Low-Voltage Electric Arc Reconstruction From Magnetic Field Measurements

The knowledge of current density distribution gives important information for the study of the electric arc in low-voltage circuit breakers. Available experimental approaches to investigate the electric arc behavior include electrical measurements, optical, and magnetic diagnostic techniques. However, noninvasive experimental methods able to obtain the electric arc current density cannot be found in the literature. This article presents a nonintrusive diagnostic technique able to reconstruct the 3-D electric arc current density from its magnetic field measurements by solving a magnetic inverse problem. This inverse problem is known to be ill-posed, and Tikhonov regularization is used together with the L-curve method. Zero-divergence condition on the current density and boundary conditions are incorporated into the formulation of the inverse problem with the help of Whitney elements. A magnetic field measurement system is developed based on a Hall-effect magnetic sensor array and a data acquisition board. The sensor array is composed of 64 mono-axial analog-bipolar sensors distributed in eight columns and eight rows. The maximum measurable magnetic field of the sensor is 9 mT. The data acquisition board consists of eight analog-to-digital converters with a maximum sampling rate of 200 kHz and a 16-bits resolution. Experimental tests are carried out using the proposed method in order to study the arc dynamics. The reconstructions are compared with those of an optical diagnostic technique based on a charge-coupled device (CCD) camera.