06-07-2012, 03:11 PM
2d analysis and compression of power quality event data
2D ANALYSIS AND COMPRESSION OF POWER QUALITY EVENT DATA.doc (Size: 268 KB / Downloads: 27)
INTRODUCTION
Two-dimensional (2D) analysis of the power quality data enables efficient event detection and localization. We first develop the method to convert the waveform data into 2D. Next, the 2D discrete wavelet transform (2D-DWT) is proposed as the tool to apply on the 2D data. The compression technique is performed through signal decomposition, thresholding of wavelet transform coefficients, and signal reconstruction.
2D ANALYSIS OF POWER QUALITY EVENT DATA
2D Representation of Event Data
2D representation consists of a matrix whose rows correspond to non-overlapping segments of the waveform data. The data can be considered as an image or a 2D surface. The time segments, which are placed in the rows, should have a duration of an integer multiple of the data period. In this way, the cyclo-stationary behaviour of the waveform is exploited well, and the image surface resembles water waves.
One level decomposition
For a 2D image of size M×N, the DWT, hence the subband, decomposition, is first applied to the rows (horizontal process), producing two M×N/2 matrices (denote by l and h). Then, the same decomposition structure is applied to each of the previously obtained matrices. The whole operation corresponds to one-level decomposition, and we obtain four images, each with sizes M/2 × N/2 (denote by ll, lh, hl, and hh).
Inverse 2D-DWT
In order to combine the above information contained in separate subspaces into a single feature datum, we synthesize the subspace signals (i.e. lh, hl, and hh images) by inverse 2D–DWT, while ignoring the ll subspace. Inverse 2D–DWT is implemented by a synthesis filter–bank as illustrated in Figure 3, where the branches consist of vertical and horizontal up–samplers (instead of down–samplers of an analysis filter–bank) followed by synthesis filters. The result of the inverse 2D–DWT is a 2D image at the original scale.