Protection
CT knee-point voltage requirement
- where
- secondary fault current (A)
- maximum through-fault current (A, entered in kA)
- CT rated secondary current (A)
- CT rated primary current (A)
- minimum knee-point voltage (V)
- dimensioning factor from the relay manual
- CT secondary winding resistance (Ω)
- lead resistance, one way (Ω)
- relay burden resistance (Ω)
Explain this equation
Finds the minimum knee-point voltage a class PX CT needs so it does not saturate before the protection operates. Use it when specifying CTs or checking an existing CT against a new relay.
Isf is the fault current on the CT secondary. Rct is the CT’s own winding resistance, 2RL the go-and-return leads, Rr the relay. Their sum is the loop the CT must drive current round. K allows for DC offset and remanence and comes from the relay maker.
The CT must produce enough EMF to push the secondary fault current through the whole loop; that EMF has to stay below the knee point where the core saturates. Ohm’s law gives the steady value and K adds headroom for transients.
Sense check: 10 kA through a 400/1 CT gives 25 A secondary; with 3.1 Ω of loop and K = 2 the CT needs about 155 V.
Watch out: the fault current is entered in kA and multiplied by 1000 internally. Use 2RL for earth faults on a residual connection; RL alone is often used for phase faults.
Minimum knee-point voltage a class PX (or equivalent) CT needs so that it does not saturate before the protection operates, from the fault current, ratio and secondary loop resistance.
Enter your values to see the result.
Good to know
The factor K comes from the relay manufacturer and allows for DC offset and remanence; typical values are 1 to 2 for overcurrent, larger for differential or distance protection, or K = 1 with a stability voltage for high-impedance schemes. The 2RL term is the full loop for an earth fault with a residual connection; for phase faults on a star-connected CT set, RL alone is often used. Take Rct at 75 °C.
Common mistake
Using the CT rated secondary current instead of the fault current referred to the secondary, or omitting the CT’s own winding resistance.
Limits
Steady-state symmetrical requirement multiplied by an empirical factor; it is not a full transient (TPX/TPY) dimensioning to IEC 61869-2.
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.