Determination of Secondary Time Constant for
Current Transformer Dimensioning
A. H. A. Bakar, H. Mokhlis, N.Nazri, C.H.Wong
UMPEDAC Research Centre
Department of Electrical Engineering
University of Malaya
Kuala Lumpur, Malaysia
a.halim@um.edu.my
Abstract—In this paper, a study has been carried out to analyze
the factors influencing the current transformer (CT) saturation
factor (KS), in particular the secondary time constant (TS) of a
CT. The study identifies and analyzes the optimum value for TS
as this value varies. This paper also analyses and discusses the
effect of TS to the KS factor in order to calculate the CT knee
point voltage (VK) in dimensioning a CT. A comparison of
guessed and measured value of TS is also done in this paper.
CTs as TS is often a few or several seconds and the influence
on KS is relatively small and almost negligible during the first
100 ms [7]. However, there was no further explanation on why
TS was set to 3.0 s. Theoretically, TS is in order of few seconds.
For TPX class CT, TS is 5.0 s or above whereas for TPY class
CT, TS is 0 to 10.0 s. For TPZ class CT, CT’s has a linear core
with a secondary time constant of 60 ± 6 ms for 50 Hz and 50 ±
5 ms for 60 Hz applications [8].
Keywords - Current transformer, saturation factor, secondary
time constant, knee point voltage.
In this paper, a study and an analysis on CT secondary time
constant was carried out for TPS class CT for transformer
differential protection in order to determine its optimum value
and hence analyze its effect to the KS factor. Value for TS will
be determined by means of iteration of KS factor. After
obtaining KS, VK will then be calculated. Values obtained from
the calculation will be compared to values obtained from
measurement at the site. The measurement has been done on a
30 MVA 132/11kV transmission substation located at one of
metropolitan substations in Kuala Lumpur [9].
I.
INTRODUCTION
In dimensioning a current transformer (CT), it is important
to determine the optimum value of knee point voltage (VK).
Beyond this point, CT will tend to saturate. Obtaining VK is by
multiplying three factors. These factors are short circuit factor
(KSSC), remanence flux factor (KR) and saturation factor (KS)
[1].
II.
In calculating CT saturation factor (KS), four parameters are
required. The parameters are primary time constant (TP),
secondary time constant (TS), time to saturation (t) and system
frequency [2]–[5]. These four values will influence the value of
KS factor which is to be calculated and therefore it is important
to have precise value for these four parameters. KS factor is
important as this value will influence the value of knee point
voltage (VK) when dimensioning a CT for protection purposes.
REQUIREMENTS OF SATURATION FACTOR (KS)
AND KNEE POINT VOLTAGE (VK)
As mentioned, in calculating VK for CT dimensioning, KS
factor is an important factor which needs to be determined
correctly. It is vital to design current transformer that will not
saturate even when there is worst external fault to be expected.
Various standards such as IEC 185, BS 3938 and ANSI/IEEE
C57.13 have given the required transient knee point voltage by
following expression [10]:
Value for TP depends on system X/R ratio whereas value
for t is depending on protection relay operating time. In
practice, value for TS is difficult to obtain as it varies from site
to site. Secondary time constant is actually a CT secondary
loop time constant. It is determined by the CT magnetising
inductance Lm and the sum of resistances in the secondary
circuit [6].
VK = K0·KS·KR·I2·R2
(1)
where:
knee point voltage defined by the intersection of the
VK =
extensions of straight line portions of the excitation
curve
symmetrical fault current in secondary amps
I2 =
total secondary resistance burden including current
R2 =
transformer secondary, wiring loop resistance, lead
resistance and load resistance
the effect of the offset present during fault
K0 =
No study has been done on the value of TS especially for
TPS and TPX Class CT. In dimensioning a CT for numerical
protection relays, P.K. Gangadharan, T.S. Sidhu and J.
Finlayson had taken the value of TS as three (3.0) seconds [1].
The value of 3.0 s was suggested by S.Holst and B. S. Palki
[7]. This value is said to be a good estimate for high remanence
___________________________________
978-1-61284-365-0/11/$26.00 ©2011 IEEE
58
KS =
KR =
saturation factor
remanence flux factor
START
In this paper, remanence flux factor will not be considered
in calculating the VK.
Enter X/R value
K0 depends on the fault inception angle. K0 will be
maximum at 0° angle and minimum at 90° angle. For a full
offset fault current, K0 is equal to 1.0 [7].
