Some developments on phase coordinates line modeling based on Idempotent decomposition

Abstract

Abstract Time-domain transmission line models remains a topic of ongoing research. The state of the art consists in using the Method of Characteristics (MoC) with a rational approximation of the characteristic admittance and propagation function matrices. The so-called universal line model (ULM) stands as among the most accurate phase-domain line models using MoC. However, it might present unstable responses due to large residue-pole ratios which amplifies the error associated with the interpolation scheme of the reflected current wave. In this work we investigate the possibility of using Idempotent Decomposition as an alternative for a full-frequency-dependent transmission line model suitable for the analysis of underground cables and overhead lines. An overview of the basic structure of time-domain transmission line modeling is presented. Results indicate that the separation of the propagation function into the sum of products of an Idempotent matrix with the corresponding exponential time-delay function avoids the stability problems related to large residue-pole ratios. A proposition to group Idempotent matrices with similar time-delays to reduce the order of the rational approximation of the propagation function matrix is also analyzed. Four test cases were considered including two previously reported cases where unstable simulation responses were found using ULM with a simple interpolation scheme. A Numerical Laplace Transform (NLT) approach was used to compare the time-domain responses. While results indicate that the Idempotent decomposition can be used to model underground cables, there is some accuracy loss in the rational approximation of the propagation function in the case of overhead transmission lines when a large number of phases is involved.