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A novel mathematical morphology filter for the accurate fault location in power transmission lines

The performance of Multi-resolution Morphology Gradient(MMG)-based fault location scheme in power transmission lines will deteriorate when the noise is imposed on the transient signals. In this paper, a novel mathematical morphology filter Dierion is proposed to effectively reduce the noise in the transient signals and improve the performance of the accurate fault location using MMG. This proposed filter with parameters (m, k) extracts the kth element in the sorted input signal according to the structure element, whose length is m. Dilation and Erosion filter, the two basic operators in Mathematical Morphology (MM), are formulated in a unified mathematical framework defined by Dierion filter based on the assumption that the structure element is symmetric with respect to its origin. The general statistical characteristics of this proposed morphological filter are discussed in details. The results show that Dierion filter with parameters (m, (m + 1)/2), which namely is Median filter, performs better in noise reduction compared with Dilation and Erosion filters. The efficiency of Dierion filter's noise reduction is verified by a variety of simulations. Therefore, the MMG protection scheme is improved significantly to be noisy tolerant.