Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation
Abstract : With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. The selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases.
? To compare the stability of Parareal algorithm with the HAM-based coarse solver, we also implemented the standard numerical-based predictor-corrector (Trap) method for the coarse operator .
? Usually, there exist an optimal number of terms for achieving the desired accuracy and time performance.
? Also, the ADM-based semi-analytical coarse solver allows users to select different number of terms for different components.
? The ADM method is a promising SAS approach which approximates solution of differential equations by infinite terms and each term can take different forms, for example, polynomial function of time.
? This simplification was necessary in the past in order to reduce the size of the problem and achieve solutions in reasonable times. It could also be justified in legacy distribution systems with passive loads and almost no sources.
? The SAS methods have been widely applied to solve nonlinear ordinary differential equations (ODEs) and DAE problems in the applied sciences and engineering.
? In addition, it is a powerful analytic technique for strongly nonlinear problems, provides a rapid convergence to a solution, and thus has shown the potential for fast power system simulations.
? This paper considers two promising SAS methods whose details will be discussed in the subsequent section.
• This paper proposes parareal in time algorithm for the dynamic simulations of large power systems. Parareal algorithm seems to be a promising approach which can achieve higher speedup ratios.
• “Parareal in Time” algorithm first proposed in provides flexibility in terms of both the numerical method and the initial seed.
• The parareal method decomposes the time evolution problem into a series of independent evolution problems on smaller time intervals.
• Parallel computing on high performance computing (HPC) architectures and parallelization techniques have become an increasingly attractive choice for researchers.
? Parareal belongs to the class of Parallelin-time algorithms for solution of systems of differential-algebraic equations in parallel over an interval of time.The selection of a reasonably fast and accurate coarse solution is crucial to improve the performance of Parareal algorithm.
? To enhance its computational performance, several parallel algorithms for power system time domain simulations have been proposed with the rapid development of high-performance parallel computing platforms.
? The objective of this paper is to investigate and improve the performance and feature of Parareal algorithm for power system dynamic simulations in two aspects.
? More terms can improve the accuracy but also brings more computation burden. Usually, there exist an optimal number of terms for achieving the desired accuracy and time performance.
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