Improved Sparsity Techniques for Solving Network Equations in Transient Stability Simulations

When solving network algebraic equations during power system transient stability simulations, the nonzero elements in the independent vector and the elements needed in the solution vector are determined by the location of source nodes. Different kinds of source nodes will have a different influence on the solution process of the network equations. According to these features of source nodes, sparsity techniques, more specifically, the node ordering algorithm and sparse vector method, are improved in this paper. A new heuristic ordering algorithm is proposed to enhance the efficiency of the sparse vector method by reducing the number of nodes in the factorization path set of source nodes while maintaining the sparsity of the factorized matrix. A multipath sparse vector method is proposed to avoid the unnecessary computation in the iterative solution process of the network equations, whereby the idea of the method is to form different paths for different types of source nodes. Different paths are used to solve different elements in the solution vector. The correctness and effectiveness of these improvements is proven by the simulation results of three practical power systems (up to 13 490 nodes) and six IEEE examples (up to 162 nodes).

[1]  R. Bacher,et al.  Approximate sparse vector techniques for power network solutions , 1991, Conference Papers Power Industry Computer Application Conference.

[2]  Hermann W. Dommel,et al.  Fast Transient Stability Soultions , 1972 .

[3]  F. Alvarado,et al.  Partitioned sparse A/sup -1/ methods (power systems) , 1990 .

[4]  R. Baharom,et al.  Modeling of power system dynamic devices incorporated in Dynamic Computation for Power Systems (DCPS) for transient stability analysis , 2011, 2011 IEEE International Electric Machines & Drives Conference (IEMDC).

[5]  H. Wilf,et al.  Direct Solutions of Sparse Network Equations by Optimally Ordered Triangular Factorization , 1967 .

[6]  Dechao Xu,et al.  A Two-Layered Parallel Static Security Assessment for Large-Scale Grids Based on GPU , 2017, IEEE Transactions on Smart Grid.

[7]  Fernando L. Alvarado,et al.  Sparse matrix inverse factors (power systems) , 1990 .

[8]  Leopoldo García Franquelo,et al.  An efficient ordering algorithm to improve sparse vector methods , 1988 .

[9]  W. F. Tinney,et al.  Sparse Vector Methods , 1985, IEEE Transactions on Power Apparatus and Systems.

[10]  Alan George,et al.  The Evolution of the Minimum Degree Ordering Algorithm , 1989, SIAM Rev..

[11]  W. F. Tinney,et al.  Sparsity-Oriented Compensation Methods for Modified Network Solutions , 1983, IEEE Transactions on Power Apparatus and Systems.

[12]  L. G. Franquelo,et al.  Mode ordering algorithms for sparse vector method improvement , 1988 .

[13]  Thomas J. Overbye,et al.  Geomagnetically induced current sensitivity to multiple substation grounding resistances , 2017, 2017 IEEE Texas Power and Energy Conference (TPEC).

[14]  Martin Head-Gordon,et al.  Fast Sparse Cholesky Decomposition and Inversion using Nested Dissection Matrix Reordering. , 2011, Journal of chemical theory and computation.

[15]  Hoay Beng Gooi,et al.  New ordering methods for sparse matrix inversion via diagonalization , 1997 .

[16]  Timothy A. Davis,et al.  Hypergraph-Based Unsymmetric Nested Dissection Ordering for Sparse LU Factorization , 2010, SIAM J. Sci. Comput..

[17]  R. Betancourt,et al.  An efficient heuristic ordering algorithm for partial matrix refactorization , 1988 .

[18]  Hai Jin,et al.  Implementation and Optimization of GPU-Based Static State Security Analysis in Power Systems , 2017, Mob. Inf. Syst..

[19]  Pierre Ramet,et al.  Reordering Strategy for Blocking Optimization in Sparse Linear Solvers , 2017, SIAM J. Matrix Anal. Appl..

[20]  Vladimir Brandwajn,et al.  Partial Matrix Refactorization , 1986, IEEE Transactions on Power Systems.

[21]  W. F. Tinney,et al.  Orthogonal sparse vector methods , 1992 .

[22]  Vahid Jalili-Marandi,et al.  Real-Time Simulation Using Transient Stability, ElectroMagnetic Transient and FPGA-Based High-Resolution Solvers , 2012, 2012 SC Companion: High Performance Computing, Networking Storage and Analysis.

[23]  G. Soykan,et al.  Parallel-in-space implementation of transient stability analysis on a Linux cluster with infiniband , 2012, 2012 North American Power Symposium (NAPS).