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In order to improve the dependability and security of transformer differential protection, the energisation conditions should be effectively distinguished from internal fault conditions. In this study, a new method with a low computational burden and high robustness against measurement noises is proposed for discriminating between the transformer inrush current and internal faults. In the proposed method, sine waves are fitted to the sample points of the normalised differential currents for different phases using recursive extended least‐squares (RELS) algorithm in an online manner. The extended kernel enables the algorithm to effectively estimate the dynamics of the measurement noises. Three residual signals which are defined as the differences between the normalised differential currents and the fitted sine wave signals are considered as the decision criteria. Based on the selected criteria, the energisation condition is identified in about a half‐cycle of power system frequency. A large number of simulation and experimental test cases are used to demonstrate the effectiveness of the proposed method. The results show that the proposed algorithm achieves an accuracy of ∼98% and has a relatively low operating time, while the computational burden for the embedded implementation is favorably low. [ABSTRACT FROM AUTHOR]