Short Circuit Presentation Lecture 14 SC Calculations According to Standard IEC 60909

Short-circuits – Lecture 14Short-circuits calculations according to standard IEC 60909

Teaching materials distributed for free.

Prof. Désiré Rasolomampionona,

Prof. dr hab. Jan Machowski

Outline of the lecture

•Definitions

•Schematic diagram of short-circuit current

•Low Voltage factors

•short-circuits fed from non-meshed networks

•Short-circuit currents inside a power station unit with on-load tap-changer

•Short-circuit currents inside a power station unit without on-load tap-changer

•short-circuits in meshed networks


•short-circuits in meshed networks

•Symmetrical short-circuit breaking current

•steady-state short-circuit current

•Joule integral and thermal equivalent short-circuit current

Short-circuits Standards

Definitions

Definition Symbol according to IEC 60909

Initial symmetrical short-circuit current

Peak short-circuit current

Symmetrical short-circuit breaking current

Factor for the calculation of the symmetrical short-circuit

breaking current

"KI

pi

bI

µ


breaking current

Decaying aperiodic component of short-circuit current

Thermal equivalent short-circuit current

Assymmetrical short-circuit breaking current

Initial symmetrical short-circuit power

Duration of the short-circuit current

dci

thI

asymbI"KS

KT

Short-circuits StandardsFig. 1. Schematic diagram of

short-circuit current

(a) short-circuit current of far

from generator short-

circuit with decaying AC

component

(b) short-circuit current of

near to generator short-

circuit with constant AC

2 2

IK

2 2

IK

A

i p

a)Current

1 - top enveloppe

2 - bottom enveloppe

i idc dc - DC component of the short-circuit current

Time


circuit with constant AC

component.

All the other symbols (A, IK, ip, Idc)

were given in the definitions,

1. Top enveloppe,

2. bottom enveloppe

dc

2 2

I K2

2 I

K

2 2

IK

A

i p

=

b)Current

1 - top enveloppe

2 - bottom enveloppe

i idc dc - DC component of the short-circuit current

Time


•Table 1. Selection of Voltage factor c (equivalent voltage source)

Nominal voltage

Un

Voltage factor c to be calculated

of maximum voltage

short-circuit

of minimum voltage short-

circuit

Low voltage (100 – 1000V)

a) 230 – 240V 1.00 0.95


a) 230 – 240V

b) Other voltages

1.00

1.05

0.95

1.00

Medium voltage (1 – 35kV) 1.10 1.00

High voltage > 35kV 1.10 1.00


Selection of Voltage factor c (equivalent voltage source)

In all hitherto used formulas the initial short-circuit and short-circuit currents were

calculated using the U0 voltage (equivalent voltage source) derived from the Thevenin’s

theorem. by corresponding to the prefault voltage at short-circuit location node. The IEC

standard defines this voltage from the network nominal voltage mutipiled by the c factor

given in the previous slide table as follows :

o UcU ⋅=


no UcU ⋅=

After defining such a voltage the initial three phase short-circuit current may be calculated

using the following expression :

K

n

2K

2K

n"K

33 Z

cU

XR

cUI =

+⋅=


Short-circuits fed from non-meshed networks

For a far-from-generator short-circuit fed from a single source (see Figure 1), the short-

circuit current is calculated using the equation presented at the bottom of the previous

slide.

When there is more than one source

contributing to the short-circuit current, and the

sources are unmeshed, as shown for instance

in the figure at right,

G3

M3

Q


in the figure at right,

The initial symmetrical short-circuit current at

the short-circuit location F is the sum of the

individual branch short-circuit currents.

