Short Circuit Calculation Sector Energy D SE PTI NC Steffen Schmidt
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Standards and Terms
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Steffen Schmidt
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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 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. Page 4
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Short-Circuit Calculations Standard IEC 60909 IEC 60909 : Short-circuit currents in threephase a.c. systems Part 0: Part 1: Part 2: Part 3:
Part 4:
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Calculation of currents Factors for the calculation of short-circuit currents Electrical equipment; data for short-circuit current calculations Currents during two separate simultaneous line-to-earth short circuits and partial short-circuit currents flowing through earth Examples for the calculation of short-circuit currents Copyright © Siemens AG 2008. All rights reserved. E D SE PTI NC
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
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Short-Circuit Calculations Types of Short Circuits
3-phase
2-phase
1-phase
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Variation of short circuit current shapes
fault at voltage peak
fault at voltage zero crossing
fault located in the network
fault located near generator
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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
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Steffen Schmidt
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 shortcircuit 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" Page 10
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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.
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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
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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
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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 Initial symmetrical shortcircuit current Ik” devices (e.g. cables) Fault duration Selective detection of partial Minimum symmetrical shortcircuit current Ik short-circuit currents
Protection setting Earthing, Interference, EMC
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Potential rise; Magnetic fields
Steffen Schmidt
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-circuit Equivalent voltage source at the short-circuit 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 Page 17
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Short circuit in meshed grid Equivalent voltage source at the short-circuit location real network
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equivalent circuit
Steffen Schmidt
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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. 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
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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
at 20°C
at maximum temperature
Resistance of lines and cables
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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
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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 = = " Sk" 3 ⋅ Ik XQ =
ZQ 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 Page 23
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Network transformer Correction of Impedance
ZTK = ZT KT general
c max K T = 0,95 ⋅ 1 + 0,6 ⋅ x T
at knownUconditions c max of operation K T = nb ⋅ U 1 + x T (IbT IrT ) sin ϕbT
no correction for impedances between star point and ground Page 24
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Steffen Schmidt
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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 KT7.5 %. Reduction of transformer impedance Increase of short-circuit currents Page 25
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Generator with direct Connection to Network Correction of Impedance
ZGK = ZG KG general KG =
Un c max ⋅ UrG 1 + x′d′ ⋅ sin ϕrG
for continuous operation above rated voltage: UrG (1+pG) instead of UrG turbine generator:
X(2) = X(1)
salient pole generator:
X(2) = 1/2Copyright (Xd" + Siemens Xq") AG 2008. All rights reserved.
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©
Steffen Schmidt
E D SE PTI NC
Generator Block (Power Station) Correction of Impedance Q
ZS(O) = (tr2 ZG +ZTHV) KS(O)
G
power station with on-load tap changer: 2 2 UnQ UrTLV c max KS = 2 ⋅ 2 ⋅ UrG UrTHV 1 + x′d′ − x T ⋅ sin ϕrG
power station without on-load tap changers: UnQ U c max K SO = ⋅ rTLV ⋅ (1 ± p t ) ⋅ UrG (1 + pG ) UrTHV 1 + x′d′ ⋅ sin ϕrG
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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
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) Page 28
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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
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Calculation of initial short circuit current
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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
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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)
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(0)
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(0)
(0)
Steffen Schmidt
zero sequence system
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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 =
network left of fault location
– Uf
U(1) = – Uf
UL2 = a2 (– Uf) UL3 = a Page 33
network right of fault location
U(2) = 0
(– Uf)
28.06.2008
fault location
U(0) = 0 Steffen Schmidt
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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
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)
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~
~
L2
Steffen Schmidt
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
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Calculation of 2-phase initial short circuit current with ground connection L1-L2-L3-system
Z(1)l
012-system
~
L1
~
~
L2 L3
~
′′ I scE2E
-Uf
Z(1)r
3⋅ c ⋅ U r = Z ( 1) + 2 Z ( 0 )
c Un
(1)
√3
Z(2)l
Z(2)r
~
~ (2)
Z(0)l
Z(0)r
~
~ (0)
I L1 = 0 2
U L2 = − a c U L3 = − a c Page 35
network left of fault location
Un 3
U (1) − U ( 2) = − c
Un 3
28.06.2008
fault location
Un 3
network right of fault location
= U (1) − U ( 0)
I(0) = I(1) = I(2) Steffen Schmidt
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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
network left of fault location
Un 3
U ( 0) + U (1) + U ( 2) = − c
IL2 = 0
network right of fault location
Un 3
I(0) = I(1) = I(2)
IL3 = 0 Page 36
fault location
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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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Feeding of short circuits single fed short circuit
S"kQ
I sc"
k3
ür:1
UnQ
multiple fed short circuit G 3~ M 3~ I“scG
I“scN
I sc" =
I“scM
" ∑ I sc_part ≅ ∑ I sc_part "
Fault Page 38
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Calculation of short circuit currents by programs (1/3) Basic equation i=Yu Y: matrix of admittances (for short circuit) 0 Y 11 0 Y 21 . . . . . . '' = I sci Y i1 . . . . . . 0 Y n1
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. .
. .
. .
.
.
.
.
.
.
. Y 1n . Y 2n . . . . Y in . . . . Y nn
U1 U 2 . . . Ur − c ⋅ 3 . . . U n
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Calculation of short circuit currents by programs (2/3) Inversion of matrix of admittances u = Y-1 i U1 U 2 . . . Ur = − c ⋅ 3 . . . U n
Page 40
Z 11 Z 21 . . . Z i1 . . . Z n1
28.06.2008
. .
