Ramesh Babu P., Ashisa Dash, Siva Nagaraju, Sangameswara Raju / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.1760-1764 1760 | P a g e The Research of Power Quality Analysis Based on family of S- Transform Ramesh Babu P., Ashisa Dash, Siva Nagaraju, Sangameswara Raju. ABSTRACT Power quality (PQ) disturbance recognition is the foundation of power quality monitoring and analysis. The S- transform (ST) is an extension of the ideas of the continuous wavelet transform (CWT) or variable window of short time Fourier transform (STFT). It is based on a moving and scalable localizing Gaussian window. S-transform has better time frequency and localization property than traditional. With the excellent time—frequency resolution (TFR) characteristics of the S-transform, ST is an attractive candidate for the analysis and feature extraction of power quality disturbances under noisy condition also has the ability to detect the disturbance correctly but it involves high computational overhead which is of the order of O(N 2 log N) . This paper overviewed the theory of basis S-transform and fast discrete S-transform (FDST) summarized their computational requirement in the area of power quality disturbance recognition. The new Fast discrete S-transform algorithm, with a new frequency scaling and band pass filtering, Computational complexity is O(N log N) in optimal conditions. So it becomes less time consuming and decreases cost overhead, tool for power signal disturbance assessment. Keywords – STFT, CWT, S-Transform, Discrete S-Transform, FDST. I. INTRODUCTION Although the Fourier transform of the entire time series does contain information about the spectral components in time series, it cannot detect the time distribution of different frequency, so for a large class of practical applications, the Fourier transform is unsuitable. So the time-frequency analysis is proposed and applied in some special situations. The STFT is most often used. But the STFT cannot track the signal dynamics properly for non-stationary signal due to the limitations of fixed window width. The WT is good at extracting information from both time and frequency domains. However, the WT is sensitive to noise. The S transform was proposed by Stockwell and his coworkers in 1996. The properties of S transform are that it has a frequency dependent resolution of time- frequency domain and entirely refer to local phase information. For example, in the beginning of earthquake, the spectral components of the P-wave clearly have a strong dependence on time. So we need the generalized S transform to emphasize the time resolution in the beginning time and the frequency resolution in the later of beginning time. Based on different purposes, we can apply different window of S transform. For example, we will introduce the Gaussian window, the bi-Gaussian window, and the hyperbolic window. The comparison between the ST- based method and other methods such as the wavelet- transform-based method for power-quality disturbance recognition shows the method has good scalability and very low sensitivity to noise levels. All of these show FDST based methods has great potential for the future development of fully automated monitoring systems with online classification capabilities. The analysis direction and emphasis of studying about the power quality (PQ) disturbance recognition also put forward. II. THE S- TRANSFORM There are some different methods of achieving the S transform. We introduce the relationship between STFT and S transform. And the type of deriving the S transform from the "phase correction" of the CWT here, learned from [1] 2.1 The Continuous S Transform 2.1.1 Relationship between S Transform and STFT The STFT of signal h(t) is defined as     dt e t g t h f SFT ft j           2 , (2.1) where τ and f denote the time of spectral localization and Fourier frequency, respectively, and g(t) denote a window function. The S transform can derive from (2.1) by replacing the window function g(t) with the Gaussian function, shown as  2 2 2 2 f t e f t g    (2.2) Then the S transform is defined as