Sensitivity analysis of impedance-based fault location methods
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Impedance-based methods are used to locate faults on distribution systems because of their simplicity and ease of implementation. These methods require fault voltage and current data along with the positive- and zero-sequence line impedance values (in ohm per unit length) to estimate the reactance or distance to fault location. Inaccuracies in line impedance values, which arise from circuit model errors, have an adverse impact on fault location estimates of the impedance-based methods. Measurement errors in current and voltage transformers can also lead to inaccuracy in estimation. Further, all methods use simplistic models to represent the system load. The load in a practical distribution system does not conform to the oversimplified models leading to errors in estimation of fault location. This thesis presents sensitivity analysis of four impedance-based methods. It focuses on the Takagi, positive-sequence reactance, loop reactance and balanced-load methods. Amongst these four methods, the first three are commonly used for fault location. The fourth method was developed as a part of this work. The objective of sensitivity analysis is to study and quantify the effect of circuit model, measurement and load model errors, on the fault location estimates of the four methods. The results of this analysis are used to establish upper and lower bounds on the estimation errors for each method. The analysis begins with creation of a baseline case using a modified version of the IEEE 34 Node Test Feeder. All the methods estimate the reactance to fault location as a part of this analysis. The baseline case uses accurate line impedances and measurement values in the four methods. The fault location estimates for this case serve as a means of comparison for all subsequent analyzes. Secondly, various circuit model errors are introduced while computing the line impedance values. These errors include inaccurate modeling of four parameters viz. phase conductor distances, conductor sizes, phase to neutral conductor distances and earth resistivity. The erroneous line impedance values, which arise from these circuit model errors, are used in the four methods. The resultant location estimates are compared with those for the baseline case. It is observed that modeling errors in earth resistivity can cause estimation errors of 2% to 5% in the Takagi and positive-sequence reactance methods. These errors can be positive or negative depending upon whether the modeled earth resistivity value is more than or less than the accurate value. The effect of inaccurate modeling of the other three parameters is marginal. Additionally, the Takagi and positive-sequence reactance methods assume line impedances to be uniform while estimating fault location. Although this assumption is a type of circuit model error, it does not lead to significant errors in estimation. The loop reactance and balanced-load methods are insensitive to circuit model errors as they do not use line impedance values while estimating reactance to fault location. The next part is analysis of effect of measurement errors on fault location estimates. Ratio and phase angle errors are deliberately introduced in the current and voltage transformers and the erroneous measurements are used to conduct fault location. This causes 5% to 6% errors in estimation for the Takagi and positive-sequence reactance methods. These estimation errors can be positive or negative depending upon the magnitude of the CT and VT ratio errors and the sign of the phase angle errors. For the loop reactance method, erroneous measurements introduce 8% to 30% errors in fault location. This indicates that the loop reactance method is highly sensitive to measurement errors. The balanced-load method is moderately sensitive and experiences 6% to 7% errors in fault location estimates. Lastly, the effect of load current on fault location estimates is analyzed. When the Takagi and positive-sequence reactance methods are used on a heavily loaded system, they estimate fault location with an error of 5% to 8%. The loop reactance method is severely affected by the level of load current in the system. This method can estimate fault location with nearly 100% accuracy, on a lightly loaded system. However, the estimation errors for this method increase significantly and are in the range of 15% to 30%, as load current in the system increases. In case of the balanced-load method, unbalanced, heavy loads can cause estimation errors of 7% to 25%. The combined effect of all the error sources is taken into account by creating a confidence interval for each method. For the Takagi and positive-sequence reactance methods, the actual fault location can be expected to lie within ±10% of the estimated value. The fault location estimation error for the loop reactance and balanced-load methods is always positive. The actual reactance-to-fault is within -30% of the value estimated by these methods.