. .
. .
. .
.
Z ii
.
.
.
.
.
.
Z 1n Z 2n . . . Z in . . . Z nn
Steffen Schmidt
0 0 . . . '' I sci . . . 0 Copyright © Siemens AG 2008. All rights reserved. E D SE PTI NC
Calculation of short circuit currents by programs (3/3)
from line i: − c Ur " = Z ii ⋅ I sci 3
⇒I " = − c U r 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
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Short Circuit Calculation Results Faults at all Buses
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Short Circuit Calculation Results Contribution for one Fault Location
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Example
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Data of sample calculation
Network feeder:
Transformer:
Overhead line:
110 kV 3 GVA R/X = 0.1
110 / 20 kV 40 MVA uk = 15 % PkrT = 100 kVA
20 kV 10 km R1’ = 0.3 Ω / km X1’ = 0.4 Ω / km
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Impedance of Network feeder
c ⋅ Un2 ZI = Sk" 1.1⋅ ( 20 kV ) ZI = 3 GVA
2
ZI = 0.1467 Ω
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RI = 0.0146 Ω
Steffen Schmidt
XI = 0.1460 Ω
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Impedance of Transformer
Un2 Z T = uk ⋅ Sn Z T = 0.15 ⋅
( 20 kV ) 2 40 MVA
Z T = 1.5000 Ω
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28.06.2008
Un2 R T = PkrT ⋅ 2 Sn
( 20 kV ) 2 R T = 100 kVA ⋅ ( 40 MVA ) 2 R T = 0.0250 Ω
Steffen Schmidt
X T = 1.4998 Ω
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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 Z TK = 1.4381 Ω
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R TK = 0.0240 Ω
Steffen Schmidt
X TK = 1.4379 Ω
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Impedance of Overhead Line
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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
Steffen Schmidt
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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 Ik" = Ik" =
c ⋅ Un 3 ⋅ ( R1 + j ⋅ X1 ) 1.1⋅ 20 kV 3⋅
( 0.0386 Ω ) 2 + (1.5839 Ω ) 2
Ik" = 8.0 kA Page 50
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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 Ik" = Ik" =
c ⋅ Un 3 ⋅ ( R1 + j ⋅ X1 ) 1.1⋅ 20 kV 3⋅
( 3.0386 Ω ) 2 + ( 5.5839 Ω) 2
Ik" = 2.0 kA Page 51
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Calculation of Peak Current
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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
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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
i p = ip1 + ip2 + ip3 + ip4 Page 54
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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 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 Page 55
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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
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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
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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
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Calculation of Breaking Current
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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”
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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
I B4 = μ∙q∙I“ k
I B = IB1 + I B2 + IB3 + IB4 Page 61
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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.
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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.
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Breaking Current Calculation in meshed Networks Simplified calculation: Ib = Ik” For increased accuracy can be used: ∆U"Mj ∆U"Gi " " Ib = I − ∑ ⋅ (1 − µi ) ⋅ IkGi − ∑ ⋅ (1 − µ jq j ) ⋅ IkMj i c ⋅ Un / 3 j c ⋅ Un / 3 " k
"
"
∆UGi = jX "diK ⋅ IkGi
X“diK X“Mj I“kGi , I“kMj
"
"
" ∆UMj = jXMj ⋅ IkMj
subtransient reactance of the synchronous machine (i) reactance of the asynchronous motors (j) contribution to initial symmetrical short-circuit current from the synchronous machines (i) and the asynchronous motors (j) as measured at the machine terminals
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Steffen Schmidt
Copyright © Siemens AG 2008. All rights reserved. E D SE PTI NC
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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Steffen Schmidt
Copyright © Siemens AG 2008. All rights reserved. E D SE PTI NC
Short-circuit with preload
Page 66
28.06.2008
Steffen Schmidt
Copyright © Siemens AG 2008. All rights reserved. E D SE PTI NC
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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28.06.2008
Steffen Schmidt
Copyright © Siemens AG 2008. All rights reserved. E D SE PTI NC
Short-circuit with preload Example A Load flow calculation
B Short circuit calculation
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28.06.2008
Steffen Schmidt
Copyright © Siemens AG 2008. All rights reserved. E D SE PTI NC
Short-circuit with preload Results
Load flow 2Ω 50A
40A 3 Ω
40A
Superposition: Load flow + feed back 2Ω
10A 2Ω 50A
10A
1000V
50. A 153.95A 203.95A
720V 900V ~
90 Ω
780V
700V
14 Ω
1000V -0V 1000V
~
40. A 157.37A 197.37A
40A 208A 168A
900. V -307.89V 592.11V
~
10A 182A 192A 720V -0V 720V
700V -364V 336V
~
365.37A
Short-circuit: feed back 153.95A 0V
3.42A
203.95A
182A
365.3A 157.37A
307.89V
Short-circuit with preload
208.0A
780V
26A
0V
197.37A 6.58A
1000V
592.11V
364V
168A
192.0A 24A 720V
336V ~
~ 365.37A
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Steffen Schmidt
Copyright © Siemens AG 2008. All rights reserved. E D SE PTI NC
Break time!
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Steffen Schmidt
Copyright Copyright©© Siemens AG 2008. All rights reserved. E D SE PTI NC
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:
[email protected]
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Steffen Schmidt
Copyright © Siemens AG 2008. All rights reserved. E D SE PTI NC
Thank you for your attention!
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Steffen Schmidt
Copyright Copyright©© Siemens AG 2008. All rights reserved. E D SE PTI NC
