scholarly journals On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2019
Author(s):  
Talal Alharbi ◽  
Marcos Tostado-Véliz ◽  
Omar Alrumayh ◽  
Francisco Jurado
Keyword(s):  
Power Flow ◽  
Order Of Convergence ◽  
Computational Cost ◽  
High Order ◽  
Sixth Order ◽  
Power Networks ◽  
Power Flow Calculation ◽  
Flow Problems ◽  
High Computational Cost ◽  
Very High

Recently, the high-order Newton-like methods have gained popularity for solving power flow problems due to their simplicity, versatility and, in some cases, efficiency. In this context, recent research studied the applicability of the 4th order Jarrat’s method as applied to power flow calculation (PFC). Despite the 4th order of convergence of this technique, it is not competitive with the conventional solvers due to its very high computational cost. This paper addresses this issue by proposing two efficient modifications of the 4th order Jarrat’s method, which present the fourth and sixth order of convergence. In addition, continuous versions of the new proposals and the 4th order Jarrat’s method extend their applicability to ill-conditioned cases. Extensive results in multiple realistic power networks serve to sow the performance of the developed solvers. Results obtained in both well and ill-conditioned cases are promising.

Power flow calculation considering power exchange control for multi-area interconnection power networks

2016 ◽  
Author(s):  
Xiaoming Dong ◽  
Yuanyuan Ding ◽  
Penghui Zhao ◽  
Chengfu Wang ◽  
Yong Wang ◽  
...  
Keyword(s):  
Power Flow ◽  
Power Networks ◽  
Power Flow Calculation ◽  
Flow Calculation ◽  
Power Exchange ◽  
Exchange Control

Efficient Family of Sixth-Order Methods for Nonlinear Models with Its Dynamics

2019 ◽  
Vol 16 (05) ◽  
pp. 1840008
Author(s):  
Ramandeep Behl ◽  
Prashanth Maroju ◽  
S. S. Motsa
Keyword(s):  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Complex Dynamics ◽  
Nonlinear Models ◽  
Computational Cost ◽  
Sixth Order ◽  
System Of Nonlinear Equations ◽  
Van Der Pol ◽  
Numerical Work ◽  
The Family

In this study, we design a new efficient family of sixth-order iterative methods for solving scalar as well as system of nonlinear equations. The main beauty of the proposed family is that we have to calculate only one inverse of the Jacobian matrix in the case of nonlinear system which reduces the computational cost. The convergence properties are fully investigated along with two main theorems describing their order of convergence. By using complex dynamics tools, its stability is analyzed, showing stable members of the family. From this study, we intend to have more information about these methods in order to detect those with best stability properties. In addition, we also presented a numerical work which confirms the order of convergence of the proposed family is well deduced for scalar, as well as system of nonlinear equations. Further, we have also shown the implementation of the proposed techniques on real world problems like Van der Pol equation, Hammerstein integral equation, etc.

Assessment of Very High Order of Accuracy in Implicit LES models

2007 ◽  
Vol 129 (12) ◽  
pp. 1497-1503 ◽  
Author(s):  
Andrew Mosedale ◽  
Dimitris Drikakis
Keyword(s):  
Computational Cost ◽  
Single Mode ◽  
Theoretical Models ◽  
Higher Order ◽  
Second Order ◽  
High Order ◽  
Good Representation ◽  
Order Reconstruction ◽  
Time Required ◽  
Very High

This paper looks at the use of high-resolution and very high-order methods for implicit large-eddy simulation (ILES), with the specific example of simulating the multicomponent two-dimensional single-mode Richtmyer–Meshkov instability for which experimental data is available. The two gases are air and SF6, making stringent demands on the models used in the code. The interface between the two gases is initialized with a simple sinusoidal perturbation over a wavelength of 59mm, and a shock of strength Mach 1.3 is passed through this interface. The main comparison is between the second-order monotone upwind-centered scheme for conservation law methods of van Leer (1979, “Towards the Ultimate Conservative Difference Scheme,” J. Comput. Phys. 32, pp. 101–136) and the current state-of-the-art weighted essentially nonoscillatory interpolation, which is presented to ninth order, concentrating on the effect on resolution of the instability on coarse grids. The higher-order methods as expected provide better resolved and more physical features than the second-order methods on the same grid resolution. While it is not possible to make a definitive statement, the simulations have indicated that the extra time required for the higher-order reconstruction is less than the time saved by being able to obtain the same or better accuracy at lower computational cost (fewer grid points). It should also be noted that all simulations give a good representation of the growth rate of the instability, comparing very favorably to the experimental results, and as such far better than the currently existing theoretical models. This serves to further indicate that the ILES approach is capable of providing accurately physical information despite the lack of any formal subgrid model.

scholarly journals TECHNIQUE FOR VERY HIGH ORDER NONLINEAR SIMULATION AND VALIDATION

2002 ◽  
Vol 10 (02) ◽  
pp. 211-229 ◽  
Author(s):  
RODGER W. DYSON
Keyword(s):  
Euler Equations ◽  
Harmonic Wave ◽  
Computational Cost ◽  
High Order ◽  
Mean Flow ◽  
Order Accuracy ◽  
Nonlinear Simulation ◽  
Fixed Design ◽  
The Mean ◽  
Very High

Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of five wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.

scholarly journals A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation

2015 ◽  
Vol 25 (3) ◽  
pp. 529-537 ◽  
Author(s):  
Ricardo Costa ◽  
Gaspar J. Machado ◽  
Stéphane Clain
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Intramedullary Nail ◽  
High Order ◽  
Sixth Order ◽  
Finite Volume Scheme ◽  
Biharmonic Operator ◽  
Mean Values ◽  
Volume Method ◽  
Very High

Abstract A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

Very High Order Residual Distribution Schemes for Steady Flow Problems

2009 ◽  
pp. 269-274
Author(s):  
Adam Larat ◽  
Rémi Abgrall ◽  
Mario Ricchiuto
Keyword(s):  
Steady Flow ◽  
High Order ◽  
Residual Distribution ◽  
Flow Problems ◽  
Residual Distribution Schemes ◽  
Very High

scholarly journals Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 992-996 ◽  
Author(s):  
Jin Li ◽  
Zilong Liu
Keyword(s):  
Computational Cost ◽  
Tensor Decomposition ◽  
Low Complexity ◽  
Transform Domain ◽  
Spatial Correlations ◽  
Compression Method ◽  
Nonnegative Tensor ◽  
Hyper Spectral ◽  
High Computational Cost ◽  
Very High

AbstractNonnegative tensor Tucker decomposition (NTD) in a transform domain (e.g., 2D-DWT, etc) has been used in the compression of hyper-spectral images because it can remove redundancies between spectrum bands and also exploit spatial correlations of each band. However, the use of a NTD has a very high computational cost. In this paper, we propose a low complexity NTD-based compression method of hyper-spectral images. This method is based on a pair-wise multilevel grouping approach for the NTD to overcome its high computational cost. The proposed method has a low complexity under a slight decrease of the coding performance compared to conventional NTD. We experimentally confirm this method, which indicates that this method has the less processing time and keeps a better coding performance than the case that the NTD is not used. The proposed approach has a potential application in the loss compression of hyper-spectral or multi-spectral images

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