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7/30/2019 Pr4PresentationSC E

1/23

1

DIgSILENT

Short-Circuit Calculation

Basics, Methodologies and Models

IEC 60909

2

Content

1 Basic Terminology

2 Superposition Method

3 Voltage Source Method

4 Short-Circuit currents of the different time zones

5 Example: Star-Point treatment in the distribution network


2/23

3Fundamentals

Short-Circuit Calculation

Operational Conditions

Online-S/C calculation

Planning Conditions

Simplified Methods

(IEC, ANSI, ...)Reduced Set of Data

Complete Method,Comprehensive set of data

Method 1:

Equivalent Voltage Source

at the fault location

Method 2.1:Superposition

Method

Method 2.2:Solution of Diff.

Equation

Initial S/C current

ISC (Ikss)

ip Ib Ith

m, n

I"k, Uki ik(t)

4

Application in Network Planning

- S/C Capacity of existing substations

- Design and Parametrization of Protection Relays

- Dimensioning of Earthing grids

- Thermal S/C capacity of cables

- Check for sufficient S/C power at load connection

- Induction problems during unsymmetric faults

Application in Network Operation

- Staying within S/C limits during network switching

- Localizing network faults based on the fault impedance

- Clarification of protection mis-operation

Fundamentals


3/23

5

Upper Amplitude

DC-Component iDC

Time

Current

Lower Amplitude

Time-Plot of S/C current (far from generator)

Fundamentals

6

Time-Plot of S/C current (close to generator)

Current

Upper Amplitude

Lower Amplitude

DC-Component iDC

Fundamentals


4/23

7

S/C close to GeneratorModel of the Synchronous Machine

xd-x'd

S

x'd-x"d x"d

E' E"E

t

Fundamentals

8

Important magnitudes in S/C calculation

ip Peak Current

idc DC Offset of the S/C current

Ik" AC Component of the initial (sub-transient) S/C/C

Ik AC Component of Transient S/C Current

Ik AC Component of Steady-State S/C current

Also of Importance:

Sk" Initial S/C Apparent Power

knk "IU3"S =

Fundamentals


5/23

9

Symmetric Components - Principle

Im

Re

1 = a3

a2

a

120

120

120

Uniform Pointer in the

complex plane

I1R

t

I1S

I1T

I1R

t

I1T

I1S

I1R

t

I1T

I1S

Pos. Sequence

System 1

Neg. Sequence

System 2Zero Sequence

System 0

2

3j2

1a +=

2

3j

2

1a

2 =

0aa12 =++

Fundamentals

10

=

2

1

0

2

2

T

S

R

I

I

I

aa1

aa1

111

I

I

I

=

T

S

R

2

2

2

1

0

I

I

I

aa1

aa1

111

3

1

I

I

I

Symmetric Components - Transformation

210R IIII ++=

21

2

0S IaIaII ++=

2

2

10T IaIaII ++=

012 RST

RST 012( )TSR0 III

3

1I ++=

( )T2SR1 IaIaI3

1I ++=

( )TS2R2 IaIaI3

1I ++=

Fundamentals


6/23

11

Symmetric Components - Impedance Measuring

Positive Sequence

System 1

Negative Sequence

System 2

Zero Sequence

System 0

Fundamentals

12

Classification of Short-Circuits

3-phase S/C

1

2

0

L1

L2

L3

ZA1

ZA2

ZA0

ZB1

ZB2

ZB0

~3nUc

1I

Fundamentals


7/23

13

2-phase S/C

(no Earth Contact)


Fundamentals

1

2

0

L1

L2

L3

ZA1

ZA2

ZA0

ZB1

ZB2

ZB0

~3

Uc n 1I

2I

14

2-phase S/C

(incl. Earth Contact)


Fundamentals

1

2

0

L1

L2

L3

ZA1

ZA2

ZA0

ZB1

ZB2

ZB0

~3nUc

1I

2I 0I


8/23

15

Phase-to-Earth S/C

1

2

0

L1

L2

L3

ZA1

ZA2

ZA0

ZB1

ZB2

ZB0

~3nUc

1I

0I

2I


Fundamentals

162 Element Models in Symmetr. Components

Model of an External Network

~U11

2

0

RN1 XN1

RN2 XN2

RN0 XN0

Parameters and Calculation

k

n1N

"I3

UcZ

=

Further Parameters:

