# Current Transformer

**Current Transformers** or CT's are Instrument Transformers that convert a generally high primary current **I _{p}** to a k-times lower secondary current

**I**that can be connected to standard measuring or protection devices. The primary and secondary windings are galvanically separated and can be on a different potential level. The transformation ratio k of a current transformer is the number of secondary turns

_{s}**N**to the number of primary turns

_{s}**N**and is equal to the primary current

_{p}**I**over the secondary current

_{p}**I**.

_{s}[math] k = \frac{N_s} {N_p} = \frac{I_p} {I_s} [/math]

[math] I_s = I_p . \frac {N_p} {N_s} [/math]

[math] I_s = \frac {I_p} {k} [/math]

## Contents

## Standards for current transformers

### According IEC

At the moment TC38 of the IEC is busy converting all the instrument transformers from the 60044-family to the new 61869 family with a general part and specific parts.

- IEC 60044-1 Consolidated Edition 1.2 (incl. am1+am2) (2003-02) TC/SC 38 Instrument transformers - Part 1: Current

transformers

- IEC 60044-3 Edition 2.0 (2002-12) TC/SC 38 Instrument transformers - Part 3: Combined transformers
- IEC 60044-6 Edition 1.0 (1992-03) TC/SC 38 Instrument transformers - Part 6: Requirements for protective current

transformers for transient performance

- IEC 60044-8 Edition 1.0 (2002-07) TC/SC 38 Instrument transformers - Part 8: Electronic current transformers
- IEC 61869-1 Edition 1.0 (2007-10) TC/SC 38 Instrument transformers - Part 1: General requirements

### Other standard organisations

- IEEE Std C57.13-1993: IEEE Standard requirements for Instrument transformers
- Canada CAN3-C13-M83: Instrument transformers
- Australia AS 1675 Current transformers - Measurement and protection
- British Standard BS3938 Specifications for Current Transformers (Withdrawn and replaced by IEC 60044-1)

## Functioning of a Current Transformer

Just like a normal voltage transformer, a CT has a primary winding, a secondary winding and a magnetic core. In the window-type and bushing-type CT's, the primary winding is reduced to one wire passing trough the round or square shaped core, accounting for 1 turn. The primary current I_{p} will produce a magnetic field with induction B round the conductor. The magnetic induction B is amplified by the core material with very high magnetic permeability µ and will produce a primary flux that will magnetise the core with cross section A and induces a secondary voltage V_{s} in the secondary winding with N turns.

[math]V_s = 4.44 \times 10^-8 f N A B [/math]

At the same time, a N times smaller voltage, opposed to the primary current will be induced in the primary wire creating a small extra resistance in the primary circuit. The induced secondary voltage will drive the secondary current I_{s} that will flow for the mayor part trough the connected load R_{b} and for a small part (the error current) I_{e} trough the internal resistance and induction. The internal resistance and induction represent the part of the current that is used to magnetise the core (Inductive part) and to heat-up the core material as iron-losses.
Actually the magnetising current is taken from the primary side but that will only make the calculation model more difficult and does not form any additional value. The secondary current I_{s} will also produce a secondary flux, opposite to the primary flux. The resulting flux in the CT core is a very small magnetising flux so that the core does not saturate at normal operation currents. The secondary current I_{s} will be N times smaller than the primary current I_{p}.

[math] I_s = \frac{I_p} {N} [/math]

The error current I_{e} exists for the major part of a purely inductive part; the magnetising current

I_{m} that can be seen on the magnetising curve of the CT and a small resistive part I_{g} that represent the iron losses. The magnetising current I_{m} is proportional to the field strength H

[math] I = \frac{l} {N} \times H[/math]

The copper losses are represented in the series resistor R_{CT}

## General properties of a Current Transformer

### The Primary current Ip

According to IEC 60044-1, the primary current I_p is standadise of the decadic series 1 - 1,25 - 1,5 - 2 - 2,5 - 3 - 4 - 5 - 6 - 7,5. When selecting a CT; the primary current of the CT must be at least the maximum current of the line in which the CT will operate. When the current is bigger than the rated primary current of the CT, the windings will overheat, age faster and finally the insulation will fail. According ANSI, the primary currents are fixed values; for single Ratio CT's Ip = 10; 15; 25; 40; 50; 75; 100; 200; 300; 400; 600; 800; 1200; 1500; 2000; 3000; 4000; 5000; 6000; 8000; 12000A.