Enter maximum value of
TS
The saturation factor, KS is given by the following equation
[1] - [5]:
−t
−t
ω ⋅ TP ⋅ TS ⎛⎜ TS
TP
e −e
KS =
TS − TP ⎜⎝
where:
TP =
TS =
ω=
t=
⎞
⎟ +1
⎟
⎠
Enter minimum value of
TS
(2)
Enter value of (t)
power system time constant
CT secondary loop time constant
system angular frequency
time to saturation of CT
Enter system frequency
For TS min ≤ TS max,
iterates KS factor
KS is depending on protection relays operating time .
Where high speed protection is employed, it is possible to
reduce CT dimensions by allowing it to saturate only after both
the protection relays and circuit breaker have tripped. With a
given VK for the CT, time taken for the CT to go into saturation
can be determined [9].Value of TS depends on the sum of the
magnetizing and the leakage inductances (Ls) and the
secondary loop resistance (Rs). This is given by the following
equation [5]-[6]:
END
Figure 1. Flow chart of a developed programme
IV.
TS = Ls / Rs
The developed programme has been tested in determining
TS for a CT used in 500 and 132 kV system voltages. TABLE I
show the parameters used which is normally used by utility
[11]. Results of iteration are shown in TABLE II.
Practically leakage inductances and secondary loop
resistances is difficult to obtain. Leakage inductances vary
from one type of CT to another type. The secondary loop
resistance is depending on the winding resistances corrected to
75°C and external connected burden unless otherwise specified
[5].
III.
RESULTS AND DISCUSSIONS
(3)
Time to saturation used in the calculation is 30 ms. This is
because high-speed operation of main protection relay must be
ensured under transient condition with severe CT saturation
due to DC transient current. Protection current transformer is
required to provide more saturation free current transformation
during this transient condition [11].
COMPUTER PROGRAMME DEVELOPMENT
It is proposed TS value to be determined by an iteration of
KS factor. A programme has been developed by using C/C++
to help the iteration process. In the developed programme, five
parameters need to be entered. The parameters are system X/R,
time to saturation, maximum and minimum estimation value of
TS, and system frequency.
TABLE I.
DATA FROM UTILITY
Voltage
I1
I2*
X/R
TP
level
500 kV
50 kA
12.5 A
20
64 ms
132 kV 31.5 kA
26.25 A
10
32 ms
I1 = Maximum symmetrical fault current in primary amps
*Current transformer turn ratio = 4000/1 (500 kV), 1200/1
(132 kV) [11].
After the programme stop iterating the KS factor, then
values of TS and KS is observed. Value of TS should be taken at
a point whenever KS starts to give constant value. The result is
verified by using Matlab. Fig. 1 shows the flow chart of the
C/C++ developed programme.
In performing the iteration, a minimum and maximum
value of TS needs to be guessed. Since TS is in order of few
second [8], the estimation of TS should range between 1.0 s to
10.0 s. In this study, the estimation of TS minimum is 3.0 s as
59
suggested in reference [1] & [7] and TS maximum is set to
8.0 s. By using equation (2) and data in TABLE I, the KS factor
of CT has been calculated and iterated. Results are shown in
TABLE II and TABLE III.
TABLE II.
TS (s)
3.0
4.0
5.0
6.0
7.0
8.0
From TABLE II and TABLE III, it is observed that KS
factor starts to give constant value after TS 3.0 s. Therefore, it
is recommended that value for TS to be taken is 3.0 s or more.
This value conforms to Fig. 2 and 3 and what has been stated in
reference [8].
ITERATION OF KS FACTOR (500 KV)
For comparison, iteration has also been made on the
measured data of a CT. This is to compare between guessed
and measured value of TS.
KS
8.48
8.49
8.49
8.50
8.50
8.50
A study had been done on the transient phenomenon of the
current transformer at one of the metropolitan substation
located nearby Kuala Lumpur. In the study, a short circuit
simulation was carried out. Computer-Aided Protection
Engineering (CAPE) simulation software was used to perform
this task. Simulation was done in order to find the maximum
possible out of zone fault current that can occur at 11 kV
system. Concurrently, TP was also obtained with the help of
CAPE software [9].
For the case of metropolitan substation, maximum fault
current will only occur during a three phase fault condition. For
a single to ground fault, current was much lower since it was
limited by the neutral earthing resistor. TABLE IV show
parameters obtained from CAPE simulation [9].
