In power-electronic-based power systems like wind farms, stability analysis requires knowledge of system impedance across a wide frequency range, from sub-harmonic frequencies to the Nyquist frequency. Although it is feasible to take the fundamental frequency measurement during power system operation, obtaining a wide-frequency impedance curve in real time is very challenging. This paper proposed an ANN-based approach to estimate wide-frequency system admittance of wind farms with power cables, through fundamental frequency measurements. Real-life uncertainties are considered, including shunt capacitor injection, filter inductance variance, cable aging, errors in voltage and current measurements, and the variance of other system parameters. The generalization ability of the ANN is validated on a new dataset with different uncertainty distributions, and the error sensitivity to the potential system parameter variance is evaluated. These results can be referenced in the data acquisition step in future neural-network-based applications.