Parallel Simulation of Power Systems Transient Stability Based on Implicit Runge–Kutta Methods and <i>W</i>-transformation

Liu, Kaipei; Liao, Xiaobing; Li, Yuye

doi:10.1080/15325008.2017.1400606

Cited by 7 publications

(3 citation statements)

References 27 publications

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“…However, these can be useful to obtain solution with higher accuracy also in interior integration points. A GPU implementation of the fully implicit IRK method is found in Reference 54, applied to a system of ODEs. There, the matrices to be solved have the same structure as in (7) and the preconditioner has a tridiagonal structure.…”

Section: A Summary Of Some Earlier Presented Stage‐parallel Precondit...mentioning

confidence: 99%

Stage‐parallel preconditioners for implicit Runge–Kutta methods of arbitrarily high order, linear problems

Axelsson,

Dravins,

Neytcheva

2023

Numerical Linear Algebra App

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Fully implicit Runge–Kutta methods offer the possibility to use high order accurate time discretization to match space discretization accuracy, an issue of significant importance for many large scale problems of current interest, where we may have fine space resolution with many millions of spatial degrees of freedom and long time intervals. In this work, we consider strongly A‐stable implicit Runge–Kutta methods of arbitrary order of accuracy, based on Radau quadratures. For the arising large algebraic systems we introduce efficient preconditioners, that (1) use only real arithmetic, (2) demonstrate robustness with respect to problem and discretization parameters, and (3) allow for fully stage‐parallel solution. The preconditioners are based on the observation that the lower‐triangular part of the coefficient matrices in the Butcher tableau has larger in magnitude values, compared to the corresponding strictly upper‐triangular part. We analyze the spectrum of the corresponding preconditioned systems and illustrate their performance with numerical experiments. Even though the observation has been made some time ago, its impact on constructing stage‐parallel preconditioners has not yet been done and its systematic study constitutes the novelty of this article.

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Section: A Summary Of Some Earlier Presented Stage‐parallel Precondit...mentioning

confidence: 99%

Stage‐parallel preconditioners for implicit Runge–Kutta methods of arbitrarily high order, linear problems

Axelsson,

Dravins,

Neytcheva

2023

Numerical Linear Algebra App

View full text Add to dashboard Cite

show abstract

“…Transient stability appears as the application where GPU is second-most used refs. [18,[61][62][63][64][65][66][67][68][69][70][71][72][73][74]. In refs.…”

Section: Transient Stabilitymentioning

confidence: 99%

A Review of Parallel Heterogeneous Computing Algorithms in Power Systems

et al. 2021

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The power system expansion and the integration of technologies, such as renewable generation, distributed generation, high voltage direct current, and energy storage, have made power system simulation challenging in multiple applications. The current computing platforms employed for planning, operation, studies, visualization, and the analysis of power systems are reaching their operational limit since the complexity and size of modern power systems results in long simulation times and high computational demand. Time reductions in simulation and analysis lead to the better and further optimized performance of power systems. Heterogeneous computing—where different processing units interact—has shown that power system applications can take advantage of the unique strengths of each type of processing unit, such as central processing units, graphics processing units, and field-programmable gate arrays interacting in on-premise or cloud environments. Parallel Heterogeneous Computing appears as an alternative to reduce simulation times by optimizing multitask execution in parallel computing architectures with different processing units working together. This paper presents a review of Parallel Heterogeneous Computing techniques, how these techniques have been applied in a wide variety of power system applications, how they help reduce the computational time of modern power system simulation and analysis, and the current tendency regarding each application. We present a wide variety of approaches classified by technique and application.

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“…e IRK method has wider stable region and higher accuracy compared with explicit Runge-Kutta methods [7]. erefore, the IRK method is suitable for solving stiff differential equations, and abundant results have been mentioned in the literature [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Study on Banded Implicit Runge–Kutta Methods for Solving Stiff Differential Equations

Liu

Zhang

2019

Mathematical Problems in Engineering

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The implicit Runge–Kutta method with A-stability is suitable for solving stiff differential equations. However, the fully implicit Runge–Kutta method is very expensive in solving large system problems. Although some implicit Runge–Kutta methods can reduce the cost of computation, their accuracy and stability are also adversely affected. Therefore, an effective banded implicit Runge–Kutta method with high accuracy and high stability is proposed, which reduces the computation cost by changing the Jacobian matrix from a full coefficient matrix to a banded matrix. Numerical solutions and results of stiff equations obtained by the methods involved are compared, and the results show that the banded implicit Runge–Kutta method is advantageous to solve large stiff problems and conducive to the development of simulation.

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Parallel Simulation of Power Systems Transient Stability Based on Implicit Runge–Kutta Methods and W-transformation

Cited by 7 publications

References 27 publications

Stage‐parallel preconditioners for implicit Runge–Kutta methods of arbitrarily high order, linear problems

Stage‐parallel preconditioners for implicit Runge–Kutta methods of arbitrarily high order, linear problems

A Review of Parallel Heterogeneous Computing Algorithms in Power Systems

Study on Banded Implicit Runge–Kutta Methods for Solving Stiff Differential Equations

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