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A methodology for the reduction of the residual flux in network transformers is proposed in this paper. The purpose is the mitigation of large inrush currents taken by numerous transformers when a long feeder is energized. Time-domain simulations are used to prove that a small-power device can substantially reduce the residual flux of all transformers simultaneously. The device consists of a low-voltage dc source, a suitable power-electronic switching unit, and a simple controller. Before a feeder is re-energized, the residual flux is reduced to a minimum and, as a consequence, the large inrush currents are reduced to an acceptable level. This greatly enhances the probability for the feeder to be successfully energized when otherwise a false trip would have occurred. Inrush current reductions of more than 60% are obtained at the head of the feeder.