Each branch short-circuit current can be

calculated as an independent single-source

three-phase short-circuit current in

accordance with equation

K

n

2K

2K

n"K

33 Z

cU

XR

cUI =

+⋅=

3

F

IiI

KPSU

pPSU

bPSU

Ii

KT

pT

IiI

KM

pM

bM

IiII

K

K

p

b K3

Fig. 2. Example of a non-meshed network



The initial symmetrical short-circuit current is calculated with the corrected impedances of

the generator and the power station unit in series with a line impedance. The short-

circuit impedances for the different cases are given by the following equations:

•short-circuit fed from one power station unit (generator and unit transformer with or

without on-load tap-changer)


( ) LTHVG2r1PSULPSUK ZZZtKZZZ ++=+=

•Equivalent circuit with unit transformer and transmission line

LTHVT2r2QK ZZKtZZ ++=

•Set of HV motors and transmission line

LMK ZZZ +=



The initial short-circuit current at the short-circuit location F is the phasor sum of the

individual partial short-circuit currents :

∑=i

iII "K

"K

Within the accuracy of this standard, it is often sufficient to determine the short-circuit


Within the accuracy of this standard, it is often sufficient to determine the short-circuit

current at the short-circuit location F as being the sum of the absolute values of the

individual partial short-circuit currents.


Short-circuit currents inside a power station unit with on-load tap-changer

For calculating the partial short-circuit currents

and with a short-circuit at F1 (Fig. 3), in the

case of a power station unit with on-load tap-

changer, the partial initial symmetrical short-circuit

currents are given by:

QGG

3

T

F1

AT

K3

K3

trAT

1

F2

KF2I

KGI

KQmaxI

KTI

1:tnQU

QU

rG"KG

cUI =

"KGI

"KTI


AF3

K3

KATIGGS

KG3 ZK

I =

+=

Qmin1

TLV

rG"KT

2r

3 ZZ

cUI

t

Where KGS is a correcting factor

given by the following expression

rG"d

maxGS

sin1 ϕX

cK

+=

Fig. 3. Short-circuit currents and partial short-circuit currents for

three-phase short-circuits between generator and unit

transformer with or without on-load tap-changer, or at the

connection to the auxiliary transformer of a power station unit

and at the auxiliary busbar A



And the rest of the symbols are defined as follows:

ZG is the subtransient impedance of the generator

is the subtransient reactance referred to the rated impedance:"dX


d

ZTLV is the transformer short-circuit impedance referred to the low-voltage side

tr is the rated transformation ratio;

ZQmin is the minimum value of the impedance of the network feeder, corresponding to

the maximum short-circuit power



For the calculation of the partial short-circuit current feeding into the short-circuit

location F2, for example at the connection to the high-voltage side of the auxiliary

transformer AT in the figure, it is sufficient to take:

+

+=

Qmin1

TLVTSGGS

rG"KF2

2

11

3 ZZKZK

cUI


+ QminTLVTS 2r

ZZKt

With KTS given by the following expression

rGTp.u.

maxTS sin1 ϕX

cK

−=

And KGS as it was given before

rG"d

maxGS

sin1 ϕX

cK

+=


Short-circuit currents inside a power station unit without

on-load tap-changer

For a power station unit without on-load tap-changer of the unit transformer, the

partial initial symmetrical short-circuit currents (the same figure) are defined by the

same formulas as for the case with on-load tap-changer, with small modifications of

the correcting factors KGS and KTS, which become KGS0 and KTS0

rG"KG

cUI =

= rG"KT

cUI


GGS0

KG3 ZK

I =

+ Qmin1

TLV

KT

2r

3 ZZt

rG"d

max

GGSO

sin1

1

1

ϕX

c

pK

+⋅

+=

rGp.u.T

max

GTSO sin1

1

1

ϕX

c

pK

−⋅

+=

( )

++=

Qmin1

TLVTS0GGS0

rG"KF2

2r

11

3 ZZKZK

cUI

t

with


Short-circuit currents inside a power station unit without

on-load tap-changer

If the unit transformer has an on-load tap-changer on the high-voltage side, it is

assumed that the operating voltage at the terminals of the generator is equal to UrG.

