A Mathematical Basis for a Protective Relay with Conic Pickup Characteristics

A mathematical basis and suggested circuitry are proposed for a distance relay having unique pickup characteristics. By simple adjustments these characteristics, when plotted on an R-X diagram, can be made to assume the shape of any conic section, including: a hyperbola, a parabola, an ellipse, and a circle. Possible applications of these characteristics for protection of power systems are mentioned, with emphasis on use of the elliptical characteristic for protecting long, heavily loaded transmission lines.