Ct Dimension Ing Principles

1

Current TransformerDimensioning

Siemens AG, PTD SE PT 5Postfach 3220, 91050 Erlangen

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Tel +49 9131 7- 34324Fax +49 9131 7- 35017

[email protected]

Power Transmission and DistributionCopyright SIEMENS AG. PTD SE PT 2005. All rights r eserv ed.

Power TechnologiesCurrent Transformer Dimensioning,

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Current Transformer Dimensioning


Power TechnologiesCurrent Transformer Dimensioning, Page 2

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Current Voltage

Inductive

Rogowski-Coil

Ohmic

Inductive/Optical

Optical

Inductive

Ohmic

Capacitive

Different Measuring Methods I

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Different Measuring Methods II




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Dimensioning Criteria

Requirements of modern relays Installation points Relay functions Relay burden, cable burden and CT burden Short-circuit current and system time constant Technical criteria

Customer criteria Requirements of relays in use Habits Tender invitation National standards

CT-Ratio, Accuracy Limiting Factor, Nominal Burden,Class, Knee- Point Voltage

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Important Standards

AdditionalCEI (Italy) SEN (Sweden) CSA (Canada) SEU (Suisse) NF (France) ABNT (Brasil)

International Standards

IEC 60044-1 1996/12 Current Transformers IEC 60044-1 2000/07 Current Transformers (amendment 1)

IEC 60044-6 1992/03 Current Transformers (transient performance TP)

IEC 60044-2 1997/02 Voltage TransformersBS EN 60044-1 CurrentTransformers

ANSI C57.13/1993 Current TransformersAS 1675-1986 Current Transformers

IEC 185/1978BS 7626/1993BS 3938/1973

VDE 0414 Specifications for Instrument Transformers

obsolete !obsolete !obsolete !




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CT: Equivalent Circuit

CT

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Saturation Effect

20 40 60 80 100 120 140 160 180 t/ms0

ipis

5 P10 60 VAU/V

900

90

0,001 0,010 0,100 1,000

Ritz

Pfiffner

IM /A

iP iM

Lh

L σσσσ RCTLZ RZ

Lb

Rb

is




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Definitions of Accuracy According to IEC 60044-1

Definition of current error:

Definition of angle error:

Definition of composite error:

prim

primnseci I

InI100F

−=

)I(angle)I(angle primseci −=ϕ∆

( )

rms.prim

T

0

2)t(primsecnT

1

i I

dti)t(in

100F

∫ −

=

5




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Qualifying Symbols According to IEC

10 P 10, 15 VA

Nominal burden

Accuracy Limiting Factor (ALF)

Core Type P = Protection

Accuracy limit in % at ALF * I n

Measuring cores are not suitable for protection!



Power TechnologiesCurrent Transformer

Dimensioning, Page 10

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IEC-60044 Accuracy Classification for Protection CT in Steady State

2 standard accuracy classes: 5P and 10PLimits of error

Example: 5 P 10 , 50 VA

accuracy limit in % at I=ALF × I n

accuracy limiting factor (ALF)nominal burden

Accuracyclass

5P10P

At nominal primary current

Current error Phase angledisplacement

Phase angledisplacement

% minutes centirad

± 1± 3

± 60-

± 1.8-

At nominal accuracy limitprimary current

Composite error

%

510

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However:

Definition for type P according toIEC 60044-1, only AC componentis taken into account

Only symmetrical saturation isconsidered

Short-circuit current consists of ACand decaying DC components

For CT-dimensioning DC componentshould also be considered

10P10, 15 VA

Isecondary/In

10

5

0 5 10 15 Iprimary /In

burden < 15 VA

burden = 15 VA

burden > 15 VA

F i = 10%

Definition of Protection CT Performance in Steady-S tate According to IEC





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IEC: Not high nominal VA or high nominal ALF fac tor leads toa better CT performance, but higher actual ALF’ fact or

Accuracy Limiting Factor ALF’

