Copy of shortckt

28.06.2008Copyright © Siemens AG 2008. All rights reserved.

E D SE PTI NC Steffen Schmidt

EXPERT SYSTEMS AND SOLUTIONS

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Copyright © Siemens AG 2008. All rights reserved.

Short Circuit Calculation

Sector Energy D SE PTI NC

Steffen Schmidt



Standards and Terms



Purpose of Short-Circuit Calculations

Dimensioning of switching devices

Dynamic dimensioning of switchgear

Thermal rating of electrical devices (e.g. cables)

Protection coordination

Fault diagnostic

Input data for

Earthing studies

Interference calculations

EMC planning

…..



Short-Circuit CalculationStandards

IEC 60909:Short-Circuit Current Calculation in Three-Phase A.C. Systems

European Standard EN 60909 German National Standard DIN VDE 0102 further National Standards

Engineering Recommendation G74 (UK)Procedure to Meet the Requirements of IEC 60909 for the Calculation of Short-Circuit Currents in Three-Phase AC Power Systems

ANSI IIEEE Std. C37.5 (US)IEEE Guide for Calculation of Fault Currents for Application of a.c. High Voltage Circuit Breakers Rated on a Total Current Basis.



Short-Circuit CalculationsStandard IEC 60909

IEC 60909 : Short-circuit currents in three-phase a.c. systems

Part 0: Calculation of currentsPart 1: Factors for the calculation of

short-circuit currentsPart 2: Electrical equipment; data for

short-circuit current calculations Part 3: Currents during two separate

simultaneous line-to-earth short circuits and partial short-circuit currents flowing through earth

Part 4: Examples for the calculation of short-circuit currents



Short-Circuit CalculationsScope of IEC 60909

three-phase a.c. systems low voltage and high voltage systems up to 500 kV nominal frequency of 50 Hz and 60 Hz balanced and unbalanced short circuits

three phase short circuits two phase short circuits (with and without earth connection) single phase line-to-earth short circuits in systems with solidly

earthed or impedance earthed neutral two separate simultaneous single-phase line-to-earth short circuits

in a systems with isolated neutral or a resonance earthed neutral (IEC 60909-3)

maximum short circuit currents minimum short circuit currents


E D SE PTI NC Steffen SchmidtCopyright © Siemens AG 2007. All rights reserved.

Short-Circuit Calculations Types of Short Circuits

3-phase

2-phase

1-phase



Short-Circuit Calculations Far-from-generator short circuit

Ik” Initial symmetrical short-circuit currentip Peak short-circuit current Ik Steady-state short-circuit current

A Initial value of the d.c component



Short-Circuit Calculations Definitions according IEC 60909 (I)

initial symmetrical short-circuit current Ik”r.m.s. value of the a.c. symmetrical component of a prospective (available) short-circuit current, applicable at the instant of short circuit if the impedance remains at zero-time value

initial symmetrical short-circuit power Sk”fictitious value determined as a product of the initial symmetrical short-circuit current Ik”, the nominal system voltage Un and the factor √3:

NOTE: Sk” is often used to calculate the internal impedance of a network feeder at the

connection point. In this case the definition given should be used in the following form:

"kn

"k IU3S

"k

2n

S

UcZ



Short-Circuit Calculations Definitions according IEC 60909 (II)

decaying (aperiodic) component id.c. of short-circuit currentmean value between the top and bottom envelope of a short-circuit current decaying from an initial value to zero

peak short-circuit current ip

maximum possible instantaneous value of the prospective (available) short-circuit current

NOTE: The magnitude of the peak short-circuit current varies in accordance with the

moment at which the short circuit occurs.



