### Current Transformer Accuracy

Instrument Transformer and Power Management (P1) Course
Chapter (6) : Current Transformers
6.6 Current Transformer Accuracy
6.6.1 Introduction  :
Instrument current transformers must change the magnitude being measured without introducing significant unknown errors.
The accuracy of a transformer must either be of a known value, so that error may be allowed for, or the accuracy must be sufficiently high that any error introduced by the instrument transformer may be ignored.
Three factors affecting accuracy  :
a) The design of instrument transformer.
b) The circuit conditions such as voltage, current and frequency.
c) The burden connected to the secondary' circuit of the transformer.

6.6.2 Composite error :
The composite error is the total result error due to the phase and magnitude errors. Under steady state condition the value of the composite error is the r.m.s value of the difference between the instantaneous values of the primary current and the instantaneous values of the actual secondary current multiplied by the rated transformation ratio.
The composite error Ec is generally expressed as a percentage of the r.m.s values of the primary current according to the formula.
Ec = 100/ Ip√((1/T) 0r(Kn Is - Ip)2 dt )
Where :
Kn = Rated transformer ratio.
Ip = r.m.s value of the primary currenthh
ip = instantaneous value of  the primary current.
is = instantaneous value of the secondary current.
T = duration of one cycle.

6.6.3 Accuracy of measuring current transformer :
6.6.3.1 Definition of C.T factor :
a) Rated accuracy limit primary current :
The value of the minimum primary current at which the composite error of the measuring current transformer is equal to or greater than 10X, the secondary burden being equal to the rated burden.
The composite error should be greater than 10% in order to protect the apparatus supplied by the instrument transformer against the high currents produced in the event of system fault.
b) Instrument security factor (FS) :
It is the ratio of rated instrument limit primary current to the rated primary current. The safety of the apparatus supplied by the transformer is greatest when the value of rated instrument security factor (FS) is small.
c) Secondary limiting e.m.f :
The product of the accuracy limit factor, the rated secondary current and the Victorian sum. of the rated burden and the impedance of secondary winding.
d) Exciting current  :
The r .m.s value of the current taken by the secondary winding of a current transformer when sinusoidal voltage of rated frequency is applied to the secondary terminals, The primary and any other winding being open circuited.

6.6.3.2 Accuracy class designation for Metering CT :
For measuring current transformer, the accuracy class is designated by the highest permissible percentage current error at rated current.
The standard accuracy classes for measuring current transformers are 0.1 , 0.2 , 0.5 , 1 , 3 , 5 . For classes 0.1 , 0.2 , 0.5 and 1 the current error and phase displacement at rated frequency shall not exceed the value given in table I, when the secondary burden is any value from 25% to 100% of rated burden.
For classes 0.2 Sand 0.5 S , The current error and phase displacement of current transformers for special applications ( in particular in connection with special electricity meters which measure correctly at a current between 50 mA and 6A that is between 1% and 120% of the rated current 5A ) at rated frequency shall not exceed the value given in table II when secondary burden is any value from 25%to 100% of the rated burden.
These classes shall mainly be used for the ratios 25/5,50 /5.and 100/5 and their decimal multiples and only for the rated secondary current 5A. For class 3 and class 5 the current error at rated frequency shall not exceed the values given in table III when the secondary burden is any value from 50% to 100%of the rated burden.
The secondary burden used for test purpose shall have a power factor of 0.8 lagging except that, when the burden is less than 5V A a power factor of 1.0 shall be used. In no case shall the test burden be less than 1 V A.

6.6.3.3 Extended current rating For Metering CT :
Current transformers of accuracy classes 0.1 to 1 may be marked as having an extended current rating provided they comply with the following two requirements.
a) The rated continuous thermal current shall be the rated extended primary current expressed as a percentage of the rated primary  current.
b) The limits of current error and phase displacement prescribed for 120% of rated primary current in table I shall be retained up to the rated extended primary current. Standard values of rated extended primary current are 120% ,150% and 200% of the rated primary current.

Limit of error for current transformers for special applications This table is applicable only to transformer having a rated secondary current of 5A.

