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Transcript of Pr4PresentationSC E
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1
DIgSILENT
Short-Circuit Calculation
Basics, Methodologies and Models
IEC 60909
2
Content
1 Basic Terminology
2 Superposition Method
3 Voltage Source Method
4 Short-Circuit currents of the different time zones
5 Example: Star-Point treatment in the distribution network
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3Fundamentals
Short-Circuit Calculation
Operational Conditions
Online-S/C calculation
Planning Conditions
Simplified Methods
(IEC, ANSI, ...)Reduced Set of Data
Complete Method,Comprehensive set of data
Method 1:
Equivalent Voltage Source
at the fault location
Method 2.1:Superposition
Method
Method 2.2:Solution of Diff.
Equation
Initial S/C current
ISC (Ikss)
ip Ib Ith
m, n
I"k, Uki ik(t)
4
Application in Network Planning
- S/C Capacity of existing substations
- Design and Parametrization of Protection Relays
- Dimensioning of Earthing grids
- Thermal S/C capacity of cables
- Check for sufficient S/C power at load connection
- Induction problems during unsymmetric faults
Application in Network Operation
- Staying within S/C limits during network switching
- Localizing network faults based on the fault impedance
- Clarification of protection mis-operation
Fundamentals
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Upper Amplitude
DC-Component iDC
Time
Current
Lower Amplitude
Time-Plot of S/C current (far from generator)
Fundamentals
6
Time-Plot of S/C current (close to generator)
Current
Upper Amplitude
Lower Amplitude
DC-Component iDC
Fundamentals
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S/C close to GeneratorModel of the Synchronous Machine
xd-x'd
S
x'd-x"d x"d
E' E"E
t
Fundamentals
8
Important magnitudes in S/C calculation
ip Peak Current
idc DC Offset of the S/C current
Ik" AC Component of the initial (sub-transient) S/C/C
Ik AC Component of Transient S/C Current
Ik AC Component of Steady-State S/C current
Also of Importance:
Sk" Initial S/C Apparent Power
knk "IU3"S =
Fundamentals
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Symmetric Components - Principle
Im
Re
1 = a3
a2
a
120
120
120
Uniform Pointer in the
complex plane
I1R
t
I1S
I1T
I1R
t
I1T
I1S
I1R
t
I1T
I1S
Pos. Sequence
System 1
Neg. Sequence
System 2Zero Sequence
System 0
2
3j2
1a +=
2
3j
2
1a
2 =
0aa12 =++
Fundamentals
10
=
2
1
0
2
2
T
S
R
I
I
I
aa1
aa1
111
I
I
I
=
T
S
R
2
2
2
1
0
I
I
I
aa1
aa1
111
3
1
I
I
I
Symmetric Components - Transformation
210R IIII ++=
21
2
0S IaIaII ++=
2
2
10T IaIaII ++=
012 RST
RST 012( )TSR0 III
3
1I ++=
( )T2SR1 IaIaI3
1I ++=
( )TS2R2 IaIaI3
1I ++=
Fundamentals
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Symmetric Components - Impedance Measuring
Positive Sequence
System 1
Negative Sequence
System 2
Zero Sequence
System 0
Fundamentals
12
Classification of Short-Circuits
3-phase S/C
1
2
0
L1
L2
L3
ZA1
ZA2
ZA0
ZB1
ZB2
ZB0
~3nUc
1I
Fundamentals
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2-phase S/C
(no Earth Contact)
Classification of Short-Circuits
Fundamentals
1
2
0
L1
L2
L3
ZA1
ZA2
ZA0
ZB1
ZB2
ZB0
~3
Uc n 1I
2I
14
2-phase S/C
(incl. Earth Contact)
Classification of Short-Circuits
Fundamentals
1
2
0
L1
L2
L3
ZA1
ZA2
ZA0
ZB1
ZB2
ZB0
~3nUc
1I
2I 0I
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Phase-to-Earth S/C
1
2
0
L1
L2
L3
ZA1
ZA2
ZA0
ZB1
ZB2
ZB0
~3nUc
1I
0I
2I
Classification of Short-Circuits
Fundamentals
162 Element Models in Symmetr. Components
Model of an External Network
~U11
2
0
RN1 XN1
RN2 XN2
RN0 XN0
Parameters and Calculation
k
n1N
"I3
UcZ
=
Further Parameters:
1N2N ZZ =
RN1, XN1 acc. to ratio1N
1N
X
R
RN0, XN0 acc. to ratio1N
0N
Z
Zand
0N
0N
X
R
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Model of Overhead Lines / Cables
