Improved Analysis of Non-Uniform Windings Using New Sectionalization Procedure

Abstract

The paper deals with the frequency and transient analysis of transmission lines and transformer windings. It presents a new solution procedure based on efficiently increasing the number of sections used for simulating these elements. The proposed technique is also applicable to non-uniform elements and is characterized by a relatively small computational burden in terms of the calculation steps and memory requirement. The increase of the number of sections is followed by the analytical solution (in Mathematica) of the simultaneous differential and algebraic equations governing the elements and the use of the ABCD generalized circuit constants of two-port networks. The new procedure is applied to a representative case study in order to show how to increase the number of transformer winding’s sections from the initial number 5 to 10, 15, or 40. The s-domain expressions for the different currents and voltages can then be derived and numerically Laplace-inverted using the Fourier series approximation algorithm. The results include, among others, the frequency and time domain performance of the source current injected into the winding and the currents flowing through the different sections as well as the voltage distribution along the winding, the input impedance and the resonance frequencies. The frequency plots are also given in a logarithmic form and occasionally interpreted through the use of a parametric polar impedance representation.