The CT’s performance under steady-state conditions is described by

A ccuracy L imiting F actorBetriebsüberstromziffer

ALF’ = Actual Accuracy Limiting FactorALFn = Nominal Accuracy Limiting FactorPn = Nominal VA Output (Nominal Burden)PCT = Internal CT BurdenP’ = Actual Connected Burden

CT

CTnn PP`

PPALFALF`

++⋅=

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Definition of Knee-Point Voltage According to BS Cl ass X and IEC Class PX

Usecondary/V

200

0 Isecondary/mA

∆∆∆∆U = 10%

50 100 150

400

∆∆∆∆I = 50%

Uknee

RCT (internal burden)

R‘(external burden)

Knee-point voltage is the voltage at which a 10% increase in rms voltage results in a 50% increase in rms magnetizing current





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BS Performance Classification for Relaying CTs

Class P: 5P and 10P similar to IEC 60044

Class X: Defined by Rated primary current Turns ratio (the error shall not exceed ± 0.25%) Rated knee-point voltage Magnetizing current at rated knee-point voltage Resistance of secondary winding corrected to 75°C

Class X CT will be applied if accuracy limits of cl ass 5P or 10P are notappropriate

Class X quantities can also be measured and given f or class 5P and 10 P

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Relation Between Accuracy Limiting Factor ALF and K nee-Point Voltage

I1N I2N

RCT(internal burden)

Rn(nominalexternalburden)

Uknee

( )1.3

ALFIRRknee

n2nCTnU ⋅⋅+=( )

n2

nCTnI3.1

ALFPP

⋅⋅+

=

( )146V

1VA1.3104VA15VA

U knee =⋅

⋅+=

Example:IEC Class 5P: 600/1A, 5P10, 15 VA, RCT= 4ΩtoIEC Class PX: 600/1A:

Usecondary/V

200

0 Isecondary/mA

∆∆∆∆U = 10%

50 100 150

400

∆∆∆∆I = 50%





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Relation Between Knee-Point Voltage and Accuracy Li miting Factor ALF

Example : An IEC PX CTI2N = 1A Rated secondary currentUknee = 600V Knee-Point VoltageRCT = 5Ω Internal burdenR‘ = 1Ω Wire and relay burden

100A1Ω5Ω

600VRR

UI

CT

kneemax =

+=

+=

100A1

A100I

I'ALF

n

max ===

245VA20VA

5VA1VA100

PPPP'

ALF'ALFCTn

CTn =

++=

++=

405VA10VA

5VA1VA100

PPPP'

ALF'ALFCTn

CTn =

++=

++=

CT with 20VA:

CT with 10VA:

For small connected burdens, like for most GIS, wit h short lines to the relay and for modern relays with a burden of ca. 0.1 VA only P-cores with small Nominal Accuracy Limiting Factors are required

Maximum transmittable AC currentwithout DC components (secondary):

I1N I2N

RCT(internal burden)

Rn(nominalexternalburden)

Uknee

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Conversion of ANSI to IEC CT Data for 1A CTs

RCT

R’Uterm

Example C200, 1A

C100 10P20, 5 VAC200 10P20, 10 VAC400 10P20, 20 VAC800 10P20, 40 VA

Nominal Accuracy Limiting Factor ALF n

Uterm is defined as terminal voltage at 20*I nand connected external standard burden.

ALFn = 20 for all class C cores

Nominal ANSI-Standard burden

Class P Nominal Burden

Ω=⋅

=⋅

= 10A120V200

I20U

'Rn

term

VA1010)A1('RIP 22nn =Ω⋅=⋅=





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Conversion of ANSI to IEC CT Data for 5A CTs

RCT

R’Uterm

Example C200typical 5A

C100 10P20, 25 VAC200 10P20, 50 VAC400 10P20, 100 VAC800 10P20, 200 VA

Nominal Accuracy Limiting Factor ALF n

Uterm is defined as terminal voltage at 20*I nand connected external standard burden.

