Introduction
Current transformer is an instrument transformer in which the secondary current, in
normal conditions of use, is substantially proportional to the primary current and differs
in phase from it by an angle which is approximately zero for an appropriate direction of
the connections.
Current error
The error which a transformer introduces into the measurement of a current arises from
the fact that the actual transformation ratio is not equal to the rated transformation ratio.
The higher the exciting current or core loss the larger the error.
The current error expressed in percent is given by the formula:
Phase displacement and accuracy class
Phase displacement = The difference in phase between the primary and secondary
current vectors, the direction of the vectors being so chosen that the angle is zero for a
perfect transformer.
Accuracy class = A designation assigned to a current transformer the error of which
(Current error, phase displacement, composite error) remain with specified limits under
prescribed conditions of use.
Burden
Burden = The impedance of the secondary circuit in ohms and power factor. The burden
is usually expressed as the apparent power (S) in volt-amperes absorbed at a specified
power-factor at the rated secondary current.
Secondary winding impedance
(internal burden) Z s
Secondary load impedance Z 0
The secondary load S = V 0 Is (cos φ = 0.8 ind for
example)
As a matter of safety, the secondary circuits of a current transformer should never be
opened under load, because these would then be no secondary mmf to oppose the
primary mmf, and all the primary current would become exciting current and thus might
induce a very high voltage in the secondary.
Rated thermal and dynamic currents
Rated short-time thermal current = The r.m.s. value of the primary current which a
transformer will withstand for one second without suffering harmful effects, the
secondary winding being short-circuited.
Rated continuous thermal current = The value of the current which can be permitted to
flow continuously in the primary winding, the secondary winding being connected to the
rated burden, without the temperature rise exceeding the values specified.
Rated dynamic current = The peak value of the primary current which a transformer will
withstand without damaged electrically or mechanically by the resulting electromagnetic
forces, the secondary winding being short-circuited.
General
Measuring current transformer = A current transformer intended to supply indicating
instruments, integrating meters and similar apparatus.
Definitions
Composite error = Under steady-state conditions, the r.m.s value of the difference
between:
a) the instantaneous values of the primary current
b) the instantaneous values of the actual secondary current multiplied by the rated
transformation ratio.
The composite error εc is generally expressed as a percentage of the r.m.s. values of the
primary current according to the formula:
K n= rated transformation ratio
I p= r.m.s. value of the primary current
i p= instantaneous value of the primary current
i s= instantaneous value of the secondary current
T= duration of one cycle
Rated instrument 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 10%, the secondary burden being equal to the rated burden
Instrument security factor = The ratio of rated instrument limit primary current to the
rated primary current.
Accuracy requirements
For measuring current transformers the accuracy class is designated by the highest
permissible percentage current error at rated current prescribed for the accuracy class
concerned.
The standard accuracy classes for measuring current transformers are: 0,1 - 0,2 - 0,5 - 1 3-5
Accuracy +/- Percentage current error at
class
percentage of rated current
shown below
0,1
0,2
0,5
1
5
0,4
0,75
1,5
3,0
Class
3
5
20
0,2
0,35
1,5
3,0
100
0,1
0,2
0,5
1,0
120
0,1
0,2
0,5
1,0
+/- Phase displacement at percentage of
rated current shown below
Minutes
Centiradians
5
20 100 120 5
20 100 120
15 8 5
5
0,45 0,24 0,15 0,15
30 15 10 10 0,9 0,45 0,3 0,3
90 45 30 30 2,7 1,35 0,9 0,9
180 90 60 60 5,4 2,7 1,8 1,8
+/- Percentage current error at percentage of rated current shown below
50
120
3
3
5
5
[SFS 2874:E]
Marking
The rating plate shall carry the appropriate information in accordance general marking.
The accuracy class and instrument security factor shall be indicated following the
indication of corresponding rated output (e.g. 15 VA Class 0,5 F s 10). F s = instrument
security factor
Current transformers having an extended current rating shall have this rating indicated
immediately following the class designation (e.g. 15 VA Class 0,5 ext. 150%).
General
Protective current transformer = A current transformer intended to supply protective
relays.
Definitions
Composite error = Under steady-state conditions, the r.m.s value of the difference
between:
a) the instantaneous values of the primary current
b) the instantaneous values of the actual secondary current multiplied by the rated
transformation ratio.
The composite error εc is generally expressed as a percentage of the r.m.s. values of the
primary current according to the formula:
K n= rated transformation ratio
I p= r.m.s. value of the primary current
i p= instantaneous value of the primary current
i s= instantaneous value of the secondary current
T= duration of one cycle
Rated accuracy limit primary current = The value of primary current up to which the
transformer will comply with the requirements for composite error.
Accuracy limit factor = The ratio of the rated accuracy limit primary current to the rated
primary current.
Secondary limiting e.m.f = The product of the accuracy limit factor, the rated secondary
current and the vectorial sum of the rated burden and the impedance of the secondary
winding.
Accuracy requirements
For protective current transformers the accuracy class is designated 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) at ratecurrent prescribed for the accuracy class concerned.
The standard accuracy classes for protective current transformers are: 5 P and 10 P
Accuracy
class
Percentage current
error at primary
current in %
5P
10 P
+/- 1
+/- 3
Phase displacement at
rated primary current
+/- 60
Composite error at rated
accuracy limit primary
current in %
Minutes
Centiradians
+/- 1,8
6
10
Marking
The rating plate shall carry the appropriate information in accordance general marking.
