.................................. 6
3. T
IME TO
M
AXIMUM
F
LUX
T
IME TO
S
ATURATION
......................................................................... 8
4. T
RIPPING
T
IMES OF
P
ROTECTION
D
EVICES
................................................................................ 11
5. R
ESULTANT
F
AULT
V
OLTAGES AND
CT D
IMENSIONING
............................................................... 12
6. T
ERMS AND
D
EFINITIONS
.......................................................................................................... 13
6.1 Rated Primary Short-circuit Current (I
Primarysc
) .................................................................. 13
6.2 Instantaneous Error Current (I ) ....................................................................................... 13
6.3 Peak Instantaneous Error ( i
) ........................................................................................... 13
6.4 Peak Instantaneous Alternating Current Component Error ( ac
) ...................................... 13
6.5 Accuracy Class................................................................................................................. 13
6.6 Class Index....................................................................................................................... 13
6.7 Limit Factor....................................................................................................................... 13
6.8 Class P Current Transformer ........................................................................................... 14
6.9 Class TPS Current Transformer....................................................................................... 14
6.10 Class TPX Current transformer ...................................................................................... 14
6.11 Class TPY Current Transformer..................................................................................... 14
6.12 Class TPZ Current Transformer ..................................................................................... 14
6.13 Primary Time Constant (T
1
)............................................................................................ 14
6.14 Secondary Loop Time Constant (T
2
).............................................................................. 14
6.15 Time to Maximum Flux (t max
) ...................................................................................... 14
6.16 Secondary Winding Resistance (R
CT
) ............................................................................ 15
6.17 Secondary Loop or Burden Resistance (R
B
) .................................................................. 15
6.18 Low Leakage Flux Current Transformer ........................................................................ 15
6.19 Saturation Flux( S
) ........................................................................................................ 15
6.20 Remanent Flux ( R)
....................................................................................................... 15 CT Dimensioning
ÿþ üûúùø ÷öõöôùóùõò
4
GER-3973
Application note
1. TRANSIENTS ON CURRENT TRANSFORMERS - FUNDAMENTALS
More than the steady state under load conditions of the CTs, the main concern is about the fault conditions
when the protections installed in their secondaries must respond correctly to the short-circuit transient,
specially during the first cycles. Because of this, it is necessary to define how much a CT must be oversized
in order to avoid the saturation due to the asymmetrical component of the fault current (the dc offset or
exponential component).
The initial value of this dc offset depending on the voltage incidence angle (the voltage value when the fault
occurs), and the line parameters may be between 0 and 2*I
sc
, being I
sc
the rms value of the short-circuit
symmetrical current.
Considering this maximum value, the transient short-circuit current is defined by the following equation:
(
)
(
)
e
1
ÿ
t
*
Sin
*
I
t
Sin
*
I
)
t
(
i
+
=
(1)
Where:
I =
Peak value of current =
2 * * f =
angle on voltage wave at which fault occurs =
arctan ( *X/R)
T
1
=
X/R (of power system)
Assuming that the secondary load is essentially resistive, the necessary flux in the CT to avoid saturation is
defined by the following expression: T
= A
[
t
Sin
T
T
T
T
e
e
2
s
1
s
T
t
T
t
2
1
2
1 ÷
]
(2)
Where:
T
1
=
Line time constant or primary time constant = L/R
T
2
=
CT time constant or secondary time constant