ALFn = 20 for all class C cores

Nominal ANSI-Standard burden

Class P Nominal Burden

Ω=⋅

=⋅

= 2A520V200

I20U

'Rn

term

VA502)A5('RIP 22nn =Ω⋅=⋅=

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Class C: indicates that the transformer ratio can be calculated (bushing type CTs)Class T: indicates that the transformer ratio must b e determined by test

800

700

600

500

400

300

200

100

0

0 10 20 30 40 50 60 70 80 90 100

8 Ω

4 Ω

2 Ω

1 Ω

C800

C400

C200

C100

wound-type CTs limits of error

secondary amperes

secondary

volts

terminal

Error will not exceed 10% for secondary voltage equivalent to or less than value described by curve

Class C: Ratio error will not exceed 10% between 1 t o 20 times nominalsecondary current.

ANSI C57.13 Performance Classification for Relaying CTs





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Effective Burden

Ri R1

RRelay

RRelay

RRelay

Ri R1

Ri R1

R2

R2

R2

3 CT Earth-Returns

RBurden = R1 + RRelay + R2PBurden = In2 (R1 + R2) + PRelay

Ri R1

Ri R1

Ri R1

R2

RRelay

RRelay

RRelay

1 CT Earth-Return

3-phase and 2-phase faults:RBurden = R1 + RRelayPBurden = In2 *R1 + PRelaynon-symmetrical earth faults:RBurden = R1 + RRelays + R2PBurden = In2 (R1 + R2) + PRelays

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Effective Secondary Cable Burden with Nominal Curre nt 1A, 5A

0 100 200 3000

10

20

30

40

50

60VA

length/m

2,5 mm2

0,70 ΩΩΩΩ / 100 m

4,0 mm2

0,44 ΩΩΩΩ / 100 m

6,0 mm2

0,29 ΩΩΩΩ / 100 m

10,0 mm2

0,17 ΩΩΩΩ / 100 m

16,0 mm2

0,11 ΩΩΩΩ / 100 m

I n = 5 A

2,5 mm2

0,70 ΩΩΩΩ / 100 m

4,0 mm2

0,44 ΩΩΩΩ / 100 m

6,0 mm2

0,29 ΩΩΩΩ / 100 m

10,0 mm2

0,17 ΩΩΩΩ / 100 m

16,0 mm2

0,11 ΩΩΩΩ / 100 m

I n = 1 A

0 100 200 300length/m

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2VA

(I n)2 = 25 A2 ⇒⇒⇒⇒ high burden (In)2 = 1,0 A2 ⇒⇒⇒⇒ low burden

better





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Steady State Dimensioning - Transmission Capability

RCT RI

……Ω ……Ω

RI

Relay

RRelay

……Ω

P’ = …… VAn = …… / 1A

CT-Transmission Capability with nominal burden

I’’ k = …… x In = …… kA

Accuracy Limiting Factor

CT-Transmission Capabilitywith actual burden

I’’ k = ALF’ x I n = …… kA

=++⋅=

CT

CTnn PP'

PPALFALF'

..................

.................. =

++

⋅=

Current Transformer CT

…… / 1A, …… P ……, …… VA

1000

2 1

0,1

1000

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Steady State Dimensioning

RCT RI

……Ω ……Ω

RI

Relay

RRelay

……Ω

P’ = …… VAn = …… / 1A


…… / 1A, …… P ……, …… VA

Short-Circuit Current

I’’ k = …… kA = …… x In

Necessary Accuracy Limiting Factor

Necessary Nominal Burden

Necessary Nominal AccurancyLimiting Factor

......I''I

'ALFn

k ==

VA......PVA......'PP nn =⇒=≥

=++⋅=

CTn

CTn PP

PP'ALF'ALF

..............................

...... =++⋅=

1000

2 1

0,1

2,1

1000 5? ?