If, even in this case, the voltage region of the generator UG = UrG(1±pG) is used

permanently, take equations for the case without on-load tap changer than those for

the case with on-load tap changer.


the case with on-load tap changer.

The total short-circuit current in F1 or F2 is found by adding the partial short-circuit

current, caused by the medium- and low-voltage auxiliary motors of the power

station unit.


Short-circuit currents in meshed networks

In meshed networks, such as those shown in figure

at right, it is generally necessary to determine the

short-circuit impedance Zk = Z(1) by network

reduction (series connection, parallel connection,

and delta-star transformation, for example) using the

positive-sequence short-circuit impedances of

electrical equipment.

G3

Q


electrical equipment.

The impedances in systems connected through

transformers to the system, in which the short-

circuit occurs, have to be transferred by the

square of the rated transformation ratio.

M3

M3

M3

F

If there are several transformers with slightly

differing rated transformation ratios (trT1 trT2... trTn),

in between two systems, the arithmetic mean

value can be used.

Fig. 4. System diagram



G3

QThe initial symmetrical short-circuit current shall

be calculated with the equivalent voltage source

at the short-circuit location using

equation

3ncU


M3

M3

M3

F

Fig. 4. System diagram

K

n

2K

2K

n"K

33 Z

cU

XR

cUI =

+⋅=



For three-phase short-circuits fed from non-meshed networks as in figures 2 and 3, the

contribution to the peak short-circuit current from each branch can be expressed by:

"Kp 2 Ii χ=

1,6

1,8

2,0

The factor χ for the R/X ratio shall be obtained

from Figure 5 or calculated by the following


Fig. 5. Factor χ for series circuit as a function of ratio R/X

0 0,2 0,4 0,6 0,8 1,0 1,21,0

1,2

1,4

1,6

x

R X/

from Figure 5 or calculated by the following

expression:

3R/Xe98,002,1 −+=χ



Equations of ip and χ of the previous slide presume that the short-circuit starts at zero

voltage, and that ip is reached approximately after one half-cycle. For a synchronous

generator use RGf..

The peak short-circuit current ip at a short-circuit location F, fed from sources which are

not meshed with one another, in accordance with Figure 2, is the sum of the partial short-


circuit currents:

And from Fig. 2



When calculating the peak short-circuit current ip in meshed networks, the equation of ipshall be used with χ determined using one of the following methods a), b), or c).

a) Uniform ratio R/X or X/R

For this method the factor χ is determined from figure 5 taking the smallest ratio of R/X

or the largest ratio of X/R of all branches of the network.


or the largest ratio of X/R of all branches of the network.

It is only necessary to choose the branches which carry partial short-circuit currents

at the nominal voltage corresponding to the short-circuit location and branches with

transformers adjacent to the short-circuit location.

Any branch may be a series combination of several impedances. In practise,

considering branches, through which the flowing current is about 80% of the short-

circuit current is sufficient.



b) Ratio R/X or X/R at the short-circuit location

For this method the factor χ is multiplied by a factor 1,15 to cover inaccuracies caused

by using the ratio Rk / Xk from a network reduction with complex impedances.


The factor χ(b) is found from figure5 for the ratio Rk / Xk given by the short-circuit

impedance Zk = Rk + jXk at the short-circuit location F, calculated for frequency f = 50 Hz

As long as R/X remains smaller than 0,3 in all branches, it is not necessary to use the

factor 1,15. It is not necessary for the product 1,15 . χ(b) to exceed 1,8 in low-voltage

networks or to exceed 2,0 in medium- and high-voltage networks.



c) Equivalent frequency fc

An equivalent impedance Zc of the system as seen from the short-circuit location is

calculated assuming a frequency fc = 20 Hz The R/X or X/R ratio is then determined

according to the following equation :

f

f

X

R

X

R c

c

c ⋅=


Zc = Rc + jXc is the equivalent impedance of the system as seen from the short-circuit

location for the assumed frequency fc;

where

Rc is the real part of Zc (Rc is generally not equal to the R at nominal frequency)

