# How to Size Current Transformers

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The correct sizing of current transformers is required to ensure satisfactory operation of measuring instruments and protection relays.  Several methods exist to size current transformers.  This note will look at several methods, with particular attention being paid to protection class CTs sized in IEC 60044, which is adopted internationally.

ABB Current
Transformer

Example of a CT specification: - a very common specification for a protection class CT would be an accuracy class 5P (1%), with rated accuracy limiting factors of 10 or 20. Typical burdens would be 5, 10, 15 or 20 VA. A typical specification would be 5P10 15 VA.

## The IEC 60044 Method

IEC 60044 specifies the requirements for protection CTs (in addition to measuring CT's, VTs and electronic sensors).

The key to CT dimensioning under the standard, is the symmetrical short circuit current and transient dimensioning factors:

• Kssc    - rated symmetrical short-circuit current factor
• Kssc   - effective symmetrical short-circuit current factor
• Ktd     - transient dimensioning factor

Example IEC 60044 Calculation

Consider a CT with the following specification and protection requirements:

• CT: 600/1 5P20 15 VA,  Rct = 4 Ω
• CT Leads: 6 mm2, 50 m long
- use R=2 ρ l /a to calculate = 0.0179 Ω/m
• Relay: Siemens 7SJ45, Ktd = 1
• Short circuit current, Iscc max = 30 kA

To find the lead resistance Rleads (two leads – supply, return) we can use the standard formulae for resistivity:

Rleads = 2 ρ l /a = 2 x 0.0175 x 50 / 6 = 0.3 Ω

Numerical relays have low burdens, typically 0.1 Ω (where possible the relay manual should be consulted).

Plugging everything into the equations:

Rb = 15 VA / 1 A2 = 15 Ω

Rb = Rleads + Rrelay = 0.3 + 0.1 = 0.4 Ω

Kscc = Kscc (Rct + Rb)/(Rct + Rb)

= 20 (4 + 15 )/ (4 + 0.4) = 86.4

Required Kscc > 1 x 30000/600 = 50

In this case the effective Kscc of 86.4 is greater than the required Kscc of 50 and the CT meets the stability criteria.

The factor Kssc is relatively easy to understand and relates to the liner portion of a CT characteristic.  The voltage and current across a CT are linear only up till a certain value (normally specified as a multiple of the nominal rating),  after which the CT will saturate and the curve will level off.  A CT rated at say 5P20 will stay linear to approximately 20 times its nominal current.  This linear limit is the  Kssc (i.e. Kssc = 20).  As a reminder, the 5 [in the 5P20] would be the CT accuracy class and the ‘P’ signifies a protection class CT.

Slightly more complicated is the effective factor, Kscc.  This is a calculated value which takes into account the burden (resistance) of the relay, resistance of the CT windings and resistance of the leads:

• Rct - secondary winding d.c. resistance at specified temperature
• Rb  - rated resistive burden of the relay
• Rb - Rleads + Rrelay;  this is thel connected burden

CTs need to be able to supply the required current to drive the relays during transient fault conditions.  The ability of the CT and relay to operate under these conditions is a function of Kscc and the transient performance of the relay, Ktd.  The factor, Ktd is supplied by the relay manufacturer.  Correct functioning is achieved by ensuring the following is valid:

• Issc max - maximum symmetrical short-circuit current
• Ipn - CT rated primary current

That it.  Once you have confirmed the above is ok, you know your CT is ok.

### What the Manufacturer Wants

There is a slight complication in the manufacturers know their relays better than we (or the IEC) do.  As general advice, you should always refer to the manufacturers information:

• firstly it is the only way to get the factor Ktd
• secondly manufacturers sometimes have additional requirements; for example Siemens’ overcurrent, motor protection, line differential (non-pilot)and transformer differential are good to go with the above, while their line differential (pilot wire) and distance relays require the above and have additional limitations on Kscc

In the sizing of protection transformers, the resistance (burden) of the connection leads can have a considerable effect.  In calculations, the resistance of the connection leads can be estimated from:

where:

l is the connection lead length in m
ρ is the resistivity in Ω mm2 m-1 (=0.0179 for copper)
A is the cross sectional area in mm2

## Other CT Sizing Methods and Requirements

### BS 3938 and BS 7626

BS 3938 and BS 7626  are older British Standards which deal the the specification and sizing of current transformers.  Both of these have been withdrawn and are superseded by the IEC 6044 standard.

The standards adopted the concept of knee voltage and it is still common to find knee voltage voltage being used as a CT sizing parameter.

Knee voltage is defined as the point at which a 10% increase in voltage across the terminals, causes a 50% increase in excitation current

Utilising the British Standards, CTs were defined by the knee point voltage UKN and the internal secondary resistance Ri. To convert an IEC design the following can be used:

where:  I2N is the nominal secondary current

### ANSI/IEEE C57.13

The IEEE standard C57.13 covers the requirements for CT sizing in the North American markets.

Class C of the standard defines CTs by their secondary terminal voltage at 20 times nominal current (for which the ratio error shall not exceed 10%). Standard classes are C100, C200, C400 and C800 for 5 A nominal secondary current.

This terminal voltage can be calculated from the IEC data as follows:

with

and

If anyone has any questions, comments or suggestions on how to improve the post, please add them below.

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Steven has over twenty five years experience working on some of the largest construction projects. He has a deep technical understanding of electrical engineering and is keen to share this knowledge. About the author

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#### View 7 Comments (old system)

1. Vinayan Chavarattil says:
10/15/2012 1:44 PM

Dear Steven,

It is a very informative technical article you shared here. Thanks for it. Could you please provide the reference clauses for the equations used for the calculations in IEC-60044. I could not find it in 60044.

Thanks,

Vinayan

• Steven says:
11/15/2012 2:26 PM

You need to derive them from the equations given in IEC 60044. If your looking for a reference where this is already done, I think you can probably check the Siemens Power Engineering Guide or maybe one of the Schneider Cahier Technique Papers (links to both these under Tools->Steven's Technical List).

2. kamila says:
11/15/2012 2:09 PM

Ktd x Issc max / Ipn = 1 x 30000/600 = 18.64
how did u come up with this result? it should be 50

• Steven says:
11/15/2012 2:58 PM

kamila,

It's good to know people read through what I write. I've corrected the example and hopefully got it a little closer to being right this time.

3. tranthanhlc says:
1/10/2013 7:50 AM

Hi Steven

Could you add a topic about sizing the ZCT for the neutral of a transformer (Star-Delta) or a generator (with the neutral solidly earthed or earthed through a resistor)? How to select the primary current for this ZCT?

Thank you.

4. Notes says:
2/8/2013 11:28 AM

Current transformers (CTs) are used to convert high level currents to a smaller more reasonable level for use as inputs to protection relays and metering equipment.  Within electrical systems, current transformers are essential to ensure the correct... ...

5/24/2013 3:15 AM

Hi Steven

Could you please give more detail example to sizing CT Class X.

Specially for transformer differential application

thanks

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