Parallel-in-Time Power System Simulation Using a Differential Transformation Based Adaptive Parareal Method

Liu, Yang; Park, Byungkwon; Sun, Kai; Dimitrovski, Aleksandar; Simunovic, Srdjan

doi:10.1109/oajpe.2022.3220112

Cited by 5 publications

(5 citation statements)

References 32 publications

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“…In addition, a shorter simulation length (e.g., the 1 second simulation) is often desired for the fast and robust convergence of the Parareal algorithm in power system simulations. In this aspect, the windowing approach can be utilized to improve the convergence of the Parareal algorithm for a longer simulation length (e.g., the 10 second simulation); the Parareal algorithm can be applied to the 1 second simulation window 10 times sequentially to obtain the 10 second simulation trajectory [23], [24], [35].…”

Section: Overview Of the Parareal Algorithmmentioning

confidence: 99%

Stochastic Power System Dynamic Simulation Using Parallel-in-Time Algorithm

Park

2024

IEEE Access

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With increasing grid modernization efforts, future electric grids will be governed by more complex and faster dynamics with the high penetration of new components such as power electronic-based control devices and large renewable resources. These lead to the importance of developing real-time dynamic security assessment under the consideration of uncertainties, whose main tool is time-domain simulation. Though there are many efforts to improve the computational performance of time-domain simulation, its focus has been on the deterministic differential-algebraic equations (DAEs) without modeling uncertainties inherent in power system networks. To this end, this paper investigates large-scale time-domain simulation including effects of stochastic perturbations and ways for its computational enhancement. Particularly, it utilizes the parallel-in-time (Parareal) algorithm, which has shown great potentials, to solve stochastic DAEs (SDAEs) efficiently. A general procedure to compute the numerical solution of SDAEs with the Parareal algorithm is described. Numerical case studies with 10-generator 39-bus system and 327-generator 2383bus system are performed to demonstrate its feasibility and efficiency. We also discuss the feasibility of employing semi-analytical solution methods, using the Adomian decomposition method, to solve SDAEs. The proposed simulation framework provides a general solution scheme and has the potential for fast and large-scale stochastic power system dynamic simulations.INDEX TERMS Brownian motion, parallel algorithms, power system dynamics, semi-analytical solution, stochastic differential algebraic equations, time domain simulation.

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Section: Overview Of the Parareal Algorithmmentioning

confidence: 99%

Stochastic Power System Dynamic Simulation Using Parallel-in-Time Algorithm

Park

2024

IEEE Access

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“…Another study focuses on the efficiency of the double Laplace-Sumudu transform (DLST) in solving partial differential equations. Theorems regarding the properties of DLST are proven, including the convolution theorem, which facilitates the solution of partial differential equations [7]. Population balance equations, prevalent in fields such as plan-etary science and chemical study, pose significant challenges due to model complexity.…”

Section: Introductionmentioning

confidence: 99%

An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical Physics

Li,

Wang

2024

IEEE Access

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The Laplace-Sumudu-Elzaki Transformation (LSET) represents a significant advancement in mathematical physics, offering versatile tools for solving differential equations and analyzing complex systems. This article provides a comprehensive introduction to LSET and explores its diverse applications in the realm of mathematical physics. Beginning with an overview of the fundamental principles and properties of the Laplace, Sumudu, and Elzaki transformations, we focus on their comparative analysis and elucidate their interrelations. Emphasizing the practical significance of these transformations, we discuss their applications in solving ordinary and partial differential equations, integral equations, delay differential equations, and fractional calculus problems. We investigate numerical techniques and algorithms for computing LSET, including implementation examples using popular software packages. We examine recent developments, emerging trends, and future directions in LSET research. Through case studies and illustrative examples, we demonstrate the efficacy of LSET in addressing real-world challenges across various domains of mathematical physics. This article serves as a valuable resource for researchers, practitioners, and students interested in harnessing the power of LSET to unravel complex phenomena and advance scientific knowledge.

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“…(2) parallel computing, which leverages high-performance computers to speed up the simulations [6][7][8][9][10][11][12][13]. In these methods, the computation burdens of solving power system DAEs are split into multiple independent sub-computational tasks so that they could be executed in multiple cores.…”

Section: Introductionmentioning

confidence: 99%

“…In these methods, the computation burdens of solving power system DAEs are split into multiple independent sub-computational tasks so that they could be executed in multiple cores. Many different methods are proposed to improve the parallelizability of power system simulation, for example, the multi-area Thévenin equivalents method [10], the waveform relaxation method [11], and the recently studied Parareal method [7,12,13]. These methods are often categorized as parallelin-time methods, parallel-in-space methods, or both.…”

Section: Introductionmentioning

confidence: 99%

“…The semi-analytical solution of power system models could be derived by many methods, for example, the differential transformation method [14] and the Adomian decomposition method [15]. Recently, researchers are also investigating the potential of combining the semi-analytical solution methods and parallel computing methods for achieving faster-than-realtime simulation, for example, [12,13]. However, the potential of these methods for practical large-scale power systems remains to be further investigated.…”

Section: Introductionmentioning

confidence: 99%

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AI-Based Faster-Than-Real-Time Stability Assessment of Large Power Systems with Applications on WECC System

et al. 2023

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Achieving clean energy goals will require significant advances in regard to addressing the computational needs for next-generation renewable-dominated power grids. One critical obstacle that lies in the way of transitioning today’s power grid to a renewable-dominated power grid is the lack of a faster-than-real-time stability assessment technology for operating a fast-changing power grid. This paper proposes an artificial intelligence (AI) -based method that predicts the system’s stability margin information (e.g., the frequency nadir in the frequency stability assessment and the critical clearing time (CCT) value in the transient stability assessment) directly from the system operating conditions without performing the conventional time-consuming time-domain simulations over detailed dynamic models. Since the AI method shifts the majority of the computational burden to offline training, the online evaluation is extremely fast. This paper has tested the AI-based stability assessment method using multiple dispatch cases that are converted and tuned from actual dispatch cases of the Western Electricity Coordinating Council (WECC) system model with more than 20,000 buses. The results show that the AI-based method could accurately predict the stability margin of such a large power system in less than 0.2 milliseconds using the offline-trained AI agent. Therefore, the proposed method has great potential to achieve faster-than-real-time stability assessment for practical large power systems while preserving sufficient accuracy.

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Parallel-in-Time Power System Simulation Using a Differential Transformation Based Adaptive Parareal Method

Cited by 5 publications

References 32 publications

Stochastic Power System Dynamic Simulation Using Parallel-in-Time Algorithm

Stochastic Power System Dynamic Simulation Using Parallel-in-Time Algorithm

An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical Physics

AI-Based Faster-Than-Real-Time Stability Assessment of Large Power Systems with Applications on WECC System

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