As a minimum, magnitude of the incoming quantity, commonly using Fourier transform concepts (RMS and some form of averaging) would be used in a simple relay function.
The relay analyzes the resultant A/D converter outputs to determine if action is required under its protection algorithm(s).
It is capable of analyzing whether the relay should trip or restrain from tripping based on parameters set by the user, compared against many functions of its analogue inputs, relay contact inputs, timing and order of event sequences.
If a fault condition is detected, output contacts operate to trip the associated circuit breaker(s).
The logic is user-configurable and can vary from simply changing front panel switches or moving of circuit board jumpers to accessing the relay's internal parameter setting webpage via communications link on another computer hundreds of kilometers away.
In a solid-state relay, the incoming voltage and current wave-forms are monitored by analog circuits, not recorded or digitized.
The analog values are compared to settings made by the user via potentiometers in the relay, and in some case, taps on transformers.
[7] The award was for "pioneering development and practical demonstration of protective relaying of electric power systems with real-time digital computer techniques."
In 1971 M. Ramamoorty was the first to describe [8] calculation of impedance for distance protection using discrete Fourier analysis.
The first practical commercially available microprocessor based digital/numeric relay was made by Edmund O. Schweitzer, III in the early 1980s.
For simplicity on one-line diagrams, the protection function is usually identified by an ANSI device number.