R-X diagram for impedance relays

R-X plane:

Impedance relays are widely used as distance relays for protection of transmission lines / feeders. Various manufacturers use different algorithms in their relays for optimum performance. R-X diagrams are used to illustrate characteristics of relay. From these diagrams protection engineers can easily understand relay behaviour during fault conditions and visualize difference in characteristics of relays of different model / manufacturer. Relay testing using secondary injection is also based on verification of operating characteristics on R-X diagrams. For example, chrematistics of some of the manufacturers are as below:

In above diagrams, horizontal axis represents Resistance and Vertical axis represents Reactance. Here, -ve value of resistance means power import, +ve value means power export, -ve value of reactance means capacitance and +ve value of reactance means inductance. Lines / feeder are have inductive behaviour in case of fault coonditions, therefore their reactance will be +ve and for forward direction fault, power will injected into fault from relay location, therefore resitance will also be positive. Therefore, Lines / feeders have their line representation in first quadrant based on per unit positive sequence reactance (X₁) and positive sequence resistance (R₁). We can represent feeder on R-X plane by calculating total X₁ and R₁ of Transmission Line / Feeder (Click here for more about line parameters).  

Zone settings parameters in relays also have R and X value (or Z and φ) for each zone. For quadrilateral characteristics resistive reach, R value for left and right blinders is also specified. From these relay setting parameters R-X diagrams can be plotted.