In essence they are "filling the bucket". Say you have a steady state fault current that results in tripping at 0.833 seconds and the relay process runs at 4 calculations per cycle. That means it's going to take 200 processor intervals to get to a trip, each interval adding .005 to the bucket. After 200 of those .005 results the sum is 1 and the trip is issued.

For varying currents, at each processor interval the relay accumulates some amount; take the trip time for the measured current and divide that into the length of the processor interval. Repeat until the sum gets to 1.

I’ll see your silver lining and raise you two black clouds. - Protection Operations

Yeah, that is what I was expecting. It makes moving on the time overcurrent charts a little bit more complicated than sliding left and right.

The microprocessor simulates the integration that an electro-mechanical relay would do.