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Copyright © Siemens AG 2008. All rights reserved.
Page 1 28.06.2008 Steffen Schmidt E D SE PTI NC

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 Calculation
Standards

 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 Calculations
Standard IEC 60909

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

Part 0: Calculation of currents
Part 1: Factors for the calculation of
short-circuit currents
Part 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


Scope 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


Types of Short Circuits

3-phase

2-phase

1-phase

Copyright © 2008.

Variation of short circuit current shapes

fault at voltage peak fault at voltage
zero crossing

fault located in
the network

fault located
near generator


Far-from-generator short circuit

Ik” Initial symmetrical short-circuit current
ip Peak short-circuit current
Ik Steady-state short-circuit current
A Initial value of the d.c component


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:

Sk = 3 ⋅ Un ⋅ Ik
" "

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:

c ⋅ Un2
Z= "
Sk

Definitions according IEC 60909 (II)

decaying (aperiodic) component id.c. of short-circuit current
mean 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.


Near-to-generator short circuit

Ik” Initial symmetrical short-circuit current
ip Peak short-circuit current
Ik Steady-state short-circuit current
A Initial value of the d.c component
IB Symmetrical short-circuit breaking current

2 ⋅ 2 ⋅ IB

tB


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


Purpose of Short-Circuit Values

Design Criterion Physical Effect Relevant short-circuit current

Breaking capacity of circuit Thermal stress to arcing Symmetrical short-circuit
breakers chamber; arc extinction breaking current Ib
Mechanical stress to Forces to electrical devices Peak short-circuit current ip
equipment (e.g. bus bars, cables…)
Thermal stress to equipment Temperature rise of electrical Initial symmetrical short-
devices (e.g. cables) circuit current Ik”
Fault duration
Protection setting Selective detection of partial Minimum symmetrical short-
short-circuit currents circuit current Ik
Earthing, Interference, EMC Potential rise; Maximum initial symmetrical
Magnetic fields 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-circuit
Equivalent voltage source at the short-circuit location

real network
Q A F

equivalent circuit
ZN Q ZT A ZL

~
c.U n
I"K
3

Operational data and the passive load of consumers are neglected
Tap-changer position of transformers is dispensable
Excitation of generators is dispensable
Load flow (local and time) is dispensable

Short circuit in meshed grid
Equivalent 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.

Voltage factor c for calculation of
Nominal voltage maximum short circuit currents minimum short circuit currents

Low voltage 100 V – 1000 V
-systems with a tolerance of 6% 1.05 0.95
-systems with a tolerance of 10% 1.10 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 minimum
short circuit currents 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”

c ⋅ Un c ⋅ Un2
ZQ = = "
3 ⋅ Ik
"
Sk

ZQ
XQ =
1 + (R / X)2

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

Network transformer
Correction of Impedance

ZTK = ZT KT

 general
c max
K T = 0,95 ⋅
1 + 0,6 ⋅ x T

 at known conditions of operation
U c max
KT = n ⋅
Ub 1 + x T (Ib IrT ) sin ϕb
T T

no correction for impedances between star point and ground

Network transformer
Impact of Correction Factor

1.05

1.00

0.95
KT

0.90
cmax = 1.10
0.85 cmax = 1.05

0.80
0 5 10 15 20
xT [%]
The Correction factor is KT<1.0 for transformers with xT >7.5 %.

Reduction of transformer impedance
Increase of short-circuit currents


Generator with direct Connection to Network

ZGK = ZG KG

 general

Un c max
KG = ⋅
UrG 1 + x′′ ⋅ sin ϕrG
d

 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")

Generator Block (Power Station)

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

 power station with on-load tap changer:
2 2
UnQ UrTLV c max
KS = 2 ⋅ 2 ⋅
UrG UrTHV 1 + x′′ − x T ⋅ sin ϕrG
d

 power station without on-load tap changers:
UnQ U c max
K SO = ⋅ rTLV ⋅ (1 ± p t ) ⋅
UrG (1 + pG ) UrTHV 1 + x′′ ⋅ sin ϕrG
d


Asynchronous Motors

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

2
1 UrM
ZM = ⋅
ILR / IrM SrM

ZM
XM =
1 + (RM / XM )2

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)

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


Procedure

 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


Equivalent circuit in symmetrical components

(1) (1) (1)

(1) (1) (1) (1)
(1)
positive sequence system

(2) (2) (2)
(2)
(2) (2) (2) (2)
negative sequence system

(0)
(0) (0)
(0)
(0) (0)
(0) (0)
zero sequence system

Copyright © 2008.

