An Analytical Evaluation of the Factor $k^{2}$ for Protective Conductors

Abstract

At the occurrence of phase-to-ground faults, abnormal levels of thermal energy <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> , due to the Joule effect, will be developed during the clearing time that protective devices take to operate. The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> , also referred to as specific energy or Joule Integral, is accumulated within the elements forming the fault loop, such as the protective conductors (also referred to as equipment grounding conductors), responsible to return ground-fault currents to the source. As a consequence, the temperature of these conductors elevates and may exceed, in the case of an incorrect design, the maximum value that their insulation can withstand. This dangerous situation can cause the failure of the conductor insulation and/or trigger fires in neighboring materials. The maximum <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> that protective conductors can endure is, therefore, crucial in order to guarantee the electrical safety. The parameters on which the maximum <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> depends are described by the factor <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , which will be herein discussed and analytically evaluated. The intention of the authors is to provide a theoretical support to the Power Systems Grounding Working Group of the Technical Books Coordinating Committee IEEE P3003.2 “Recommended Practice for Equipment Grounding and Bonding in Industrial and Commercial Power Systems”; the working group is currently elaborating a dot standard based on IEEE Standard 142-2007, also referred to as the Green Book. To this purpose, a comparison with existing formulas, currently present in codes, standards of the International Electrotechnical Commission and of the IEEE, as well in the literature, will be also presented.