Knee point voltage and CT errors

Typical knee point voltage

The knee point voltage (Vk) of a CT is the secondary e.m.f. at which a 10 % rise in voltage causes a 50 % rise in exciting current. It is the boundary between the linear part of the excitation curve and saturation.

 Vs │           ______ saturation
    │       Vk ●
    │        /
    │       /  linear (accurate) region
    └──────/──────────────── Ie

• Below Vk the CT transforms current accurately; above it the core saturates and secondary current is distorted and reduced.
• A protective CT must have Vk higher than the voltage needed to drive the maximum fault current through its burden: Vk ≥ K·I_f(sec)·(R_ct + R_lead + R_relay). Typical values are a few hundred volts for protection CTs and much lower for metering CTs.

Errors of CT and their causes

An ideal CT has I_s = I_p / K_n exactly in phase opposition. In practice part of the primary ampere-turns is used to supply the exciting current I₀, causing errors.

1. Ratio (current) error: difference between actual and nominal ratio, Current error % = (K_n·I_s − I_p) / I_p × 100 Cause: the loss component of I₀ (in phase with I_s) reduces I_s; also burden power factor.
2. Phase angle error (phase displacement, β): angle between the primary current and the reversed secondary current. Cause: the magnetising component of I₀ (in phase with flux) makes I_s lag/lead the ideal phasor.
3. Composite error: r.m.s. value of the difference between ideal and actual secondary current over a cycle, including harmonics caused by saturation (important for protective CTs).

Causes and factors increasing errors

• High exciting current due to poor core material or high flux density.
• High burden (impedance of relays + leads) – requires more e.m.f., more flux, more I₀.
• Burden power factor (inductive burden increases ratio error; resistive increases phase error).
• Saturation due to high fault current or DC offset; remanent flux in core.
• Low primary current (operating near ankle region, low permeability).
• Frequency different from rated.

Errors are reduced by using high-permeability cores (CRGO, nickel-iron), low flux density, low burden and turn compensation.