Análise computacional da proteção direcional de sobrecorrente 67F/67N aplicada à linha de transmissão de 345 kV Furnas–Poços de Caldas

Abstract

The Brazilian electrical power system comprises an extensive interconnected grid in which transmission lines connect different generation and load centers at high voltage levels. In transmission lines supplied from both ends, short-circuit current may receive contributions from different sources and flow in different directions, making current magnitude alone insufficient to determine the fault direction. In this context, this work presents a computational analysis of directional overcurrent functions 67F and 67N applied to the 345 kV transmission line connecting the Furnas and Poços de Caldas substations in Minas Gerais, Brazil. The 131 km transmission system was modeled in ATP/ATPDraw using Thévenin equivalents to represent the external networks and an equivalent π model for the transmission line. Twenty-seven short-circuit scenarios were simulated, covering three-phase, phase-to-phase-to-ground, phaseto- phase, and single-phase-to-ground faults. Variations in fault location, fault resistance, and fault inception angle were considered, including faults internal and external to the protected line section. A Python routine was developed to process the waveforms exported from ATP/PlotXY in COMTRADE format and extract voltage and current phasors using the Discrete Fourier Transform. For the analysis of function 67F, phase-A current and the quadrature polarizing voltage VBC were used. For function 67N, zero-sequence voltage V0 and inverted zero-sequence current −I0 were employed. The phasor diagrams allowed the faults to be classified as forward or reverse for the relays installed at both ends of the transmission line. The sensitivity analysis showed that, for function 67F, maximum torque angle values between 30◦ and 90◦ correctly classified all evaluated cases, with 45◦ presenting the lowest mean angular distance from the maximum sensitivity axis. For function 67N, values between −15◦ and −90◦ produced consistent classifications in all cases, while −90◦ provided the best overall alignment among the evaluated values. The results demonstrated the influence of the maximum torque angle on directional classification and contributed to understanding the behavior of functions 67F and 67N in a transmission line supplied from both ends. The study was limited to the behavior of the directional element and did not include pickup settings, time delays, or circuit-breaker tripping commands.