Efficient iterative methods for ill-conditioned linear and nonlinear network problems.

摘要

We propose two methods in this thesis: an iterative method for solving a complex-symmetric linear system arising in electric power networks, and a method for numerical solution of the swing equations. The swing equations are a system of differential-algebraic equations (DAE) used to determine transient stability of electrical power networks. Our iterative method extends Gremban, Miller, and Zagha's [11] support-tree preconditioner to handle complex weights and vastly different admittances. The underlying iteration is a modification to BiCG-STAB to enhance accuracy. Our method for numerical solution of the swing equations is based on a standard linear multi-step method for solving DAEs combined with the linear solver described above. In the case of “islanding,” our method represents a significant improvement over methods currently used. Since the linear solver does not apply directly to the transient stability equations, we include analysis to show that the DAE solver's inner loop can be reduced to a problem amenable to the technique proposed in the first part of this thesis. Computational results for both methods are described.