A Simple Mathematical Expression for Nonlinear Resistive Characteristics of Metal Oxide Elements in Lightning Surge Analysis

Abstract

Accurate simulations of transient phenomena in electric power systems with metal oxide varistors (MOVs) or lightning arresters (LAs) using the finite-difference time-domain (FDTD) method for solving Maxwell's equations require simple and accurate representations of MOVs or LAs. By representing a small cell within a MOV or LA with resistivity (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</i>) dependent on electric field (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i>), these components can be modeled in three dimensions and seamlessly integrated into FDTD simulations. Achieving computational efficiency in FDTD simulation necessitates avoiding iterative computations for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</i> from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i>. Hence, there is a significant need for a simple and accurate mathematical expression of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</i> in terms of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i>. This study presents a methodology for deriving a three-coefficient exponential function from experimental data. By using integration properties, this method transforms nonlinear characteristics into linear ones without iterative processes or uniform data sampling. It also incorporates data weighting and outlier discrimination for enhanced accuracy. Comparative analysis with previous methods based on the ordinary least squares method and experimental data, using an applied current with a rise time of approximately 8 μs, confirms high accuracy and effectiveness in computing residual voltages resulting from impulse current injection using the FDTD method.