Xc is the imaginary part of Zc (Xc is generally not equal to the X at nominal frequency).

fXX c



c) Equivalent frequency fc

The factor χ is found from figure 5 using the R/X or X/R ratio from equation (*), or with

equation (**). Method c) is recommended in meshed networks (see IEC 60909-1).

f

f

X

R

X

R cc ⋅= (*) 3R/Xe98,002,1 −+=χ (**)


When using this method in meshed networks with transformers, generators and

power station units, the impedance correction factors KT, KG and KS, respectively KSO,

shall be introduced with the same values as for the 50 Hz or 60 Hz calculations.

fXX c(*) e98,002,1 +=χ (**)


Symmetrical short-circuit breaking current:

Single-fed three- phase short-circuit

For a near-to-generator short-circuit, in the case of a single fed short-circuit or from non-

meshed networks (fig. 2), the decay to the symmetrical short-circuit breaking current Ib(*) is taken into account by the factor m according to equations (**).

"Kb II µ=

rG"KG

rG"KG

/300min

/260min

e 51,071,0 s 05,0for -

e 26,084,0 s 02,0for -

II,-

II,-

t

t

+==

+==

µ

µ(*)

(**)The factor m depends on the minimum


rG"KG

rG"KG

/380min

/320min

min

e 0,940,56 s 0,25for -

e 72,062,0 s 10,0for -

e 51,071,0 s 05,0for -

II,-

II,-

t

t

t

+=≥

+==

+==

µ

µ

µ(**)

The factor m depends on the minimum

time delay tmin and the ratio rG"K / II

where IrG is the rated generator current.

The values of m in equation (**) apply if synchronous machines are excited by rotating

exciters or by static converter exciters (provided, for static exciters, the minimum time

delay tmin is less than 0,25 s and the maximum excitation voltage is less than 1,6 times

rated load excitation-voltage). For all other cases take if the exact value is

unknown.

1=µ



Single-fed three- phase short-circuit

If is not greater than 2, apply for all values of

the minimum time delay tmin. rG

"K / II 1=µ

1,0

0,9

0,8

0,02 s

0,05 s

Minimum time delay tmin

The factor µ may also be obtained from figure 6.


Fig. 6. Factor µ

For other values of minimum time delay, linear

interpolation between curves is acceptable.

Figure 6 can be used also for compound excited

low-voltage generators with a minimum time

delay tmin not greater than 0,1 s.

0,8

0,7

0,6

0,50 1 2 3 4 5 6 7 8 9

Three-phase short circuit or I /I I /IkG rG kM rM

0,05 s

0,1 s

0,25 s

µ



Single-fed three- phase short-circuitFor three-phase short-circuits in non-meshed networks as in figure 2, the symmetrical

breaking current at the short-circuit location can be calculated by the summation of the

individual breaking current contributions:

whereMb"KTPSU bb IIII ++= "

KMbM IqI µ=

m is taken from equation (** - slide 24) or figure 6 for synchronous generators and

asynchronous motors.


asynchronous motors.

The factor q for the calculation of the symmetrical short-circuit breaking current for

asynchronous motors may be determined as a function of the minimum time delay tmin

(fig. 7).

mqst

mqst

mqst

mqst

ln 10,026,0 25,0for

ln 12,057,0 10,0for

ln 12,079,0 05,0for

ln 12,003,1 02,0for

min

min

min

min

+=≥−+==−+==−+==− Where m is the ratio between is the rated

active power in MW and the number of

pairs of poles of the motor.

pPm /rM=

(*)



Three-phase short-circuit in meshed networks

At first the current at the short-circuit

The short-circuit breaking current Ib in

meshed networks shall be calculated by:

"Kb II =

0,4

0,5

0,6

0,7

0,8

0,9

1,0

q

0,02 s

0,05 s

0,1 s

Minimum time delay tmin


Fig. 7. Factor q for the calculation of the

symmetrical short-circuit breaking current

of asynchronous motors

At first the current at the short-circuit

location is calculated for the time of

breaking, and then the partial currents in

the branches where the circuit breakers

are located.

