Characteristic Frequency of Travelling Waves Applied for Transmission Lines Fault Location Estimation L.U. Iurinic; R.G. Ferraz; A.S. Bretas Electrical Engineering Department Federal University of Rio Grande do Sul Porto Alegre, Brazil Abstract—This paper presents an analytical approach for determining the characteristic frequency of transient signals generated from transmission lines faults. Transient signals of travelling waves generated by faults contain very important information about the fault distance. Therefore, the characteristic frequency can be used for transmission lines fault distance estimation. In order to demonstrate the effectiveness of the developed equations, five cases are simulated using different values for equivalent impedance of local terminal and maintaining the fault distance at 120 km from the sending-end. Results obtained show a good correlation between measured and calculated characteristic frequency allowing very good accuracy for fault distance estimation. Index Terms-- characteristic frequency, fault location, frequency spectrum, travelling waves, wavefronts. I. INTRODUCTION Transmission lines are used to transmit electric power and are constantly exposed to faults, especially overhead lines. Fault location methods are very important because they can aid power supply restoration. There are many approaches for fault location analyzing the travelling wave phenomenon, where the basic principle is to use incident and reflected wavefront propagation observed at the measuring end(s) of the line [1]. The fault distance is performed using synchronized or unsynchronized measurements [2-3] and travelling waves can be detected using different approaches such as wavelets transform [2], filtering [4] or Park’s transformation [5]. In [5] is proposed a fault location algorithm for smart distribution and transmission grids using voltage measurements at two points of the network based on the transient detection. In [6] the time delay between successive wave reflections is identified for the fault distance estimation. Implementing one-end travelling wave methods for fault distance estimation are a difficult task, because also reflections from the remote terminal can be observed. The current or voltage transient spectrum can be used as a signature to estimate the fault distance, eliminating the problem of identifying wave fronts arrival. In [7] the existence of natural frequencies of voltages and currents inversely proportional with line length is proved. This theory can be used to estimate the fault distance by identifying the peaks in the Fourier transform of current or voltage signal. However, the equations are valid only for extreme values of the upstream impedance from Digital Fault Recorder (DFR). In [8] a formulation to solve the problem by implementing a mother wavelet inferred from the own measured signal is identified. Nevertheless this method has hard to design parameters. In this paper a formulation for calculate the dominant frequency of spectrum transient that includes the value of the equivalent impedance upstream the measurement point is derived. The formulation is implemented using Matlab program and validated with Alternative Transient Program (ATP) simulations. II. CHARACTERISTIC FREQUENCIES AND WAVE INTERFERENCE Fig. 1 shows the line-to-ground fault in a single-phase transmission line, where Zc is the characteristic impedance of the transmission line and Zs is the Thévenin's impedance viewed from the bus S. S R transmission line fault Z c Z s Figure 1. Faulted single-phase transmission line Consider a pure resistive or close to zero fault, which occurs at some instant. Then, the voltage at end R is collapsed to zero by a negative step surge which travels back to S in the transit time IJ, cancelling out the voltage as it travels. As explained in [9], the surge will be reflected at both ends generating a noise superposed with the source voltage and the dominant noise frequency can be represented as: 1 . p noise f n W  (1) Where IJ is the transit time and n p is related to the propagation of the travelling wave along the transmission line. The authors gratefully acknowledge Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) for the financial support of this study.