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Current Transformer Explained with Calculations

We use a Current Transformer (C.T.) as an “instrument transformer.” It creates an alternating current in its secondary winding that matches the current in its primary winding.

Current transformers lower high voltage currents to safer levels. They help us monitor the actual electrical current in an AC transmission line using a standard ammeter.

The way a basic current transformer works is different from a regular voltage transformer. A current transformer usually has only one or a few turns in its primary winding. This primary can be a single flat turn, a heavy-duty wire coil around the core or just a conductor or bus bar passing through a central hole.

So when we talk about this kind of setup, people often call the current transformer a “series transformer.”

This is because the primary winding which really only has a handful of turns, is connected in series with the conductor that is actually carrying the current and supplying power to a load.

Now the secondary winding can have a whole lot of coil turns wrapped around a laminated core made from some low-loss magnetic material. The core is designed with a pretty big cross-sectional area.

This helps keep the magnetic flux density nice and low and it allows for the use of much thinner wire in terms of cross-sectional area.

The amount of current that needs to be stepped down will depend on how much current we want to output while keeping it constant, no matter what kind of load is connected.

When it comes to the secondary winding it will send out current either into a short circuit—like when you are using an ammeter—or into some kind of resistive load.

It will keep doing this until the voltage that gets induced in the secondary winding becomes high enough to saturate that core or even cause it to fail because of too much voltage breakdown.

Now as we know, the current transformer is very different to a voltage transformer. The primary current in a current transformer does not depend on the current flowing through the secondary load. Instead it is controlled by an external load.

Typically the secondary current is rated at either 1 Ampere or 5 Amperes especially when we are dealing with larger primary current ratings.

Types of Current Transformers

When we talk of current transformers there are basically three main types that you should know about: wound, toroidal, and bar.

Wound Current Transformer

Let us start with the wound current transformer. In this type the primary winding is actually connected directly in series with the conductor that is carrying the current we want to measure in the circuit.

The amount of current that comes out of the secondary side is determined by what we call the transformer’s turns ratio.

So basically how many turns there are in the winding compared to the primary side will dictate how much current you are going to see on the secondary side.

Toroidal Current Transformer

Next up is the toroidal current transformer. This one is a bit different because it doesnt have a primary winding at all. Instead what happens is that the conductor carrying the current just gets passed through a sort of window or opening in the toroidal transformer itself.

Some versions of this transformer even come with what is known as a “split core.” This means you can open it up and put it around the conductor without having to disconnect anything in the circuit that it is associated with, which is super convenient.

Bar-type Current Transformer

Finally we have the bar-type current transformer. This type actually uses the main cable or bus-bar from the circuit as its primary winding which means it essentially acts like a single turn.

These transformers are completely insulated from any high operating voltage that might be present in the system and they are usually mounted securely onto whatever device is carrying the current.

Current transformers are really cool because they can lower super high current levels, sometimes reaching thousands of amperes, to a safer and more manageable outputs, usually either 5 Amps or 1 Amp.

This makes it possible to use smaller and more accurate tools and control devices safely since these devices are kept away from any dangerous high-voltage power lines. There are many different ways to use current transformers.

They can work with devices like wattmeters, power factor meters, watt-hour meters, protective relays and even trip coils in magnetic circuit breakers which are often called MCBs.

Understanding Current Transformer Winding

Current transformers and ammeters usually work together as a team. The current transformer is designed to produce a secondary current that matches the full-scale reading on the ammeter.

Most current transformers have a turns ratio that is roughly the opposite of the currents in the primary and secondary windings. This is why the current transformer is often calibrated to fit a specific type of ammeter.

Typically the current transformers are set to have a secondary rating of 5 amps. The relationship between the primary and secondary currents is shown as a ratio, like 100/5.

This means that the primary current is twenty times larger than the secondary current. So if there is 100 amps flowing in the primary wire then the secondary will show 5 amps.

For example a current transformer rated at 500/5 will produce 5 amps in the secondary when there is 500 amps in the primary, showing a ratio of 100 to 1.

Increasing the number of secondary windings called Ns, allows us to lower the secondary current compared to the current in the primary circuit we are looking at.

This happens because when we add more secondary windings, then the secondary current Is, decreases in a way that matches the increase in windings. In simpler terms, there is a reverse relationship between the number of turns and the currents in both the primary and secondary windings.

A current transformer just like any other transformer must follow the amp-turn equation. From what we’ have talked about with double wound voltage transformers, we know that this turns ratio can be shown like this:

T.R. = n = NP/NS = IS/IP

And so this gives us the following equation:

Secondary Current, IS = IP(NP/NS)

The current ratio is really important for figuring out the turns ratio of a transformer. Usually the primary winding has just one or two turns while the secondary winding can have hundreds of turns creating a big difference between the two.

For example if the primary winding is rated at 100A then secondary winding is usually rated at 5A. This means that the current in the primary winding is 100A compared to 5A in the secondary which simplifies to a ratio of 20:1.

This shows that the current in the primary winding is twenty times higher than in the secondary winding.

It’s also important to understand that a current transformer labeled as 100/5 is not the same as one labeled 20/1 or any other similar ratios.

