I. Introduction
Due to the nonlinearity of the transformer core, the magnetizing inrush possibly occurs when a transformer is energized. In this case, the security of the differential protection will be challenged [1], [2]. To solve this problem, many criteria have been proposed [3]–[11] to prevent differential protection from mal-operation due to inrush. Among these, second harmonic restraint criterion is the most prevalent. The effectiveness of this criterion has been verified with amounts of industrial applications in past decades. However, some differential protections equipped with second harmonic restraint mal-operate under some abnormal disturbances or operations. For instance, some mal-operations of the transformer differential protections during loaded transformer energization have been reported recently [12], [13]. A concept called the “ultra saturation state” is put forward in [12] to explain this phenomenon. According to the analysis in [12], the amplitude of the magnetizing inrush should be very high when the transformer experiences “ultra saturation state”. In this case, the protection shall detect a quite a high bias current, a high operating current, and low second harmonic of differential current, and it therefore mal-operates at the biased operating region since the percentage bias characteristic is employed by most differential protection. However, the data from the field fault recorder [13] show that some mal-operation cases occurred at the non-restraint region in the percentage bias characteristic plane, and the operating current was only somewhat higher than the threshold. Of course, the second harmonic restraint criterion failed to block the differential protection as well in these cases. Obviously, the ultra saturation model of transformer is not suitable for explaining such scenarios. Furthermore, the loaded transformer energization model in [12] needs to be improved in that the non-linear magnetizing inductance of transformer is simplified as an average inductance being a constant, which does not coincide with the real situation. Therefore, a novel model for analyzing the transient course of the loaded transformer energization is proposed in this paper. Together with the existing CT models, the waveform characteristics of the primary and secondary inrushes are analyzed. On basis of above models, the mal-operations reported by [13] can be explained rationally.