# Knee Point Voltage Calculator, Formula, Knee Point Voltage Calculation

## Knee Point Voltage Calculator:

Enter the values of fault current, IF(A), secondary winding resistance, RCT(Ω), lead resistance, RL(Ω), relay burden, RL(Ω) and CT ratio to determine the value of Knee point voltage, V(V).

 Enter Fault Current : A Enter Secondary Winding Resistance : Ω Enter Lead Resistance : Ω Enter Relay Burden: Ω Enter CT Ratio: Result – Knee Point Voltage: V

## Knee Point Voltage Formula:

Knee point voltage is a crucial concept in the design and analysis of current transformers (CTs) used in electrical power systems.

It defines the voltage at which the CT’s core begins to saturate, meaning the CT can no longer accurately transform the current due to nonlinear behaviour.

Accurate determination of the knee point voltage is essential for ensuring the CT operates correctly under fault conditions and provides reliable measurements for protection systems.

Knee point voltage, V(V) in volts is calculated by dividing the product of two times of fault current, IF(A) in amperes with the sum of secondary winding resistance, RCT(Ω) in ohms, lead resistance, RL(Ω) in ohms and relay burden, RB(Ω) in ohms by CT ratio.

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Knee point voltage, V(V) =  2 * IF(A) * (RCT(Ω) + RL(Ω) + RB(Ω)) / CT

V(V) = knee point voltage in volts, V.

IF(A) = fault current in amps, A.

RCT(Ω) = secondary winding resistance in ohms, Ω.

RL(Ω) = lead resistance in ohms, Ω .

RB(Ω) = relay burden in ohms, Ω.

CT = CT ratio.

### Knee Point Voltage Calculation:

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

Given: IF(A) = 20A, CT = 200, RCT(Ω) = 1 Ω, RL(Ω) = 0.5 Ω, RB(Ω) = 2 Ω.

Knee point voltage, V(V) =  2 * IF(A) * (RCT(Ω) + RL(Ω) + RB(Ω)) / CT

V(V) =  2 * 20 * (1 + 0.5 + 2) / 200

V(V) =  2 * 0.1 * 3.5

V(V) =  0.7V.

1. Determine the knee point voltage for a current transformer with a fault current of 50A, acquired voltage is 0.9V with secondary winding resistance of 2Ω, lead resistance of 1Ω, and burden resistance of 1.5Ω:
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Given: IF(A) = 50A, V(V) =  0.9V, RCT(Ω) = 2Ω, RL(Ω) = 1 Ω, RB(Ω) = 1.5 Ω.

\ Knee point voltage, V(V) =  2 * IF(A) * (RCT(Ω) + RL(Ω) + RB(Ω)) / CT

CT = 2 * IF(A) * (RCT(Ω) + RL(Ω) + RB(Ω)) / V(V)

CT = 2 * 50 * (2 + 1 + 1.5) / 0.9

CT = 100 * 4.5 / 0.9

CT = 500.

### Applications and Considerations:

• Current Transformer Design: Knee point voltage calculations are critical for designing current transformers that accurately measure high currents without saturation.
• Protection Systems: Ensuring the correct knee point voltage is essential for the reliable operation of protection systems in power networks.
• Fault Analysis: Accurate knee point voltage helps in analyzing and responding to fault conditions in electrical systems.