The rated accuracy limit factor shall be indicated following the corresponding output and
accuracy class (e.g. 30 VA Class 5 P 10). 10 = Accuracy limit factor
A current transformer satisfying the requirements of several combinations of output and
accuracy class and accuracy class limit factor may be marked according to all of them.
15 VA Class 0,5
or 15 VA Class 0,5
30 VA Class 1
15 VA Class 1 ext 150%
30 VA Class 5 P 10 15 VA Class 5 P 20
Standard values of rated currents and outputs
The standard values of rated primary current are:
10 - 12,5 - 15 - 20 - 25 - 30 - 40 - 50 - 60 - 75 amperes
And their decimal multiples of fractions. The preferred values are those underlined.
The standard values of rated secondary current are:
1,2 and 5 amperes, but the preferred value is 5A.
The standard values of rated output up to 30 VA are:
2,5 - 5,0 - 10 - 15 and 30 VA.
Value above 30 VA may be selected to suit the application. (Recommended values:
45,60 VA)
Short-time current ratings
Current transformer supplied with a fixed primary winding of conductor shall comply
with the requirements of rating below.
Thermal rating = A rated short-time thermal current shall be assigned to the transformer.
Dynamic rating = The values of the rated dynamic current shall normally be 2,5 times
the rated short-time thermal current and it shall be indicated on the rating plate when it is
different from this value.
Limits of temperature rise
The temperature rise of a current transformer when carrying a primary current equal to
the rated continuous thermal current, with a unity power-factor burden corresponding to
the rated output, shall not exceed the appropriate value given in the table below.
Class of insulation (in accordance with IEC
Publication 85)
All classes immersed in oil
All classes immersed in oil and hermetically sealed
All classes immersed in bituminous compound
Classes not immersed in oil or bituminous compound
Y
A
E
B
F
H
Maximum temperature rise
0
C
60
65
50
45
60
75
85
110
135
Terminal markings - general rules
The terminal markings shall identify: the primary and secondary windings; the winding
sections, if any; the relative polarities of windings and winding sections; the intermediate
tapings, if any.
[SFS 2874:E]
Graphic symbols of current transformers
current transformer: one output at
two coils with the same
the secondary
core
two alternative symbols
double core current
transformer
Introduction
In current transformer design, the core characteristics must be carefully selected because
excitation current I e essentially subtracts from the metered current and affects the ratio
and phase angle of the output current.
The higher the exciting current or core loss the larger the error
Measuring or protective current transformers?
Measuring current transformer
Permeability of the core material high and core loss low => exciting current small (I
fe<<) => current error small. The exciting current determines the maximum accuracy that
can be achieved with a current transformer => Study accuracy classes
Protective current transformer
Permeability of the core material is low => When remanence is reduced to a lower level
(increase the useful flux density, gapping), the voltage spikes produced by the leakage
inductance due to the transformer saturation will be eliminated. In linear current
transformers there are generally air gaps in the iron core to reduce the time constant and
remanence. Such current transformers are used only to protect objects of major
importance that require a short tripping time.
Selecting core material
When choosing a core material a reasonable value for B m (0,2 ... 0,3 T) typically results
in L c and R fe values large enough to reduce the current flowing in these elements so as
to satisfy the ratio and phase requirements.
Window utilization factor
The window utilization factor (K u = S 1 x S 2 x S 3 x S 4 ) is the amount of copper that
appears in the window area or transformer of inductor. The window utilization factor is
influenced by four different factors: (1) wire insulation, (2) wire lay (fill factor), (3)
bobbin area and (4) insulation required for multilayer windings or between windings. In
the design of high-current of low-current transformers, the ratio of conductor area over
total wire area can vary from 0,941 to 0,673 depending on the wire size. The wire lay or
fill factor can vary from 0,7 to 0,5, depending on the winding technique. The amount and
the type of insulation are dependent on the voltage. [McLyman.]
A transformer intended to supply measuring instruments, meters, relays and other similar
apparatus
Effect of Gapping
[McLyman.]
Air gap increases the effective length of the magnetic path
Air-gapped current transformers
These are auxiliary current transformers in which a small air gap is included in the core
to produce a secondary voltage output proportional in magnitude to current in the
primary winding. Sometimes termed ´transactors´ or ´quadrature current transformers´,
this form of current transformer has been used as an auxiliary component of unit
protection schemes in which the outputs into multiple secondary circuits must remain
linear for and proportioned to the widest practical range of input currents.
[Protective Relays Application Guide.]
Anti-remanence current transformers
A variation in the overdimensioned class of current transformer has small gap(s) in the
core magnetic circuit, thus reducing the possible remanent flux from approximately 90%
of saturation value to some 10% only. These gap(s) are quite small, for example 0.12mm
total, and so within the core saturation limits. Errors in current transformation are
thereby significantly reduced when compared with those with the gapless type of core.
[Protective Relays Application Guide.]
Linear current transformers
The ´linear´ current transformer constitutes an even more radial departure from the
normal solid core CT in that it incorporates an appreciable air cap, for example 7.510mm. As its name implies the magnetic behaviour tends to linearization by the
inclusion of this gap in the magnetic circuit. However, the purpose of introducing more
reluctance into the magnetic circuit is to reduce the value of magnetizing reactance, this
in turn reduces the secondary time-constant of the CT thereby reducing the
overdimensioning factor necessary for faithful transformation.
[Protective Relays Application Guide.]
The time constant of the circuit depends on the inductance of the coil and on the
resistance in the circuit in accordance to the following simple formula: