Transient Power and Quality Events Analysed Using Hilbert Transforms

This work presents an advanced mathematical tool applicable to the recognition and classification of power system transients and disturbances. Disturbances without a periodic pattern or with a non-linear pattern require a more suitable tool than the Fourier series （Fast Fourier or Windowed Fourier Transforms）. To overcome these drawbacks, other tools have been broadly used, such as the wavelet transform. However, the wavelet transform also has some drawbacks such as the lack of adaptivity or interpretation of nonlinear phenomena that the Hilbert and Hilbert Huang Transform techniques could mitigate. The Hilbert techniques transform a time domain function into a space representation both in time and frequency. In the paper, the technique is applied to analyse several short-term and steady events, like a short circuit, a capacitor-switching transient, or a line energisation, showing the abilities of the Hilbert-based transforms.

Analysis of temperature time series based on Hilbert-Huang Transform

In this paper, with consideration of the nonlinear and non-stationary properties of the temperature time series, we employ the Hilbert-Huang Transform, based on the empirical mode decomposition（EMD）, to analyze the temperature time series from 1959 to 2012 in the Fengxian district of Shanghai, obtained from a certain monitoring station. The oscillating mode is drawn from the data, and its characteristics of the time series are investigated. The results show that the intrinsic modes of 1, 2 and 6 represent the periodic properties of 1 year, 2.5 years, and 27 years. The mean temperature shows periodic variations, but the main trend of this fluctuation is the rising of the temperature in the recent 50 years. The analysis of the reconstructed modes with the wave pattern shows that the variations are quite large from 1963 to 1964, from 1977 to 1982 and from 2003 to 2006, which indicates that the temperature rises and falls dramatically in these periods. The volatility from 1993 to 1994 is far more dramatic than in other periods. And the volatility is the most remarkable in recent 50 years. The log-linear plots of the mean time scales T and M show that each mode associated with a time scale almost twice as large as the time scale of the preceding mode. The Hilbert spectrum shows that the energy is concentrated in the range of low frequency from 0.05 to 0.1 Hz, and a very small amount of energy is distributed in the range of higher frequency over 0.1 Hz. In conclusion, the HHT is better than other traditional signal analysis methods in processing the nonlinear signals to obtain the periodic variation and volatility＇s properties of different time scales.