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Knee point voltage and CT selection

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.

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

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

 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.
 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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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