Short-Circuit Calculations Near-to-generator short circuit

Ik” Initial symmetrical short-circuit currentip Peak short-circuit current Ik Steady-state short-circuit currentA Initial value of the d.c componentIB Symmetrical short-circuit breaking current

tB

BI22



Short-Circuit Calculations Definitions according IEC 60909 (III)

steady-state short-circuit current Ik

r.m.s. value of the short-circuit current which remains after the decay of the transient phenomena

symmetrical short-circuit breaking current Ib

r.m.s. value of an integral cycle of the symmetrical a.c. component of the prospective short-circuit current at the instant of contact separation of the first pole to open of a switching device



Short-Circuit Calculations Purpose of Short-Circuit Values

Design Criterion Physical Effect Relevant short-circuit current

Breaking capacity of circuit

breakers

Thermal stress to arcing

chamber; arc extinction

Symmetrical short-circuit breaking current Ib

Mechanical stress to

equipment

Forces to electrical devices

(e.g. bus bars, cables…)

Peak short-circuit current ip

Thermal stress to equipment Temperature rise of electrical

devices (e.g. cables)

Initial symmetrical short-circuit current Ik”

Fault duration

Protection setting Selective detection of partial

short-circuit currents

Minimum symmetrical short-circuit current Ik

Earthing, Interference, EMC Potential rise;

Magnetic fields

Maximum initial symmetrical short-circuit current Ik”



Standard IEC 60909 Simplifications and Assumption

Assumptions

quasi-static state instead of dynamic calculation

no change in the type of short circuit during fault duration

no change in the network during fault duration

arc resistances are not taken into account

impedance of transformers is referred to tap changer in main position

neglecting of all shunt impedances except for C0

-> safe assumptions



Equivalent Voltage Source



Short-circuitEquivalent voltage source at the short-circuit location

AQ

Q A ZLZTZN

F

~

I"K3

. nUc

real network

equivalent circuit

Operational data and the passive load of consumers are neglectedTap-changer position of transformers is dispensableExcitation of generators is dispensableLoad flow (local and time) is dispensable



Short circuit in meshed gridEquivalent voltage source at the short-circuit location

real network equivalent circuit



Voltage Factor c

c is a safety factor to consider the following effects: voltage variations depending on time and place, changing of transformer taps, neglecting loads and capacitances by calculations, the subtransient behaviour of generators and motors.

Nominal voltage

Voltage factor c for calculation of

maximum short circuit currents minimum short circuit currents

Low voltage 100 V – 1000 V

-systems with a tolerance of 6%

-systems with a tolerance of 10%

1.05

1.10

0.95

0.95

Medium voltage >1 kV – 35 kV 1.10 1.00

High voltage >35 kV 1.10 1.00



Maximum and minimum Short-Circuit Currents

maximum

short circuit currents

minimum

short circuit currents

Voltage factor Cmax Cmin

Power plants Maximum contribution Minimum contribution

Network feeders Minimum impedance Maximum impedance

Motors shall be considered shall be neglected

Resistance of lines and cables at 20°C at maximum temperature



Short Circuit Impedances and Correction Factors



Short Circuit Impedances

For network feeders, transformer, overhead lines, cable etc.

impedance of positive sequence system = impedance of negative sequence system

impedance of zero sequence system usually different

topology can be different for zero sequence system

Correction factors for

generators,

generator blocks,

network transformer

factors are valid in zero, positive, negative sequence system



Network feeders

At a feeder connection point usually one of the following values is given: the initial symmetrical short circuit current Ik” the initial short-circuit power Sk”

If R/X of the network feeder is unknown, one of the following values can be used: R/X = 0.1 R/X = 0.0 for high voltage systems >35 kV fed by overhead lines

"k

2n

"k

nQ S

Uc

I3

UcZ

2

QQ

)X/R(1

ZX



Network transformer Correction of Impedance

ZTK = ZT KT

general

at known conditions of operation

no correction for impedances between star point and ground

T

maxT x6,01

c95,0K

bTrT

bTT

maxbn

T sin)II(x1

c

U

UK



Network transformer Impact of Correction Factor

The Correction factor is KT<1.0 for transformers with xT >7.5 %.

Reduction of transformer impedanceIncrease of short-circuit currents

0.80

0.85

0.90

0.95

1.00

1.05

0 5 10 15 20

xT [%]

KT

cmax = 1.10

cmax = 1.05



Generator with direct Connection to NetworkCorrection of Impedance

ZGK = ZG KG

general

for continuous operation above rated voltage:

UrG (1+pG) instead of UrG

turbine generator: X(2) = X(1)

salient pole generator: X(2) = 1/2 (Xd" + Xq")

rGd

max

rG

nG sinx1

c

U

UK



Generator Block (Power Station)Correction of Impedance

ZS(O) = (tr2 ZG +ZTHV) KS(O)

power station with on-load tap changer:

power station without on-load tap changers:

rGTd

max2rTHV

2rTLV

2rG

2nQ

S sinxx1

c

U

U

U

UK

G

Q

rGd

maxt

rTHV

rTLV

GrG

nQSO sinx1

cp1

U

U

)p1(U

UK



Asynchronous Motors

Motors contribute to the short circuit currents and have to be considered for calculation of maximum short circuit currents

If R/X is unknown, the following values can be used: R/X = 0.1 medium voltage motors power per pole pair > 1 MW R/X = 0.15 medium voltage motors power per pole pair ≤ 1 MW R/X = 0.42 low voltage motors (including connection cables)

rM

2rM

rMLRM S

U

I/I

1Z

2MM

MM

)X/R(1

ZX



Special Regulations for low Voltage Motors

low voltage motors can be neglected if ∑IrM ≤ Ik” groups of motors can be combined to a equivalent motor ILR/IrM = 5 can be used



Calculation of initial short circuit current



Calculation of initial short circuit currentProcedure

Set up equivalent circuit in symmetrical components

Consider fault conditions in 3-phase system transformation into symmetrical components

Calculation of fault currents in symmetrical components transformation into 3-phase system


E D SE PTI NC Steffen SchmidtCopyright © Siemens AG 2007. All rights reserved.

Calculation of initial short circuit currentEquivalent circuit in symmetrical components

positive sequence system

negative sequence system

zero sequence system

(1) (1) (1)

(1) (1) (1) (1)

(1)

(2)

(2)

(2)

(2)

(2)

(2) (2)

(2)

(0)(0)

(0)

(0)

(0)

(0)

(0)

(0)



Calculation of initial short circuit current3-phase short circuit

L1L2L3

~ -Uf

012-system

UL1 = – Uf

UL2 = a2 (– Uf)

UL3 = a (– Uf)

U(1) = – Uf

U(2) = 0

U(0) = 0

(1)

rsc3

3 Z

UcI

L1-L2-L3-system~ ~

Z(1)l Z(1)r

~ ~

Z(2)l Z(2)r

~ ~

Z(0)l Z(0)r

(1)

(2)

(0)

network left of fault location

network right of fault location

fault location

~ c Un

3

~~



Calculation of 2-phase initial short circuit current

L1-L2-L3-system 012-system

IL1 = 0

IL2 = – IL3

UL3 – UL2 = – Uf

I(0) = 0

I(1) = – I(2)

3n

)2()1(

UcUU

~ ~

Z(1)l Z(1)r

~ ~

Z(2)l Z(2)r

~ ~

Z(0)l Z(0)r

(1)

(2)

(0)



fault location

~ c Un

3

21

rsc2

ZZ

UcI

2

3

2 sc3

sc2

1

rsc2

I

I

Z

UcI

L1

L2

L3

~

-Uf



Calculation of 2-phase initial short circuit current with ground connection

L1-L2-L3-system 012-system

0L1 I

3n2

L2

UcaU

3n

L3

UcaU

I(0) = I(1) = I(2)

)0()1(n

)2()1(3

UUU

cUU

~ ~

Z(1)l Z(1)r

~ ~

Z(2)l Z(2)r

~ ~

Z(0)l Z(0)r

(1)

