We shall discuss current transformer – Construction, Phasor and Errors in this post. Current transformer are widely used for measuring the high current.The Current transformer steps down high value of current to low value which measuring instrument can read. If 2000 Amperes current to be read by a meter, it is not possible to read because a small shunt resistance of high power rating in parallel to the galvanometer is required to be used. However, it is impractical to use a small value shunt resistance of high power rating to read high current directly by meter. That is why current transformer is used to lower the magnitude of the current so that measuring instrument and protective relay can read the current.

**Construction of Current Transformer(CT)**

The current transformer has two winding called primary and secondary. The primary winding has fewer number of turns and it is connected in series with primary circuit. The whole circuit current passes through the primary winding and it is desirable that the voltage drop across primary winding must be as low as possible. The current transformer has fewer turns of large cross section and, thus the voltage drop in the primary winding gets reduced up to a great extent.

The secondary winding has more number of turns compared to the primary winding and it is connected with ampere meter, energy meter, watt meter,transducer and protection relay. The secondary winding of the CT must be connected with low impedance meter to keep the magnetic flux in the core up to its rated flux capacity. The flux in the core above the rated capacity cause saturation of the magnetic core which leads to complete failure of current transformer. The CT secondary must not be left open because in this condition, the flux in the core increases manifold and it cause CT core saturation.

Based on the construction, there are two types of current transformer- Live Tank CT and Dead Tank CT. In both types of CTs, the core and winding are enclosed in a porcelain structure and this structure is filled with mineral insulated oil which acts as cooling media, and it also provide required electrical insulation.

**Symbol of Current Transformer(CT)**

**Equivalent Circuit of Current Transformer(CT)**

The primary of CT has few turns and it has very less resistance. The primary winding resistance and reactance is denoted by R_{p} and X_{p} respectively. The secondary winding resistance and reactance is denoted by R_{s} and X_{s} respectively. The magnetization components of the current transformer are Rc and X_{m}. R_{c} is responsible for the core loss component, and X_{m} is the magnetization reactance of CT. The other CT parameters are as given below.

**Phasor Diagram of Current Transformer(CT)**

The equivalent circuit of the current transformer is similar to that of power transformer and induction motor. **The current transformer has two types of errors.**

**Ratio Error****Phase Angle Error**

From the phasor diagram, the CT ratio error and phase angle error can be calculated.

### CT Transformation Ratio

_{p}as per definition and then divide it by secondary current Is.

## CT Ratio Error Formula Derivation

_{p}as shown below.

From the above phasor, the primary current Ip is phasor sum of nI_{s} and I_{0}. The CT primary current Ip can be calculated using vector addition formula.

The magnetizing current Io is very small compared to the primary current I_{p}. Therefore, the above expression can be simplified as follows.

From above expression, it is clear that transformation ratio is not equal to turn ratio. The transformation ratio and turn ratio will be equal if α=0 and δ=0.This condition can be achieved **if the core loss is equal to zero and the burden is purely resistive.** This is **an ideal condition**, however this condition is practically impossible.

**Phase Angle Error of Current Transformer**

Phase angle of current transformer is defined as the angle between the primary current Ip and secondary current I_{s}. In above phasor diagram, θ is the phase angle.

**CT Phase Angle Error Formula Derivation**

Consider right angle triangle obc in the above phasor diagram.

**Ratio Error of Current Transformer**

**Phase Angle Error of Current Transformer**

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hello how we can measure or calculate ( Im) in ct to calculate phase angle error.

thanks.