Rigorous Mathematical Steps for Sensitivity Analysis of High Impedance Ground Fault Detection in Power Distribution Systems

A literature survey indicated that high impedance fault (HIF) detection methods employ simulation techniques using very low voltage signals generated using software such as PSCAD, and MATLAB, among others. While software platforms are used to derive satisfactory results, small fault current signals cannot be accurately tapped from high transformation ratio current transformers owing to the dominant load currents in real power systems. Therefore, a sensitivity analysis based on a power system background is considered essential. A set of well-known power system equations are used to analyse and select a parameter to tune this sensitivity, from several available parameters, such as source, transformer, line, neutral, and earth impedance. The analysis reveals that when the detection of HIF in the field is challenging, then fault or neutral impedance emerges as an important parameter for tuning the system. To achieve this, certain rigorous mathematical steps are derived to develop a suitable formulation for sensitivity analysis using differential calculus. Based on the analysis, the sensitivity results and tuning parameters are tabulated, and sensitivity dependency curves are plotted.