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parallel solution of transient stability constrained optimal power flow by exact optimality condition decomposition

IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第21期12卷 5858-5866页

作者： Yang, Yude Qin, Zhijun Liu, Bin Liu, Hui Hou, Yunhe Wei, Hua Guangxi Univ Coll Elect Engn Nanning Peoples R China Guangxi Key Lab Power Syst Optimizat & Energy Tec Nanning Peoples R China Univ Hong Kong Dept Elect & Elect Engn Hong Kong Hong Kong Peoples R China

Power systems are required to achieve an optimally economic operating point while maintaining security and stability in the presence of credible contingencies. Transient stability constrained optimal power flow (TSCOPF) is a tool to bridge steady-state optimal power flow (OPF) with transient processes under a predefined set of simulated contingencies to guarantee post-fault rotor angle stability in a simulation time window. A parallel solution of TSCOPF using exact optimality condition (OC) decomposition is proposed, where generator swing equations are utilised recursively by exploring the structure of OCs of TSCOPF from the end of simulation time window to its beginning to derive an exact explicit expression consisting of generator-dynamics-related variables in terms of the steady-state variables. The OCs of the TSCOPF model are then decomposed into the OC of OPF, along with a parallel evaluation of this expression for each contingency. Multi-core processing units are applied to accelerate the evaluation process. Case studies with up to 1047 buses over 16 contingences demonstrate an 8x improvement in the computation for realistically sized power systems using the proposed decomposition strategy.

关键词： power system security rotors power system stability power system transient stability power system control optimisation load flow realistically sized power systems parallel evaluation TSCOPF model steady-state variables generator-dynamics-related variables exact explicit expression OC simulation time window post-fault rotor angle stability simulated contingencies transient processes steady-state optimal power flow credible contingencies optimally economic operating point exact optimality condition decomposition transient stability parallel solution

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parallel solution Methods and Preconditioners for Evolution Equations

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MATHEMATICAL MODELLING AND ANALYSIS 2018年第2期23卷 287-308页

作者： Axelsson, Owe Neytcheva, Maya Liang, Zhao-Zheng Czech Acad Sci Inst Geon Ostrava Czech Republic Uppsala Univ Dept Informat Technol Uppsala Sweden Lanzhou Univ Sch Math & Stat Lanzhou Gansu Peoples R China

The recent development of the high performance computer platforms shows a clear trend towards heterogeneity and hierarchy. In order to utilize the computational power, particular attention must be paid to finding new algorithms or adjust existing ones so that they better match the HPC computer architecture. In this work we consider an alternative to classical time-stepping methods based on use of time-harmonic properties and discuss solution approaches that allow efficient utilization of modern HPC resources. The method in focus is based on a truncated Fourier expansion of the solution of an evolutionary problem. The analysis is done for linear equations and it is remarked on the possibility to use two- or multilevel mesh methods for nonlinear problems, which can enable further, even higher degree of parallelization. The arising block matrix system to be solved admits a two-by-two block form with square blocks, for which a very efficient preconditioner exists. It leads to tight eigenvalue bounds for the preconditioned matrix and, hence, to a very fast convergence of a preconditioned Krylov subspace or iterative refinement method. The analytical background is shown as well as some illustrating numerical examples.

关键词： parallel solution evolution equation preconditioning PDE-constrained optimization

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A systolic array for the parallel solution of block tridiagonal linear systems (SATS)

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1999年第1期71卷 57-70页

作者： Evans, DJ Nottingham Trent Univ Dept Comp Nottingham NG1 4BU England

In this paper the parallel solution of block tridiagonal linear systems derived from the finite difference/element discretisation of 2D/3D elliptic partial differential equations which occur frequently in scientific and engineering applications is presented. The direct solution by the Gaussian elimination algorithm is used and a parallel architecture designed employing a systolic array (SATS) which comprises of triangular and rectangular systolic arrays to perform the block triangularisation of the system. The block triangular system is then solved by a pipeline using local memory systems. The results show that when the system order is > 10 then the speedup of the parallel system is significant.

