• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
• /
• v.29 no.10
• /
• pp.89-96
• /
• 2015

Explicit numerical integration methods for power system transient stability simulation require very small time steps to avoid numerical instability. The EXST1 exciter model is a primary source of fast dynamics in power system transients. In case of the EXST1, the required small integration time step for entire system simulation increases the computational demands in terms of running time and storage. This paper presents a practical exciter model reduction approach which allows the increase of the required step size and thus the method can decrease the computational demands. The fast dynamics in the original EXST1 are eliminated in the reduced exciter model. The use of a larger time step improves the computational efficiency. This paper describes the way to eliminate the fast dynamics from the original exciter model based on linear system theory. In order to validate the performance of the proposed method, case studies with the GSO-37 bus system are provided. Comparisons between the original and reduced models are made in simulation accuracy and critical clearing time.

• Structural Engineering and Mechanics
• /
• v.48 no.5
• /
• pp.711-736
• /
• 2013

In this paper new implicit time integration called N-IHOA is presented for dynamic analysis of high damping systems. Here, current displacement and velocity are assumed to be functions of the velocities and accelerations of several previous time steps, respectively. This definition causes that only one set of weighted factors is calculated from the Taylor series expansion which leads to a simple approach and reduce the computational efforts. Moreover a comprehensive study on stability of the proposed method i.e., N-IHOA compared with IHOA integration which is performed based on amplification matrices proves the ability of the N-IHOA in high damping vibrations such as control systems. Also, wide range of numerical examples which contains single/multi degrees of freedom, damped/un-damped, free/forced vibrations from finite element/finite difference demonstrate that the accuracy and efficiency of the proposed time integration is more than the common approaches such as the IHOA, the Wilson-${\theta}$ and the Newmark-${\beta}$.

• Journal of the Korean Society of Industry Convergence
• /
• v.12 no.3
• /
• pp.149-155
• /
• 2009

A new finite element equation is derived by applying quadratic and cubic time integration scheme to the variational formulation in time-integral for the analysis of the transient elastodynamic problems to increase the numerical accuracy and stability. Emphasis is focused on methodology for cubic time integration scheme procedure which are never presented before. In this semidiscrete approximations of the field variables, the time axis is divided equally and quadratic and cubic time variation is assumed in those intervals, and space is approximated by the usual finite element discretization technique. It is found that unconditionally stable numerical results are obtained in case of the cubic time variation. Some numerical examples are given to show the versatility of the presented formulation.

• Earthquakes and Structures
• /
• v.8 no.6
• /
• pp.1325-1348
• /
• 2015

Real-time hybrid testing (RTHT) involves virtual splitting of the structure into two parts: physical substructure that contains the key region of interest which is tested in a laboratory and numerical substructure that contains the remaining part of the structure in the form of a numerical model. This paper numerically assesses four step-by-step integration methods (Central difference method (CDM), Operator splitting method (OSM), Rosenbrock based method (RBM) and CR-integration method (CR)) which are widely used in RTHT. The methods have been assessed in terms of stability and accuracy for various realistic damping ratios of the physical substructure. The stability is assessed in terms of the spectral radii of the amplification matrix while the accuracy in terms of numerical damping and period distortion. In order to evaluate the performance of the methods, five carefully chosen examples have been studied - undamped SDOF, damped SDOF, instantaneous softening, instantaneous hardening and hysteretic system. The performance of the methods is measured in terms of a non-dimensional error index for displacement and velocity. Based on the error indices, it is observed that OSM and RBM are robust and performs fairly well in all the cases. CDM performed well for undamped SDOF system. CR method can be used for the system showing softening behaviour. The error indices indicate that accuracy of OSM is more than other method in case of hysteretic system. The accuracy of the results obtained through time integration methods for different damping ratios of the physical substructure is addressed in the present study. In the presence of a number of integration methods, it is preferable to have criteria for the selection of the time integration scheme. As such criteria are not available presently, this paper attempts to fill this gap by numerically assessing the four commonly used step-by-step methods.