TABLE IV.
I1
12.129 kA
TS (s)
3.0
4.0
5.0
6.0
7.0
8.0
I2*
6.74 A
X/R
17.31
TP
55 ms
I1 = Symmetrical fault current in primary amps
*Current transformer turn ratio = 1800/1
Figure 2. Graph of Ks vs. Ts for t=30 ms and Tp=64 ms (500 kV)
TABLE III.
DATA FROM CAPE SIMULATION
As for analysis, K0 = 1 since full offset primary fault
current was assumed.
ITERATION OF KS FACTOR (132 KV)
KS
7.07
7.08
7.08
7.09
7.09
7.09
CT Analyzer test set from Omicron was used to measure
the current transformer parameters used for protection scheme
at the metropolitan substation. Results are shown in TABLE V
[9].
TABLE V.
Current
Transformer
Red
Yellow
Blue
DATA FROM MEASUREMENT AT SITE
VK (V)
R2 (Ω)
TS (s)
302.38
293.55
296.35
5.251
5.396
6.629
6.005
4.826
4.981
Time to
saturation (t)
31.67 ms
29.10 ms
21.75 ms
By using equation (2) and data in TABLE IV and
TABLE V, the KS factor of CT for each phase has been
calculated. Results are shown in TABLE VI.
TABLE VI.
SATURATION FACTOR (KS)
Current Transformer
Red Phase
Yellow Phase
Blue Phase
Figure 3. Graph of Ks vs. Ts for t=30 ms and Tp=32
ms (132kV)
60
CT saturation factor, KS
8.54
8.08
6.63
As mentioned earlier, values of secondary time constant
(TS) from TABLE V are measured values. It can be seen that
the values measured are close to 5.0 s for yellow and blue
phase CT whereas for red phase CT, TS is 6.005 s. These
values of TS are actually close to the values of TS obtained
from the iteration of KS factor. To verify these values and for
comparison, iteration of KS factor was also done by using data
in TABLE IV and TABLE V. The results are shown in
TABLE VII, TABLE VIII and TABLE IX for red, yellow and
blue phase CT respectively.
TABLE VII.
RED PHASE CURRENT TRANSFORMER
TS (s)
3.0
4.0
5.0
6.0
7.0
8.0
KS
8.52
8.53
8.54
8.55
8.55
8.55
Figure 5. Graph of Ks vs. Ts for t=29.10 ms and Tp=55 ms
(yellow phase CT)
From TABLE VIII, value of KS factor is constant at TS 5.0 s
to 7.0 s. This value of TS which is 5.0 s where KS starts to give
constant value is actually close to the measured value in
TABLE V where TS for yellow phase CT is 4.826 s. Values of
KS factor obtained from iteration are still close to the calculated
value in TABLE VI. Fig. 5 confirms the result.
TABLE IX.
TS (s)
3.0
4.0
5.0
6.0
7.0
8.0
BLUE PHASE CURRENT TRANSFORMER
KS
6.62
6.63
6.63
6.63
6.63
6.64
Figure 4. Graph of Ks vs. Ts for t=31.67 ms and Tp=55 ms (red phase CT)
From TABLE VII, it can be seen that value of KS factor is
constant after TS 5.0 s. The value of TS where KS starts to give
constant value is actually close to the measured value in
TABLE V where TS for red phase CT is measured as 6.005 s.
Values of KS factor obtained from iteration are also close to the
calculated value in TABLE VI. Fig. 4 conforms the result.
TABLE VIII.
YELLOW PHASE CURRENT TRANSFORMER
TS (s)
3.0
4.0
5.0
6.0
7.0
8.0
KS
8.06
8.07
8.08
8.08
8.08
8.09
Figure 6. Graph of Ks vs. Ts for t=21.75 ms and tp=55 ms (yellow phase CT)
In TABLE IX, it is observed that value of KS factor is
giving a constant value at TS 4.0 s until 7.0 s. It is encouraged
to choose the value of TS to be 4.0 s since it started to give
constant KS. However, the TS for blue phase measured on site
is 4.981 s, which is slightly different to the simulation result.
Since the TS 4.0 s and 5.0 s give same value of KS, therefore it
does give any significant meaning to its knee point voltage.
Once again, Fig. 6 confirms the result.