1N2N ZZ =

RN1, XN1 acc. to ratio1N

1N

X

R

RN0, XN0 acc. to ratio1N

0N

Z

Zand

0N

0N

X

R


9/23

17

Model of Overhead Lines / Cables

1

2

0

RL1 XL1

RL2 XL2

RL0 XL0CL0/2 CL0/2


RL1, XL1 according to conductors/geometry andmanufacturer's data respectively

1L2L ZZ =

RL0, XL0 according to conductors/geometry and underconsideration of parallel paths through earth andneighbouring conducting materials

Temperature coefficient of the resistance forminimum S/C value:

( )[ ] 20,LeL RC201R +=


18

Model of 2-Winding Transformer

Parameters and Calculation:

rT

2HV,rT

kr1HV,TS

UuZ =

rT

2 HV,rTRr1HV,T

S

UuR =

1HV,T2HV,T ZZ =


1

2

0

RT,HV1 XT,HV1

RT,HV2 XT,HV2

3ZE1 3ZE2

ZT0


10/23

19

Model of 3-Winding-Transformer (1)Parameters and Calculation:

12rT

2HV,rT

12kr1,12S

UuZ =

12rT

2

HV,rT12Rr1,12

SUuR =

23rT

2HV,rT

23kr1,23S

UuZ =

23rT

2HV,rT

23Rr1,23S

UuR =

31rT

2HV,rT

31kr1,31S

UuZ =

31rT

2

HV,rT31Rr1,31S

UuR =


1

0

RT,HV11 XT,HV11

3ZE13Z

E3

ZT0

RT,HV31

XT,HV21RT,HV21

XT,HV31

2

3ZE2

RT,HV12 XT,HV11 RT,HV32

XT,HV22 RT,HV22

XT,HV32

20

Model of 3-Winding-Transformer (2)

( )1,311,231,1211HV,T ZZZ2

1Z +=

( )1,311,231,1221HV,T ZZZ2

1Z +=

( )1,311,231,1231HV,T ZZZ2

1Z ++=

1,HVi,T2,HVi,T ZZ =


1

0

RT,HV11 XT,HV11

3ZE1 3ZE3

ZT0

RT,HV31

XT,HV21RT,HV21

XT,HV31

2

3ZE2

RT,HV12 XT,HV11 RT,HV32

XT,HV22 RT,HV22

XT,HV32


11/23

21

Model of Series Reactor

1

2

0

RR1 XR1

RR2 XR2

RR0 XR0


rR

2

nkr1R

I3

UuZ

=

rT

2rT

Rr1RS

UuR =

In case of symmetry:

1R0R2R ZZZ ==


22

Model of the Synchr. Machine (RG acc. to IEC)

RS/X"d UrG SrG

0.15 1kV any

0.07 > 1kV < 100 MVA

0.05 > 1kV 100 MVA


dSS "jXRZ +=

Further Parameters:

2S2S2S jXR"jXRZ +=+=

Normally applicable: X2

= X"d

If x"d different from xq", it may be set:

( )qd22 "X"X2

1X"X +==


~U"11

2

0

RS1 X"S1

RS2 X"S2

RS0 X"S0

ZE

3ZE

S


12/23

23

Model of the Asynchronous Machine


rM

2

rM

rM

LR

AKS

U

I

I

1Z

=

RM/XM UrM PrM per PolePair

0.1 > 1kV 1 MW

0.15 > 1kV < 1 MW

0.42 1kV, incl.cables

any

ASM

~U"11

2

0

RA1 X"A1

RA2 X"A2

RA0 X"A0


24

Model of Load/Shunt Compensation

1

2

0

RLoad1

XLoad1

not

forIEC60909

CLoad1

RLoad2

XLoad2

CLoad2

RLoad0

XLoad0

CLoad0

0



13/23

25

Model of Converter Drives


Calculation in general like in case of anAsynchronous Machine:

rM

2

rM

rM

LR

K,ConvS

U

I

I

1Z

=

where

ILR/IrM = 3

RM/XM = 0.10


~U11

2

0

RConv1 XConv1

3ZE

3

RConv2 XConv2

RConv0 XConv0

263 Superposition Method

~

~

~

US1

US2

US3

UOp,0

~ UOp,0

+

=

UOp,0

~

~

~

US1

US2

US3

USC

= 0

IOp

IOp

IOp

ISC

ISC

ISC

ISC + IOp

ISC + IOp

ISC

+ IOp

a)

b)

c)