• Structural Engineering and Mechanics
• /
• v.4 no.6
• /
• pp.589-600
• /
• 1996

An explicit 4th order time integration scheme for solving the convection-diffusion equation is discussed in this paper. A system of ordinary differential equations are derived first by discretizing the spatial derivatives of the relevant PDE using the finite difference method. The integration of the ODEs is then carried out using a 4th order scheme and a self-adaptive technique based on the spatial grid spacing. For a non-uniform spatial grid, different time step sizes are used for the integration of the ODEs defined at different spatial points, which improves the computational efficiency significantly. A numerical example is also discussed in the paper to demonstrate the implementation and effectiveness of the method.

• Earthquakes and Structures
• /
• v.7 no.2
• /
• pp.159-178
• /
• 2014

Although the family methods with unconditional stability and numerical dissipation have been developed for structural dynamics they all are implicit methods and thus an iterative procedure is generally involved for each time step. In this work, a new family method is proposed. It involves no nonlinear iterations in addition to unconditional stability and favorable numerical dissipation, which can be continuously controlled. In particular, it can have a zero damping ratio. The most important improvement of this family method is that it involves no nonlinear iterations for each time step and thus it can save many computationally efforts when compared to the currently available dissipative implicit integration methods.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.31 no.7
• /
• pp.1-8
• /
• 2003

Numerical characteristics of air chemistry associated with hypersonic flows are described and are compared with those of hydrogen oxygen combustion, applying the partially implicit time integration method to air chemistry. This paper reveals that the time integration of air chemistry needs a chemical Jacobian for stable calculations. However the positive real eigenvalues in air chemistry are relatively smaller than those of hydrogen combustion, and the numerical integration is less sensitive than that with combustion. lt is also found that the application of the partia1ly irnplicit method reduces the computing time without numerical instabilities.

• Aerospace Engineering and Technology
• /
• v.13 no.2
• /
• pp.60-65
• /
• 2014

In this paper, numerical integration method using operational matrix of integration is studied. Using the operational matrix of integration, modified fixed point iteration method is introduced in order to solve rapidly an initial value problem for non-linear equation of motion. As an example, an initial value problem for orbital motion is considered. Through the numerical example, it is shown that the algorithm is efficient from the computational time point of view.

• Smart Structures and Systems
• /
• v.14 no.6
• /
• pp.1131-1150
• /
• 2014

One of the issues in extending the range of applicable problems of real-time hybrid simulation is the computation speed of the simulator when large-scale computational models with a large number of DOF are used. In this study, functionality of real-time dynamic simulation of MDOF systems is achieved by creating a logic circuit that performs the step-by-step numerical time integration of the equations of motion of the system. The designed logic circuit can be implemented to an FPGA-based system; FPGA (Field Programmable Gate Array) allows large-scale parallel computing by implementing a number of arithmetic operators within the device. The operator splitting method is used as the numerical time integration scheme. The logic circuit consists of blocks of circuits that perform numerical arithmetic operations that appear in the integration scheme, including addition and multiplication of floating-point numbers, registers to store the intermediate data, and data busses connecting these elements to transmit various information including the floating-point numerical data among them. Case study on several types of linear and nonlinear MDOF system models shows that use of resource sharing in logic synthesis is crucial for effective application of FPGA to real-time dynamic simulation of structural response with time step interval of 1 ms.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.2 no.1
• /
• pp.106-115
• /
• 1994

A parallel integration approach is proposed for real-time simulation of controlled mechanical systems. The proposed approach, which employs the dual-rate integration method in a parallel computing environment, is developed to deal with stiffness and high frequency characteristics of the controlled mechanical systems effectively. Numerical experiments are performed to demonstrate the effectiveness of the approach in shared memory multiprocessors, Alliant FX/8 and Alliant FX/80.