A digital-computer-programmed topological method of coordinate selection for numerical computations in an electrical network

• Main Author: Lock, Kenneth
• Format: Others
• Published: 1962
• Online Access: https://thesis.library.caltech.edu/6604/1/Lock_k_1962.pdf; Lock, Kenneth (1962) A digital-computer-programmed topological method of coordinate selection for numerical computations in an electrical network. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1KC2-ZF72. https://resolver.caltech.edu/CaltechTHESIS:08192011-102613198 <https://resolver.caltech.edu/CaltechTHESIS:08192011-102613198>

In this thesis an algorithm is developed for setting up the differential equations and initial conditions of an electrical network of arbitrarily connected capacitors, resistors, inductors, multiwinding ideal transformers, and ideal voltage and current sources that topologically represents a large class of systems. The algorithm formulates the equation in a set of coordinates such that all matrices to be inverted are nonsingular. The topological description of the circuit is used to select a nonsingular set of coordinates which enables the computation of the transient responses and the short circuit admittances to a set of arbitrarily chosen ports of a network. Transformers are accounted for by appropriately selecting a set of dependent variables from the set of transformer linear equations. The algorithm for selecting a nonsingular set of coordinates, being mainly symbol manipulations, is coded in LISP. It is also shown that the same method may be applied to systems with nonlinear parameter matrices.