3-phase short circuit
L1-L2-L3-system Z(1)l
012-system Z(1)r
L1 ~ ~
L2 ~ c Un (1)
√3
L3
Z(2)l Z(2)r
~ ~ ~ -Uf ~ ~
c ⋅ Ur
′′
I sc3 = (2)
3 ⋅ Z (1)
Z(0)l Z(0)r
~ ~
(0)

network left of fault location network right of
UL1 = – Uf fault location fault location
U(1) = – Uf
UL2 = a2 (– Uf)
U(2) = 0
UL3 = a (– Uf)
U(0) = 0

Calculation of 2-phase initial short circuit current

L1-L2-L3-system Z(1)l
012-system Z(1)r
L1 ~ ~
L2 ~ c Un (1)
L3 √3
~

Z(2)l Z(2)r
-Uf c ⋅U r ~ ~
′′
I sc2 = (2)
Z ( 1) + Z ( 2 )
Z(0)l Z(0)r
~ ~
c ⋅U r ′′
I sc2 3
′′
I sc2 = ⇒ = (0)
2 Z ( 1) ′′
I sc3 2
network left of network right of
IL1 = 0 U fault location
U (1) − U ( 2 ) = −c n fault location fault location
3
IL2 = – IL3 I(0) = 0

UL3 – UL2 = – Uf I(1) = – I(2)

with ground connection

L1-L2-L3-system 012-system
Z(1)l Z(1)r
~ ~
L1
~ c Un (1)
L2
√3
L3
Z(2)l Z(2)r
~ ~
~ 3⋅ c ⋅ U r
-Uf ′′
I scE2E = (2)
Z ( 1) + 2 Z ( 0 )
Z(0)l Z(0)r
~ ~
(0)

I L1 = 0
fault location
2 Un fault location fault location
U L2 = − a c
3 Un
U (1) − U ( 2) = − c = U (1) − U ( 0)
Un 3
U L3 = − a c
3 I(0) = I(1) = I(2)


L1-L2-L3-System Z(1)l 012-System Z(1)r
~ ~
(1)
L1
L2
Z(2)l Z(2)r
L3
~ ~
3⋅ c ⋅ U r c Un
I sc1 =
"
~
(2)
~ -Uf Z (1) + Z ( 2 ) + Z ( 0 ) √3

Z(0)l Z(0)r
~ ~
(0)

fault location
Un fault location fault location
U L1 = − c
3 Un
U ( 0) + U (1) + U ( 2) = − c
IL2 = 0 3
I(0) = I(1) = I(2)
IL3 = 0

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)


Feeding of short circuits

single fed short circuit

"
I sc
ür:1 k3
S"
kQ
UnQ

multiple fed short circuit
G
3~

M
3~

∑ I sc_part ≅ ∑ I sc_part
"
I“scG I“scN I“scM I sc =
" "

Fault


Calculation of short circuit currents by programs (1/3)

Basic equation
i=Yu Y: matrix of admittances (for short circuit)

0  Y 11 . . . . Y 1n   U1 
0  Y  U 
   21 . . . . Y 2n 
  2 
 .   . .   . 
     
.  . 
  . .  
 .   . .   . 
 ''  =    Ur 
 I sci   Y i1 . . . . Y in  − c ⋅ 
 3
 .   . . 
     . 
 .   . .   . 
 .   .  
.   . 
   
0 
  Y n1
 . . . . Y nn 
  U 
 n 



Inversion of matrix of admittances
u = Y-1 i

 U1   Z 11 . . . . Z 1n  0 
 U  Z
 2   21 . . . . Z 2n 

0 
 
 .   . .   . 
     
. 
  . .   . 
 .   . .   . 
 Ur  =    '' 
− c ⋅   Z i1 . Z ii . . Z in   I sci 
 3
 . .   . 
 .     
 .   . .   . 
   .
 .  .   . 
   
 U   Z n1
 . . . . Z nn 
 0 
 
 n 



from line i:
− c Ur "
⇒I " = − c U r
= Z ii ⋅ I sci
3 sci
3 ⋅ Z ii

from the remaining lines:

"
U sc = Z sci ⋅ I sci

 calculation of all node voltages
 from there -> calculation of all short circuit currents


Short Circuit Calculation Results
Faults at all Buses


Short Circuit Calculation Results
Contribution for one Fault Location


Example


Data of sample calculation

Network feeder: Transformer: Overhead line:

110 kV 110 / 20 kV 20 kV
3 GVA 40 MVA 10 km
R/X = 0.1 uk = 15 % R1’ = 0.3 Ω / km
PkrT = 100 kVA X1’ = 0.4 Ω / km


