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In this paper, a new numerical algorithm for medium-voltage overhead lines, autoreclosure, is described. The subfunction of the autoreclosure scheme that would inhibit the first shot after detecting a solid fault (as compared with an arc fault) is evaluated and presented. It is based on one terminal data processing and it is derived in the time domain. In the algorithm the fault nature (arcing or arcless fault) is estimated using linear least error squares estimation technique. The arc, occurring on the fault point during arcing faults on overhead lines, is included in the problem consideration. In addition, by introducing the prefault load current in the existing model, better algorithm performances and a more reliable adaptive algorithm for autoreclosure are achieved. The algorithm is derived for the case of three-phase symmetrical fault. The results of the algorithm testing through computer simulation are presented. Particularly the algorithm sensitivity to arc elongation effects, supplying network parameters, and processing of the signals in the presence of harmonics are tested and analyzed.