Mathematical Study on Traveling Waves Phenomena on Three Phase Transmission Lines – Part II: Reflection and Refraction Matrices

In this paper, the study initiated in its first part on traveling waves (TWs) launched by faults on three-phase transmission lines is continued, with major focus on TW reflection and refraction coefficient matrices at line terminations and fault point. By doing so, mathematical expressions that represent the behavior of reflected and refracted voltage and current TWs are obtained in modal domain, for all fault types, allowing the proper estimation of wavefronts measured at the line terminals. Hence, once the amplitude and polarity of wavefronts measured at the line terminals can be estimated for specific fault features, the setup of TW detection thresholds and polarity evaluation schemes can be enhanced in practical applications. To demonstrate the validity of the obtained results, the Alternative Transients Program (ATP) is used to simulate fault-induced transients, from which several TWs are analyzed to compare the obtained analytical mathematical wavefront representation with those verified in the assessed fault records. From the obtained results, the mixing mode phenomena is proven, and the TW reflection and refraction matrices are validated, highlighting the usefulness of the presented mathematical study during the development of modern TW-based applications.