Directional Overcurrent
In DOC protection, the fault direction is detected using the angle between current and voltage. For example, if a fault occurs in phase A, the voltage level might drop so low that the voltage and its angle are no longer reliable for the relay. In such cases, the voltage from the healthy phases is used to determine the fault direction. So, if there is a fault in phase A, the voltage from phase BC is used to determine the fault angle (assuming that the voltage angle in the non-fault phases remains constant).
Since a reference angle is needed to detect the fault direction, VBC(ref) must be rotated by an angle ϕ to match the current angle. This ϕ is typically chosen from three values: 30°, 45°, or 60°. At this angle, it can be said that the fault has occurred directly in front of the relay. This angle is referred to as the MTA (Maximum Torque Angle).
The range from MTA + 90° to MTA – 90° is considered the forward direction. However, due to a measurement error of 4 degrees on both sides, a margin is considered. Therefore, the ‘sector opening’ for this condition is set from MTA + 86° to MTA – 86, which equals 172°.
Note on Two-Phase Fault Testing
In two-phase fault testing, to prevent the generation of residual voltage, the angle of the voltages in each phase must be adjusted so that the residual voltage equals zero. Therefore, if the user inputs the phase-to-phase fault voltage (for a BC fault), the relationships shown will apply:
f the phase-to-phase fault voltage is set to 55V and the nominal voltage is 63.51V, α will be 40.9°
In this phase-to-phase fault, to detect the fault, we use an OR condition for faults in phases B and C, where MTA and sector opening need to be calculated separately for each phase, and the union of the two should be considered.
For Phase B:
For Phase C:
As shown in the diagram, the sector opening exceeds 180° by half of the overlap area, unlike the single-phase fault where the sector opening was 180° or less. In general, if the fault voltage is equal to the nominal value, the sector opening increases by 30° on both sides, and this value decreases linearly with the voltage drop
