basics of current and voltage transformers - siemens

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Page 1: Basics of Current and Voltage Transformers - SIEMENS

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Power Transmission and Distribution

Author

Page 241 2007-08

Copyright © Siemens AG 2007. All rights reserved.

PTD SE PTI Author

Basics of

Current and Voltage Transformers

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Power Transmission and Distribution

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Page 242 2007-08

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PTD SE PTI Author

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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Power Transmission and Distribution

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PTD SE PTI Author

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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Power Transmission and Distribution

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PTD SE PTI Author

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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Power Transmission and Distribution

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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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PTD SE PTI Author Tp

⎟⎟⎟

⎜⎜⎜

⋅+=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

1Ttt

Tt

Tt

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

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)