basics of current and voltage transformers - siemens
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Basics of
Current and Voltage Transformers
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2
1
12
N
N ⋅=′ I I
R1 jX1 jX2 R2I 1 I 2
Zb
S2P2 Ideal CT
S1P1 I m
N1 N2 ZmU
2
Equivalent current transformer circuit
X1 = Primary leakage reactance
R1 = Primary winding resistance
X2 = Secondary leakage reactanceZ0 = Magnetizing impedance
R2 = Secondary winding resistance
Zb = Secondary load
Note: Normally the leakage fluxes X1 and X2 can be neglected
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jX2
i2 ZB
i1
1 : N2
R2
RB
i'1 = ⋅ i1 i21
N2
LW
L2<< LW
R2
im
Current transformer, simplified equivalent circuit
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N1
I 1
I 2
N2
Zb
I 2
ε
I 1
I m
. N1
N2
Current transformer:Phase displacement (δ) and current ratio error (ε)
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CT classes to IEC 60044-1: 5P or 10P
Specification: 300/1 A 5P10, 30 VA
5% accuracyat I= n x In Accuracy
limit factor ALF
Rated burden
(nominal power) P NBRatio In -Prim / In -Sek.
BB P i P
NB P i P ALF ALF +
+×='
Actual accuracy limit factor
in operation is higher as the CT
is normally underburdened :
Operating ALF: ALF‘
Dimension criterium:
TF K
n
I
SC I ALF ×−≥ max'
K TF (over-dimensioning factor) considers the single sided CT over-magnetising due to the d.c.
component in short circuit current ISC.
K TF values required in practice depend on relay type and design.
Recommendations are provided by manufacturers (see Application Guides)
R CT ≤ 5 Ohm
CT2
.seci R IP ×=
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UKN
10 %
50 %
U2
Im
Definition of the CT knee-point voltage
IEC 60044-1 Class PX
formerly
British Standard BS3938:
Class X
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Accuracy classCurrent error
at nominal
current (In)
Angle errorat rated current
In
Total error at n x In
(rated accuracy limit)
5P
10P
± 1 %
± 5%
± 60 minutes 5 %
10 %
IEC 60044-1 specifies the following classes:
Current transformer, Standard for steady-state performance
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Current transformers, Standard for transient performance
IEC 60044-6 specifies four classes:
Class
Ratio error Angle error
Maximum error at
rated accuracy limit
TPX(closed iron core)
TPYwith anti-remanence
air gap
TPZlinear core
± 30 min
± 30 min
± 180 ± 18 min
± 0,5 %
± 1,0 %
± 1,0 %
%10ˆ ≤ε
only)current(a.c.
%10ˆ ≤ε
%10ˆ ≤ε
Error at rated current
TPSclosed iron core
Special version for high impedance protection
(Knee point voltage, internal secondary resistance)
Remanence
no limit
< 10 %
negligible
No limit
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Current transformer saturation
Steady-state saturation with AC current
Transient saturation with offset current
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S
ISC
Im
DC flux non-saturated
AC flux
Magnetising current
Short circuit current
Transient CT saturation due to DC component
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Ι P primary current
TN
B
total flux
a.c. flux
transientd.c. flux
BMax
B~
t
t
d.c. component
B~
)(ω
1 TS
t
TN
t
SN
SN
~
−−
−−
⋅⋅+= ee
T T
T T
B
B
ˆ
TNTS
TS
S
NS
Maxω1
~
−⎜⎜⎝
⎛ ⎟ ⎠
⎞⋅⋅+=T
T T
B
B
N
S
NS
SN
MaxBnT
T l
T T
T T t ⋅−= ⋅
δ tanω
1
Bi
W
S
⋅=
+=
R R
LT
[ ]
[ ] ms10900
min
S
δ =T For 50 Hz:
Course of CT-flux during off-set short-circuit current
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CT transient over-dimensioning factor KTF
KTF
TS [ms]
50 100 150 200
10
2
0
3
0
4
0
5
0
6
0
100
250
500
1000
5000
∞ (KTF ≈ 1+ωTN)
Closed iron core
Linear core
TN = network time constant
(short-circuit time constant)
TS = CT secondary time constantTN [ms]
NS
S
TT
T
S
N
STF ω
1
−
⎜⎜⎝
⎛
⎟⎟ ⎠
⎞
+= T
T T K