6.6.4 Accuracy requirements for Protective current transformer   :
For certain protective systems where the current transformer characteristic are dependent on the overall design of the protective equipment, additional requirements may be necessary and in particular for the forms of protection in which the prime requirement is the maintenance of accuracy up to several times the rated current.
6.6.4.1 Definition :
a)  Rated accuracy limit primary current:
The value of primary current up to which the transformer will comply with the requirements for composite error.
b) Accuracy limit factor:
The ratio of the rated accuracy limit primary current to the rated primary current. The standard accuracy limit factors are 5 , 10 , 15 , 20 , 30.
c) Secondary limiting e.m.f :
The product of the accuracy limit factor, the rated secondary current and the Victorian sum. of the rated burden and the impedance of secondary winding.
d) Exciting current :
The r .m.s value of the current taken by the secondary winding of a current transformer when sinusoidal voltage of rated frequency is applied to the secondary terminals, The primary and any other winding being open circuited.
6.6.4.2 Accuracy: classes:
For protective current transformer the accuracy class is designed by the highest permissible percentage composite error at the rated accuracy limit primary current prescribed for the accuracy class concerned, followed by the letter “ P ” (  meaning protection).
The standard accuracy classes for protective current transformers are 5P and l0P. The rated frequency and with rated burden connection the current error, phase displacement and composite error shall not exceed the value given in table IV.
For testing purposes when determining current error and phase displacement, the burden shall have a power factor of 0.8 inductive except that where the burden is less than 5V A , A power factor of 1.0 is permissible.
For the determination of composite error, the burden shall have a power factor between 0.8 inductive and unity at the discretion of the manufacturer.

6.6.5 Class X protective C. T :
Class X  C. T is used for differential relay. The performance of class X current transformer of the low ( secondary ) reactance type shall be specified in terms of each of the following:
1) Rated primary current.
2)Turns ratio ( The error in turns ratio shall not exceed 0.25% ).
3) Knee -point voltage.
4) Exciting current at the knee point voltage and / or at a stated  percentage.
5) Resistance of secondary winding.

6.6.7 Factors affecting accuracy :
6.6.7.1 Secondary burden power factor:
The burden power factor will affect the phase angle error. As the power factor increased, the phase angle error increased and the ratio error decrease. The maximum error would occur when the secondary current is 180 degrees out of phase with the exciting current.

6.6.7.1 Effect of current on accuracy :
The value of the exciting current depends upon the secondary voltage which is requiring forcing the secondary current through the total secondary impedance.
As the primary current decreases, the secondary current will decreased in the same ratio.
However, as the current transformer are designed, normally, to operate at low flux densities in the core below the point of maximum effective permeability , the exciting current will not decrease as rapidly as the secondary current. This means that the ratio errors will increase at low current unless the transformer is compensated.

6.6.7.2 Compensation:
The actual turns ratio of a current transformer may be changed to compensate for the exciting current and core losses. There may be, in addition to them special compensating windings to give still greater accuracy and to reduce phase angle error. These windings are generally used in wound primary current transformer. The compensating windings are wound in series with the main secondary windings.

6.6.7.3 Frequency variation :
Current transformer may be used over a wide frequency range without greatly affecting their accuracy. The errors do increase with lower frequency and the name plate ratings should be observed.
The newer transformers will have separate accuracy classifications for the standard frequencies on which they are employed.

6.6.7.4 Return conductor effect :
Conductors carrying large currents, such as those that might be used for return conductors on current transformers of 2000 A rating and above, produce a relatively large flux pattern about their axis. If such conductors are placed too near the transformer core, their flux may concentrate in the core, causing error.

6.6.7.5 Thermal and mechanical ratings :
The ability to withstand the mechanical effect of the initial current caused by the short circuit is called" the mechanical rating " of the transformer. It is expressed as the r .m.s value of the AC component of a completely displaced primary current wave which the transformer is capable of withstanding with the secondary short circuited.
The ability to withstand the heating effect of the initial current caused by the short circuit is called" the thermal rating " of the transformer. It is given as the  r.m.s value of a steady current which a transformer can withstand without exceeding 250°c ( 450 F ) ( normally) for the period of one second ( usually).
Both of the above ratings are associated with short circuit currents. When current transformers are associated with breakers , it is important that both the current transformer and breakers , have an adequate short circuit rating.

6.6.7.6 Magnetic bias  :
The accuracy of a current transformer may be affected by magnetization of the core. This may result from one of the following: .
a) The passage of DC through one winding or the passage of AC while the other winding is open circuited.
b) The application of a high over current, particularly if it is interrupted at a peak value.