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Short Circuit Current

Constant AC component 50/60 Hz Decaying DC component Time constants:

Medium voltage 10ms .. 50msHigh voltage 50ms .. 100msExtra high voltage 80ms .. 150ms

Decaying AC component 50/60 Hz Decaying DC component Time constants:

Medium voltage 10ms .. 100msHigh voltage 50ms .. 250msExtra high voltage 80ms .. 250msGenerator level up to 500ms

Fault far from generator Fault near to generator

A

i p

'' 22 kI

'' 22 22 kk II =

Bottom envelope

Decaying component iDC

Top envelope

Time

Current

Bottom envelope

Decaying component iDC

Top envelope

Time

Current

A

i p'' 22 kIk 22 I

IK'' = Subtransient short-circuit current

ip = Peak value of short-circuit value

IK = Steady short-circuit current

iDC = Decaying DC component

A = Initial value of DC component

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Power Transmission and DistributionCopyright SIEMENS AG. P TD SE P T 2005. All rights r eserv ed.



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Meaning of the accuracy limiting factor ALF‘

The multiplication of the accuracy limiting factor and nominal CT-current specifies the symmetrical short-circuit current which can be transmitted without saturation.

Relation between magnetic flux density and secondary nominal CT-current.

dti*)R(RdtuB s(t)Bcts(t) ∫∫ +=≈

-1,5

-1

-0,5

0

0,5

1

1,5

-1,5

-1

-0,5

0

0,5

1

1,5

+Bmax

-Bmax

In* ALF´ x 1.41

maxBB

kmax

s

Ii





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Transient Dimensioning Factor I

Asymmetrical short circuit current with a superposing DC-component

The DC-component of an asymmetrical short circuit is causing an additional magnetic flux.

Transient dimensioning factor

TN : System time constant

-0,5

0

0,5

1

1,5

2

2,5

0

2

4

6

8

10

12

kmax

s

Ii

maxBB

tfrei

10ms

=

=ACmax

DC/ACmax

B

B

∞=+≈ freeNtd for t T1K ω

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Bsat Magnetic Flux

secondary current

primary current

The DC-component is producing a steep rising of the magnetic flux density

A CT can be saturated by an asymmetrical current DC-component nevertheless it will not be saturated by the pure symmetrical current

t free

Transient Dimensioning Factor II





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CT - Dimensioning according to saturation-free trans mission time

Overdimensioning factor for saturation-freetransmission time t free:

)e(1T1K NTfreet

Ntd

−−+= ω(iron-cored CT with T S >> TN)

tfree = 10 ms

0 0,05 0,10 0,15 0,20

tfree = 20 ms

tfree = 30 ms

tfree = ∞Ktd

0

5

10

15

TN

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CT-Dimensioning for Transformer Differential Protec tion

A transformer differential protection should be sta ble on external short-circuit faults.The CT saturation detection of 7UT612 relays needs an unsaturated transmission ofmaximum short-circuit current in

For high CT time constants, the maximum transmittab le current must not exceed

tfree = 10 ms

0 0,05 0,10 0,15 0,20

tfree = 20 ms

tfree = 30 ms

tfree = ∞Ktd

0

5

10

15

mit ALF'tdK

nSC

⋅= II

TN





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CT-Dimensioning for Line Differential Protection

A current differential protection should be stable on external short-circuit faults.The CT saturation detection of 7SD51 relays need an unsaturated transmission ofmaximum short-circuit current in

For high CT time constants, the maximum transmittab le current must not exceed

tfree = 10 ms

0 0,05 0,10 0,15 0,20

tfree = 20 ms

tfree = 30 ms

tfree = ∞Ktd

0

5

10

15

mit ALF'tdK

nSC

⋅= II

TN

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CT-Dimensioning for Distance Relay

General:

The CT may be saturated, but any short circuit faul ts in zone 1 mustbe cleared undelayed, short circuit faults outside zone 1 must be cleared delayed.

CT may be saturated, but the remainingmagnitude of fundamental current and its phase angle must lead toimpedance within zone 1.

