In power-electronic-based power systems like wind farms, conducting stability analysis necessitates a comprehensive understanding of the system impedance across a wide frequency range, from sub-harmonic frequencies up to the Nyquist frequency of control systems of power converters. The cable aging effect can significantly impact the cable impedance, while accurately estimating the degree of aging proves challenging. To avoid the requirement for precise aging prognostic, this paper proposes an approach based on Artificial Neural Networks (ANN) that enables the estimation of AC cable impedance in a wind farm solely through fundamental frequency measurements. The data used for training the ANN is obtained from the cable model in PSCAD, incorporating physical and geometrical parameters, which accurately approximates real cables within power systems. The training results of the ANN validate the accuracy of the proposed identification approach. As a result, the proposed approach effectively eliminates the potential misjudgment of system stability caused by the aging effect of power cables.