The knee-point voltage (V_k) is the point where a CT begins to saturate. For differential protection, the CT must be able to reproduce the full fault current without saturation. IEEE C37.109 specifies V_k ≥ 1.6 × I_fault × R_ct (where R_ct is the burden resistance). If V_k is too low, the CT saturates during faults, causing incorrect differential relay operation.
When a transformer is energised, the magnetic flux can reach twice the normal peak, causing a magnetising inrush current of 6–12× nominal for 0.1–0.3 seconds. This looks like an internal fault to a differential relay. Restraint is achieved by detecting 2nd harmonic content (typically ≥15–20% of fundamental) and increasing the bias setting or delaying operation during the inrush period.
Bias slope (or percentage restraint) ensures stability during external faults, which cause large differential currents due to CT saturation. The operating characteristic: I_diff > slope × I_bias + I_pu. Slope 1 (unrestrained) is for internal faults where speed is critical. Slope 2 (restrained, 0.2–0.3) provides stability during external faults and inrush by requiring a higher differential current relative to bias (restraint) current.
CT ratio = I_nom_sec / I_sec_rated. For a 630 kVA 400 V transformer, I_nom = 909 A, so a 1000:5 CT gives ratio = 200. Select the next standard ratio above the calculated value to avoid CT saturation. For the primary side, use the primary nominal current: 630 kVA at 20 kV → I_nom_pri = 18.2 A, so 20:5 CT (ratio 4:1) or 30:5 CT (ratio 6:1) is appropriate.
Class C (standard) CTs have accuracy limit factors of 5–7.5 and are used for standard overcurrent and differential protection. Class KM (extended) CTs have F_ks = 10 and higher knee-point voltage, used for demanding applications. Class X CTs have F_ks = 20, the highest accuracy class, used where maximum security against CT saturation is required (e.g., high-current busbar protection).
If the differential pickup (I_pu) is below the inrush peak current, the relay will mis-operate every time the transformer is energised. The standard practice is to set I_pu ≥ 1.2–1.5× the estimated inrush peak, or to use harmonic restraint (2nd harmonic blocking) which overrides the amplitude check when harmonic content is high. The calculator flags this with an inrush_pass warning.