CT should keep to transmit short circuitcurrents without saturation in a longer time than relay operating time.





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CT-Dimensioning for Overcurrent Relays

General:

The CT may be saturated, but the remaining magnitud e of fundamentalcurrent has to be higher than the relay settings I >>.

IS > I> or I S > I>>

nCT

CTnn I

IPP'PP

ALF >>>++⋅

nII

ALF >>>

In systems with high time constants the tripping co mmand for therelay can be delayed for faults at the zone boundar ies.

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......kA......kA............

IK

ALF'I n

tdk =×=⋅=

Transient Dimensioning - Transmission Capability

RCT RI

……Ω ……Ω

RI

Relay

RRelay

……Ω

P’ = …… VAn = …… / 1A


…… / 1A, …… P ……, …… VA

Accuracy Limiting Factor

......PP'PP

ALFALF'CT

CTnn =

++⋅=

Tsys = 0 ms, t free = ∞, steady stateIk = ALF’ * I n = …… kA

Tsys = 50 ms, t free = ∞, transient

Tsys = 50 ms, t free = 10 ms, transient

1000

2 1

0,1

2,1

1000 5 10 10

.......kA......kA............

IK

ALF'I n

tdk =×=⋅=





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Transient Dimensioning

RCT RI

……Ω ……Ω

RI

Relay

RRelay

……Ω

P’ = …… VAn = …… / 1A


…… / 1A, …… P ……, …… VA

Short-Circuit Current

I’’ k = …… kA = …… x InTsys = …… ms

Necessary Transient Accuracy Limiting Factor

Necessary Nominal Burden

Necessary Nominal AccuracyLimiting Factor

VA......PVA......'PP nn =⇒=≥

.................................... =⋅=

++

1000

2 1

0,1

2,1

1000 5? ?

7UT612

............KI'I'

ALF' ...................

tdn

k =×=⋅=

=++⋅=

CTn

CTn PP

PP'ALF'ALF

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CT - Demagnetizing

circuit breaker switched-off at current zero crossing

Maximum of induction





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TP - current transformer classes acc. IEC 60044 - 6

- Iron - cored CT without limited remanence- Mechanical construction corresponds to class P (IE C 60044 - 1)- transient behavior is specified additionally

- same as TPX- remanence limited to < 10% (anti - remanence air ga p)

- remanence neglectable- error limit is only formulated for AC component- DC - component will be shortened considerably

TPX

TPY

TPZ

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Exemplary magnetizing characteristics of Class TP - CTs:





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CT - Induction curve during AR

−

−⋅⋅++⋅

−

−⋅+=

== −−−−−

∝

+

)e(eTTTTω

1e)e(eTTTωT

1B

BK ST

F2t

NTF2t

STF2tSpt

STF1t

NTF1t

SN

S1

SN

SNmaxtd ˆ

tF1 tSp tF2 t

A

B

BR

BR

A – Iron cored CT TPX

B – Iron cored CT with anti - remanenceair gap TPY

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• Advantages by AR• Cost intensive partitioned core • very short sec. Time constant (<100ms): sec. DC component is no longer transformed correctly• high demagnetizing current

CT - Induction curve during AR

Linear core CTTPZ

−

−⋅+=

== −−

∝

)e(eTTTT

1B

BK ST

F2t

NTF2t

SN

SNmaxtd

ωˆ

Ip

Is

Im

B





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Error limits of TP - current transformer classes acc. to IEC 60044 - 6

class Error at rated currentratio angle

Peak error at ratedovercurrent

TPX

TPY

TPZ

± 0,5% ± 30 min

± 1,0% ± 60 min

± 1,0% ± 180 ± 18 min

ε ≤ 10%

ε ≤ 10%

ε ≤ 10% (only I ~)

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CTDim 3.2 - Current Transformer Dimensioning Program

Technical Optimization

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Automatic Report Generation

Standard Conversion

Dynamic Simulation

Ct Dimension Ing Principles

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