Current Transformer - Definition, Principle, Equivalent Circuit, Errors, and Types

Updated on January 2, 2017
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Electrical and Automation Engineer . Specialized in LV Switchgear Design and process automation


A current transformer is an instrument transformer, used along with measuring or protective devices, in which the secondary current is proportional to the primary current (under normal conditions of operation) and differs from it by an angle that is approximately zero.


Current transformers perform the following functions:

  • Current transformers supply the protective relays with currents of magnitude proportional to those of power circuit but sufficiently reduced in magnitude.
  • The measuring devices cannot be directly connected to the high magnitude supplies. Hence current transformers are used to supply those devices with currents of magnitude proportional to those of power.
  • A current transformer also isolates the measuring instruments from high voltage circuits.

Current Transformer


The basic principle of the current transformer is the same as that of the power transformer. Like the power transformer, the current transformer also contains a primary and a secondary winding. Whenever an alternating current flows through the primary winding, alternating magnetic flux is produced, which then induces alternating current in the secondary winding. In the case of current transformers, the load impedance or “burden” is very small. Therefore the current transformer operates under short circuit conditions. Also the current in the secondary winding does not depend on load impedance but instead depends on the current flowing in the primary winding.

The current transformer basically consists of an iron core upon which primary and secondary windings are wound. The primary winding of the transformer is connected in series with the load and carries the actual current flowing to the load, while the secondary winding is connected to a measuring device or a relay. The number of secondary turns is proportional to the current flowing through the primary; i.e., the larger the magnitude of current flowing through the primary, more the number of secondary turns.

The ratio of primary current to the secondary current is known as the current transformation ratio of the CT. Usually the current transformation ratio of the CT is high. Normally the secondary ratings are of the order 5 A, 1 A, 0.1 A, whereas the primary ratings vary from 10 A to 3000 A or more.

The CT handles much less power. Rated burden can be defined as the product of current and voltage at the secondary side of the CT. It is measured in volt ampere (VA).

The secondary of a current transformer should not be disconnected from its rated burden while current is flowing in the primary. As the primary current is independent of the secondary current, the entire primary current acts as a magnetizing current when secondary is opened. This results in deep saturation of the core, which cannot return to normal state and so the CT is no longer usable.

Types: Bar, Wound, and Window

Bar type current transformer
Bar type current transformer
Wound type current transformer
Wound type current transformer
Window type current transformer
Window type current transformer


Based on the function performed by the current transformer, it can be classified is follows:

  1. Measuring current transformers. These current transformers are used along with the measuring devices for the measurement of current, energy, and power.
  2. Protective current transformers. These current transformers are used along with the protection equipments such as trip coils, relays, etc.

Based on the function construction, it can also be classified as follows:

  1. Bar Type. This type consists of a bar of suitable size and material forming an integral part of the transformer.
  2. Wound Type. This type has a primary winding of ore than one full turn wound over the core.
  3. Window Type. This type has no primary winding. The secondary wind of the CT is placed around the current flowing conductor. The magnetic electric field created by current flowing through the conductor induces current in the secondary winding, which is used for measurement.

Figure 1 - Phasor diagram of an ideal CT

Figure 2 - Phasor diagram of an actual CT


The ideal current transformer may be defined as one in which any primary condition is reproduced in the secondary circuit in the exact ratio and phase relationship. The phasor diagram for an ideal current transformer is shown in Figure 1.

For an ideal transformer:

Ip Tp = Is Ts

Ip / Is = Ts / Tp

Therefore the ratio of primary and secondary winding currents equal to the turns ratio. Also the primary and secondary winding currents are exactly 1800 in phase.

In an actual transformer, the windings have resistance and reactance and also the transformer has magnetizing and loss component of current to maintain the flux (see Figure 2). Therefore, in an actual transformer the ratio of current is not equal to the turns ratio and also there is a phase difference between the primary current and the secondary currents reflected back on the primary side and consequently we have ratio error and phase angle error.

Kn = turns ratio

= number of secondary winding turns / number of primary winding turns,

rs, xs = resistance and reactance respectively of the secondary winding,

rp, xp = resistance and reactance respectively of the primary winding,

Ep, Es = primary and secondary induced voltages respectively,

Tp, Ts = number of primary winding and secondary winding turns respectively,

Ip, Is = primary and secondary winding currents respectively,

θ = phase angle of the transformer

Φm = working flux of the transformer

δ = angle between secondary induced voltage and secondary current,

Io = exciting current,

Im = magnetizing component of exciting current

Il = loss component of exciting current,

α = angle between Io and Φm

Actual transformation ratio

R = Ip / Is

= Kn + (Il cos δ + Im sin δ)/ KnIs

Phase angle θ = 180/ π (Il cos δ + Im sin δ)/ KnIs

Ratio error = (KnIs - Ip)/ Ip x 100%

= (Kn – R) / R x 100 %

Secondary Current Rating

The value of the rated secondary current is 5A. A secondary current rating of 2A and 1A may also be used in some cases if the number of secondary turns is low and the ratio cannot be adjusted within the required limits by the addition or removal of one turn, if the length of secondary connecting lead is such that the burden due to them at higher secondary current would be excessive.

