copy of shortckt
TRANSCRIPT
Page 1 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
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Standards and Terms
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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
…..
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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.
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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
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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
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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
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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
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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
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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.
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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
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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
Page 15 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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”
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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
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Equivalent Voltage Source
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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
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Short circuit in meshed gridEquivalent voltage source at the short-circuit location
real network equivalent circuit
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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
Page 21 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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
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Short Circuit Impedances and Correction Factors
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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
Page 24 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
E D SE PTI NC Steffen Schmidt
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
)X/R(1
ZX
Page 25 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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
Page 26 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
E D SE PTI NC Steffen Schmidt
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
Page 27 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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
Page 28 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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
Page 29 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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
Page 30 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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
Page 31 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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Calculation of initial short circuit current
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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
Page 33 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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)
Page 34 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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
~~
Page 35 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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)
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
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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)
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
Page 37 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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)
network left of fault location
network right of fault location
fault location
~c Un
3~ -Uf )0()2()1(
r"sc1
3
ZZZ
UcI
Page 38 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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)
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Short Circuit Calculation ResultsFaults at all Buses
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Short Circuit Calculation ResultsContribution for one Fault Location
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Example
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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
Page 47 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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Impedance of Network feeder
"k
2n
I S
UcZ
GVA3
kV201.1Z
2
I
1467.0ZI 0146.0RI 1460.0XI
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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
Page 49 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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Impedance of TransformerCorrection Factor
T
maxT x6.01
c95.0K
14998.06.01
1.195.0KT
95873.0KT
4381.1ZTK 0240.0RTK 4379.1XTK
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Impedance of Overhead Line
'RRL
0000.3RL 0000.4XI
km10km/3.0RL
'XXL
km10km/4.0XL
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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
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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
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Calculation of Peak Current
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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
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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
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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
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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
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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
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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
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Calculation of Breaking Current
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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”
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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
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Breaking currentDecay of Current fed from Generators
IB = μ ∙ I“k
Factor μ to consider the decay of short circuit current fed from generators.
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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.
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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
Page 66 28.06.2008Copyright © Siemens AG 2008. All rights reserved.
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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
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Short-circuit with preload
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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
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Short-circuit with preload Example
A Load flow calculation
B Short circuit calculation
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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
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Break time!
Copyright © Siemens AG 2008. All rights reserved.
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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]
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