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**Current transformer:**

A **current transformer** or a **CT** is a type of **transformer** which converts a high value of **current** and **voltage** into a smaller value of **current** and **voltage**. The **high voltage** and **low voltage current** quantities are linearly proportional by the CT turns ratio during normal operating conditions although the voltage quantity on the low-voltage side is smaller it is not linearly proportional.

So **current transformer**s are used for step-down current quantities while potential transformers are used for step down voltage quantities and a power transformer is used to transfer power. it can be either step-down or step up. **Current transformer**s are a very special application of a step-down transformer. in order to have a smaller amount of current on the secondary side of the CT the number of turns on the secondary side must be greater than the number of turns on the primary side.

CTR= I_{P}/I_{s} = N_{S}/N_{P}

I_{P}= Primary current

I_{s}= Secondary current which should below

N_{P}= Primary turns

N_{S}= Secondary turns

Suppose we have a conductor passing through a CT since the conductor passes through the window the number of primary turns is simply 1 the number of secondary turns should be much higher with this being an ideal transformer primary current over secondary current should be equal to the number of secondary turns over the number of primary turns. So the number of turns on the primary side is equal to 1 and let’s assume we have four secondary turns this is a step-down transformer. So if primary current equals 100 amps and CTR equals four then we should expect the secondary current to be equal to 100 divided by four or 25 amps.

I_{s}= 100/4=25A

## Current transformer CT Equivalent Model:

Now consider the equivalent model of a current transformer there are various parameters to consider we will be going through them one by one.

Let’s begin by considering the parameters on the primary side of the current transformer first we have the parameter V_{P} which can be defined as the rated voltage on the primary side of the current transformer. This is the line side of the CTR connection. Next up we have I_{P} which is the current flowing through the primary side of the CT. The resistance components R_{P} and R_{S} are impedance parameters driven by CT construction and due to the generation of flux in the primary and secondary windings. This results in the generation of a leakage reactance which can be observed in the equivalent model on both sides XL-p and XL-s are parameters that describe the leakage reactance of the current transformer. It is responsible for a voltage reduction on the secondary terminal of the current transformer moving over to the secondary side we have V s which is the rated voltage on the secondary side of the current transformer. We have the excitation current Ie which is used to energize the magnetic core of the CT it is also useful in calculations involving CT saturation. Furthermore this excitation current quantifies the amount of CT error which is present in the circuit the greater the value of Ie the more error being produced in the current transformer and vice versa. The final current value is I_{s} which flows from the secondary winding towards the load RC can be defined as the resistance responsible for the core losses which include the losses occured due to eddy currents as well as hysteresis under normal conditions. These losses are constant since they are derived from CT construction and finally we have Zm which is an inductance responsible for producing the magnetic flux. This flux is critical for proper transformer operation another important parameter to consider is the CT burden which can be defined as the load connected to the secondary side the CT burden is typically relay and meter impedance as well as impedance of the wires that connect relays and meters again these loads are connected directly to the secondary terminal.

## CT Accuracy:

Let us first define the meaning of CT accuracy in simple terms it is the extent to which the current present in the secondary side of a current transformer is able to faithfully reproduce the current flowing in the primary side under practical conditions. There will always be some error in the output current when compared to the original current in the primary winding. The error is due to the magnetization current present in the secondary branch. Let us consider the importance of CT accuracy for protection if we consider a fault on a low voltage but in a three-phase system we would require the connected CT to be able to operate effectively at the highest current level present on that particular bus this is because we want the CT to accurately recognize the fault level and deliver the signal to the relay connected to its secondary winding which in turn would cause the circuit breaker to trip for protection CTS are required to carry the fault currents which can be 10 times the rate at full load current for this reason we require protection Class C T’s to saturate at a high value as this will enable the CT to properly identify the high fault level signature for protective relays examples of protection Class C T’s include the 5P20, 10C400 as well. Let us consider the importance of CT accuracy class for metering purposes we would want metering Class CT’s to accurately measure the current flowing on the primary side to the full load current and beyond these CTS are designed to have a lower saturation value this is because under fault conditions we do not want our metering CT to become permanently damaged. The lower saturation limits the amount of maximum current which can flow through the core thereby protecting it from damage. These type of CTS are normally used for energy metering and instrumentation purposes. Since the accuracy class holds critical importance for metering applications. The percentage ratio error is only acceptable within a very small percentage typically less than 1%. Examples of metering Class C T’s include 0.15, 0.3, 0.3s and various others these values tell us about the percentage error.

