4. Discussion and conclusion
This paper proposes a new approach to estimate the parameters of the elliptical model which is applied to detect faults in transmission lines. In addition, it successfully applies non-linear quantile regression to estimate upper and lower control limits. The simulation study and the real case scenario show that our proposal achieves more accurate values for the parameters of the model and provides false detection rates closer to the α-level chosen by the user. Therefore, it provides more reliable control regions than previous approaches.It is worth mentioning that in energy transmission fault detection methods, voltage and current signals are successively evaluated in order to detect faults as soon as possible. Faults are deviations of the signals from normal operating conditions. Extreme deviations from normal operating conditions are detected quickly and easily. On the contrary, subtle deviations from normal operating conditions are difficult to detect because they approximate normal operating conditions. Therefore, it is crucial to represent normal operating conditions as accurately as possible, thereby establishing a proper boundary between normal and fault conditions. Furthermore, the larger the boundary the more difficult to detect faults. On the contrary, the narrower the boundary, the faster a fault is detected but the greater the chance of false faults. This work proposes new estimate procedures to create a more accurate mathematical representation of the current and voltage signals under normal operating conditions. In addition, new parametric upper and lower bounds are proposed and estimated using quantile regression. This approach does not require any statistical assumption about data uncertainties and create an accurate region under normal operating conditions. The user can change the width of the region in order to adjust the expected number of false faults. A real case scenario shows that this approach can detect faults in one eighth of a cycle, on average. The main limitation of our proposal, and previous proposals, is the fact that each phase of the transmission line is controlled independently. In a real case scenario, faults may affect more than one phase simultaneously. Therefore, future studies aim at developing a three-dimensional control region which controls, simultaneously, the current signals for all three phases of the transmission line. Furthermore, it is of interest to classify fault conditions, i.e., to use signal information under fault conditions to identify the types of faults. Such conditions may include a fire close to the transmission line, or cable entanglement, or electrical lightning, or falling tree, or any other condition. This information is crucial for preparing maintenance teams for line repair. For instance, statistics calculated from the residuals under fault conditions can be used as input variables for fault type classification models. Finally, the proposed approach can be easily employed in different research areas as control schemes.