Initial State before S/C

Superposition as result

Backward-Infeed at faultlocation

Superposition Method


14/23

274 Voltage Source Method according to IEC 60909

Initial State before S/C:

No-Load Case

Superposition as result

approximation

Backward-Infeed at fault

location (incl. Security

Factor)

Explanation of Method

~

~

~ US3

=Un3

UOp,0=Un

~

+

Un

~

~

~

Un1

Un2

Un3

USC= 0

IOp=0

ISC

ISC

ISC

ISC

ISC

ISC

a)

b)

c)

US2

=Un2

US1

=Un1

IOp

=0

IOp=0

c Un

28

IEC 60909: Principle of Correction Factors

~U"k Zk I"k

~c Un K Zk I"k,IEC



15/23

29

IEC 60909: Voltage Correction Factors

Nominal Voltage Calc. max. S/C Current

cmax

Calc. min S/C Current

cmin

Low Voltage

Un 1 kV

1.05 (bei Umax 1.06 Un)

1.10 (bei Umax 1.10 Un) 0.95

Medium Voltage

1 kV < Un 35 kV1.10 1.00

High Voltage

35 kV < Un

1.10

If Un not defined:

cmaxUn Um

1.00

If Un not defined:

cminUn 0.9Um

In general must be considered: cmaxUn Um


30

IEC 60909: Transformer Impedance Correction

krT

maxT

x6.01

c95.0K

+=

resp.

max,TbrT

max,TbrT

max

max,b

nT

sinI

Ix1

c

U

UK

+

=

3-Winding Transformers:

12kr

max12T

x6.01

c95.0K

+

=

23kr

max23T

x6.01

c95.0K

+

=

31kr

max31T

x6.01

c95.0K

+

=



16/23

31

IEC 60909: Synch. Machine Impedance Correction

Impedance Correction(Z1, Z2, Z0, with exception of Ze)

rGd

max

rG

nG

sin"x1

c

U

UK

+

=

RS/X"d UrG SrG

0.15 1kV any

0.07 > 1kV < 100 MVA

0.05 > 1kV 100 MVA


32

IEC 60909: Modeling Asynchronous Machines

- No Correction Factor

- IEC 60909 formulating Conditions under which ASM shouldnot be neglected (not relevant for Software implementations)

- Estimation of RM

RM/XM UrM PrM per PolePair

0.1 > 1kV 1 MW

0.15 > 1kV < 1 MW

0.42 1kV, incl.cables

any



17/23

33

IEC 60909: Power Station Correction Factors

Power Stations with on-load tap changer at unit transformer

rGTd

max

2

r

2

rG

2

Netw,n

PS

sinx"x1

c

t

1

U

UK

+

=

Power Stations with no-load tap changer at unit transformer

( )( )

rGd

maxT

rGrG

Netw,n

PSsin"x1

cp1

t

1

p1U

UK

++

+=

IEC60909 formulates modification rules for these factors


34

Comparison between IEC 909:1988 and IEC 60909:2001 (1)

IEC 909:1988 EC60909:2001

Netw.-Transf. No Impedance Correction Factor

Special considerations in the followingcases:

- A single-fed S/C current has samedirection as operational current

- Tap Changer with voltage range >5%

- S/C voltage Uk,min significantly smallerthan rated S/C voltage Ukr

- Voltage during operation significantlyhigher than Un (U>1.05 Un)

Special Correction Factor

SynM Impedance correction based on UrG Impedance correction based on (1.0 + pG)UrG (instead of UrG), when operationalvoltage permanently different from UrG

Unit with on-load tapchanger

Optional Choice between

- Single correction of transformer andSynchronous Machine

- Unit Correction

Only Unit Correction admissible

Unit with no-load tapchanger

No Correction Specific Correction Factor



18/23

35

Comparison between IEC 909:1988 and IEC 60909:2001 (2)

IEC 909:1988 EC60909:2001

Lines max = 80 C max according to max. possible conductortemperature

cmax in case of

LV networks

c max = 1.00 c max = 1.05 (if Ub < 1.06 Un)

else cmax = 1.10S/Ccontribution ofASM

- Consideration when calculation of 3P and2P(E)

