8698462 short circuit calculations

8/3/2019 8698462 Short Circuit Calculations

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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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Page 2 28.06.2008Copyright Siemens AG 2008. All rights reserved.

E D SE PTI NCSteffen Schmidt

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 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 theCalculation 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 Calculations

Standard 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 calculationsPart 3: Currents during two separate

simultaneous line-to-earth shortcircuits and partial short-circuitcurrents flowing through earth

Part 4: Examples for the calculation ofshort-circuit currents


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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


7/72Page 7 28.06.2008Copyright Siemens AG 2008. All rights reserved.

E D SE PTI NCSteffen SchmidtCopyright Siemens AG 2007. All rights reserved.


Types of Short Circuits

3-phase

2-phase

1-phase




Variation of short circuit current shapes

fault at voltage peak fault at voltagezero crossing

fault located inthe network

fault locatednear generator





Far-from-generator short circuit

Ik Initial symmetrical short-circuit currentip Peak short-circuit currentIk Steady-state short-circuit current

A Initial value of the d.c component





Definitions according IEC 60909 (I)

initial symmetrical short-circuit current Ikr.m.s. value of the a.c. symmetrical component of a prospective(available) short-circuit current, applicable at the instant of short circuit ifthe impedance remains at zero-time value

initial symmetrical short-circuit powerSkfictitious 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

=


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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-circuitcurrent decaying from an initial value to zero

peak short-circuit current ipmaximum 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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Copyright Siemens AG 2008. All rights reserved.E D SE PTI NCSteffen Schmidt


Near-to-generator short circuit

Ik Initial symmetrical short-circuit currentip Peak short-circuit currentIk Steady-state short-circuit currentA Initial value of the d.c componentIB Symmetrical short-circuit breaking current

tB

BI22


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Definitions according IEC 60909 (III)

steady-state short-circuit current Ikr.m.s. value of the short-circuit current which remains after the decay ofthe transient phenomena

symmetrical short-circuit breaking current Ibr.m.s. value of an integral cycle of the symmetrical a.c. component of theprospective short-circuit current at the instant of contact separation ofthe first pole to open of a switching device


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Purpose of Short-Circuit Values

Minimum symmetrical short-circuit current IkSelective detection of partialshort-circuit currents

Protection setting

Maximum initial symmetricalshort-circuit current Ik

Potential rise;

Magnetic fields

Earthing, Interference, EMC

Initial symmetrical short-circuit current Ik

Fault duration

Temperature rise of electrical

devices (e.g. cables)

Thermal stress to equipment

Peak short-circuit currentipForces to electrical devices

(e.g. bus bars, cables)Mechanical stress toequipment

Symmetrical short-circuitbreaking current Ib

Thermal stress to arcing

chamber; arc extinction

Breaking capacity of circuit

breakers

Relevant short-circuit currentPhysical EffectDesign Criterion


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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

AQ

Q A ZLZTZN

F

~

I"K3

.n

Uc

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 grid

Equivalent voltage source at the short-circuit location

real network equivalent circuit


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Voltage Factor c

c is a safety factorto 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.

1.001.10Medium voltage >1 kV 35 kV

0.950.95

1.051.10

Low voltage 100 V 1000 V

-systems with a tolerance of 6%-systems with a tolerance of 10%

1.001.10High voltage >35 kV

minimum short circuit currentsmaximum short circuit currentsNominal voltage

Voltage factor c for calculation of


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Maximum and minimum Short-Circuit Currents

shall be neglectedshall be consideredMotors

Maximum impedanceMinimum impedanceNetwork feeders

minimum

short circuit currents

maximum

short circuit currents

Minimum contributionMaximum contributionPower plants

CminCmaxVoltage factor

at maximum temperatureat 20CResistance 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 negativesequence 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

If R/X of the network feeder is unknown, one of the following values canbe used: R/X = 0.1 R/X = 0.0 for high voltage systems >35 kV fed by overhead lines

"k

2n

"k

n

Q S

Uc

I3

Uc

Z

=

=

2

QQ

)X/R(1

ZX

+=


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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

maxTx6,01

c95,0K +=

b

TrT

b

TT

maxbnT sin)II(x1

c

U

UK +=


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Network transformer

Impact of Correction Factor

The Correction factor is KT7.5 %.

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


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Generator with direct Connection to Network


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

sinx1c

UUK

+=


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Generator Block (Power Station)


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

2rTLV

2

rG

2nQS

sinxx1c

UU

UUK

+=

G

Q

( )rGd

maxt

rTHV

rTLV

GrG

nQSO

sinx1

cp1

U

U

)p1(U

UK

+

+=


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Asynchronous Motors

Motors contribute to the short circuit currents and have to be consideredfor 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

rMLRM S

U

I/I

1

Z=

2

MM

MM

)X/R(1

ZX

+=


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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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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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E D SE PTI NCSteffen SchmidtCopyright Siemens AG 2007. All rights reserved.


