What is the knee point voltage of a CT?

Knee point voltage (Vk) is a critical parameter when it comes to the selection and application of Current Transformers (CTs) in power systems, especially in protection and metering circuits. It helps define the performance and suitability of a CT in applications like differential protection, where accurate measurement is crucial even under fault conditions.

What is a Knee Point Voltage?

The knee point voltage is the voltage at which a CT core starts to saturate, meaning that a small increase in applied voltage results in a large increase in magnetizing current. This parameter is important because once the CT core saturates, it no longer produces an accurate transformation ratio between primary and secondary currents, leading to potential errors in protective relay operations.

Mathematically, the knee point is defined as the voltage where a 10% increase in the applied voltage causes a 50% increase in the magnetizing current.

Importance of Knee Point Voltage

The knee point voltage is particularly significant for protection-class CTs, such as those used in differential or distance protection schemes. In such protection applications, the CT must remain linear and accurate up to a certain fault current level to ensure that the protection system functions correctly.

Why is it important?

• Accurate Relay Operation: In protection applications, relays rely on accurate current measurement from CTs to determine whether a fault condition exists. A CT that saturates prematurely may provide a distorted current signal, leading to incorrect operation of the relay.
• Avoid False Trips: A high knee point voltage ensures that the CT remains unsaturated during high fault conditions, thereby preventing false tripping of protective devices.
• Differential Protection Systems: In systems like transformer differential protection, accurate current measurement is required to detect internal faults versus external faults. The knee point voltage ensures that CTs on either side of a transformer have similar characteristics to avoid differential errors during external faults.

How to Determine the Knee Point Voltage?

The knee point voltage can be determined by performing an excitation (magnetization) test on a CT. This test plots the relationship between the applied voltage and the resulting magnetizing current (excitation curve).

Excitation Test Procedure:

1. Apply a variable AC voltage across the secondary winding of the CT (keeping the primary open-circuited).
2. Measure the resulting magnetizing current at each voltage level.
3. Plot the voltage vs. magnetizing current curve.

The knee point is identified as the point where the curve significantly bends, meaning the current starts increasing disproportionately with voltage.

For example:

• If at a certain voltage (Vk), a 10% increase in voltage results in a 50% increase in magnetizing current, then that voltage is considered the knee point voltage.

Formula for Knee Point Voltage

The knee point voltage (Vk) is often defined in CT specifications by standards such as IEC 60044-1 or IEEE C57.13. A common formula for estimating Vk for a CT used in protection circuits is:

$Vk = 2 \times I_s \times (Rct + RL)$

Where:

• $I_s$: The secondary current of the CT.
• $Rct$: The internal resistance of the CT secondary winding.
• $RL$: The resistance of the secondary circuit (including leads and burden).

This formula ensures that the CT is capable of producing the necessary voltage to drive the required secondary current without significant saturation.

Application of Knee Point Voltage

The knee point voltage is typically specified when selecting CTs for:

• Differential Protection: Transformer differential protection requires CTs with matched knee point voltages on both sides of the transformer to ensure consistent behavior during faults.
• Distance Protection: In transmission lines, distance protection schemes rely on accurate current and voltage measurements, where a CT with a high knee point voltage can remain unsaturated even during high fault currents.
• Overcurrent Relays: High knee point CTs ensure accurate measurement in overcurrent protection, especially when high fault currents are expected.

Practical Considerations for Knee Point Voltage

1. Selecting CTs Based on Vk:

   • When designing a protection scheme, select CTs with a knee point voltage that is at least twice the expected secondary voltage during fault conditions. This ensures that the CT remains linear and accurate.
   • Consider the CT accuracy class. For example, a Class PS (Protection Special) CT will have a specific knee point voltage, along with accuracy limits.

2. Impact of Saturation:

   • If a CT operates beyond its knee point, it will saturate, causing significant measurement errors.
   • Saturation can delay the operation of protective relays, making the system less responsive during faults.

3. Matching CTs:

   • For differential protection schemes (e.g., transformers), it’s essential that CTs on both sides have similar knee point voltages to ensure that their behavior under fault conditions is matched, preventing unwanted trips.