- In case of low-impedance grounding alsoconsideration for 1PE (no guideline forcalculation)

- Concrete calculation guideline for all faulttypes

- Concrete rules for consideration of ASM(saving effort in case of manualcalculation)

Additionalcalculationprocedures

- Calculation guideline for 1-phaseconductor interruption in MV network (fusereaction) and a fault in the LV network

- Calculation guideline for the thermal S/Ccurrent taken over from EC 865-1


36

Types of S/C current feeding

Single-fed One-sided

Single-fed Multiple-sided

Meshed feeding



19/23

37

Maximum Initial AC S/C Current Ik,max

k

2

nmaxmax,k

Z

1

3

Uc"I

=

Minimum Initial AC S/C Current Ik,min

k

2

nminmin,k

Z

1

3

Uc"I

=

To be considered:

- Factor cmin instead of cmax.

- For OHL & Cables application of Resistance values not for 20C

but for the max. possible conductor temperature.

- Network topology and Generator activity should be set for

minimum S/C current expectation.


38

Peak Current ip (1)

kp "I2i =

Single-fed networks

k

k

X

R3

k

k e98.002.1

X

R +=

=

used for all fault types (3p,2pE,2p,1p)



20/23

39

Peak Current ip (2)

Calculation of in case of meshed feeding

Method A: Uniform Ratio R/X

R/X according to the minimal ratio of all branches contributing to the S/Ccurrent (series connections count as one branch only)

i: Branches contributing to the S/C current

Pros/Cons:

+ Easy in Application

- R/X mostly too pessimistic (too small)

=

i

i

min X

RMin

X

R


40

Peak S/C current ip (3)

Calculation of in case of meshed feedingMethod B: Ratio R/X at fault location

Modificationsa) In case of a ratio R/X < 0.3 in all branches the factor 1.15 need not

be applied

b) In LV networks is to be applied (1.15 b) max = 1.8c) In MVnetworks is to be applied (1.15 b) max = 2.0

Pros/Cons:

+ more exact than procedure b

=

k

kb

X

Rkbp "I215.1i =



21/23

41

Peak Current ip (4)

Calculation of in case of meshed feedingMethod C: Method of Equivalent Frequency

- All network impedances calculated for Frequency fe

- S/C impedance Zk,e calculated at Frequency fe- Factor Kappa based on R/X ratio of Zk,e

Pros/Cons:

+ most exact

- high calculation effort for manual evaluation

i

*

i RR =

e

ni

*

if

fXX =

fn fe

50 Hz 20 Hz

60 Hz 24 Hz

=

e

e

f,k

f,k

cX

R


42

DC Component iDC

tX

Rf2

kDC e"I2i

=

R/X calculated based on

- Method A (Uniform Ratio R/X)

- Method C (Equivalent Frequency Method) with value of fe depending ontime interval

ft


22/23

43

Breaker Current ib(not considered here, see IEC-60909)

Steady-State S/C current Ik(not discussed here, see IEC-60909)

Thermal S/C current Ith

( ) k2

thk

2

k

T

0

2 TITnm"Idtik

=+=

k

Tk

0

2

thT

dti

I

=

m Thermal contribution of the DC component

n Thermal contribution of the AC component


445 Star-Point Treatment in Distribution Networks

Example

Application

~U11

2

0

ZN1 ZT1 ZL1

ZN2 ZT2 ZL2

ZN0 ZT0ZL0

ZE

3 ZE

1PE

CL/2CL/2


23/23

45

Low-Impedance Grounding

~U11

2

0

ZN1 ZT1 ZL1

ZN2 ZT2 ZL2

ZN0 ZT0ZL0

3 ZE

CL/2CL/2

~U11

2

0

ZN1 ZT1 ZL1

ZN2 ZT2 ZL2

ZN0 ZT0ZL0

3 ZE

CL/2CL/2

Isolated Star-Point

5 Star-Point Treatment in Distribution Networks

Star-Point Compensation

~U11

2

0

ZN1 ZT1 ZL1

ZN2 ZT2 ZL2

ZN0 ZT0ZL0

3 XE

CL/2CL/2

1CL3 LE2

0 =

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