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Impedance characteristics of shipboard power systems provide important information for studies on system stability and integration. Existing injection based impedance measurement techniques require multiple tests on the system to obtain characteristics over wide frequency ranges. In this paper, recurrent neural networks (RNNs) are used to model the small signal dynamics of power electronic systems based on a single test in which randomized signals are injected into the system. The trained RNN is then used to extract the small-signal impedances/admittances of the system. A number of tests have been carried out in simulation to verify the effectiveness of the proposed method.