The disadvantage of making transformers with lower secondary current ratings is that they produce much higher voltage if they are ever accidentally left open circuited. For this reason, it is better to adopt 5 A rating at the secondary.

Turns Compensation

Turns compensation is used in current transformers in order to reduce ratio error. If the phase angle of secondary is zero;

R = Kn + Il/ Is

The reduction in the number of secondary turns will reduce the actual transformation ratio b an equal percentage. Usually the best number of secondary turns is 1 or 2 fewer than the number that will make Kn equal to the nominal current ratio of the transformer.

Terminology of Current Transformer

Rated transformation ratio. The ratio transformation ratio is defined as the ratio of the rated primary current to the rated secondary current.

Current error (ratio error). The percentage error in the magnitude of the secondary current is defined by the following formula:

Ratio error = (KnIs - Ip)/ Ip x 100%

Ip, Is = primary and secondary winding currents respectively,

Kn = turns ratio

Accuracy class. Accuracy class tells you how accurate the current transformer is. Accuracy class shall be 0.2, 0.5, 1, 3 or 5. For example, if the accuracy class of a current transformer is 1, then the ratio error will be ±1% at the rated primary value.

Phase displacement. The difference in phase between the primary and the secondary current phasors, the direction of the phasors being chosen such that the angle is zero for a perfect transformer.

Rated secondary current. The value of rated secondary current shall be 5 A. The secondary currents rating of 2 and 1 A may also be used in some case.

Rated burden. The product of current and voltage at the secondary side of the CT is called the rated burden. It is measured in volt ampere (VA).

Table 1 - Rated Primary Current


Temperature Rise

The temperature rise of the current transformer's winding when carrying a rated primary current, at rated frequency and with rated burden, should not exceed the approximate values given in Table 2.

Table 2 - Limits of Temperature Rise of Windings

Class of Insulation
Max Temperature Rise (Deg. Celsius)
All classes immersed in oil
All classes immersed in bituminous compound
If the current transformer is specified for service at altitudes exceeding 100 m and tested at an altitude below 1000m, limits of the temperature rise given in this table shall be reduced in the following amounts for each 100 m excess over 1000m alti


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    • profile image

      Jagadeesh 2 months ago

      Can you explain simply about ct

    • profile image 6 months ago

      nice explanation of c.t.

    • profile image

      Fayzan Ali Awan 6 months ago

      Oh nice dear

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      OSBERT JOEL C 9 months ago from CHENNAI

      Please check your CT rating and input the primary in the controller.

    • profile image

      abel 9 months ago

      ive just replace a Power Factor Regulator at a switch board.

      Ive got to key in the Current Transformer Primary Value.

      The range is between 5 - 10000.

      What does it mean by that..

      Please advice.


    • goodnews11 profile image

      OSBERT JOEL C 9 months ago from CHENNAI

      Kindly let me know the primary current.

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      Anudeep 11 months ago

      i want to know what happens to a 500.5A, class 5p15 , 30VA CT When 12 KA fault current flows through it?

      Secondary total burden along with CT resistance is 1.25ohms.

      How is error calculated with Burden ?

    • profile image

      ravindra napit 13 months ago

      Very nice

    • profile image

      saud alam 23 months ago

      Thanks sir

    • profile image

      chintan vyas 2 years ago

      To good.....all the information is on the mark.

      Bt i suggest you to represent the explanation in point wise method.

      Thank you sir

    • profile image

      wkaar 2 years ago

      current transformer mathematical equations?

    • profile image

      jitender chauhan 2 years ago

      Up to point contents are include.Nice

    • profile image

      sijil rajan 2 years ago

      Thank you for this site

    • profile image

      abilash 2 years ago

      Very good answers,to be showing point wise is good to study.

    • profile image

      trilok sinha 2 years ago

      Thank you for knowdge in this site

    • profile image

      chandan kumar 2 years ago

      thank you sir for this

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      OSBERT JOEL C 3 years ago from CHENNAI

      Did you mean high temperature type transformer?

      These are designed for metering inside high ambient temperature

      environments (135ºC). these transformers can be mounted directly upon the energized busbar.

    • profile image

      fazlullah 3 years ago

      what's hot temperature Current transfarmar.

    • profile image

      Mohit yadav 3 years ago

      Good answer but i suggest important points are write in point wise. Thank you sir

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      OSBERT JOEL C 4 years ago from CHENNAI

      thank you rabindra sahoo

    • profile image

      rabindra sahoo 4 years ago

      Good answer