This study deals with a method for discrimination between magnetising inrush and internal fault currents in three-phase transformers based on sine-wave curve fitting. A sine wave is fitted to the normalised differential current by using the leastsquares technique for each phase. The difference between the normalised differential currents and the fitted signals are calculated, which are hereafter named residual signals (RSs). Maximum range of the RSs variations is utilised for the definition of a simple criterion. Based on this criterion, the discrimination is realised within less than a half cycle of power frequency. In order to eliminate the impact of the current transformer (CT) saturation on the performance of the proposed technique, the currents are compensated by a CT saturation compensation algorithm in the first step. The proposed method is evaluated and compared with some well-known methods by a large number of simulation and experimental data. Furthermore, the proposed algorithm is evaluated in the case of a transformer, which is fed through a feeder with series capacitors. The results confirm that reliability, accuracy and speed response of the proposed technique is more than the other methods.

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The atom-bond connectivity (ABC) index of a graph G is defined as the sum over all pairs of adjacent vertices u, v, of the termsdenotes the degree of the vertex v of the graph G. Whereas the finding of the graphs with the greatest ABC-value is an easy task, the characterization of the graphs with smallest ABC-value, in spite of numerous attempts, is still an open problem. What only is known is that the connected graph with minimal ABC index must be a tree, and some structural features of such trees have been determined. Several conjectures on the structure of the minimal-ABC trees, were disproved by counterexamples.In this review we present the state of art of the search for minimal-ABC trees, and provide a complete bibliography on ABC index.

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