### The Secondary current Is

According IEC the secondary current can be 0.5, 1 , 2 or 5A. According ANSI the secondary current is allways 5A.

### Dual or Multi-Ratio CT's

Dual ratio CT's exist in all standards but only according the ANSI standard, the ratio's are standardised. Note the for multi ratio CT's, many primary currents are mentionned and only one secondary current but in reality there is only one primary connection and 5 secondary terminals that allow 10 different ratings.

### Ratio k

As already mentionned, the most important property of the current transformer is the **ratio k** that is both the ratio of secundary turns to primary turns and the ratio of primary current to secondary current. Note the often the primary is only one turn and practically it's just the conductor passing trough the core. Since a small amount of energy is necessary to magnetising the core and to produce heat as iron loss in the core, the secondary output Ampere-turns is a bit less than the primary Ampere-turns. The difference in current is the error current or magnetising current. In case of very critical CT's, ratio-turn-correction is applied; remove some secondary turns so that the ratio is a bit higher and the output is thus a bit higher at rated current. Of course this can only be applied when the CT meets all accuracy requirements after ratio-turn correction.

### R_{CT} The internal copper resistance

R_{CT} is often called the secondary DC resistance at 75°C. It's value depends on the length en cross section of the secondary winding wire Pouillet's law. So R_{CT} also depends on the core dimensions; bigger core cross section implies a longer wire length per turn. The smaller R_{CT}; the more the current transformer approaches the ideal current source.

### Accuracy

The accuracy of a CT is given by it's "class". The division into accuracy classes depends on the type of CT; we mainly distinguish measuring class CT's and Protection class CT's who are defined quite differently. We will discuss accuracy for both types further. Of course they both have a primary current I_p, a secondary current I_s and a ratio k. From these 3 parameters we can define some important property's related to accuracy.

- The primary current vector Ip.
- The secondary current vector Is that is here represented k times larger to be able to compare them and to have an idea of the error current. In case the error would be 0, both vectors I_p and k.I_s would be identical.
- The total error vector (composite error) can be seen as the composition of:
- an amplitude error (ratio error), expressed in % and
- an angle error, expressed in radians or seconds.

Note that for protection CT's, the angle error is disregarded and only the total composite error is given in %. When examining the equivalent diagram, one would easily conclude that the error current can only be the magnetising current of the CT. Indeed, normally the magnetising current is very low but at the saturation point of the core, 50% increase in magnetising current produces only 10% extra secondary voltage so at saturation the error current rises quickly. Therefore, the property's accuracy and saturation of the core are closely linked. Hense the error vector is allways a reducion in secondary output current; negative error. Positive error is only possible by ratio-turn correction.

### Load, Rated load and Burden

A Voltage transformer is unloaded when the secondary terminals are open; it behaves like a normal voltage source. A current transformer is just the opposite and is unloaded with the secondary terminals short-circuited. Stonger even, when the secondary terminals of a CT are open, there is no secondary flux to oppose the primary flux and the core goes to positive saturation on the positive current-sine and to negative saturation on the negative current sine. The induced seconday voltage is proportional to [math] -N.d\phi/dt[/math] and from -Vsat to +Vsat is a huge voltage. One might also conclude that the current transformen is raising the voltage in trying to drive the secondary current trough the open terminals. The insulation of the CT is not calculated for this situation and it will distroy the CT secondary winding and may cause fire at the terminals & high voltage injury.
The nominal load of a CT is the rated resistive burden R_{B}; expressed in VA. The correct resistance can be calculated with below formula

[math] P = R_B.I_s^2 [/math]

[math] R_B = \frac{P} {I_s^2} [/math]

Example: A 50VA CT with rated secondary current of 5A is designed for a connected load of 50VA/5² = 2 Ohm. Measuring transformers are tested at rated load and at 1/4 of the rated load so this CT should be loaded within these limits to be sure the accuracy is within specification.