关键词： systolic array block tridiagonal system parallel solution

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Iterative methods and parallel solution of the dam problem

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2001年第3-5期191卷 295-309页

作者： Laitinen, E Lapin, A Pieskä, J Univ Oulu Dept Math Sci FIN-90014 Oulu Finland Kazan VI Lenin State Univ Dept Comp Math & Cybernet Kazan 4200008 Russia

A free boundary problem of fluid flow in the porous medium is considered. A finite difference scheme is constructed and written in the form of the inclusion for the sum of several multi-valued operators. The study of this mesh scheme and iterative algorithms of its numerical solution is performed. solution of the mesh problem by Gauss-Seidel and by Schwarz alternating methods was executed. The numerical results are reported which confirm the theoretical results. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： dam problem domain decomposition methods parallel solution

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Approximation of Voronoi cell attributes using parallel solution

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ADVANCES IN ENGINEERING SOFTWARE 2019年 132卷 7-17页

作者： Masek, Jan Vorechovsky, Miroslav Brno Univ Technol Inst Struct Mech Veveri 331-95 Brno 60200 Czech Republic

This paper concerns an algorithm for fast parallel approximation of selected attributes of hyper-dimensional Voronoi cells in a unit hypercube. The presented algorithm does not require the construction of a corresponding Voronoi diagram (usually by employing the Quick Hull algorithm) which typically is a highly computationally demanding task, especially when performed in higher dimensions. The algorithm is suitable for both the clipped and periodic variants of Voronoi tessellation and provides a significant speedup in a convenient range of practical usage. For the purposes of approximation of selected scalar properties of Voronoi cells, only the distances of points in sample are evaluated using an adequately fine underlying orthogonal mesh. The algorithm estimates e.g. the volumes and centroids of Voronoi cells, radii and coordinates of centers of the corresponding Delaunay hyper-circles. The paper also provides quite accurate explicit error estimators for the extracted attributes due to rasterization and thus the user is given a control over the accuracy by selecting an appropriate discretization density. Among numerous fields in which Voronoi diagrams are being utilized, the authors are concerned with optimization of point samples for the Design of Experiments and also with weighting of integration points in Monte Carlo type integration. In these applications, selected scalar topological descriptors of Voronoi diagrams are being repeatedly computed. As the full Voronoi diagram is not of interest but the resulting cell volumes or shape descriptions have to be repeatedly computed, the presented parallel solution seems highly suitable for these applications.

关键词： Voronoi diagram approximation by rasterization parallel solution error of hyper-dimensional raster

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A NEW QUADRANT INTERLOCKING FACTORIZATION FOR parallel solution OF TRIDIAGONAL LINEAR-SYSTEMS

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1991年第1-2期39卷 99-107页

作者： CHAWLA, MM PASSI, K Department of Mathematics Indian Institute of Technology Hauz Khas New Delhi-110016 India

We introduce a new quadrant interlocking factorization (Q.I.F.) for use with the partition method for the solution of tridiagonal linear systems. A given linear system of sizeNis partitioned intorblocks each of sizen(N=rnneven). The new factorizationWZof the coefficient matrix in each block has the properties that the vectoris invariant under the transformationWand the solution process with coefficient matrixZproceeds from the first and the last unknowns towards the middle ones. These properties of the new factorization help us uncouple the partitioned systems for parallel execution once a core system of order 2ris solved. The scalar count for the resulting algorithm isO(17N) which is the count for cyclic reduction and the partition method of Wang [9]. We also note that for the parallel algorithm based on modified Q.I.F. given in Evanset al. [6] the number of processors required for the algorithm is in terms of semibandwidth and the size of the system; on the other hand, the number of processors required for the present algorithm is in terms of the number of blocks into which the system is partitioned.