A
=
Peak value of symmetrical ac flux
t
s
=
Any given time during which maximum transient flux will remain
without CT saturation, or the time after which saturation is permitted.
For T2 >> T1 (the case of TPY and TPX class CTs with and without air gaps),
Equation (2) turns to: T
= A
[
t
Sin
1
T
e
1
s
T
t
1 ÷
]
(3)
As the load and wiring are mainly resistive, we can consider Sin t = -1; and then equation (3) is reduced to: T
= A
[
1
T
e
1
s
T
t
1
1
+
÷
÷
] ÿþ üûúùø ÷öõöôùóùõò
CT Dimensioning
Application note
GER3973
5
Finally because T
s
(relay response time + Circuit Breaker operating time) is normally much higher than T1,
the expression can be reduced as follows: T
= A
( T
1
+ 1)
(4)
During faults the CTs will be forced to develop a flux necessary to feed fault current to the secondary with
two components: the exponential (dc offset asymmetrical component) and the ac component (symmetrical
component). The resultant voltage must be higher than that necessary to feed the load connected in the
secondary side of CTs without distortions caused by saturation. Hence, the necessary oversize factor Ks is
defined by: transient
= dc
+ ac
= * K
s ac
where the overdimensioning or transient factor is:
K
s
=
t
Sin
1
T
e
1
s
T
t
1 ÷
(5) CT Dimensioning
ÿþ üûúùø ÷öõöôùóùõò
6
GER-3973
Application note
2. RESULTANT VOLTAGES ON CT SECONDARIES DURING FAULTS
In general, testing and experience have shown that the performance of many relays will not be adversely
affected by moderate degrees of CT saturation. However, since it is not economically feasible to test and
determine the performance of all types of relays with different degrees of saturation, it is common practice to
specify CT requirements for various protective schemes. The requirement generally specified is that the CTs
should not saturate before the relays operate for some specified fault location.
To meet this criterion, the required transient performance for a current transformer can be specified by
calculating the minimum required saturation voltage. In general different standards as IEC 185, BS3938 or
ANSI/IEEE C5713 fix this voltage by the general expression:
2
2
R
s
0
s
R
I
k
k
k
V
=
(6)
where:
V
s
=
Saturation voltage as defined by the intersection point of the extensions of the straight line portions
(the unsaturated and the saturated regions) of the excitation curve
I
2
=
Symmetrical fault current in secondary Amperes
R
2
=
Total secondary resistance burden including CT secondary, wiring loop resistance, lead resistance
and load resistance.
k
s
=
Saturation or transient factor =
1
T
T
T
T
e
e
2
s
1
s
T
t
T
t
2
1
2
1
+
÷
÷
(as per Eq. 2)
where
T
2
=
Secondary time constant
T
1
=
Time constant of the dc component of fault component. It is proportional to the X/R ratio of the
system. =
System angular frequency
t
s
=
Time to saturation. This is equal or greater than the relay operating time.
K
0
=
Represents the effect of the offset present during the fault. This offset is a function of the time when
the fault occurs, being maximum at zero voltage (0º or 180º). Experience states that the incidence
angle of the faulted voltage is near 90º that produce a lower offset effect. Therefore this factor will
apply in those cases where offset exceeds 0.5 p.u
K
R
=
Remanent flux factor. The remanent flux can remain in the core due to the following: The excitation current leads the load current by 90º and thereby under normal control
open commands, the load current is cut near or at zero crosses, but the excitation
current in the CT has significant value. DC tests performed on the CTs The effect of the dc component on offset fault currents (exponential component) which is
interrupted when tripping the circuit breaker. ÿþ üûúùø ÷öõöôùóùõò
CT Dimensioning
Application note
GER3973
7
Equation (2) is valid for CTs with air-gapped cores because of their low magnetizing impedance and then with
low secondary time constant T
2
. The air-gaps used in CTs tends to reduce drastically the effect of the
remanent flux left in the core due to its lower magnetizing impedance and therefore much lower secondary
time constant. The effect of the remanent flux is also to reduce the time to saturation. This factor may vary
from 1.4 to 2.6 times the rated flux in the core.
For a closed-core CTs (normal CTs), the secondary time constant T
2
is too high (L
magnetizing

before
saturation), equation (5) does no include it, and then a conservative value for time to saturation will result. CT Dimensioning
ÿþ üûúùø ÷öõöôùóùõò
8
GER-3973
Application note
3. TIME TO MAXIMUM FLUX TIME TO SATURATION
After the initiation of the short-circuit the flux




0
and the corresponding magnetizing current I
0
will reach a
maximum at a time defined by:
÷
÷
÷
÷
=
2
1
2
1
2
1
x
a
m
T
T
n
T
T
T
T
l
t
(7)
Finally the time to saturation is given by the following expression:
Where:
K
s
= V
Saturation
/( I
fault
* R
2
)
V
Saturation
= Saturation voltage as defined in page 5
I
fault
= Secondary fault current
R
2
= Total loop resistance as defined in page 5
X/R = Reactance to resistance ratio of any given circuit, generator, e