In electrical protection design, safeguarding key assets like generators, power transformers, and busbars requires instantaneous relay coordination. High-impedance protection schemes, such as Differential Protection and Restricted Earth Fault (REF) Protection, are used because they are highly sensitive to internal faults while remaining stable during external faults.

To prevent protective relays from maloperating during heavy external short circuits, standard protection CTs (like 5P10 or 5P20) are not suitable. Instead, design engineers must specify Class PX (previously Class PS in IS 2705) current transformers, defined by their Knee-Point Voltage (Vk).

In this technical guide, we break down Knee-Point Voltage, explore the calculation formulas, and explain why it is vital for system coordination.

1. What is Knee-Point Voltage (Vk)?

The Knee-Point Voltage is the point on the CT's magnetization (excitation) curve where the core transitions from a highly linear magnetic state to a saturated magnetic state.

According to IS 2705 and IEC 61869-2, the Knee-Point Voltage is formally defined as the sinusoidal secondary voltage which, when increased by 10%, causes the excitation current to increase by 50%.

Below Vk: The CT operates linearly, accurately replicating primary currents on the secondary terminals.
Above Vk: The magnetic flux saturates the core, the secondary output drops, and the CT secondary behaves almost as a short circuit, preventing the relays from receiving the true fault current.

2. The Knee-Point Voltage Formula for REF and Differential Schemes

In high-impedance protection schemes, the required Knee-Point Voltage is calculated based on the maximum fault current, loop resistance of the cables, and internal resistance of the CT secondary winding.

The standard formula used by relay protection engineers is:

Vk = 2 × I_f × (R_ct + 2 × R_lead + R_relay)

Where:

$I_f$ = The maximum secondary fault current during a through-fault (external short circuit).
$R_ct$ = The internal DC resistance of the CT secondary winding at 75°C.
$R_lead$ = The one-way resistance of the copper lead wire from the CT to the relay panel. (Multiplied by 2 for the loop return path).
$R_relay$ = The internal resistance of the protective relay (which is negligible for modern numerical relays).

Practical Example Calculation

Suppose you are designing a protection scheme with the following parameters:

Maximum primary fault current: 20,000A
CT Ratio: 1000/1A (Secondary fault current $I_f$ = 20A)
Internal CT winding resistance ($R_ct$): 3.0 Ω
Lead wire distance to relay: 50 meters using a 2.5 mm² copper cable ($R_lead$ = 0.37 Ω)

Plugging these values into the formula:

Vk = 2 × 20 × (3.0 + (2 × 0.37))

Vk = 40 × (3.0 + 0.74) = 40 × 3.74 = 149.6 V

To ensure stability, the CT must be designed with a Knee-Point Voltage of at least 150 Volts.

3. Winding Resistance ($R_ct$) and Magnetizing Current ($I_e$) Limits

A Class PX CT is not fully specified by Vk alone. The designer must also specify:

Maximum Winding Resistance ($R_ct$): Must be kept low to reduce the required Vk. Winding resistance is controlled during manufacturing by using thicker copper conductor sizes.
Maximum Magnetizing Current ($I_e$): The exciting current at a specific voltage (usually $Vk/2$ or $Vk/4$) must be extremely low (typically < 20mA or 30mA) to prevent loss of relay sensitivity during small internal faults.

Conclusion

Calculating and verifying the Knee-Point Voltage is vital to ensure that Class PX CTs do not saturate during heavy faults, maintaining protection system integrity.

At Alliance Engineering's Chandigarh facility, we custom-manufacture Class PX current transformers with precision-wound cores to meet specific $R_ct$ and $Vk$ calculations. We perform excitation test sweeps and knee-point validations on our automated test bench for every unit. For design support, drawing approvals, or custom quotes, email us at info@allianceengineeringco.com.