Impedance of Network feeder

c ⋅ Un2
ZI = "
Sk

1.1⋅ ( 20 kV )
2

ZI =
3 GVA

ZI = 0.1467 Ω RI = 0.0146 Ω XI = 0.1460 Ω


Impedance of Transformer

2
Un 2
Un
Z T = uk ⋅ R T = PkrT ⋅ 2
Sn Sn
( 20 kV ) 2 ( 20 kV ) 2
Z T = 0.15 ⋅ R T = 100 kVA ⋅
40 MVA ( 40 MVA ) 2

Z T = 1.5000 Ω R T = 0.0250 Ω X T = 1.4998 Ω


Impedance of Transformer
Correction Factor

c max
K T = 0.95 ⋅
1 + 0.6 ⋅ x T
1 .1
K T = 0.95 ⋅
1 + 0.6 ⋅ 0.14998

K T = 0.95873

Z TK = 1.4381 Ω R TK = 0.0240 Ω X TK = 1.4379 Ω


Impedance of Overhead Line

RL = R'⋅ XL = X'⋅

RL = 0.3 Ω / km ⋅ 10 km XL = 0.4 Ω / km ⋅ 10 km

RL = 3.0000 Ω XI = 4.0000 Ω


Initial Short-Circuit Current – Fault location 1

R = RI + R TK X = XI + X TK
R = 0.0146 Ω + 0.0240 Ω X = 0.1460 Ω + 1.4379 Ω
R = 0.0386 Ω X = 1.5839 Ω
c ⋅ Un
Ik =
"

3 ⋅ ( R1 + j ⋅ X1 )
1.1⋅ 20 kV
Ik =
"

3⋅ ( 0.0386 Ω ) 2 + (1.5839 Ω ) 2
Ik = 8.0 kA
"


Initial Short-Circuit Current – Fault location 2

R = RI + R TK + RL X = XI + X TK + XL
R = 0.0146 Ω + 0.0240 Ω + 3.0000 Ω X = 0.1460 Ω + 1.4379 Ω + 4.0000 Ω
R = 3.0386 Ω X = 5.5839 Ω
c ⋅ Un
Ik =
"

3 ⋅ ( R1 + j ⋅ X1 )
1.1⋅ 20 kV
Ik =
"

3⋅ ( 3.0386 Ω ) 2 + ( 5.5839 Ω) 2
Ik = 2.0 kA
"


Calculation of Peak Current


Peak Short-Circuit Current
Calculation acc. IEC 60909

maximum possible instantaneous value of expected short circuit current

equation for calculation: ip = κ ⋅ 2 ⋅ Ik
"

κ = 1.02 + 0.98 ⋅ e −3R / X


Calculation 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:


Calculation 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 κb from relation R/X at the fault location (equation or diagram)
 κ =1,15 κb

Method C: procedure with substitute frequency
 factor κ from relation Rc/Xc with substitute frequency fc = 20 Hz
R R c fc
 = ⋅
X Xc f
 best results for meshed networks


Fictitious 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

Ik = 8.0 kA
"

R = 0.0386 Ω X = 1.5839 Ω

R / X = 0.0244
κ = 1.02 + 0.98 ⋅ e −3R / X
κ = 1.93

ip = κ ⋅ 2 ⋅ Ik
"

ip = 21.8 kA


Peak Short-Circuit Current – Fault location 2

Ik = 2.0 kA
"

R = 3.0386 Ω X = 5.5839 Ω

R / X = 0.5442
κ = 1.02 + 0.98 ⋅ e −3R / X
κ = 1.21

ip = κ ⋅ 2 ⋅ Ik
"

ip = 3.4 kA


Calculation of Breaking Current


Breaking Current
Differentiation

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 Current
Calculation 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:


Breaking current
Decay of Current fed from Generators

 IB = μ ∙ I“k

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


Breaking current
Decay 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 Current
Calculation in meshed Networks

Simplified calculation:

Ib = Ik”

For increased accuracy can be used:
∆U"Gi ∆U"Mj
Ib = I − ∑ ⋅ (1 − µi ) ⋅ IkGi − ∑
" " "
k ⋅ (1 − µ jq j ) ⋅ IkMj
i c ⋅ Un / 3 j c ⋅ Un / 3

" "
"
∆UGi = jX " ⋅ IkGi
diK
"
∆UMj = jXMj ⋅ IkMj
"

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


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


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


Example

A Load flow calculation

B Short circuit calculation


Results

Load flow Superposition: Load flow + feed back
50. A 40. A 40A 10A
153.95A 157.37A 208A 182A
2Ω 50A 40A 3 Ω 40A 2Ω 10A 2Ω 203.95A 197.37A 168A 192A

1000V 720V
10A 50A
1000V -0V -0V
720V 1000V 720V
900V 780V 700V 900. V 700V
90 Ω 14 Ω ~
-307.89V -364V
~ ~ 592.11V 336V ~
365.37A

Short-circuit: feed back Short-circuit with preload
153.95A 365.3A 182A 203.95A 197.37A 168A 192.0A

157.37A 208.0A 26A
0V 3.42A 1000V 6.58A 24A
0V
720V
592.11V 336V
307.89V 780V 364V ~ ~
365.37A


Contact

Steffen Schmidt
Senior Consultant
Siemens AG, Energy Sector
E D SE PTI NC

Freyeslebenstr. 1
91058 Erlangen

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

E-mail: steffen.schmidt@siemens.com


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