## Abstract

The relationship between the electric current and the magnetism is well demonstrated by the Faraday's induction and conductivity laws. Under this concept, it follows that, through intensive laboratory experiments, it has been established that the arcing fault current path related sparks are indeed source of ElectroMagnetic Radiated (EMR) signals waves. These EMR can be detected and located at a relatively remote distance, with the aid of directional antennas arrays, at considerable and reasonable accuracy. Under this novel concept of power arcing fault source point triangulation, the arc EMR data play a critical role in providing essential timing information onto which the arc fault detection and location algorithm is based. Thus, from these arc EMR recorded and gathered data, the signals Time Differences Of Arrival (TDOA) information or signatures can be easily extracted from a pair of antennas, with the aid of an appropriate signal processing tool, namely the cross-correlation (Xcorr) function. Since the electric arc phenomenon is unpredictable practically, therefore, the use of the arc signal Time Of Arrival (TOA), is impossible for the fault source point triangulation solution. In contrast, the values of TDOA seem to be efficient for solving the system of hyperbolic equations which has been imposed by this particular field measurement structure and constraints. It is of interest to mention that, the arc fault EMR field measurement structure and constraints are given and determined by the distributed antennas arrays locations or positions only. In other words, with the knowledge of both the antennas arrays locations Cartesian Coordinates (CC), together with the TDOA values, it is possible to pinpoint the unknown target power arcing fault exact source point position or location, not only in two-dimensions (2D), but also in three-dimensions (3D) Euclidean plane. Thus, this kind of arc fault source point position or location solution finding is generally referred to as a source point triangulation method. This source point triangulation method consists of solving a system of hyperbolic equations as aforementioned. In fact, under a geometry analysis process, it follows that, if only if the arcing fault hazard formation time is known in advance, therefore, the solution of a system of hyperbolic equations consists of finding the intersection point of at least two or more circles. Such that, each of these circles, will be centered at each antenna in such a way that each circle will have a radius given by the distance derived from the value of TOA together with the power arcing fault hazard ignition time stamp or signature. In contrast, since the arcing fault hazard formation stage time is unknown in practice, therefore the solution of the system of hyperbolic equations consists of finding the intersection point of at least two or more hyperbolas. Such that each of these hyperbolas will have a focal point determined by the location of each antenna and the distance between pair of foci will be given by the values of TDOA. However, generally, a system of hyperbolic equations can be solved either with the aid of an analytic method or with that of a numerical method (also known as iterative method). Unlike the majority of this research field related relevant published literature into which the iterative methods have been used intensively, this paper presents an accurate analytic geometry method in order to solve the electric arc faults EMR source point exact location or position. As a result, it appears that, this novel proposed analytic geometry method has shown its potential in clarifying d considerable accuracy.

Original language | English |
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Pages (from-to) | 327-345 |

Number of pages | 19 |

Journal | International Review of Electrical Engineering |

Volume | 17 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Jul 2022 |

MoE publication type | A1 Journal article-refereed |

## Keywords

- Analytical Method
- Arc Fault Detection and Location Algorithm
- arc Fault Source Solution
- Arc Source Point Position
- Electromagnetic Signals Time Difference of Arrival
- Foci of Hyperbolas Determination
- Intersection Points of Hyperbolas
- Power Arcing Faults
- System of Hyperbolic Equations
- Translation and Rotation of Axes