The 100/5 label specifically indicates the “input/output current rating” and not the actual current ratio between the primary and secondary windings. Additionally the relationship between the number of turns and the currents in both windings is inversely proportional.

You can change the turns ratio of a current transformer by adjusting how many times the primary wire goes through the CT’s window. Each time the wire goes through, it counts as one turn and if you loop the wire through the window more than once, it changes the electrical ratio.

For example if you have a current transformer rated at 300/5A then you can loop the primary wire through the window two or three times. This would change the rating to 150/5A or even 100/5A. This method allows a current transformer with a higher rating to provide the maximum output current to the ammeter when used in circuits with lower primary current levels.

Solving Primary Turns Ratio in Current Transformers #1

Imagine a bar-type current transformer having 2 turns on its primary winding and a large 200 turns on its secondary winding. It’s designed to work with regular ammeters that have an internal resistance of 0.3 ohms. The ammeter needs to show full-scale deflection when the primary current hits a big 900 Amps. So, now let us calculate the maximum secondary current and the voltage that will show up across the ammeter.

The relationship between primary and secondary currents in a current transformer is given by the formula:

Ip / Is = Ns / Np

Where:

Is is the secondary current.

Rearranging this gives:

Is = Ip * (Np / Ns)

Substituting in the known values:

Is = 900 Amps * (2 / 200)

= 900 Amps * 0.01

= 9 Amps

Thus the maximum secondary current is 9 Amps.

Calculating Voltage Across the Ammeter:

The voltage across the ammeter can be calculated using Ohm’s Law:

V = Is * RA

Substituting the values we have:

V = 9 Amps * 0.3 ohms

= 2.7 Volts

Therefore the voltage across the ammeter is 2.7 Volts.

It’s clear from above that the secondary side of the current transformer is connected to the ammeter, which has very low resistance. Because of this when the primary current is at its highest, the voltage drop across the secondary winding is only 2.7 volts.

On the other hand if the ammeter gets disconnected, the secondary winding acts like an open circuit. In this case the transformer works like a step-up transformer.

This happens because there’s a big increase in magnetizing flux in the secondary core and the secondary leakage reactance has a big effect on the voltage that gets induced in the secondary winding. This is due to the fact that there’s no current in the secondary winding to balance it out.

As a result a very high voltage is created in the secondary winding which can be calculated using the formula Vp(Ns/Np), where this voltage appears across the secondary winding.

To give an example let’s think about the current transformer we mentioned before which is used on a three-phase power line that runs at 440 volts to the ground.

So using this formula, we get:

T.R. = n = VP/VS = NP/NS

VS = VP(NS/NP)

= 440(200/2)

= 44000 Volts or 44 kV

The high voltage seen in this situation happens because the ratio of volts per turn in both the primary and secondary coils stays almost the same. Using the formula Vs = Ns * Vp where both Ns and Vp are really big numbers we can see that the secondary voltage Vs becomes extremely high.

Because of this, it’s very important not to leave a current transformer disconnected or to use it without a load while the primary current is still flowing.

Also a voltage transformer should never be short-circuited. If you need to disconnect an ammeter or load, you should first connect a short circuit across the secondary terminals to avoid any shock risks.

The reason for the high secondary voltage is that when the secondary is left open, the iron core of the transformer gets really saturated.

Without a load to control the output, this leads to an extremely high secondary voltage which in our simple example was calculated to be an incredible 76.8 kV.

This kind of voltage is very dangerous because it could damage the insulation or cause electric shock if by mistake someone touches the current transformer terminals.

What are Handheld Current Transformers

There are many different types of current transformers available today, each one made for specific measurement tasks. One popular and easy-to-use option is the clamp meter which is great for checking how much load is in a circuit, as shown in the picture below.

Clamp meters work by wrapping around a wire that carries current. They can measure the flow of current by looking at the magnetic field created around the wire. This clever design lets users get quick readings, usually shown on a digital display and without having to unplug or stop the circuit.

Besides the handheld clamp meters there are also split core current transformers. These have a part that can be removed, making it easy to install them without disconnecting the load conductor or bus bar. They can measure currents from 100 to 5000 amps and the square openings can range from 1 inch to more than 12 inches (25 to 300 millimeters).

Conclusions

The Current Transformer or CT for short, is a special type of instrument transformer that changes a primary current into a smaller secondary current using a magnetic process.

This smaller current can help detect different situations like too much current, too little current, peak current, or average current.

The primary coil of a current transformer is always connected in series with the main conductor which is why it’s sometimes called a series transformer.

The secondary current usually comes in two standard sizes: 1A or 5A making it easier to measure. These transformers can be built in different ways like having a single primary turn in Toroidal, Doughnut, or Bar types, or having multiple turns when dealing with low current ratios.

Current transformers are made to work as proportional current devices. This means that the secondary winding should never be left open, just like you wouldn’t want to run a voltage transformer with a short circuit.

If the secondary circuit of a working current transformer is left open then it can create very high voltages.

So it’s really important to short-circuit the terminals of the current transformer if you need to disconnect the ammeter or when the CT isn’t being used before turning on the system.

References:

Current transformer

How do current transformers work?

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