---
title: "Knee point voltage and CT selection"
subject: "Switchgear and Protection"
chapter: 2
key: "semester_6/switchgear_and_protection:knee-point-ct-selection"
source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/knee-point-ct-selection
site: BCT Engineering
---

# Knee point voltage and CT selection

Switchgear and Protection · Chapter 2: Current and Potential Transformers

- Asked in: 2079 Chaitra, 5 marks
- Video: [magnetizing characteristics of CT](https://www.youtube.com/watch?v=DMOjU1ORqss) — Electrical Engineering, ITNU
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/knee-point-ct-selection
- Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-2

## Question

Explain knee point voltage in CT with the help of necessary plots. Explain its importance in selection of CT for protection system.

## Short answer

Knee point voltage (Vk) on CT excitation curve is where 10% voltage increase gives50% exciting current rise, marking core saturation. For protection, Vk must be high enough to avoid saturation at maximum fault current: Vk ≥ K × If(sec) × total secondary resistance. This ensures accurate fault sensing and prevents maloperation in differential schemes.

## Answer

The **knee point voltage (Vk)** is the secondary e.m.f. on the CT excitation curve at which a 10 % increase in voltage produces a 50 % increase in exciting current. It marks the beginning of core saturation.

#### Excitation characteristic
```text
 Vs (V)
  │                 ________ saturation
  │             _--     (flat)
  │        Vk ●         10% ↑V → 50% ↑Ie
  │         /│
  │        / │ ankle-to-knee
  │       /  │ (linear) region
  │      /   │
  │ ankle    │
  └─/────────┴──────────────── Ie (A)
```
- **Ankle region:** at very low flux, permeability is low; Ie relatively high.
- **Linear region:** Ie is small and proportional to Vs; CT is accurate (ratio error small).
- **Knee point:** beyond Vk the core saturates; a small increase in Vs needs a large Ie.
- **Saturation region:** most of the primary ampere-turns are used to magnetise the core; the secondary current waveform is distorted and lower than expected.

```text
 i_s ideal   ╱╲    ╱╲
 i_s saturated ╱▔╲__╱▔╲__ (clipped)
```

#### Importance in CT selection for protection
1. A protective CT must remain unsaturated up to the **maximum fault current**, otherwise the relay sees less current and may operate slowly or not at all.
2. **Required knee point:**
   `Vk ≥ K · I_f(sec) · (R_ct + 2R_lead + R_relay)`
   where I_f(sec) is the maximum fault current referred to the secondary and K (typically 1.5–2, higher with DC offset) allows for transient saturation.
3. In **differential and restricted earth-fault** schemes, CTs on the two sides must have matched, high Vk (class PS/PX) so that one CT saturating during a through-fault does not create a false spill current; a stabilising resistor is chosen using Vk.
4. Measuring CTs are intentionally given a **low** knee point so that they saturate and protect meters during faults.
5. Higher Vk needs a larger core and more turns, so cost rises; the designer chooses the minimum Vk that meets the fault level and burden.

*Example:* For I_f(sec) = 20 × 1 A = 20 A, R_ct + leads + relay = 5 Ω and K = 2: Vk ≥ 2 × 20 × 5 = 200 V.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which expression gives the required knee point voltage?
   A. Vk <= I_f(sec) / burden
   B. Vk >= K x I_f(sec) x (R_ct + 2R_lead + R_relay)
   C. Vk = K x primary voltage
   D. Vk >= R_relay only
   Answer: B. Vk must exceed the voltage to drive max fault current through the secondary burden. (Key point: Vk formula)

2. For I_f(sec) = 20 A, total resistance 5 ohm and K = 2, what is minimum Vk?
   A. 200 V
   B. 100 V
   C. 50 V
   D. 20 V
   Answer: A. 2 x 20 x 5 = 200 V. (Key point: Example)

3. What if a protective CT saturates at max fault current?
   A. Relay operates faster
   B. Nothing changes
   C. Secondary current is increased
   D. Relay sees less current and may operate slowly or not at all
   Answer: D. Saturation distorts and reduces secondary current. (Key point: Saturation effect)

4. Why match high Vk CTs in differential/REF schemes?
   A. To increase the spill current
   B. To lower CT cost
   C. So one CT saturating in a through-fault does not give false spill current
   D. To avoid using a stabilising resistor
   Answer: C. Matched high-Vk (PS/PX) CTs keep the scheme stable. (Key point: Differential schemes)

## Related in Switchgear and Protection

- [Knee point voltage; measuring vs protective CT](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aknee-point-measuring-protective-ct) — Switchgear and Protection, chapter 2
- [Knee point voltage and CT errors](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aknee-point-ct-errors) — Switchgear and Protection, chapter 2

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- [Transformer protection, selection and vector group](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Atransformer-protection-vector-group) — Power Plant Design, chapter 4