Full-Wave 3-D Transient Analysis With Method of Moments and Numerical Laplace Transform Including Resistive Non-Linear Elements

Abstract

Methods based on both time ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> )-domain and frequency ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> )-domain have been used for electromagnetic transient (EMT) analysis using both circuit-theory and field-theory approaches. Methods based on circuit theory are fast and convenient but may become inapplicable to many engineering problems due to simplifications such as the transverse electromagnetic assumptions. Moreover, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> -domain-based techniques rely on approximate methods to account for frequency dependence, which is an essential characteristic of electric conductors, equipment and soil environment. In this paper, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> -domain solutions obtained from the method of moments (MoM) discretization of the electric field integral equation (EFIE) are converted to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t-</i> domain using the numerical Laplace transform (NLT) by means of post-processing. This circumvents the need to formulate the EFIE and MoM based on the complex frequency which would be required for their application to conventional NLT. Hence, existing MoM implementations can be used to perform a full-wave 3-D EMT analysis for a wide range of power system applications. Examples include energizations of 3-D power system networks with fast and non-vanishing excitations such as step functions, as well as modeling non-linear elements using the piecewise linear approximation. Results from experimental measurements, finite-difference <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> -domain method, and EMT-type software confirm the validity of the proposed method for power system transients in the range of microseconds down to nanoseconds.