillatory problem is then computed by the Levin method. Results of the proposed methods are more reliable and accurate than some state-of-the-art methods such as asymptotic method, etc. The improved results are shown in the numerical section.

Simultaneous Estimation of Parameters and the State of an Optical Parametric Oscillator System

In this paper, we consider the filtering problem of an optical parametric oscillator (OPO). The OPO pump power may fluctuate due to environmental disturbances, resulting in uncertainty in the system modeling. Thus, both the state and the unknown parameter may need to be estimated simultaneously. We formulate this problem using a state-space representation of the OPO dynamics. Under the assumption of Gaussianity and proper constraints, the dual Kalman filter method and the joint extended Kalman filter method are employed to simultaneously estimate the system state and the pump power. Numerical examples demonstrate the effectiveness of the proposed algorithms.

Two-scale expansion method in the problem of temperature oscillations in frozen soil

Two-scale expansion method in the problem of temperature oscillations in frozen soil

Efficient Numerical Optimal Control for Highly Oscillatory Systems

We present an efficient transcription method for highly oscillatory optimal control problems. For these problems, the optimal state trajectory consists of fast oscillations that change slowly over the time horizon. Out of a large number of oscillations, we only simulate a subset to approximate the slow change by constructing a semi-explicit differential-algebraic equation that can be integrated with integration steps much larger than one period. For the solution of optimal control problems with direct methods, we provide a way to parametrize the controls and regularize the state trajectory. Finally, we utilize the method to find a fuel-optimal orbit transfer of a low-thrust satellite. Using the novel method, we reduce the size of the resulting nonlinear program by more than one order of magnitude.

Exponential integrator method for solving the nonlinear Helmholtz equation

<abstract><p>In this paper, we study the exponential integrator method (EIM) for solving the nonlinear Helmholtz equation (NLHE). As the wave number or the characteristic coefficient in the nonlinear term is large, the NLHE becomes a highly oscillatory and indefinite nonlinear problem, which makes most of numerical methods lose their expected computational effects. Based on the shooting method, the NLHE is firstly transformed into an initial-value-type problem. Then, the EIM is utilized for solving the deduced problem, by which we not only can capture the oscillation very well, but also avoid to search the nonlinear iteration method and to solve indefinite linear equations at each iteration step. Therefore, the high accuracy simulations with relative large physical parameters in the NLHE become possible and lots of computational costs can be saved. Some numerical examples, including the extension to the nonlinear Helmholtz system, are shown to verify the accuracy and efficiency of the proposed method.</p></abstract>