This paper proposes a novel automatic Segmented Hilbert Huang Transform (SHHT) method for the evaluating and characterizing the phase angle jump (PAJ) of voltage sag events caused by different types of symmetrical and unsymmetrical faults in transmission and distribution networks. The Hilbert Huang Transform (HHT) is a new data analysis method based on the Empirical Mode Decomposition (EMD) technique, which can generate a set of Intrinsic Mode Functions (IMFs). The IMF waveforms have well-behaved characteristics for analysis by the Hilbert transform, from which the instantaneous frequencies, amplitudes and phase angles of the IMFs can be evaluated. Because of the nonstationary characteristics of the voltage sag waveform, the conventional Fast Fourier Transform (FFT) and HHT methods show ambiguities at the starting and the recovery points of the voltage sag. This can lead to errors in the calculation of the PAJ. This paper introduces an automated segmentation of the voltage sag signal to overcome the transition time ambiguities by using a novel frequency detection method. Different examination on simulated signals from an Australian MV/LV distribution grid network shows that the proposed automatic segmentation method can successfully compute the voltage phase angle from different types of symmetrical and asymmetrical fault induced voltage sag accurately at the actual voltage sag starting and ending point. The results obtained from the simulations are also compared with the analytical results to verify the accuracy.