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)


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3-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 offault location

network right offault locationfault location

~ c Un3

~~


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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 right offault location

fault location

c Un

3~

( ) ( )01

r

scE2E 2

3

ZZ

UcI

+

=

L1

L2

L3

~ -Uf


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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

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 right offault location

fault location

~

c Un

3~ -Uf )0()2()1(

r"

sc1

3

ZZZ

UcI

++

=


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Largest initial short circuit current

Because of Z1 Z2 thelargest short circuit current canbe observed

forZ1 / Z0 < 1

3-phase short circuitforZ1 / Z0 > 1 2-phase short circuit with

earth connection(current in earth connection)


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Page 38 28.06.2008Copyright

Siemens AG 2008. All rights reserved.E D SE PTI NCSteffen Schmidt

Feeding of short circuits

single fed short circuit

multiple fed short circuit

= "sc_part"

sc_part

"

sc III

SkQ

UnQ

"r:1

k3

"

scI

G3~

M3~

IscG IscN IscM

Fault


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Calculation of short circuit currents by programs (1/3)

Basic equationi = Yu Y: matrix of admittances (for short circuit)

=

n

r

2

1

nnn1

ini1

2n21

1n11

''

sci

.

.

.3

.

.

.

....

..

..

..

....

..

..

..

....

....

0

.

.

.

.

.

.

0

0

U

Uc

U

U

YY

YY

YY

YY

I


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Inversion of matrix of admittancesu = Y-1i

=

0

.

.

.

.

.

.

0

0

....

..

..

..

...

..

..

..

....

....

.

.

.3

.

.

.

''

sci

nnn1

iniii1

2n21

1n11

n

r

2

1

I

ZZ

ZZZ

ZZ

ZZ

U

Uc

U

U


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from line i:

from the remaining lines:

calculation of all node voltages

from there -> calculation of all short circuit currents

3

"

sciiir

IZUc

=

3 ii

r"

sciZ

UcI

=

"

sciscisc IZU =


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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:

110 kV3 GVAR/X = 0.1

Transformer:

110 / 20 kV40 MVAuk = 15 %

PkrT = 100 kVA

Overhead line:

20 kV10 kmR1 = 0.3 / km

X1 = 0.4 / km


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Impedance of Network feeder

"

k

2

nI

S

UcZ

=

( )GVA3

kV201.1Z

2

I

=

= 1467.0ZI = 0146.0RI = 1460.0XI


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Impedance of Transformer

n

2

nkT

S

UuZ =

= 5000.1ZT = 0250.0RT = 4998.1XT

( )

MVA40

kV2015.0Z

2

T =

2n

2n

krTT S

UPR =

( )

( )2

2

TMVA40

kV20kVA100R =


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Impedance of Transformer

Correction Factor

T

max

Tx6.01

c

95.0K +=

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"

kXjR3

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"

kXjR3

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 Current

Calculation 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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Calculation in non-meshed Networks

The peak short-circuit current ip at a short-circuit location, fed fromsources which are not meshed with one another is the sum of the partialshort-circuit currents:

M

G

M

ip1 ip2 ip3 ip4

ip = ip1 + ip2 + ip3 + ip4


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Calculation in meshed Networks

Method A: uniform ratio R/X smallest value of all network branches quite inexact

Method B: ratio R/Xat the fault location

factorb from relation R/Xat the fault location (equation or diagram) =1,15 b

Method C: procedure with substitute frequency factor from relation R

c/X

cwith substitute frequency fc = 20 Hz

best results for meshed networks

ff

XR

XR c

c

c =


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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 ofpeak 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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Page 58 28.06.2008 Copyright


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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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,Generatoror Ikwith motor > 1.05 Ikwithout 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 whichare not meshed is the sum of the partial short-circuit currents:

M

G

M

IB1 = Ik

IB = IB1 + IB2 + IB3 + IB4

IB2 = Ik IB3 = qIk IB4 = qIk


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Breaking current

Decay of Current fed from Generators

IB

= Ik

Factor to consider the decay of short circuit current fed fromgenerators.


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Breaking current

Decay of Current fed from Asynchronous Motors

IB

= q Ik

Factor q to consider the decay of short circuit current fed fromasynchronous motors.

C


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Breaking Current

Calculation in meshed Networks

Simplified calculation:

Ib = Ik

For increased accuracy can be used:

XdiK subtransient reactance of the synchronous machine (i)XMj reactance of the asynchronous motors (j)IkGi , IkMj 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 =

C ti h t i it t


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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 transienteffects

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 bynetwork calculation programs.

For short circuits far from generator and as worst case estimation

Ik = Ik


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Short-circuit with preload

Sh t i it ith l d


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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

Sh t i it ith l d


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Example

A Load flow calculation

B Short circuit calculation

Sh t i it ith l d


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Results

720V336V592.11V

1000V

192.0A168A197.37A203.95A


~ ~

365.37A

720V

-0V

720V700V

-364V

336V

900. V

-307.89V

592.11V

1000V

-0V

1000V

10A

182A

192A

40A

208A

168A

40. A

157.37A

197.37A

50. A

153.95A

203.95A

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!



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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]
mailto:[email protected]:[email protected]


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8698462 short circuit calculations

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