## CT Sizing:

When we talk about CT sizing there are various parameters to consider including the rated power the safety factor. The accuracy class and the CT burden but the most important factor to consider when sizing a current transformer is the CT ratio as discussed above the current transformer ratio can be defined as the secondary number of turns divided by the primary number of turns.

CTR= I_{P}/I_{s} = N_{S}/N_{P}

In other words we can also specify it as the current flowing through the primary winding divided by the current on the secondary winding.

Let us now consider an example circuit where we have a current transformer connected to breaker be let’s assume that the current flowing through breaker B is 80 amps.

we already know that most CTS have a secondary current rating of either one arms or five amps keep in mind that for maximum primary load current the secondary current produced does not exceed. The continuous thermal current rating of any part of the CT total secondary circuit for this case. Let’s select a rating of 5 amps if we put at in the ratio formula then the resulting ratio is 16 which is 80 full load amps divided by 5 amps rated current on the secondary CT circuit.

CTR= I_{P}/I_{s} = 80/5 = 16

Practically speaking the closest CT ratio available to our calculated value is 20 which means that a current transformer with the ratings of 100 to 5 should be applicable for our example the 100 to 5 ratio means that we are expecting 100 amps of full load current on the primary side which is equivalent to 5 amps a full load current on the secondary side. Maximum fault currents should be considered when sizing a current transformer for protection purposes. The current transformer ratio should be large enough so that the CT secondary current does not exceed 20 times rated current under the maximum symmetrical primary fault current while the acceptable error of 10% is not exceeded. This is a bit difficult to understand first but let us break this statement down briefly for our example let’s assume that the maximum fault current is at 10 times the rated load current the resulting value turns out to be 80 times 10 which equals 800 amps.

I_{fault}=10 ×80

I_{fault}=800 Amp

Under fault conditions this 800 amps is divided by a ratio of 20 which results in a current of 40 Amps on the secondary side of the current transformer.

CTR= I_{P}/I_{s}

20= 800/I_{s}

I_{s}=40 Amp

On the other hand the CT rated current of 5 amps times 20 comes out to be 100 amps. Since the maximum secondary current of 40 amps is less than 100 amps therefore we can safely assume our CT ratio to be correct on the other hand we can face issues like saturation and reduced mechanical capability by applying the wrong CT ratio saturation can cause improper functioning of the CT and even permanently damaging in the worst case scenario. These effects can be minimized by using the highest CT ratio that is compatible with the system to conclude this discussion knowledge of CT sizing is critical for power systems protection.

## Use of CT:

Although the use of CT is a wide and varied they are mainly used for either protection or metering purposes. In order to protect a distribution feeder a current transformer can be wired to provide current quantities to a protective relay. If an abnormality occurs the primary line current would increase which is transformed to secondary values this increase in current would indicate an abnormality and the protective relay would issue a trip in command to a circuit breaker.

## Protection class transformer:

Protection class current transformers are designed to transform wide range of line current with manageable amount of error typical range is five to twenty times the load current because short-circuit currents can be very high values we can expect up to 10% for the CT error. so protection Class CT’s should be carefully sized to make sure the CTS do not saturate it is important to remember that the metering class current transformer must be highly accurate typically with less than one percent error at full load. metering Class CT’s are used for revenue metering or instrumentation or purposes a wide range of current is not required for metering Class CT’s however high accuracy is required to avoid CT error. We must carefully size metering Class CT’s because it can become inaccurate when the load current exceeds the CT rating.