Programmed overcurrent protection control apparatus with selectable time-overcurrent operation to govern the interruption of current through at least one power line associated with either a ground phase or a power phase of a power system network is disclosed. A programmed processor is included to derive an overcurrent time-to-trip in accordance with sampled measurement current values of the power line and selected derivation constants stored in a memory look-up table. The derivation constants are selected from the look-up table based on derivation parameters which may be set and read by the programmed processor from time to time. The programmed processor utilizes the selected derivation constants to derive the time-to-trip over a number of predetermined time intervals during which the overcurrent condition persists. An alternate overcurrent time-to-trip relationship utilizing different derivation parameters selected from the look-up table may be utilized for the conditions in which overcurrent exists in an initial predetermined range. In some situations, both of the derivation relationships may be used concurrently to derive the overcurrent time-to-trip.