Network Reduction and Gauss Elimination

In this chapter, sparse vector and sparse matrix techniques are discussed. The principal properties on which sparse techniques are based are first presented using network concepts such as network reduction and network expansion. Gauss elimination is then introduced so these ideas can be used for solving large sparse network problems.

[1]  William F. Tinney,et al.  Adaptive Reductions for Power Flow Equivalents , 1987, IEEE Transactions on Power Systems.

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

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

[4]  F. Broussolle,et al.  State Estimation in Power Systems: Detecting Bad Data through the Sparse Inverse Matrix Method , 1978, IEEE Transactions on Power Apparatus and Systems.

[5]  S. Deckmann,et al.  Studies on Power System Load Flow Equivalencing , 1980, IEEE Transactions on Power Apparatus and Systems.

[6]  William F. Tinney,et al.  Compensation Methods for Network Solutions by Optimally Ordered Triangular Factorization , 1972 .

[7]  I. Duff,et al.  A Comparison of Some Methods for the Solution of Sparse Overdetermined Systems of Linear Equations , 1976 .

[8]  David S. Watkins,et al.  Fundamentals of matrix computations , 1991 .

[9]  William F. Tinney,et al.  Power Flow Solution by Newton's Method , 1967 .

[10]  J. B. Ward.  Equivalent Circuits for Power-Flow Studies , 1949, Transactions of the American Institute of Electrical Engineers.

[11]  I. Duff,et al.  Direct Methods for Sparse Matrices , 1987 .

[12]  Felix F. Wu,et al.  Critical review of external network modelling for online security analysis , 1983 .

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

[14]  S. Deckmann,et al.  Numerical Testing of Power System Load Flow Equivalents , 1980, IEEE Transactions on Power Apparatus and Systems.

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

[16]  R. Bacher,et al.  Faster Local Power Flow Solutions: The Zero Mismatch Approach , 1989, IEEE Power Engineering Review.

[17]  Richard A. Smith,et al.  EXTERNAL NETWORK MODELING - RECENT PRACTICAL EXPERIENCE , 1994 .

[18]  W. F. Tinney,et al.  Partial refactorization with unrestricted topology changes , 1995 .