Short circuit calculations
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
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
Short-Circuit Calculations
Types of Short Circuits
3-phase
2-phase
1-phase
Copyright © Siemens AG 2007. All rights reserved.
Variation of short circuit current shapes
fault at voltage peak
fault located in
the network
fault located
near generator
fault at voltage
zero crossing
Short-Circuit Calculations
Far-from-generator short circuit
Ik”
ip
Ik
A
Initial symmetrical short-circuit current
Peak short-circuit current
Steady-state short-circuit current
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
S" factor
 3 √3:
 U  I"
k
•
n
k
NOTE: Sk” is often used to calculate the internal impedance of a network feeder at the connection
point. In this
2 case the definition given should be used in the following form:
c  Un
Z
Sk"
Short-Circuit Calculations
Definitions according IEC 60909 (II)
• decaying (aperiodic) component id.c. of short-circuit current
• mean value between the top and bottom envelope of a shortcircuit 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”
ip
Ik
A
IB
Initial symmetrical short-circuit current
Peak short-circuit current
Steady-state short-circuit current
Initial value of the d.c component
Symmetrical short-circuit breaking current
2  2  IB
tB
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 Initial symmetrical shortdevices (e.g. cables)
circuit current Ik”
Fault duration
Selective detection of partial Minimum symmetrical shortshort-circuit currents
circuit current Ik
Protection setting
Earthing, Interference, EMC
Potential rise;
Magnetic fields
Maximum initial symmetrical
short-circuit current Ik”
Equivalent Voltage Source
Short-circuit
Equivalent voltage source at the shortcircuit location
real network
Q
A
F
equivalent circuit
ZN
Q
ZT
A
ZL
~
I"K
c.U n
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
-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
Low voltage 100 V – 1000 V
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 U n
c U n2
ZN 
 "
"
Sk
3  Ik
XN 
•
ZN
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
KT 
c max
Un

Ub 1  x T (IbT IrT ) sinbT
• no correction for impedances between star point and ground
Network transformer
Impact of Correction Factor
1.05
1.00
KT
0.95
0.90
cmax = 1.10
cmax = 1.05
0.85
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
Correction of Impedance
ZGK = ZG KG
– general
KG 
c max
Un

UrG 1  xd  sinrG
– 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)
Correction of Impedance
2
ZS(O) = (tr ZG +ZTHV) KS(O)
Q
G
– power station with on-load tap changer:
2
2
UnQ
c max
UrTLV
KS  2  2 
UrG UrTHV 1  xd  x T  sinrG
– power station without on-load tap changers:
K SO 
UnQ
c max
U
 rTLV  1  p t  
UrG (1  pG ) UrTHV
1  xd  sinrG
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
XM 
•
ZM
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
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
Calculation of initial short circuit current
Equivalent circuit in symmetrical components
(1)
(0)
(1)
(1)
(1)
(2)
(2)
(2)
(2)
(1)
(1)
(1)
positive sequence system
(2)
negative sequence system
(1)
(2)
(2)
(2)
(0)
(0)
(0)
(0)
(0)
(0)
(0)
zero sequence system
Copyright © Siemens AG 2007. All rights reserved.
Calculation of initial short circuit current
3-phase short circuit
L1-L2-L3-system
Z(1)l
L1
L2
L3
~ ~ ~ -Uf
012-system
~
~
~
 
I sc3
c  Ur
3  Z (1)
Z(1)r
c Un
3
(1)
Z(2)l
Z(2)r
~
~
(2)
Z(0)l
Z(0)r
~
~
(0)
UL1 =
– Uf
UL2 = a2 (– Uf)
UL3 = a
(– Uf)
network left of
fault location
fault location
U(1) = – Uf
U(2) = 0
U(0) = 0
network right of
fault location
Calculation of 2-phase initial short circuit current
L1-L2-L3-system
Z(1)l
012-system
~
L1
L3
~
c U r
 
I sc2
Z 1  Z 2 
-Uf
 
I sc2
~
~
L2
c U r
2 Z 1


I sc2
3


I sc3
2
U
 c n
3
IL1 = 0
U (1)  U ( 2)
IL2 = – IL3
I(0) = 0
UL3 – UL2 = – Uf
I(1) = – I(2)
Z(1)r
c Un
(1)
3
Z(2)l
Z(2)r
~
~
(2)
Z(0)l
Z(0)r
~
~
(0)
network left of
fault location
fault location
network right of
fault location
Calculation of 2-phase initial short circuit
current with ground connection
L1-L2-L3-system
Z(1)l
012-system
Z(1)r
~
L1
~
~
L2
c Un
(1)
3
L3
~

