A Novel Methodology for the Determination of Impulse Response Coefficients Applied to Transmission Line Protection Relays

Impulse Response Coefficients (IRC) of digital filters is an imperative step in the development of transmission line protection relay algorithms. Traditionally, Fourier-based filters are used in real applications, where IRC are fixed values of sine and cosine functions with a data window of one or more cycles. Based on state-of-the-art, Mother Wavelet coefficients used in Multiresolution Analysis, and Structuring Element coefficients used in Mathematical Morphology are usually proposed to develop protection algorithms. However, the proper choice of these coefficients is based on empirical process of trial and error. This paper proposes a novel methodology for optimally determining coefficients that depend on the waveform structure analyzed, which is determined using variance as the metric. Assessment of methodology for three case studies considering requirements of relay manufactures (response time, design, harmonic attenuation and other) is presented. The first assessment is to extract coefficients useful for distinguishing among non-fault conditions, harmonics, and arcing faults. The second one is to extract coefficients to filter harmonic components. The assessment is carried out considering different data windows and sampling rates. Test results highlight the efficiency of the model to determine specific coefficients for each case study analyzed. Interestingly, results also showed that the discovered coefficients can be used in another filtering technique. Thus, the third case study involves developing two fault classifiers, which are developed using mathematical morphology where the structuring elements used correspond to the coefficient vectors determined through the proposed methodology. There is a notable paucity of scientific literature focusing on this topic. Therefore, there are several important areas where this study makes an original contribution regarding protection relays.