On Estimation of Zero-Sequence Impedances of Parallel Transmission Lines from Fault Data

The problem of estimating zero-sequence parameters of a parallel transmission line from fault data is considered. This paper analytically demonstrates that the zero-sequence impedances of a parallel transmission line are not, in general, attainable using the synchronized measurements taken at the line terminals following a ground fault on the line. To this end, Kirchhoff's voltage law (KVL) and current law (KCL) are employed to establish the system of equations that relate the measurements to the zero-sequence impedances of the line. The paper also highlights two rather theoretical exceptions to this generalization: first, the scenario of bolted faults, and second, situations where the fault resistance value is known beforehand (although this assumption is not valid in practice). A lemma is introduced and proved demonstrating that under specific conditions the zero-sequence reactances of the line can be accurately estimated while the zero-sequence resistances of the line remain unattainable. Simulation results, under a variety of conditions such as time-varying fault resistance and untransposed parallel lines, support the theoretical findings that zero-sequence resistances cannot be obtained from fault data while for short transposed lines or untransposed lines without earth wire zero-sequence reactances can be estimated quite accurately. Realistic measurement errors undermine the reliability of estimates, further questioning the attainability of zero-sequence parameters of parallel lines from fault data.