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⎟⎟⎟
⎟
⎠
⎞
⎜⎜⎜
⎜
⎝
⎛
⋅+=N
M
TFT
t-
e-1N1 T K' ω
N
NNTF 11
R
X T K +=+= ω
0 20 40 60 80 100
5
10
15
40 ms
50 ms
30 ms
10 ms
20 ms
tM
K‘td
[ ms]
∞→Mt
14
6
CT with closed iron core,
Over-dimensioning factor K TF
‘ for specified time to saturation (tM
)
:tM ∞→
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0 20 40 60 80 1000
20
40
60
80
100
120
140
160
180
0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3
3.5
4
KTF
TN in ms
10 ms
8 ms
6 ms
4 ms
2 ms
2 ms
6 ms4 ms
8 ms
10 ms
tM
tMΘ
(tM,TN)(el. degree)
CT over-dimensioning factor K TF (tM,T N)
in the case of short time to saturation (tM)
TN in ms
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Current transformer
magnetising and de-magnetising
Ι P
BBMax
Ι m
BR
t Ι m
BMax
BR
B
t
( ) TSt
RMax.R
−
⋅−+= eBBBB
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Current transformer
Course of flux in the case of non-successful auto-reclosure
tF1 tDT tF2
tF1 = duration of 1st fault
tDT dead time
tF2 =duration of 2nd fault
B
t
Bmax
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−
⋅⋅++
+
⋅
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−
⋅⋅+=
−−−−−S
F2
N
F2
SN
SNS
F2DT
S
F1
N
F1
SN
SN Tt
Tt
(ω
1Ttt
Tt
Tt
(ω
1~
maxee
T T
T T eee
T T
T T
B
B
ˆ
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Current transformer
magnetising curve and point of remanence
BI II III
H = im ⋅ w
I: closed iron core (TPX)
II: core with anti-remanence air-gaps (TPY)
III: Linearised core (TPZ)
up to 80%
< 10%
negligible
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Current transformers TPX und TPY
Course of the flux with non-successful auto-reclosure
tF1tDT tF2 t
BR
BR
closed iron core (TPX)
core with anti-
remanence air-gaps (TPY)
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Standards of voltage transformers
Class
designation
5P
3P
Voltage error FU Angle error δ
Permissible error at 0.05 ·UN and 1.0 · UN
± 3.0 %
± 6.0 %
120 minutes
240 minutes
Class
designation at 1.0 · UN at 1.0·UN
0.1
0.2
0.5
1
3
0.1
0.2
0.5
1
3
10
5
20
30
Not determined
Permissible voltage error in % Permissible angle error in minutes
VT classes to IEC 60044-2
VT classes for measurement IEC 60044-2
All 3P and 5P protection CTs must
additionally comply with one of the
below VT metering classes!
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Capacitive voltage transformer,
Equivalent circuit
ZBLF CF
RF 100 V
3
20 kV
3
400 kV
3
C1 = 5 nF
C2 = 95 nF
R'BLF CF
RF
LTRTCT
C E = C 1 + C 2
RE
LO
U *1 = U P ⋅ C 1
C 1 + C 2U*2
L'B
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Legend:
UP(t) Primary voltage
US(t) Secondary voltage
(1) Fault inception
(2) Aperiodic damping of US(t)
(3) Periodic damping of US(t)
Time
Tsin ms
Ratio
Classes
3PT1
6PT1
3PT2
6PT2
3PT3
6PT3
10 --- ≤ 25 ≤ 4
20 ≤ 10 ≤ 10 ≤ 2
40 ≤ 10 ≤ 2 ≤ 2
60 ≤ 10 ≤ 0.6 ≤ 2
90 ≤ 10 ≤ 0.2 ≤ 2
%100U2
)t(U
s
s ⋅⋅
t
Measured voltage transients after fault at
voltage maximum and zero-crossing
(Example)
Recommendations to IEC 60044-5
Transient performance of CVTs,
Recommendations acc. to IEC 60044-5
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BCT
BNCT
B
BNi ALF
i R R
R R
P P
P P ALF ALF'
+
+⋅=
+
+⋅=
rated CT burden: P BN
internal burden of the CT: P i=R i ⋅ I 2N2
Actual connected burden : P B= R B ⋅ I 2N2
RB=Rl +RR= burden resistance
Rl = resistance of connecting cables
RR= burden resistance of the relayBNCT
BCT
BNi
B ALF'i
R R
R R
P P
P P ALF' ALF
+
+⋅=
+
+⋅=
N
K OD
I
IK ' ⋅≥ ALF No saturation
for the total
short-circuit duration:N
N
N
~
Max
TF 11R
X T
B
BK' +=+== ω
ˆ
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−−
⋅⋅+=
−−
S
M
N
M
SN
SN
T
t
T
t
(ω
1 eeT T
T T TF K ''
No saturation for
the specified time tM:mTF OD
K K K Re
⋅≥
100
Remanence%1
1K mRe
−
=
with
CT dimensioning
Theory:
Practice:
TF K OD K =
Remanence only considered in extra high voltage systems (EHV)
KTF-values acc. to relay manufacturers‘ guides
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Practical CT requirements
Transient over-dimensioning factors KTF
(AR not considered)
5 K TF ≥
Distance
7SA6 and 7SA522 30ms)T if 1( 2 K N TF <≥≥
Fault atbalance point:Close-in fault:
Internal fault External fault
Transformer Differential KTF≥ 0.75 KTF≥ 1.27UT6 (Saturation free (Saturation free
time ≥ 4 ms) time ≥ 5 ms)
Line differential KTF≥ 0.5 KTF≥ 1.2
7SD61 (Saturation free (Saturation free
time ≥ 3 ms) time ≥ 5 ms)
Bus differential KTF≥ 0.5 KTF≥ 0.5
7SS52 (Saturation free (Saturation free
time ≥ 3 ms) time ≥ 3 ms)
Overcurrent ALF‘≥ I>>setting/ IN, at least 20
7SJ56
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CT dimensioning for
Example differential protection (1)
1. Calculation of fault currents
Net
∆ IL ∆ IL∆ IT
F1 F2 F3 F4
7UT617SD61
Impedances related to 20 kV:
[ ]
Ω0.13
3000
220
MVA''SCS
2kV2 NU
N Z: Net ==⎥⎦⎤
⎢⎣⎡
=
[ ][ ]
Ω1.2100
%12
40
220
100
%
MVAT- NP
2kV2 NU
T Z:Transf. =⋅=⋅⎥⎦⎤
⎢⎣⎡
= T u
[ ] [ ] Ω3,20,48Ω/km'LzkmlL Z:Line =⋅=⋅=
Impedances related to 110 kV:
[ ]
Ω4.03
3000
2110
MVA''SCS
2kV2 NU
N Z: Net ==⎥⎦⎤
⎢⎣⎡
=
110 kV, 3 GVA
110/20 kV
40 MVA
uT=12%OH-line:
l = 8 km,zL‘= 0,4 Ω/km
300/1A 1200/1A 200/1A 200/1A
[ ][ ]
Ω36.3100
%12
40
2110
100
%
MVAT- NP
2kV2 NU
T Z:Transf. =⋅=⋅⎥⎦⎤
⎢⎣⎡
= T u
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F1 kA17.34.03Ω
3110kV/1.1
NZ
3/ NU1.1F1I =
⋅=
⋅=
kA1.7336.3Ω4.03Ω
3110kV/1,1
TZ NZ
3/ NU1.1F2I =
+
⋅=
+
⋅= kA2.8
3.21.2Ω0.13Ω
320kV/1,1
LZTZ NZ
3/ NU1.1F4I =
Ω++⋅=
++⋅=F2
Dimensioning of the 110 kV CTs for the transformer differential protection:
Manufacturer recommends for relay 7UT61: 1) Saturation free time ≥ 4ms for internal faults2) Over-dimensioning factor KTF ≥ 1,2
for through flowing currents (external faults)The saturation free time of 3 ms
corresponds to KTF≥ 0,75See diagram, page 59
Criterion 1) therefore reads:
43300
173000,75
NI
F1ITFK ALF' =⋅=⋅≥
7300
17301,2
NI
F2ITFK ALF' =⋅=⋅≥
For criterion 2) we get:
kA9.551.2Ω0.13Ω
320kV/ 1.1
Z Z
3 / U 1.1 I
T N
N F3 =
+
⋅=
+
⋅=F3
F4
The 110 kV CTs must be dimensioned according to criterion 1).
CT dimensioning for
Example differential protection (2)
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CT dimensioning for
Example differential protection (3)
We try to use a CT type: 300/1, 10 VA, 5P?, internal burden 2 VA.
1.1643102
5.22' =⋅+
+=⋅
+
+≥ ALF
rated P
i P
operation P i P ALF
Specification of the CTs at the 20 kV side of the transformer:
Chosen, with a security margin : 300 /1 A, 5P20, 10 VA, R2≤ 2 Ohm (Pi ≤ 2VA)
It is good relaying practice to choose the same dimensioning as for the CTs on the 110 kV side:
1200/1, 10 VA, 5P20, R2≤ 2 Ohm (Pi ≤ 2VA)
Dimensioning of the 20 kV CTs for line protection:
For relay 7SD61, it is required: 1‘) Saturation free time ≥ 3ms for internal faults
2‘) Over-dimensioning factor KTF ≥ 1.2for through flowing currents (external faults)
24200
95500.5
NI
F3ITFK ALF' =⋅=⋅≥ 8.16=⋅=⋅≥
200
28001.2
I
I K ALF'
N
F4TF
The 20 kV line CTs
must be dimensioned
according to criterion 1‘).
(Connected burden estimated to about 2.5 VA)
The saturation free time of 3 ms corresponds
to KTF≥ 0.5See diagram, page 59
Criterion 1‘) therefore reads: For criterion 2‘) we get:
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For the 20 kV line we have considered the CT type: 200/5 A, 5 VA, 5P?, internal burden ca. 1 VA
8245111' =⋅++=⋅
++≥ ALF
rated P i P operation P i P ALF
Specification of line CTs:
We choose the next higher standard accuracy limit factor ALF=10 :
Herewith, we can specify: CT Type TPX, 200/5 A, 5 VA, 5P10, R2≤ 0.04 Ohm ( Pi≤ 1 VA)
(Connected burden about 1 VA)
CT dimensioning for
Example differential protection (4)