CT purpose, phasor diagram and errors

Purpose of a CT

A current transformer steps down a high line current to a standard low value (1 A or 5 A) for meters and relays, and isolates them from the high-voltage circuit, so that standard low-rated instruments can be used safely.

Phasor diagram of CT

 Flux Φ is the reference (horizontal).

        −E_s   −n·I_s
          ▲      ▲       ▲ I_p
          │ δ   ╱   β   ╱
          │    ╱       ╱
          │   ╱      ╱
          │  ╱     ╱
          │ ╱    ╱   _ ─▶ I₀
          │╱  ╱_ ─ α
          O──────────────────► Φ
 I_m = I₀ cos α (along Φ), I_w = I₀ sin α (⊥ Φ)
 E_s lags Φ by 90°; I_s lags E_s by δ.
 I_p = (−n·I_s) + I₀  (phasor sum)

Where: Φ = core flux, E_s = secondary induced e.m.f., I_s = secondary current (lags E_s by the burden angle δ), −n·I_s = reversed secondary current referred to the primary, I₀ = exciting current, leading Φ by α, = I_m (magnetising, in phase with Φ) + I_w (loss, leading Φ by 90°), n = turns ratio N_s/N_p.

The primary current I_p is the phasor sum of the reversed secondary current (n·I_s) and the exciting current I₀. Because of I₀, I_p is neither exactly n·I_s in magnitude nor exactly in phase with it; the reversed secondary current leads I_p by the small angle β.

Ratio error

The actual ratio R = I_p/I_s differs from the nominal ratio K_n:

 R ≈ n + I₀ sin(δ + α) / I_s
 Ratio error (%) = (K_n − R) / R × 100

It arises mainly from the loss component of I₀ and depends on the burden.

Phase angle error

β is the angle between I_p and the reversed I_s:

 β ≈ (180/π) · I₀ cos(δ + α) / (n·I_s)  degrees

It arises mainly from the magnetising component I_m. It is important for wattmeters, energy meters and directional relays.