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When designing and building power systems that contain power electronic switching sources and loads, system integrators must consider the frequency-dependent impedance characteristics at an interface to ensure system stability. Stability criteria have been developed in terms of source and load impedance, and it is often necessary to measure system impedance through experiments. Traditional injection-based impedance measurement techniques require multiple online testing that lead to many disadvantages, including prolonged test time, operating point variations, and impedance values at limited frequency points. The impedance identification method proposed in this paper greatly reduces online testing time by modeling the system with recurrent neural networks with adequate accuracy. The recurrent networks are trained with measured signals from the system with only one stimulus injection per frequency decade. The measurement and identification processes are developed, and the effectiveness of this new technique is demonstrated by simulation and laboratory tests.