1
2
0
RL1 XL1
RL2 XL2
RL0 XL0CL0/2 CL0/2
Parameters and Calculation
RL1, XL1 according to conductors/geometry andmanufacturer's data respectively
1L2L ZZ =
RL0, XL0 according to conductors/geometry and underconsideration of parallel paths through earth andneighbouring conducting materials
Temperature coefficient of the resistance forminimum S/C value:
( )[ ] 20,LeL RC201R +=
2 Element Models in Symmetr. Components
18
Model of 2-Winding Transformer
Parameters and Calculation:
rT
2HV,rT
kr1HV,TS
UuZ =
rT
2 HV,rTRr1HV,T
S
UuR =
1HV,T2HV,T ZZ =
2 Element Models in Symmetr. Components
1
2
0
RT,HV1 XT,HV1
RT,HV2 XT,HV2
3ZE1 3ZE2
ZT0
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Model of 3-Winding-Transformer (1)Parameters and Calculation:
12rT
2HV,rT
12kr1,12S
UuZ =
12rT
2
HV,rT12Rr1,12
SUuR =
23rT
2HV,rT
23kr1,23S
UuZ =
23rT
2HV,rT
23Rr1,23S
UuR =
31rT
2HV,rT
31kr1,31S
UuZ =
31rT
2
HV,rT31Rr1,31S
UuR =
2 Element Models in Symmetr. Components
1
0
RT,HV11 XT,HV11
3ZE13Z
E3
ZT0
RT,HV31
XT,HV21RT,HV21
XT,HV31
2
3ZE2
RT,HV12 XT,HV11 RT,HV32
XT,HV22 RT,HV22
XT,HV32
20
Model of 3-Winding-Transformer (2)
( )1,311,231,1211HV,T ZZZ2
1Z +=
( )1,311,231,1221HV,T ZZZ2
1Z +=
( )1,311,231,1231HV,T ZZZ2
1Z ++=
1,HVi,T2,HVi,T ZZ =
2 Element Models in Symmetr. Components
1
0
RT,HV11 XT,HV11
3ZE1 3ZE3
ZT0
RT,HV31
XT,HV21RT,HV21
XT,HV31
2
3ZE2
RT,HV12 XT,HV11 RT,HV32
XT,HV22 RT,HV22
XT,HV32
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Model of Series Reactor
1
2
0
RR1 XR1
RR2 XR2
RR0 XR0
Parameters and Calculation
rR
2
nkr1R
I3
UuZ
=
rT
2rT
Rr1RS
UuR =
In case of symmetry:
1R0R2R ZZZ ==
2 Element Models in Symmetr. Components
22
Model of the Synchr. Machine (RG acc. to IEC)
RS/X"d UrG SrG
0.15 1kV any
0.07 > 1kV < 100 MVA
0.05 > 1kV 100 MVA
Parameters and Calculation:
dSS "jXRZ +=
Further Parameters:
2S2S2S jXR"jXRZ +=+=
Normally applicable: X2
= X"d
If x"d different from xq", it may be set:
( )qd22 "X"X2
1X"X +==
2 Element Models in Symmetr. Components
~U"11
2
0
RS1 X"S1
RS2 X"S2
RS0 X"S0
ZE
3ZE
S
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Model of the Asynchronous Machine
Parameters and Calculation:
rM
2
rM
rM
LR
AKS
U
I
I
1Z
=
RM/XM UrM PrM per PolePair
0.1 > 1kV 1 MW
0.15 > 1kV < 1 MW
0.42 1kV, incl.cables
any
ASM
~U"11
2
0
RA1 X"A1
RA2 X"A2
RA0 X"A0
2 Element Models in Symmetr. Components
24
Model of Load/Shunt Compensation
1
2
0
RLoad1
XLoad1
not
forIEC60909
CLoad1
RLoad2
XLoad2
CLoad2
RLoad0
XLoad0
CLoad0
0
2 Element Models in Symmetr. Components
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Model of Converter Drives
Parameters and Calculation:
Calculation in general like in case of anAsynchronous Machine:
rM
2
rM
rM
LR
K,ConvS
U
I
I
1Z
=
where
ILR/IrM = 3
RM/XM = 0.10
2 Element Models in Symmetr. Components
~U11
2
0
RConv1 XConv1
3ZE
3
RConv2 XConv2
RConv0 XConv0
263 Superposition Method
~
~
~
US1
US2
US3
UOp,0
~ UOp,0
+
=
UOp,0
~
~
~
US1
US2
US3
USC
= 0
IOp
IOp
IOp
ISC
ISC
ISC
ISC + IOp
ISC + IOp
ISC
+ IOp
a)
b)
c)
Initial State before S/C
Superposition as result
Backward-Infeed at faultlocation
Superposition Method
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274 Voltage Source Method according to IEC 60909
Initial State before S/C:
No-Load Case
Superposition as result
approximation
Backward-Infeed at fault
location (incl. Security
Factor)
Explanation of Method
~
~
~ US3
=Un3
UOp,0=Un
~
+
Un
~
~
~
Un1
Un2
Un3
USC= 0
IOp=0
ISC
ISC
ISC
ISC
ISC
ISC
a)
b)
c)
US2
=Un2
US1
=Un1
IOp
=0
IOp=0
c Un
28
IEC 60909: Principle of Correction Factors
~U"k Zk I"k
~c Un K Zk I"k,IEC
4 Voltage Source Method according to IEC 60909
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IEC 60909: Voltage Correction Factors
Nominal Voltage Calc. max. S/C Current
cmax
Calc. min S/C Current
