Ct Saturation Calculator

CT Saturation Calculator

Determine the required knee-point voltage for a current transformer to avoid saturation during a fault.

Required Knee-Point Voltage (Vk)

What is CT Saturation?

A Current Transformer (CT) is a critical component in power system protection, designed to step down high primary currents to a lower, measurable secondary current for relays and meters. CT saturation is a phenomenon where the CT's iron core becomes magnetically saturated due to a very high primary current, typically during a system fault. When saturated, the CT can no longer produce a secondary current that is an accurate, proportional representation of the primary current. The output waveform becomes distorted and its magnitude is significantly reduced, which can cause protective relays to misoperate or fail to operate entirely.

Why is Calculating Saturation Voltage Important?

Ensuring a CT does not saturate during a fault is paramount for the reliability of a protection system. If a CT saturates, the connected protective relay may not see the true magnitude of the fault current. This can lead to:

• Delayed Tripping: The relay takes longer to command the circuit breaker to open, increasing the duration of the fault and potential damage to equipment.
• Failure to Trip: In severe cases, the secondary current might be too low to meet the relay's pickup threshold, meaning the fault is never cleared by that protection zone.
• Incorrect Operation: Distorted waveforms can confuse sophisticated relays, potentially leading to incorrect tripping of healthy circuits.

By calculating the required knee-point voltage, engineers can select a CT that will perform accurately under the worst-case fault conditions for its specific application.

Formula Explained

The calculator determines the minimum required knee-point voltage (Vk) using the simplified ANSI/IEEE formula for a steady-state symmetrical fault:

Vk_required = If_secondary * R_total_burden

Where:

• Vk_required: The minimum voltage the CT must be able to produce at its secondary terminals without saturating. This is the value our calculator provides.
• If_secondary: The maximum fault current reflected on the CT's secondary side. It's calculated as Primary Fault Current / CT Ratio.
• R_total_burden: The total resistance connected to the CT secondary. This includes the CT's own internal winding resistance (Rct), the resistance of the connecting wires or leads (Rleads), and the resistance of the connected device, such as a relay (Rrelay).

How to Use the Calculator and Find Values

1. Maximum Primary Fault Current (A): This value is obtained from a power system fault study. It represents the highest symmetrical fault current that the CT is expected to see.
2. CT Primary/Secondary Rating (A): These values are found on the CT's nameplate. For example, a 1200:5 CT has a primary rating of 1200 A and a secondary rating of 5 A.
3. CT Secondary Winding Resistance (Ω): This is specified by the manufacturer on the CT's datasheet or test report.
4. Lead/Wire Resistance (Ω): This is the resistance of the two wires running from the CT to the relay. It can be calculated based on the wire gauge (AWG) and the total loop length (to the relay and back).
5. Relay Burden Resistance (Ω): This value is found on the relay's datasheet. It's often given in VA at a specific current. To convert to Ohms, use the formula: Resistance (Ω) = VA / (Current)². For a 5A CT, you would use 5A as the current. For example, a 0.5 VA burden at 5A is 0.5 / 5² = 0.02 Ω. Some datasheets provide the resistance directly.

Example Calculation

Let's consider a protection scheme with the following parameters:

• Maximum Primary Fault Current: 20,000 A
• CT Ratio: 1200:5
• CT Secondary Winding Resistance: 0.4 Ω
• Lead Resistance for the wiring loop: 0.3 Ω
• Relay Burden Resistance: 0.2 Ω

1. Calculate the CT Ratio:
CTR = 1200 / 5 = 240

2. Calculate the Secondary Fault Current:
If_secondary = 20,000 A / 240 = 83.33 A

3. Calculate the Total Burden Resistance:
R_total_burden = 0.4 Ω + 0.3 Ω + 0.2 Ω = 0.9 Ω

4. Calculate the Required Knee-Point Voltage:
Vk_required = 83.33 A * 0.9 Ω = 75.00 V

Conclusion: To avoid saturation, the selected CT must have a nameplate knee-point voltage of at least 75 V. If the CT is rated, for example, as C100, its knee-point voltage is at least 100V, making it suitable for this application.

Disclaimer: This calculator is intended for educational and preliminary estimation purposes only. It uses a simplified formula for symmetrical faults. For critical applications, a detailed analysis considering factors like DC offset (X/R ratio), remanence, and specific protection standards should be performed by a qualified electrical engineer.