This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON POWER DELIVERY 1 The Directional Feature of Current Transients, Application in High-Speed Transmission-Line Protection Rommel Aguilar, Fabián Pérez, Member, IEEE, Eduardo Orduña, and Christian Rehtanz, Senior Member, IEEE Abstract—This paper presents an orthogonal decomposition method, which is used to extract information from the current transient signals generated after a fault. The orthogonal basis functions are obtained under the condition of maximizing vari- ability (variance) of input signals which, in turn, allows for finding an optimal representation of fault data. The results of the decom- position bring remarkable patterns described by transient signals into sight. Directionality, which appears as one of the foremost features, is highly related to the fault inception angle. This relation is then used to determine the fault direction just by comparing the steady-state prefault voltage angle and the angle of the vector resulting from the representation of the current signal in the space given by the first two orthogonal functions. Time windows shorter than 2 ms are used. Thus, the methodology can be applied in high-speed protection schemes. Index Terms—Empirical orthogonal functions, power system transients, principal component analysis, transmission-line pro- tection. I. INTRODUCTION D EFINING the fault direction is indispensable for guar- anteeing selectivity in power system protection. For this purpose, methods based on phasor estimation techniques are generally used in protection relaying. In this field, the most re- cently proposed approaches present significant improvements [1]–[3]. However, their operation time is limited to one cycle of power frequency since these methods require at least one- cycle of postfault data in order to operate properly. Thus, these methods are unsuitable for power systems growing in size and complexity where faster fault detection is essential in order to guarantee transient stability. The requirement for high-speed protection motivated in- tense research on using fault-generated transients for relaying purposes. In fact, it has long been recognized that offnominal frequency components contained in current and voltage signals Manuscript received September 14, 2012; revised December 20, 2012; ac- cepted January 22, 2013. This work was supported in part by the German Aca- demic Exchange Service (DAAD), in part by the Instituto de Energía Eléctrica of Universidad Nacional de San Juan, and in part by the Institute of Energy Systems, Energy Efficiency and Energy Economics of TU Dortmund Univer- sity. Paper no. TPWRD-00963-2012. R. Aguilar, F. Pérez, and E. A. Orduña are with Instituto de Energía Eléc- trica, Universidad Nacional de San Juan, San Juan 5400, Argentina (e-mail: raguilar@iee.unsj.edu.ar). C. Rehtanz is with the Institute of Energy Systems, Energy Efficiency and Energy Economics of TU Dortmund University, Dortmund 44227, Germany. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2013.2243762 give more information about the fault than the power fre- quency [4]. In this field, the use of travelling-wave techniques for high-speed protection has been widely explored [5]–[8]. However, these protection schemes encounter some reliability problems, particularly for detecting close-in faults and faults occurring at small inception voltages. In the last decade, some interesting proposals appeared on the transient-based protection area [9]–[13]. With the aid of sophisticated signal-processing techniques, these proposals achieve some degree of de- velopment and contribution for high-speed transmission-line directional protection. However, all of them depend on high-fre- quency measurement of voltage signals. That is a major issue, since high-fidelity voltage signals are impossible to obtain from a capacitor voltage transducer (CVT). The attenuation of high-frequency components can significantly degrade the performance of a transient-based protection algorithm using voltage signals. The present proposal does not require high-frequency voltage measurements since the directional feature of fault-generated transients can be attained just from current signals. Then, an or- thogonal decomposition method is employed to extract informa- tion from the transient current signals generated after the fault. The orthogonal basis functions, so-called empirical orthogonal functions (EOFs), are obtained from fault data itself, under the constraint of preserving the total data variability as much as pos- sible after the decomposition. Thus, representation of faults on these orthogonal basis functions leads to a better understanding of fault data. Results show that current signals decomposed in terms of EOFs clearly reveal the directional feature of fault-gen- erated transients, which is closely linked to the fault inception angle. The fault direction is defined simply by comparing the steady-state prefault voltage angle and the angle of the vector resulting from the representation of current signals in the EOF space. II. SUPERIMPOSED QUANTITIES A fault causes the postfault voltage and current signals to de- viate from the steady-state prefault signals. This, due to the su- perposition theorem, can be interpreted as (1) (2) where and are the prefault voltage and current sig- nals, and represent the fault-generated deviations from the steady-state signals, and and are the total measured signals. The incremental signals are obtained by removing the 0885-8977/$31.00 © 2013 IEEE