I scE2E
-Uf
3 c U r

Z 1  2Z 0 
Z(2)l
Z(2)r
~
~
(2)
Z(0)l
Z(0)r
~
~
(0)
I L1  0
U L2   a c
2
U L3   a c
Un
3
Un
3
network left of
fault location
U (1)  U ( 2)   c
fault location
Un
3
network right of
fault location
 U (1)  U (0)
I(0) = I(1) = I(2)
Calculation of 1-phase initial short circuit current
L1-L2-L3-System
Z(1)l
012-System
Z(1)r
~
~
(1)
L1
L2
L3
~
"
I sc1

-Uf
3 c U r
Z (1)  Z ( 2)  Z ( 0)
Z(2)l
Z(2)r
~
~
c Un
3
(2)
~
Z(0)l
Z(0)r
~
~
(0)
U L1   c
IL2 = 0
IL3 = 0
Un
3
network left of
fault location
fault location
U (0)  U (1)  U ( 2)   c
I(0) = I(1) = I(2)
network right of
fault location
Un
3
Short Circuit Calculation Results
Faults at all Buses
Short Circuit Calculation Results
Contribution for one Fault Location
Example
Data of sample calculation
• Network
feeder:
• 110 kV
• 3 GVA
• R/X = 0.1
Transformer:
Overhead line:
110 / 20 kV
40 MVA
uk = 15 %
PkrT = 100 kVA
20 kV
10 km
R1’ = 0.3 Ω / km
X1’ = 0.4 Ω / km
Impedance of Network feeder
c  Un2
ZI 
Sk"
1.1 20 kV 
ZI 
3 GVA
2
ZI  0.1467 
RI  0.0146 
XI  0.1460 
Impedance of Transformer
Un2
Z T  uk 
Sn
Z T  0.15 
20 kV 2
40 MVA
ZT  1.5000 
Un2
R T  PkrT  2
Sn
20 kV 2
RT  100 kVA 
40MVA 2
RT  0.0250 
XT  1.4998 
Impedance of Transformer
Correction Factor
K T  0.95 
c max
1  0.6  x T
K T  0.95 
1.1
1  0.6  0.14998
K T  0.95873
ZTK  1.4381
RTK  0.0240 
XTK  1.4379 
Impedance of Overhead Line
RL  R'
XL  X'
RL  0.3  / km  10 km
XL  0.4  / km  10 km
RL  3.0000 
XI  4.0000 
Initial Short-Circuit Current – Fault location 1
R  RI  RTK
X  XI  XTK
R  0.0146  0.0240
X  0.1460  1.4379
R  0.0386
X  1.5839
Ik" 
Ik" 
c  Un
3  R1  j  X1 
1.1 20 kV
3
0.03862  1.58392
Ik"  8.0 kA
Initial Short-Circuit Current – Fault location 2
R  RI  RTK  RL
X  XI  XTK  XL
R  0.0146  0.0240  3.0000
X  0.1460  1.4379  4.0000
R  3.0386
X  5.5839
Ik" 
Ik" 
c  Un
3  R1  j  X1 
1.1 20 kV
3
3.0386 2  5.58392
Ik"  2.0 kA
Peak current
Peak Short-Circuit Current
Calculation acc. IEC 60909
• maximum possible instantaneous value of expected short
"
i



2

I
circuit current
p
k
  1.02  0.98  e3R / X
• equation for calculation:
Peak Short-Circuit Current
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:
M
G
M
ip1
ip2
ip3
ip = ip1 + ip2 + ip3 + ip4
ip4
Peak Short-Circuit Current
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 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
R Rc fc


–
X Xc f
– best results for meshed networks
Peak Short-Circuit Current
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
X  1.5839
R / X  0.0244
  1.02  0.98  e3R / X
  1.93
ip    2  Ik"
ip  21.8 kA
Peak Short-Circuit Current – Fault location 2
Ik"  2.0 kA
R  3.0386
X  5.5839
R / X  0.5442
  1.02  0.98  e3R / X
  1.21
ip    2  Ik"
ip  3.4 kA
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:
M
G
M
IB1 = μ∙I“k
IB2 = I“k
IB3 = μ∙q∙I“k
IB = IB1 + IB2 + IB3 + IB4
IB4 = μ∙q∙I“k
Breaking current
Decay
Current
fed from Generators
 IB =of
μ ∙ I“
k
Factor μ to consider the decay of short circuit current fed from
generators.
Breaking current
Decay
fed from Asynchronous Motors
 IB =of
μ ∙Current
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:
I b = I k”
•
For increased accuracy can be used:
U"Mj
U"Gi
"
"
Ib  I  
 (1   i )  IkGi  
 (1   jq j )  IkMj
i c  Un / 3
j c  Un / 3
"
k
UGi  jX"diK  IkGi
"
•
•
•
"
"
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)
asynchronous motors (j) as measured at the machine terminals
and the
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