61
the value of TS which the CT analyzer gives. Therefore,
without using a CT analyser, TS value of a CT can still be
obtained by using the above mentioned method. However, in
implementing the iteration of KS factor in order to determine
the value of TS, it is important to get the accurate value of
system X/R and time to saturation of a CT as these two values
will have great influence to the KS factor value.
By assuming TS 5.0 s and using data from TABLE IV, KS
factor and knee point voltage for red, yellow and blue CTs are
calculated by using equation (1) and (2). Results are shown in
TABLE X.
TABLE X.
Current
Transformer
Red
Yellow
Blue
CALCULATED VALUE
KS
R2 (Ω)
8.54
8.08
6.63
5.251
5.396
6.629
VK
(V)
302.21
293.78
296.26
VI.
This study has been done in order to obtain the optimum
value of secondary time constant, TS. It has also shown how the
TS will influence the KS factor. Even though TS has no great
effect in determining KS factor, it is recommended that value of
TS to be used is when it started to give two or more constant
reading of KS factor. This range of TS is the best estimate for
CTs with high remanence in order to get optimum value of KS.
It is an evident that KS has a great influence to knee point
voltage (VK).
For comparison, say TS 6.0 s and using data from TABLE
V, again KS factor and knee point voltage for red, yellow and
blue CTs are calculated by using equation (1) and (2). Results
are shown in TABLE XI.
TABLE XI.
Current
Transformer
Red
Yellow
Blue
CALCULATED VALUE
KS
R2 (Ω)
8.55
8.08
6.63
5.251
5.396
6.629
VK
(V)
302.37
293.78
296.26
REFERENCES
[1]
P.K. Gangadharan, T.S. Sidhu, G.J. Finlayson, “Current Transformer
Dimensioning for Numerical Protection Relays”, IEEE Transactions on
Power Delivery, Vol.22,No.1,2007.
[2] IEC60044-1(2003-02), Instrument Transformers – Part 1: Current
Transformers.
[3] IEEE Standard Requirements for Instrument Transformers, IEEE Std.
C57.13, 1993.
[4] IEEE Guide for the Application of Current Transformers Used for
Protective Relaying Purposes, IEEE Std. C37.110, 1996.
[5] IEC 60044-6(1992-03), Instrument Transformers – Part 6: Requirements
for Protective Current Transformers for Transient Performance.
[6] Ziegler.G., “Numerical Differential Protection: Principles and
Application”, Khunkh Publicis Corporate Publishing, Earlangen, 2005.
[7] S.Holst and B.S. Palki, “Co-ordination of Fast Numerical Relays and
Current Transformers – Over Dimensioning Factors and Influencing
Factors,” presented at the CIGRE 2001 Session, SC 34 Colloquium,
Sibiu, Romania, Sep.2001, 305, unpublished.
[8] W.A.Elmore., “Protective Relaying Theory and Applications 2nd ed.,
Revised and Expanded”, Marcel Dekker Inc., New York, 2004.
[9] K.J. Abdul Jalil, A.H. Abu Bakar, W.N. Wan Mahadi, F.H. Mohamad
Salleh, “Performance of Restricted Earth Fault Protection Scheme in the
Presence of Current Transformer Remanence”, 2nd IEEE International
Conf. On Power and Energy (PECon 08), Johor Baharu, Malaysia, Dec
1-3, 2008.
[10] GE Publication No.: GER-3973B, “Dimensioning of Current
Transformers for Protection Applications”.
[11] Aminuddin Musa, Hasmarizal Hassan, “Current Transformer
Application Guide”, Tenaga Nasional Berhad, Malaysia, 2003.
From TABLE X and TABLE XI, it is observed that values
of VK for each CT show a slight difference compared to
measured value in TABLE V. The difference may be due to
values of TS that had been used in the calculation. However,
margin between measured and calculated values are still
considered very small.
V.
CONCLUSIONS
DISCUSSION
The objective of performing iteration of current transformer
saturation factor is to determine the value of secondary time
constant. From the iteration done, it is recommended that the
value for TS to be used is when it started to give two or more
constant reading of KS factor.
This range of values had been proved by comparing the
measured with calculation values. It is observed that by taking
TS 5.0 s or above, there is not much difference in KS factor
value.
It is also seen that, by means of iteration of KS factor by
using guessed minimum and maximum value of TS, the point
where TS starts to give constant KS value is almost the same to
62