Fast time domain simulation of power systems using multilevel preconditioners with adaptive reconstruction strategies

Time domain simulation (TDS) is an important tool for the analysis of the dynamic behavior of power systems. TDS is a hard computational problem due to the complexity in solving a sequence of large linear systems based on Jacobian matrices. Iterative solvers with various preconditioning techniques have been applied to solve these systems, and among which GMRES is reported to be the most robust. This paper explores the use of multilevel preconditioning technique based on INDependent SETs (INDSETs) and with fill-in guidance. To reduce the system size more effectively, we propose the use of large supernodes instead of single vertices for INDSET choice. Furthermore, a dynamic preconditioner reconstruction strategy is proposed to incorporate the runtime convergence information of the linear system solving process during the simulation. Experiments show that the proposed multilevel preconditioners have a much lower memory usage and computational overhead than their ILU counterparts. By using supernodes and fill-in guidance, we further reduce the size of the multilevel system and total number of nonzeros by 40% and 13%, respectively. The proposed preconditioner reconstruction strategy shows good adaptivity and performance compared with the strategies based on fixed time intervals.

[1]  M. A. Pai,et al.  Transient Stability Simulation by Waveform Relaxation Methods , 1987, IEEE Power Engineering Review.

[2]  F. Alvarado,et al.  Computational complexity in power systems , 1976, IEEE Transactions on Power Apparatus and Systems.

[3]  Svetozar Margenov,et al.  On Multilevel Preconditioners which are Optimal with Respect to Both Problem and Discretization Parameters , 2003 .

[4]  Hai-Xiang Lin,et al.  A unifying graph model for designing parallel algorithms for tridiagonal systems , 2001, Parallel Comput..

[5]  S. Parter.  The Use of Linear Graphs in Gauss Elimination , 1961 .

[6]  K. W. Chan.  Parallel algorithms for direct solution of large sparse power system matrix equations , 2001 .

[7]  Peter W. Sauer,et al.  A preconditioned iterative solver for dynamic simulation of power systems , 1995, Proceedings of ISCAS'95 - International Symposium on Circuits and Systems.

[8]  H. Chiang,et al.  Solving the nonlinear power flow equations with an inexact Newton method using GMRES , 1998 .

[9]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[10]  M. A. Pai,et al.  Iterative solver techniques in large scale power system computation , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[11]  P. Kundur,et al.  Power system stability and control , 1994 .

[12]  Weimin Zheng,et al.  Updating preconditioner for iterative method in time domain simulation of power systems , 2011 .

[13]  Peter W. Sauer,et al.  Iterative solver techniques in fast dynamic calculations of power systems , 2001 .

[14]  Y. Saad.  BILUM : Block versions of multi-elimination ILU preconditioner for general sparse linear systems , 1999 .

[15]  Wayne J. Pullan,et al.  Simple ingredients leading to very efficient heuristics for the maximum clique problem , 2008, J. Heuristics.

[16]  M. La Scala,et al.  Parallel-in-time implementation of transient stability simulations on a transputer network , 1994 .

[17]  Sun Hongbin.  Decomposition and Coordination Modes for Transient Stability Simulation , 2005 .

[18]  Yousef Saad,et al.  ILUM: A Multi-Elimination ILU Preconditioner for General Sparse Matrices , 1996, SIAM J. Sci. Comput..

[19]  A. Semlyen,et al.  A New Preconditioned Conjugate Gradient Power Flow , 2002, IEEE Power Engineering Review.

[20]  Diogo Vieira Andrade,et al.  Fast local search for the maximum independent set problem , 2008, Journal of Heuristics.

[21]  J. Shu,et al.  A parallel transient stability simulation for power systems , 2005, IEEE Transactions on Power Systems.

[22]  Roberto Battiti,et al.  Reactive Local Search for the Maximum Clique Problem1 , 2001, Algorithmica.

[23]  Peter W. Sauer,et al.  Power System Dynamics and Stability , 1997 .

[24]  M. Pai.  Energy function analysis for power system stability , 1989 .

[25]  M. Pai,et al.  Iterative solver techniques in the dynamic simulation of power systems , 2000, 2000 Power Engineering Society Summer Meeting (Cat. No.00CH37134).