---
title: "Different errors of CT"
subject: "Switchgear and Protection"
chapter: 2
key: "semester_6/switchgear_and_protection:errors-of-ct"
source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/errors-of-ct
site: BCT Engineering
---

# Different errors of CT

Switchgear and Protection · Chapter 2: Current and Potential Transformers

- Asked in: 2072 Asoj, 4 marks
- Video: [Accuracy class of Current Transformer | Explained | TheElectricalGuy](https://www.youtube.com/watch?v=28sWUdVGqb8) — Gaurav J - TheElectricalGuy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/errors-of-ct
- Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-2

## Question

What are the different errors of CT? Explain briefly.

## Short answer

CT errors are ratio error (difference between actual and nominal ratio), phase angle error (angle between primary and reversed secondary current), and composite error (rms difference including harmonics). They arise from the exciting current needed for core magnetization, and are increased by high burden, saturation, and remanent flux.

## Answer

A practical CT does not give a secondary current exactly equal to I_p/K_n, because part of the primary ampere-turns is used to set up flux in the core (exciting current I₀ = magnetising component I_m + loss component I_w). This causes the following errors:

#### 1. Ratio (current) error
The actual ratio R = I_p / I_s differs from the nominal ratio K_n.
```text
 Current error (%) = (K_n·I_s − I_p) / I_p × 100
 Approximately   R ≈ n + (I₀ sin(δ+α)) / I_s
```
where n is the turns ratio N_s/N_p, δ is the burden phase angle and α the angle by which I₀ leads the flux. It is mainly caused by the loss (in-phase) component of I₀.

#### 2. Phase angle error (phase displacement)
The angle β between the primary current phasor and the reversed secondary current phasor.
```text
 β ≈ (180/π) · I₀ cos(δ+α) / (n·I_s)   degrees
```
It is mainly caused by the magnetising component of I₀. It matters for wattmeters, energy meters and directional/distance relays.

#### 3. Composite error
The r.m.s. difference between (K_n × instantaneous i_s) and instantaneous i_p over one cycle, as a percentage of the r.m.s. value of I_p. It includes ratio error, phase error and harmonic distortion due to saturation. It is the main error specified for protective CTs (5P, 10P).

#### Factors affecting errors
- Exciting current (core material, flux density, core size).
- Burden magnitude and power factor.
- Saturation due to fault current or DC offset; remanent flux.
- Supply frequency.

Errors are reduced by low-loss, high-permeability cores, low flux density, small burden and turns compensation (one or two secondary turns fewer than nominal).

## Check yourself

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

1. Why does a practical CT have errors?
   A. Secondary has no turns
   B. Part of primary ampere-turns supplies exciting current I0
   C. Primary current is DC
   D. The burden is zero
   Answer: B. I0 = Im + Iw is drawn from primary. (Key point: Cause of errors)

2. Which gives current error (%)?
   A. (K_n I_s - I_p)/I_p x 100
   B. (I_p - I_s)/K_n x 100
   C. K_n/I_s x 100
   D. (I_s/I_p) x 100
   Answer: A. This is the standard definition. (Key point: Current error formula)

3. How can errors be reduced?
   A. Large burden
   B. High flux density
   C. High-permeability cores, low flux density, small burden, turns compensation
   D. Lower-permeability core
   Answer: C. These reduce exciting current. (Key point: Reduction)

4. For which devices is phase angle error important?
   A. Only ammeters
   B. Only overcurrent relays
   C. Only fuses
   D. Wattmeters, energy meters and directional/distance relays
   Answer: D. These depend on phase relation. (Key point: Phase error importance)

## Related in Switchgear and Protection

- [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
- [Need of instrument transformers; CT errors](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Ainstrument-transformers-need-ct-errors) — Switchgear and Protection, chapter 2
- [CT purpose, phasor diagram and errors](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Act-phasor-ratio-phase-error) — Switchgear and Protection, chapter 2