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In this paper, a novel power-based algorithm to discriminate between switching and internal fault conditions in power transformers is proposed and evaluated. First, the differential power signal is scrutinized and its intrinsic features during inrush conditions are introduced. Afterwards, a combined time-domain-based waveshape classification technique is proposed. This technique exploits the suggested features and provides two discriminative indices. Based on the values of these indices, inrush power signals are identified after only half a cycle. This method is founded upon some inherent low-frequency features of power waveforms and is independent of the magnitude of differential power. The approach is also unaffected by power system parameters, operating conditions, noise and transformer magnetizing curves. Simplicity of the suggested features and equations describe how the proposed method can help make it a practical solution for the inrush problem. Extensive simulations carried out in PSCAD/EMTDC software validate the merit of this technique for various conditions, such as current-transformer saturation. Furthermore, real-time testing of the proposed method using real fault and inrush signals confirms the possibility of implementing this algorithm for industrial applications.