Knee Point Voltage Calculator

What is Knee Voltage?

Knee point voltage, also referred to as “knee voltage” or “knee point,” is a word that is utilized to define current transformers (CTs), which serves as essential equipment in power systems that measure and control the flow of electromagnetic current & protect electrical equipment.

Knee Point Voltage in Current Transformers (CTs)

In a current transformer (CT), the knee point voltage is a point on magnetization curve at which the secondary current increases significantly while the primary current increases only slightly.

The magnetization curve (also known as the saturation curve) illustrates the relationship between primary and secondary currents at various levels of magnetic flux.

As the primary current rises, the core of the CT becomes saturated, making the secondary current to rise disproportionately to primary current.

This point of fast increase is commonly recognized as the knee point.

The knee point voltage is an important parameter because it determines how much fault current a CT can reliably measure prior to saturation occurs.

Beyond knee point voltage, the CT’s accuracy deteriorates, and it may be unable to produce accurate current readings under fault conditions.

Formula

The knee point voltage formula is essential for designing and analyzing current transformers (CTs) utilized in electrical power networks.

The accurate estimation of the knee point voltage is important for ensuring that the CT functions properly during fault conditions & gives reliable measurements for the protective systems.

The knee point voltage, V(V) in volts, is derived by dividing the product of two times the fault current, I_F(A) in amperes, with sum of

• Secondary Winding Resistance, R_CT(Ω) in ohms,
• Lead Resistance, R_L(Ω) in ohms, and
• Relay Burden,
• R_B(Ω) in ohms by the CT Ratio.

V(V) = 2 x I_F(A) x (R_CT(Ω) + _RL(Ω) + R_B(Ω))/CT

Where                                                                         

V(V) – Knee Point Voltage (volts) (V)

I_F(A) – Fault Current (Amps) (A)

R_CT(Ω) – Secondary Winding Resistance (Ohms) (Ω)

R_L(Ω) – Lead Resistance (Ohms) (Ω)

R_B(Ω) – Relay Burden in Ohms, Ω.

CT – CT Ratio

Solved Example

Calculate the knee point voltage of a current transformer with a fault current of 20 A, CT ratio of 200, CT resistance of 1 Ω, lead resistance of 0.5 Ω, and load resistance of 2 Ω.

Given

I_F(A) – 20 A

R_CT(Ω) – 1 Ω

R_L(Ω) – 0.5 Ω

R_B(Ω) – 2 Ω

CT – 200

Formula

V(V) = 2 x I_F(A) x (R_CT(Ω) + _RL(Ω) + R_B(Ω))/CT

Solution

V(V)=2 x 20 x (1 + 0.5 + 2)/200

       =2 x 0.1 x 3.5

V(V)=0.7 V

Answer

V(V) =  0.7 V

Application of Knee Point Voltage Calculator

• Knee point voltage calculations are essential for creating current transformers that can accurately measure high currents without saturation.
• The accurate knee point voltage serves as essential for the effective functioning of protective devices in power networks.
• Accurate knee point voltage is useful for assessing & responding to the fault conditions in the electrical systems.

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