关键词： NEW QUADRANT INTERLOCKING FACTORIZATION PARTITION METHOD TRIDIAGONAL LINEAR SYSTEM parallel solution

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An Efficient parallel solution Framework for the Linear solution of Large Systems on PC Clusters

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Tsinghua Science and Technology 2008年第S1期13卷 65-70页

作者： Ozgur Kurc Semih Ozmen Structural Mechanics Laboratory Department of Civil Engineering Middle East Technical University

In this paper, a parallel solution framework for the linear static analysis of large structures on PC clusters is presented. The framework consists of two main steps: data preparation and parallel solution. The parallel solution is performed by a substructure based method with direct solvers. The aim of the data preparation step is to create the best possible substructures so that the parallel solution time is minimized. An actual structural model was solved utilizing both homogeneous and heterogeneous PC clusters to illustrate the performance and applicability of the presented framework.

关键词： substructure parallel solution heterogeneous clusters homogeneous clusters workload bal-ancing partitioning repartitioning

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Analysis of the effectiveness of the DVM / DVMH technology for the parallel solution of the Burgers parametric equation

Analysis of the effectiveness of the DVM / DVMH technology f...

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Ivannikov Memorial Workshop (IVMEM)

作者： Bondarev, Alexander Galaktionov, Vladimir Nnikov, Artem Kuvsh RAS Keldysh Inst Appl Math Moscow Russia

ISBN: (纸本)9781538676905

The work presents a study of the effectiveness of DVM / DVMH technology for parallel solution of one-dimensional parametric problems of gas dynamics. A description is given of the numerical experiments carried out to investigate the problem of finding the optimal ratio between the given number of computational nodes given by the parameters of these nodes and the allocated graphic coprocessors for various problems on specific program codes representing one-dimensional parametric problems of gas dynamics. The results of calculations and the characteristics of efficiency and acceleration are presented.

关键词： Burgers parametric equation parallel solution DVM / DVMH computing technology effectiveness

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A Comparative Study on Two Different Direct parallel solution Strategies for Large-Scale Problems

A Comparative Study on Two Different Direct Parallel Solutio...

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1st International Conference on parallel, Distributed and Grid Computing for Engineering

作者： Bahcecioglu, T. Ozmen, S. Kurc, O. Middle E Tech Univ Dept Civil Engn TR-06531 Ankara Turkey

ISBN: (纸本)9781905088294

This paper presents a comparative study on two different direct parallel solution strategies for the linear solution of large scale actual finite element models: global and domain-by-domain. The global solution strategy was examined by utilizing the parallel multi-frontal equation solver, MUMPS [1], together with a finite element program. In a similar manner a substructure based parallel solution framework [2] was utilized for investigating the domain-by-domain strategy. Various large-scale structural models were solved with both solution strategies in order to illustrate the efficiencies and weaknesses of each solution strategy. The test runs were performed on a homogeneous PC cluster composed of eight computers connected with an ordinary 1 GBit network switch.

关键词： parallel solution multi-frontal substructure large-scale PC cluster

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Research on parallel solution of GRAPES Helmholtz equation

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CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE 2019年第12期31卷

作者： Li, Jingmei Tian, Qiao Zheng, Fangyuan Wu, Weifei Wang, Jiaxiang Harbin Engn Univ Coll Comp Sci & Technol Harbin 150001 Heilongjiang Peoples R China

GRAPES is a new generation of numerical weather prediction system developed and used by Chinese researchers. As the accuracy requirement of weather prediction system is increasing, the grid resolution of the global model is greatly increasing;therefore, the computing power becomes one of the important factors restricting the performance of the numerical weather prediction system. In order to solve the problem, the paper introduces the geometric multi-grid solution to solve the GRAPES Helmholtz equation. The core idea of multi-grid solution is to eliminate the swing component of the residual by iterative algorithm and eliminate the smooth components of the residuals by using the coarse grid interpolation to correct the fine grid solution. This paper designs a parallel solution for GRAPES multi-grid, including grid coarsening operation, smooth operation, and the coarsest grid accurate solution operation. Finally, the actual data with the resolution of 1 is tested, achieving the better acceleration effect. At the same time, the analysis and explanations of the test results have some useful conclusions.

关键词： GRAPES multi-grid parallel solution

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