1 Distance Protection Using a Novel Phasor Estimation Algorithm Based on Wavelet Transform K. M. Silva, Student Member, IEEE, W. L. A. Neves, Member, IEEE, and B. A. Souza, Senior Member, IEEE. Abstract— This paper presents a novel phasor estimation algo- rithm, which combines the filtering characteristics of the maximal overlap discrete wavelet transform (MODWT) and the least error square (LES) algorithm. Time and frequency response of the designed filters are compared to the ones of traditional discrete Fourier transform (DFT) filters. The obtained results indicate that the designed filters have time responses compatible half cycle DFT-based filters, with the advantage that their frequency responses are close to the ones of full cycle DFT-based filters. According to these characteristics, the designed filters may be used in secure high-speed distance protection. Keywords— Distance protection, wavelet transform, phasor estimation. I. I NTRODUCTION D ISTANCE protection relays are widely used to protect transmission lines. Its operation depends on voltage and current fundamental frequency phasors. The accuracy, speed and security of distance relays are associated with fast response and secure operation of the digital filtering algorithms used to estimate fundamental frequency phasors [1]. The digital filtering algorithms used to estimate fundamental frequency phasors must have certain characteristics, such as: bandpass response about the system frequency, decaying DC elimination, harmonic attenuation or elimination and good transient behavior [2]. The most popular phasor estimation algorithms are the full and half cycle DFT-based algorithms [3]. It is well known that full cycle DFT (FCDFT) filters have better frequency responses than half cycle DFT (HCDFT) filters, because the former eliminate all harmonics, whereas the latter do not eliminate even harmonics. In addition, although the latter are faster than the former, they suffer from inaccuracies due to the decaying dc and off nominal frequency components [2]. Many improvements in DFT-based algorithms have been reported [4]–[6], but the majority of these improved half cycle filters do not eliminate even harmonics and there is no significant improvement in their speed responses. To overcome these drawbacks, some algorithms based on the least error square (LES) technique have been developed [7]–[11]. Some of them use adaptive strategies to vary the window length after detecting the fault, resulting in better frequency responses. However, they are still slower than HCDFT algorithm. Alternatively to traditional algorithms, the discrete wavelet transform (DWT) have been also used to estimate phasors This work was supported by Brazilian National Research Council (CNPq). The authors are with Department of Electrical Engineering at Federal University of Campina Grande, 882 Apr´ ıgio Veloso Av, Bodocong´ o, Camp- ina Grande - PB, CEP:58.109-970, Brazil. E-mail: {kms, waneves, bene- mar}@ee.ufcg.edu.br. [12], [13]. In [12], the authors use the orthonormality property of the DWT to compute phasors. This method was used in [14] to obtain a new DWT-based transmission line distance protection algorithm, but although good results are reported, this algorithm suffers from many inaccuracies because it does not eliminate any harmonic. An algorithm based on MODWT was reported in [13]. It uses the good signal approximation characteristic of MODWT to compute fundamental frequency phasors. The obtained results indicate that this algorithm is faster than FCDFT. The authors only analyzed the MODWT filtering characteristics, but did not analyze the frequency response of the overall filtering system, which reveals informa- tion regarding the phasor estimation performance during the stead state condition. This paper presents a novel phasor estimation algorithm, which combines the filtering characteristics of MODWT and the LES algorithm. This technique may be understood as a generalization of the phasor computation algorithm reported in [13]. Time and frequency responses of proposed filters are compared with the ones of traditional DFT-based filters. The obtained results indicate that proposed and HCDFT filters have similar time responses, with the advantage that the frequency responses of proposed filters are close to the ones of FCDFT filters. These characteristics indicate that the filters developed here are suitable to secure high-speed distance protection. II. DISTANCE RELAY FUNDAMENTALS The basic principle of distance relay is to compute the pos- itive sequence impedance of the line segment from the relay location to the fault point. In digital relays, this impedance is obtained using the fundamental frequency phasors, computed from the voltage and current sampled waveforms [1]. Distance relay operating characteristic is defined by a fixed shape in the R-X diagram. The best known operating characteristic is the mho-circle, which represents a circle passing through the origin of the R-X diagram and therefore inherently combines directional and distance measurements (self-polarized mho characteristic). Fig. 1(a) depicts the mho-circle in the R-X diagram, where: Z L and θ L are the line impedance and its angle, respectively; Z R and θ R are the relay reach and the relay characteristic angle, respectively. It is a general practice to set θ R smaller than θ L in order to improve the fault resistance coverage. Z R is set to cover a percentage of Z L , typically 80 to 90% for the first protection zone. With a healthy line, the apparent impedance seen by the relay stays outside the mho-circle (Fig. 1(b)). This impedance results from a load flow condition, for which the relay oper- ation must be restrained. Under fault conditions, the apparent