CT Saturation & Knee Point Analyzer

Commercial-grade Protection Engineering tool. Calculates Knee Point Voltage ($V_k$), Time-to-Saturate ($t_{sat}$), and simulates waveform distortion. Supports ANSI (C-Class) and IEC (P/TPX) standards with transient remanence analysis.

1. Current Transformer Data
:
2. System Fault Data
3. Connected Burden

Technical Deep Dive: CT Saturation

Table of Contents

1. Physics of Saturation: The Magnetic Funnel

A Current Transformer (CT) works like a magnetic funnel. It transfers energy from the primary high-current conductor to the secondary circuit via a magnetic core (usually iron). Think of the core flux density ($B$) as water flowing through a pipe.

Saturation occurs when the "pipe" is full. The iron core cannot carry any more magnetic flux. When this happens, the coupling between primary and secondary breaks down. The secondary output current drops to zero (or near zero) for parts of the cycle, resulting in a distorted, "chopped" waveform.

The limit is defined by the Knee Point Voltage ($V_k$). If the voltage required to push the fault current through the secondary burden ($V_{req} = I_{sec} \times Z_b$) exceeds $V_k$, the CT saturates.

2. The DC Offset Killer

AC Faults are rarely pure sine waves. Because inductance opposes current change, a fault happening at voltage zero creates a massive DC Offset in the current to maintain flux continuity. This DC component decays exponentially based on the System X/R ratio.

Transient Dimensioning Factor ($K_{td}$)

The DC flux adds to the AC flux. To avoid saturation during a fully offset fault, the CT must be sized vastly larger than for steady-state. The theoretical max flux is $(1 + X/R)$ times the AC flux. For a system with X/R=20, the CT needs to be 21 times larger to avoid transient saturation completely!

3. Remanence: The Hidden Risk

Iron cores have "memory". If a fault is cleared while flux is high, magnetic domains may remain aligned, leaving Remanent Flux ($\Psi_r$) trapped in the core. This reduces the available headroom for the next fault.

If an autoreclose operation occurs onto a fault with the same polarity, the core starts with, say, 80% flux already used up. Saturation happens almost instantly ($< 2ms$).
Solution: Use gapped cores (IEC Class TPY, TPZ) which have low remanence ($K_{rem} < 10\%$).

4. Accuracy Limit Factor (ALF)

For IEC protection CTs (e.g., 5P20), the ALF defines how many times the rated current the CT can handle before error exceeds 5%. However, the Rated ALF is valid only at Rated Burden. If your connected burden is lower than rated, the Actual ALF increases significantly:

$$ ALF_{actual} = ALF_{rated} \times \frac{S_{rated} + S_{internal}}{S_{actual} + S_{internal}} $$

A CT rated 5P20 at 30VA might effectively perform as 5P40 if only 10VA of burden is connected.

5. Time-to-Saturate ($t_{sat}$)

Relays don't trip instantly; they need measurement time (e.g., 1 cycle or 20ms). Even if a CT saturates, it's acceptable IF it saturates after the relay has made its decision.

This calculator estimates $t_{sat}$. If $t_{sat} > \text{Relay Time}$, the protection is secure. If $t_{sat} < 5ms$, differential relays may misoperate (trip incorrectly) due to the distorted waveform looking like an internal fault.

6. Applicable Standards

  • IEEE C57.13 (ANSI): Defines "C" class (e.g., C400). Knee point is defined at 45° tangent on log-log curve. Focuses on terminal voltage capability.
  • IEC 61869-2 (formerly 60044): Defines "P" class (e.g., 5P20). Knee point is where 10% voltage increase causes 50% current increase. Includes TPX (closed core), TPY (gapped), TPZ (linear) for transient performance.
  • IEEE C37.110: Guide for the Application of Current Transformers Used for Protective Relaying Purposes (Source of the $t_{sat}$ formulas).