## The use and specification of Current Transformers

Current transformers are used to measure high currents; higher than 5A. So the most important parameter in defining a CT is indeed the Ratio that gives us the Magnetude of primary current and the secondary current. But for the following specifications of the current transformer, the purpose of the CT is needed since measuring CT's and Protection CT's require different specifications. Indeed, there will be two mayor groups of Current Transformers:

- Protection current transformers
- Measurement current transformers

Regarding specification, different standards have different ways in specifying CT's but it all comes down to specifying core property's (saturation point or knee-point) and secondary wire property's (R_{CT}) although it may look a totally different.

### Protection CT's

Protection CT's:

- are meant to protect an elektrical installation in case of overcurrent or short circuit and their operating current range is above nominal current I
_{n}or more specific from I_{n}to ALF times I_{n}. It is important for the good functionning of the protection relays that the CT's are NOT saturated at ALF times rated current. Where ALF is the ratio of the expected maximum fault current over the rated current. It is thus important that the core material has a high saturation induction. - their accuracy is not very high but most important is that the accuracy in fault conditions is high enough. This can only be the case when the core is not saturated in case of a fault current. Therefore their accuracy is best described with an Accuracy Limit and an Accuracy Limit Factor (ALF).E.g. a 5P20 CT has an Accuracy limit of 5% at 20 times rated current (Accuracy Limit Factor). The accuracy of this CT at rated current is 1%.
- They will be connected to one or more protection relays
- according the application, they can be defined in a few ways:
- The standard IEC protection class CT's are of class "P" that only takes the AC behaviour into account in IEC 60044-1
- Class PX CT's are defined by the position of the knee-point (saturation point or knee-point voltage and magnetising current) and the secondary wire resistance R
_{CT}. - Class PR CT's are defined like the PX CT's but they have a low remanence; less than 10%. Note that remanence in CT's can be 60-80% that may cause quick saturation in case of a fault-current DC offset in the remanent direction. A class PX CT can't have that problem.
- CT's for transient response class "TP" are defined by their connected load R
_{B}, time constant T_{S}and their overcurrent figure K_{SSC}. These linearised CT's have air-gaps in the core to obtain extreme high saturation voltage and current.

Ex. A 5P10 CT at 10 times rated current has a maximum error of 5% and only 1% at nominal current. A 10P15 CT at 15 times rated current has a maximum error of 10% and 3% at nominal current.

### Measurement CT's

- Are aimed to measure accurately within their normal operating range of 0 to I
_{n}. Therefore, the core material must have a high permeability (µ-metal) so that the magnetising current is low. - Measurement CT's are often being used for billing of electrical power consumption and their accuracy is determinent for a lot of money.
- For the protection of the measuring instruments in case of a fault current, it is favorable that for currents far above rated current I
_{n}, the core is saturated and the output lowers so that the fault-current trough the meter is only a part of the expected current trough the meter. This is expressed by the**Instrument Security Factor SF**. Of course, the dilemma is that the CT must be accurate at I_{n}(and 1,2 x I_{n}) but at f.i. 5 times rated current ( FS 5) the CT may be saturated for at least 10%. - The accuracy of a measurement CT is given by it's accuracy class that corresponds to the error% at rated current and at 1.2 times rated current I
_{n}. The standard accuracy classes according IEC are class 0.2, 0.5, 1, 3 en 5. For classes 3 and 5, no angle error is specified. The classes 0.2S and 0.5S have their accuracy shifted toward the lower currents. This means that they have 5 measuring points instead of 4 (or 2 for class 3 & 5).

- The accuracy of the CT must be within these limits at the given currents and with rated load and at 1/4 of the rated load. A measurement CT that is not loaded is therefore not necessary accurate! Ratio turn correction may have been applied to get the CT ratings witthin spec and then not loading gives a higher error.