An Asymptotic Regression Predictive Model for Sphere Gap Voltage with Gap Diameter and Gap Spacing

Abstract

This document develops two asymptotic regression models to estimate the value of sphere gap breakdown voltage from any value of gap diameter and gap spacing under IEC 60052 table 2 and table 3 to facilitate those two IEC tables that provide limited values consisting of 12 sizes in sphere diameter ranging from 20 mm to 2000 mm and sphere gap spacing range from 0.5 mm to 1500 mm. In those two IEC tables, the relationship of sphere gap voltages from sphere gap diameter and gap spacing is nonlinear in which asymptotic regression models are proposed is in the form Voltage = b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> + b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> e <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Spacing + b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> Diameter that follows the law of diminishing returns that imitates the relationship between sphere gap voltages versus sphere gap diameter and gap spacing. By using this asymptotic regression, this document provides expressions of standard sphere gap voltages as functions of the sphere gap diameter and gap spacing. The expressions are in high accuracy measured by r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> values. These proposed asymptotic regression equations can be used to estimate sphere gap voltage breakdown from any values of sphere gap diameter and gap spacing that are not specified by IEC 60052 tables.