All distance relays compare voltages and currents to create impedance-plane and directional characteristics. Electromechanical relays do so by developing torques. Most static-analog implementations use coincidence-timing techniques.

Numerical techniques are the newest way to implement distance and directional relay elements. These relays use torque-like products and other methods to accomplish their operating characteristics. How do these new techniques relate to the classical electro-mechanical and static phase-angle comparators?

This paper presents basic distance and directional element design. A large emphasis is placed on relating the newer digital and numerical methods to the established electromechanical and static-analog methods of designing relay elements. In addition, we discuss:

A new method for characterizing distance elements; i.e., equations for mapping points on a relay characteristic onto a single point on a number line.

How multi-input comparators can be viewed as a family of two-input comparators.

Which characteristics result from various combinations of comparator inputs.

Classical element-security problems and remedies.

A new negative-sequence directional element.

A different approach to the load-encroachment problem.

Finally, we point out a problem with fault-type selection logic which uses the angle between the negative- and zero-sequence currents. It can select the wrong phase for certain resistive line-line-ground faults. We present a solution to this problem which compares ground and phase fault-resistance estimates

Distance Relay Design