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Short circuit calculations
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
Copyright © Siemens AG 2007. All rights reserved.
Short-Circuit Calculations Types of Short Circuits
3-phase
2-phase
1-phase
Variation of short circuit current shapes
fault at voltage peak fault at voltage zero crossing
fault located in the network
fault located near generator
Short-Circuit Calculations 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
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
2
n
S
UcZ
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 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 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
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”
Equivalent Voltage Source
Short-circuit Equivalent 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 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.
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
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
"
2
"3 k
n
k
nN
S
Uc
I
UcZ
2)/(1 XR
ZX N
N
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
b
TrT
b
TT
max
b
nT
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 impedance Increase 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 Network Correction 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
max
2
rTHV
2
rTLV
2
rG
2
nQS
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
2
rM
rMLR
MS
U
I/I
1Z
2
MM
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 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
Copyright © Siemens AG 2007. All rights reserved.
Calculation of initial short circuit current Equivalent 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 current 3-phase short circuit
L1 L2 L3
~ -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)
3
n)2()1(
UcUU
~ ~
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
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
3
n2
L2
UcaU
3
nL3
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)
network left of
fault location
network right of
fault location 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
3
nL1
UcU
3
n)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)
network left of
fault location
network right of
fault location fault location
~ c Un
3
~ -Uf )0()2()1(
r"
sc1
3
ZZZ
UcI
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:
110 / 20 kV
40 MVA
uk = 15 %
PkrT = 100 kVA
Overhead line:
20 kV
10 km
R1’ = 0.3 Ω / km
X1’ = 0.4 Ω / km
Impedance of Network feeder
"
k
2
nI
S
UcZ
GVA3
kV201.1Z
2
I
1467.0ZI 0146.0RI 1460.0XI
Impedance of Transformer
n
2
nkT
S
UuZ
5000.1ZT 0250.0RT 4998.1XT
MVA40
kV2015.0Z
2
T
2
n
2
nkrTT
S
UPR
2
2
TMVA40
kV20kVA100R
Impedance of Transformer Correction 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"
kXjR3
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"
kXjR3
UcI
22
"
k
5839.50386.33
kV201.1I
kA0.2I"k
Peak current
Peak Short-Circuit Current Calculation acc. IEC 60909
• maximum possible instantaneous value of expected short circuit current
• equation for calculation:
"
kp I2i
X/R3e98.002.1
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 ip4
ip = ip1 + ip2 + ip3 + 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
–
– best results for meshed networks
f
f
X
R
X
R c
c
c
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
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
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
IB = IB1 + IB2 + IB3 + IB4
IB2 = I“k IB3 = μ∙q∙I“kIB4 = μ∙q∙I“k
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:
• 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
"
kMjjjj n
Mj"
kGiii 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