(2)

(0)



fault location

c Un

3~

01

rscE2E

2

3

ZZ

UcI

L1

L2

L3

~ -Uf



Calculation of 1-phase initial short circuit current

L1

L2

L3

L1-L2-L3-System 012-System

IL2 = 0

IL3 = 0

3n

L1

UcU

3n

)2()1()0(

UcUUU

I(0) = I(1) = I(2)

~ ~

Z(1)l Z(1)r

~ ~

Z(2)l Z(2)r

~ ~

Z(0)l Z(0)r

(1)

(2)

(0)



fault location

~c Un

3~ -Uf )0()2()1(

r"sc1

3

ZZZ

UcI



Largest initial short circuit current

Because of Z1 Z2 the largest short circuit current can be observed

for Z1 / Z0 < 1 3-phase short circuit

for Z1 / Z0 > 1 2-phase short circuit with

earth connection(current in earth connection)



Short Circuit Calculation ResultsFaults at all Buses



Short Circuit Calculation ResultsContribution for one Fault Location



Example



Data of sample calculation

Network feeder:

110 kV3 GVAR/X = 0.1

Transformer:

110 / 20 kV40 MVAuk = 15 %PkrT = 100 kVA

Overhead line:

20 kV10 kmR1’ = 0.3 Ω / kmX1’ = 0.4 Ω / km



Impedance of Network feeder

"k

2n

I S

UcZ

GVA3

kV201.1Z

2

I

1467.0ZI 0146.0RI 1460.0XI



Impedance of Transformer

n

2n

kT S

UuZ

5000.1ZT 0250.0RT 4998.1XT

MVA40

kV2015.0Z

2

T

2n

2n

krTT S

UPR

2

2

TMVA40

kV20kVA100R



Impedance of TransformerCorrection Factor

T

maxT x6.01

c95.0K

14998.06.01

1.195.0KT

95873.0KT

4381.1ZTK 0240.0RTK 4379.1XTK



Impedance of Overhead Line

'RRL

0000.3RL 0000.4XI

km10km/3.0RL

'XXL

km10km/4.0XL



Initial Short-Circuit Current – Fault location 1

TKI RRR TKI XXX

0240.00146.0R 4379.11460.0X

0386.0R 5839.1X

11

n"k

XjR3

UcI

22

"k

5839.10386.03

kV201.1I

kA0.8I"k



Initial Short-Circuit Current – Fault location 2

LTKI RRRR LTKI XXXX

0000.30240.00146.0R 0000.44379.11460.0X

0386.3R 5839.5X

11

n"k

XjR3

UcI

22

"k

5839.50386.33

kV201.1I

kA0.2I"k



Calculation of Peak Current



Peak Short-Circuit CurrentCalculation acc. IEC 60909

maximum possible instantaneous value of expected short circuit current

equation for calculation: "kp I2i

X/R3e98.002.1



Peak Short-Circuit CurrentCalculation in non-meshed Networks

The peak short-circuit current ip at a short-circuit location, fed from sources which are not meshed with one another is the sum of the partial short-circuit currents:

M

G

M

ip1 ip2 ip3 ip4

ip = ip1 + ip2 + ip3 + ip4



Peak Short-Circuit CurrentCalculation in meshed Networks

Method A: uniform ratio R/X smallest value of all network branches quite inexact

Method B: ratio R/X at the fault location factor b from relation R/X at the fault location (equation or diagram) =1,15 b

