An Effective Approximate Mathematical Expression for Non-Linear Resistance Characteristics of Metal Oxide Elements

Abstract

A metal oxide varistor (MOV), manufactured from a blend of zinc oxide and other metal oxides, undergoes changes in resistance or resistivity depending on changes in applied voltage or electric field strength. Typically, the nonlinear resistive characteristics of MOV elements are determined through experimental measurements of voltage and current. This article introduces a mathematical expression comprising two power functions and a constant term with five adjustable coefficients. It is utilized to describe the voltage-current or electric field-current density characteristics across a wide range of current or current density, spanning from microamperes to several tens of kiloamperes or from several hundred A/m<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> to a few hundred of kA/m<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>, respectively. This expression accurately reproduces the observed nonlinear resistive behaviors of several low-voltage MOV elements. A noniterative fitting method is developed to determine the expression's five coefficients, using integration to linearize nonlinear characteristics without requiring iterations or uniform data sampling. Through comparison with a previously proposed expression and experimental data, the proposed technique demonstrates remarkably high accuracy. Furthermore, the proposed technique is applied to accurately estimate the parasitic inductance of an MOV and its lead wires during a residual voltage test conducted with an 8/20-microsecond impulse current.