cmin
Low Voltage
Un 1 kV
1.05 (bei Umax 1.06 Un)
1.10 (bei Umax 1.10 Un) 0.95
Medium Voltage
1 kV < Un 35 kV1.10 1.00
High Voltage
35 kV < Un
1.10
If Un not defined:
cmaxUn Um
1.00
If Un not defined:
cminUn 0.9Um
In general must be considered: cmaxUn Um
4 Voltage Source Method according to IEC 60909
30
IEC 60909: Transformer Impedance Correction
krT
maxT
x6.01
c95.0K
+=
resp.
max,TbrT
max,TbrT
max
max,b
nT
sinI
Ix1
c
U
UK
+
=
3-Winding Transformers:
12kr
max12T
x6.01
c95.0K
+
=
23kr
max23T
x6.01
c95.0K
+
=
31kr
max31T
x6.01
c95.0K
+
=
4 Voltage Source Method according to IEC 60909
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IEC 60909: Synch. Machine Impedance Correction
Impedance Correction(Z1, Z2, Z0, with exception of Ze)
rGd
max
rG
nG
sin"x1
c
U
UK
+
=
RS/X"d UrG SrG
0.15 1kV any
0.07 > 1kV < 100 MVA
0.05 > 1kV 100 MVA
4 Voltage Source Method according to IEC 60909
32
IEC 60909: Modeling Asynchronous Machines
- No Correction Factor
- IEC 60909 formulating Conditions under which ASM shouldnot be neglected (not relevant for Software implementations)
- Estimation of RM
RM/XM UrM PrM per PolePair
0.1 > 1kV 1 MW
0.15 > 1kV < 1 MW
0.42 1kV, incl.cables
any
4 Voltage Source Method according to IEC 60909
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IEC 60909: Power Station Correction Factors
Power Stations with on-load tap changer at unit transformer
rGTd
max
2
r
2
rG
2
Netw,n
PS
sinx"x1
c
t
1
U
UK
+
=
Power Stations with no-load tap changer at unit transformer
( )( )
rGd
maxT
rGrG
Netw,n
PSsin"x1
cp1
t
1
p1U
UK
++
+=
IEC60909 formulates modification rules for these factors
4 Voltage Source Method according to IEC 60909
34
Comparison between IEC 909:1988 and IEC 60909:2001 (1)
IEC 909:1988 EC60909:2001
Netw.-Transf. No Impedance Correction Factor
Special considerations in the followingcases:
- A single-fed S/C current has samedirection as operational current
- Tap Changer with voltage range >5%
- S/C voltage Uk,min significantly smallerthan rated S/C voltage Ukr
- Voltage during operation significantlyhigher than Un (U>1.05 Un)
Special Correction Factor
SynM Impedance correction based on UrG Impedance correction based on (1.0 + pG)UrG (instead of UrG), when operationalvoltage permanently different from UrG
Unit with on-load tapchanger
Optional Choice between
- Single correction of transformer andSynchronous Machine
- Unit Correction
Only Unit Correction admissible
Unit with no-load tapchanger
No Correction Specific Correction Factor
4 Voltage Source Method according to IEC 60909
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Comparison between IEC 909:1988 and IEC 60909:2001 (2)
IEC 909:1988 EC60909:2001
Lines max = 80 C max according to max. possible conductortemperature
cmax in case of
LV networks
c max = 1.00 c max = 1.05 (if Ub < 1.06 Un)
else cmax = 1.10S/Ccontribution ofASM
- Consideration when calculation of 3P and2P(E)
- In case of low-impedance grounding alsoconsideration for 1PE (no guideline forcalculation)
- Concrete calculation guideline for all faulttypes
- Concrete rules for consideration of ASM(saving effort in case of manualcalculation)
Additionalcalculationprocedures
- Calculation guideline for 1-phaseconductor interruption in MV network (fusereaction) and a fault in the LV network
- Calculation guideline for the thermal S/Ccurrent taken over from EC 865-1
4 Voltage Source Method according to IEC 60909
36
Types of S/C current feeding
Single-fed One-sided
Single-fed Multiple-sided
Meshed feeding
4 Voltage Source Method according to IEC 60909
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Maximum Initial AC S/C Current Ik,max
k
2
nmaxmax,k
Z
1
3
Uc"I
=
Minimum Initial AC S/C Current Ik,min
k
2
nminmin,k
Z
1
3
Uc"I
=
To be considered:
- Factor cmin instead of cmax.