Method C: procedure with substitute frequency factor from relation Rc/Xc with substitute frequency fc = 20 Hz

best results for meshed networks

f

f

X

R

X

R c

c

c



Peak Short-Circuit CurrentFictitious Resistance of Generator

RGf = 0,05 Xd" for generators with UrG > 1 kV and SrG 100 MVA

RGf = 0,07 Xd" for generators with UrG > 1 kV and SrG < 100 MVA

RGf = 0,15 Xd" for generators with UrG 1000 V

NOTE: Only for calculation of peak short circuit current



Peak Short-Circuit Current – Fault location 1

0386.0R 5839.1X

kA0.8I"k

0244.0X/R

"kp I2i

X/R3e98.002.1

93.1

kA8.21ip



Peak Short-Circuit Current – Fault location 2

0386.3R 5839.5X

kA0.2I"k

5442.0X/R

"kp I2i

X/R3e98.002.1

21.1

kA4.3ip



Calculation of Breaking Current



Breaking CurrentDifferentiation

Differentiation between short circuits ”near“ or “far“ from generator

Definition short circuit ”near“ to generator

for at least one synchronous machine is: Ik” > 2 ∙ Ir,Generator

or Ik”with motor > 1.05 ∙ Ik”without motor

Breaking current Ib for short circuit “far“ from generator

Ib = Ik”



Breaking CurrentCalculation in non-meshed Networks

The breaking current IB at a short-circuit location, fed from sources which are not meshed is the sum of the partial short-circuit currents:

M

G

M

IB1 = μ∙I“k

IB = IB1 + IB2 + IB3 + IB4

IB2 = I“k IB3 = μ∙q∙I“kIB4 = μ∙q∙I“k



Breaking currentDecay of Current fed from Generators

IB = μ ∙ I“k

Factor μ to consider the decay of short circuit current fed from generators.



Breaking currentDecay of Current fed from Asynchronous Motors

IB = μ ∙ q ∙ I“k

Factor q to consider the decay of short circuit current fed from asynchronous motors.



Breaking CurrentCalculation in meshed Networks

Simplified calculation:

Ib = Ik”

For increased accuracy can be used:

X“diK subtransient reactance of the synchronous machine (i)

X“Mj reactance of the asynchronous motors (j)

I“kGi , I“kMj contribution to initial symmetrical short-circuit current from the synchronous machines (i)

and the asynchronous motors (j) as measured at the machine terminals

"kMjjj

j n

Mj"kGii

i n

Gi"kb I)q1(

3/Uc

"UI)1(

3/Uc

"UII

"kGi

"diK

"Gi IjXU

"kMj

"Mj

"Mj IjXU



Continuous short circuit current

Continuous short circuit current Ik

r.m.s. value of short circuit current after decay of all transient effects

depending on type and excitation of generators statement in standard only for single fed short circuit calculation by factors (similar to breaking current)

Continuous short circuit current is normally not calculated by network calculation programs.

For short circuits far from generator and as worst case estimation

Ik = I”k



Short-circuit with preload



Short-circuit with preload Principle

A Load flow calculation that considers all network parameters, such as loads, tap positions, etc.

B Place voltage source with the voltage that was determined by the load flow calculation at the fault location.

C Superposition of A and B



Short-circuit with preload Example

A Load flow calculation

B Short circuit calculation



Short-circuit with preloadResults

720V336V592.11V

1000V

192.0A168A197.37A203.95A

Short-circuit with preload

~ ~

365.37A

720V-0V

720V700V-364V336V

900. V-307.89V592.11V

1000V-0V

1000V

10A182A192A

40A208A168A

40. A157.37A197.37A

50. A153.95A203.95A

Superposition: Load flow + feed back

~ ~

365.37A

24A6.58A

720V1000V

40A40A50A

Load flow

~ ~

50A10A

2 3 2 10A 2

14780V900V

90700V

0V0V208.0A

365.3A153.95A

Short-circuit: feed back

26A3.42A

182A

780V307.89V 364V

157.37A



Break time!




Contact

Steffen SchmidtSenior ConsultantSiemens AG, Energy SectorE D SE PTI NC

Freyeslebenstr. 191058 Erlangen

Phone: +49 9131 - 7 32764Fax: +49 9131 - 7 32525

E-mail: [email protected]



Thank you for your attention!


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