Conclusion

The knee point voltage is a critical parameter for CTs in protection applications, as it defines the limit up to which the CT can provide accurate measurements without core saturation. Proper understanding and selection of CTs with appropriate knee point voltages ensure reliable operation of protective relays, improving the safety and stability of power systems. When designing or maintaining electrical protection systems, always verify the knee point voltage to ensure compliance with system requirements and standards.

Current Transformer (CT) Knee Point Voltage: Explanation and Example

Knee point voltage is a critical parameter when working with protection-class current transformers (CTs). It is especially relevant for CTs used in differential protection, distance protection, or applications where precise measurement is required at high currents and voltages.

What is Knee Point Voltage?

Knee point voltage (Vk) is the voltage at which the CT core begins to saturate. Saturation means that the CT can no longer accurately transform the primary current into the secondary current. Beyond this point, even a small increase in voltage results in a large increase in current, leading to non-linear behavior.

Why is it important?

• Protection Accuracy: It ensures that the CT can accurately measure high fault currents without saturation, enabling protective relays to operate correctly.
• Core Saturation: If the CT enters saturation during a fault condition, it may not relay the actual fault current correctly, causing delayed or incorrect operation of protection devices.
• Safety and Design: The knee point voltage helps determine the correct CT for specific protection schemes, ensuring that it can handle expected fault currents without compromising safety.

How to Identify the Knee Point Voltage?

To determine the knee point voltage (Vk) experimentally, the CT is tested by applying a voltage to the secondary winding and measuring the resulting secondary current. The knee point is typically defined by the IEC standard as:

Vk = The voltage at which a 10% increase in applied voltage results in a 50% increase in the secondary current.

The saturation region starts when the relationship between voltage and current becomes non-linear.

Knee Point Voltage Calculation Example

Let’s consider an example calculation of the knee point voltage for a CT.

Example:

Suppose you have a 1000/5A CT used in a protection circuit with the following parameters:

• Burden resistance (R): 2 ohms
• Magnetizing impedance (Zm) of the core can be approximated for simplification.

We need to determine the knee point voltage (Vk).

Step-by-Step Calculation:

1. Identify the CT Rating and Turns Ratio:

   • Primary current (Ip): 1000 A
   • Secondary current (Is): 5 A
   • Turns ratio (N): 1000/5 = 200.

2. Calculate the Magnetizing Current (Im):

   • Apply increasing voltage across the secondary winding and plot the resulting magnetizing current.
   • The knee point occurs where a 10% increase in voltage results in a 50% increase in current.

3. Approximate the Knee Point Voltage (Vk): For a rough approximation, the knee point voltage can also be estimated using:

   $$V_k \approx 2 \times (I_s \times R_b)$$

   where:

   • $I_s$ is the rated secondary current of the CT.
   • $R_b$ is the burden resistance.

   In this case:

   $$V_k \approx 2 \times (5A \times 2 \Omega) = 20 \, V$$

   This means the knee point voltage is approximately 20 volts.

4. Interpretation of the Result:

   • The CT will maintain its accuracy until about 20 volts across the secondary winding. Beyond this voltage, the CT will start to saturate.
   • For protection circuits, it is important to ensure that the voltage across the CT secondary (due to fault currents) does not exceed this knee point voltage.

Testing the Knee Point Voltage:

To confirm this calculation, you can perform a CT saturation test:

• Gradually increase the applied voltage on the CT secondary.
• Record the secondary current.
• Plot the results on a graph (voltage vs. current).
• The point where the curve becomes non-linear is the knee point.

Application in Differential Protection:

In differential protection schemes, like transformer differential protection, CTs are used to detect differences in current between the primary and secondary sides. If the CTs saturate during a fault, it may result in incorrect readings, causing the protection system to malfunction.

For example:

• If a fault occurs on a transformer and the CTs saturate, they might not accurately reflect the fault current, causing the protective relay to fail to trip.
• By selecting CTs with an appropriate knee point voltage, you ensure that they remain accurate during high current conditions, allowing the relay to operate correctly.

Conclusion:

The knee point voltage is a crucial parameter for protection CTs, ensuring accurate operation during fault conditions and preventing unwanted relay operation. Understanding and calculating the knee point voltage helps in selecting the right CT for protection applications, ensuring the safety and reliability of the power system.

By choosing a CT with a knee point voltage higher than the expected fault voltage across the CT's secondary, you ensure that the CT will operate in its linear region, providing accurate readings for protective relays.