- For OHL & Cables application of Resistance values not for 20C
but for the max. possible conductor temperature.
- Network topology and Generator activity should be set for
minimum S/C current expectation.
4 Voltage Source Method according to IEC 60909
38
Peak Current ip (1)
kp "I2i =
Single-fed networks
k
k
X
R3
k
k e98.002.1
X
R +=
=
used for all fault types (3p,2pE,2p,1p)
4 Voltage Source Method according to IEC 60909
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Peak Current ip (2)
Calculation of in case of meshed feeding
Method A: Uniform Ratio R/X
R/X according to the minimal ratio of all branches contributing to the S/Ccurrent (series connections count as one branch only)
i: Branches contributing to the S/C current
Pros/Cons:
+ Easy in Application
- R/X mostly too pessimistic (too small)
=
i
i
min X
RMin
X
R
4 Voltage Source Method according to IEC 60909
40
Peak S/C current ip (3)
Calculation of in case of meshed feedingMethod B: Ratio R/X at fault location
Modificationsa) In case of a ratio R/X < 0.3 in all branches the factor 1.15 need not
be applied
b) In LV networks is to be applied (1.15 b) max = 1.8c) In MVnetworks is to be applied (1.15 b) max = 2.0
Pros/Cons:
+ more exact than procedure b
=
k
kb
X
Rkbp "I215.1i =
4 Voltage Source Method according to IEC 60909
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Peak Current ip (4)
Calculation of in case of meshed feedingMethod C: Method of Equivalent Frequency
- All network impedances calculated for Frequency fe
- S/C impedance Zk,e calculated at Frequency fe- Factor Kappa based on R/X ratio of Zk,e
Pros/Cons:
+ most exact
- high calculation effort for manual evaluation
i
*
i RR =
e
ni
*
if
fXX =
fn fe
50 Hz 20 Hz
60 Hz 24 Hz
=
e
e
f,k
f,k
cX
R
4 Voltage Source Method according to IEC 60909
42
DC Component iDC
tX
Rf2
kDC e"I2i
=
R/X calculated based on
- Method A (Uniform Ratio R/X)
- Method C (Equivalent Frequency Method) with value of fe depending ontime interval
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Breaker Current ib(not considered here, see IEC-60909)
Steady-State S/C current Ik(not discussed here, see IEC-60909)
Thermal S/C current Ith
( ) k2
thk
2
k
T
0
2 TITnm"Idtik
=+=
k
Tk
0
2
thT
dti
I
=
m Thermal contribution of the DC component
n Thermal contribution of the AC component
4 Voltage Source Method according to IEC 60909
445 Star-Point Treatment in Distribution Networks
Example
Application
~U11
2
0
ZN1 ZT1 ZL1
ZN2 ZT2 ZL2
ZN0 ZT0ZL0
ZE
3 ZE
1PE
CL/2CL/2
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Low-Impedance Grounding
~U11
2
0
ZN1 ZT1 ZL1
ZN2 ZT2 ZL2
ZN0 ZT0ZL0
3 ZE
CL/2CL/2
~U11
2
0
ZN1 ZT1 ZL1
ZN2 ZT2 ZL2
ZN0 ZT0ZL0
3 ZE
CL/2CL/2
Isolated Star-Point
5 Star-Point Treatment in Distribution Networks
Star-Point Compensation
~U11
2
0
ZN1 ZT1 ZL1
ZN2 ZT2 ZL2
ZN0 ZT0ZL0
3 XE
CL/2CL/2
1CL3 LE2
0 =