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UBC Theses and Dissertations

Transform based algorithms for transient analysis of nonlinear networks Agnew, David George

Abstract

In this thesis, computer methods for the transient analysis of networks are investigated. Numerical transform techniques are developed to solve the differential equations a rising in network simulation. Extensions to permit inclusion of some nonlinear elements are considered. Efficient methods for implementing the techniques are developed. For the transform techniques, error estimates are derived. Using these estimates, algorithms for the automatic determination of solution parameters are developed. Advantages over other numerical transform and numerical integration techniques are revealed. For nonlinear networks, it is shown that use of a Newton-Raphson scheme for solving nonlinear algebraic equations is difficult when coupled with transform methods for solving differential equations. Instead, an alternative technique is developed. Steps which are easily generated, but which only approximate Newton-Raphson steps, are used. The implementation of the transform techniques and the nonlinear solution is considered. A program using a sparse tableau form of network equations is discussed. The program is in two sections. The first reads in the network descriptions, and writes a series of Fortran subroutines for performing the analysis efficiently. The subroutines must be compiled, and are used by the second part of the program to perform the actual analysis. Examples which illustrate the performance of the various techniques are presented.

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