# Current Transformer CT class Ratio Error Phase Angle Error in Current Transformer

## Definition of Instrument Transformer

Instrument transformers means**current transformer**& voltage transformer are used in electrical power system for stepping down currents and voltages of the system for metering and protection purpose. Actually relays and meters used for protection and metering, are not designed for high currents and voltages. High currents or voltages of electrical power system can not be directly fed to relays and meters. CT steps down rated system current to 1 Amp or 5 Amp similarly voltage transformer steps down system voltages to 110 V. The relays and meters are generally designed for 1 Amp, 5 Amp and 110 V.

## Definition of Current Transformer(CT)

A CT is an instrument transformer in which the secondary current is substantially proportional to primary current and differs in phase from it by ideally zero degree.## CT Accuracy Class or Current Transformer Class

A CT is similar to a electrical power transformer to some extent, but there are some difference in construction and operation principle. For metering and indication purpose, accuracy of ratio, between primary and secondary currents are essential within normal working range. Normally accuracy of**current transformer**required up to 125% of rated current; as because allowable system current must be below 125% of rated current. Rather it is desirable the CT core to be saturated after this limit since the unnecessary electrical stresses due to system over current can be prevented from the metering instrument connected to the secondary of the CT as secondary current does not go above a desired limit even primary current of the CT rises to a very high value than its ratings. So accuracy within working range is main criteria of a CT used for metering purpose. The degree of accuracy of a metering CT is expressed by

**CT accuracy class**or simply

**current transformer class**or

**CT class**. But in the case of protection, the CT may not have the accuracy level as good as metering CT although it is desired not to be saturated during high fault current passes through primary. So core of protection CT is so designed that it would not be saturated for long range of currents. If saturation of the core comes at lower level of primary current the proper reflection of primary current will not come to secondary, hence relays connected to the secondary may not function properly and protection system losses its reliability.

Suppose you have one CT with current ratio 400/1 A and its protection core is situated at 500 A. If the primary current of the CT becomes 1000 A the secondary current will still be 1.25 A as because the secondary current will not increase after 1.25 A because of saturation. If actuating current of the relay connected the secondary circuit of the CT is 1.5 A, it will not be operated at all even fault level of the power circuit is 1000 A.
The degree of accuracy of a protection CT may not be as fine as metering CT but it is also expressed by **CT accuracy class** or simply **current transformer class** or **CT class** as in the case of metering current transformer but in little bit different manner.

## Theory of Current Transformer or CT

A CT functions with the same basic working principle of electrical power transformer, as we discussed earlier, but here is some difference. If a electrical power transformer or other general purpose transformer, primary current varies with load or secondary current. In case of CT, primary current is the system current and this primary current or system current transforms to the CT secondary, hence secondary current or burden current depends upon primary current of the current transformer.Are you confused? OK let us clear you.

In a power transformer, if load is disconnected, there will be only magnetizing current flows in the primary. The primary of the power transformer takes current from the source proportional to the load connected with secondary . But in case of CT, the primary is connected in series with power line. So current through its primary is nothing but the current flows through that power line. The primary current of the CT, hence does not depend upon whether the load or burden is connected to the secondary or not or what is the impedance value of burden. Generally CT has very few turns in primary where as secondary turns is large in number. Say N_{p} is number of turns in CT primary and I_{p} is the current through primary. Hence the primary AT is equal to N_{p}I_{p} AT.

If number of turns in secondary and secondary current in that current transformer are N_{s} and I_{s} respectively then Secondary AT is equal to N_{s}I_{s} AT.

In an ideal CT the primary AT is exactly is equal in magnitude to secondary AT.

So from the above statement it is clear that if a CT has one turn in primary and 400 turns in secondary winding, if it has 400 A current in primary then it will have 1 A in secondary burden.

Thus the turn ratio of the CT is 400/1 A

## Error in Current Transformer or CT

But in an actual CT, errors with which we are connected can best be considered through a study of phasor diagram for a CT, I_{s}- Secondary current. E

_{s}- Secondary induced emf. I

_{p}- Primary current. E

_{p}- Primary induced emf. K

_{T}- Turns ratio = Numbers of secondary turns/number of primary turns. I

_{0}- Excitation current. I

_{m}- Magnetizing component of I

_{0}. I

_{w}- Core loss component of I

_{0}. Φ

_{m}- Main flux.

Let us take flux as reference. EMF E_{s} and E_{p} lags behind the flux by 90°. The magnitude of the passers E_{s} and E_{p} are proportional to secondary and primary turns. The excitation current I_{o} which is made up of two components I_{m} and I_{w}.

The secondary current I_{0} lags behind the secondary induced emf E_{s} by an angle Φ _{s}. The secondary current is now transferred to the primary side by reversing I_{s} and multiplied by the turns ratio K_{T}. The total current flows through the primary I_{p} is then vector sum of K_{T} I_{s} and I_{0}.

### The Current Error or Ratio Error in Current Transformer or CT

From above passer diagram it is clear that primary current I_{p}is not exactly equal to the secondary current multiplied by turns ratio, i.e. K

_{T}I

_{s}. This difference is due to the primary current is contributed by the core excitation current. The

**error in current transformer**introduced due to this difference is called current error of CT or some times

**ratio error in current transformer**.

### Phase Error or Phase Angle Error in Current Transformer

For a ideal CT the angle between the primary and reversed secondary current vector is zero. But for an actual CT there is always a difference in phase between two due to the fact that primary current has to supply the component of the exiting current. The angle between the above two phases in termed as**phase angle error in current transformer**or CT. Here in the pharos diagram it is β the phase angle error is usually expressed in minutes.

### Cause of Error in Current Transformer

The total primary current is not actually transformed in CT. One part of the primary current is consumed for core excitation and remaining is actually transformers with turns ratio of CT so there is**error in current transformer**means there are both

**ratio error in current transformer**as well as a

**phase angle error in current transformer**.

#### How to Reduce Error in Current Transformer

It is desirable to reduce these errors, for better performance. For achieving minimum error in current transformer, one can follow the following,- Using a core of high permeability and low hysteresis loss magnetic materials.
- Keeping the rated burden to the nearer value of the actual burden.
- Ensuring minimum length of flux path and increasing cross-sectional area of the core, minimizing joint of the core.
- Lowering the secondary internal impedance.