( ) ( ) "KM

n

"M"

KGn

"G"

Kb 1

3

1

3

jjjj

jii

i

i IqcUU

IcUU

II µµ −∆

−−∆−= ∑∑

0,01 0,02 0,04 0,1 0,2 0,4 1 2 4 10MW0

0,1

0,2

0,3

Active power of the motor per pair of poles m

0,25 s



Three-phase short-circuit in meshed networks

where

µi, µj are the values given in equation (** - slide 24) for both synchronous (i) and

asynchronous (j) machines;

q are the values given in equation (* - slide 26) for asynchronous (j) motors;

( ) ( ) "KM

n

"M"

KGn

"G"

Kb 1

3

1

3

jjjj

jii

i

i IqcUU

IcUU

II µµ −∆

−−∆−= ∑∑


qj are the values given in equation (* - slide 26) for asynchronous (j) motors;

are respectively the initial symmetrical short-circuit current and the symmetrical short-

circuit breaking current with influence of all network feeders, synchronous machines and

asynchronous motors;

are the initial voltage drops at the terminals of the synchronous machines (i)

and the asynchronous motors (j);

"M

"G , ji UU ∆∆

are the contributions to the initial symmetrical short-circuit current from the

synchronous machines (i) and the asynchronous motors (j) as measured at the terminals of

the machines.

"KM

"KG , ji II

"Kb,II



IK1IK2

IK3

IK4IK5

IK6I ,IK b

The symmetrical short-circuit breaking

current may be considered as :

the difference between the symmetrical

short-circuit breaking current with influence

of all network feeders, synchronous machines

and asynchronous motors and


Fig. 8. Calculation of short-circuit

breaking current Ib in meshed networks

∑ ∑−−=i j

ji IIII zMzG"Kb

the contributions to the initial symmetrical

short-circuit current from the synchronous

machines (i) and the asynchronous motors (j)

as measured at the terminals of the

machines.

Both last current sum can be considered as decaying components and can be

determined using the following equations, providing that the short-circuit occurs at

the terminals of the ith generator (jth motor ) :( ) ( ) "

KMzM"KGzG 1 , 1 jjjjiii IqIII µµ −=−=

(*)

(**)



(*)

The short-circuit is a far-from-generator short-circuit, hence the decaying process of

the short-circuit current sinusoidal component is dynamic (Fig. 1). We can assume

that the decaying factor is equal to a coefficient αi, which is a real number, the absolute

value of which less than 1 (αj for motors), multiplied by the current defined for near-to-

generator short-circuit.

( ) ( ) "KMzM

"KGzG 1 , 1 jjjjjiiii IqIII µαµα −=−=


(*)( ) ( ) KMzMKGzG 1 , 1 jjjjjiiii IqIII µαµα −=−=

The coefficient αi defines the distance between the short-circuit location and the

generator terminals (for near-to-generator short-circuits, its value is near 1, for very far-

from-generator short-circuits almost equal to 0).

In case of non-meshed networks this coefficient can be determined in correlation with

the impedance of the portion of line from the short-circuit location and the generator.



In case of meshed networks it is difficult to define such a line, then the distance between

the short-circuit location and the generator is assumed as equal to the ration of voltage

drop in the corrected generator (motor) reactance and the network phase voltage, hence.

""" XIU∆ " XIU∆


3

"dK

"KG

3

"G

n ncUi

cUi

iXIU

=∆

=α33

"

nn cU

MkMj

cU

Mjj

XIU=

∆=α

Considering the equations (* - previous slide), (*) and (**) leads to a new form of the

equation (* - slide nr 28). In case of greater number of voltage sources, it is much more

convenient to use special computer methods for short-circuit calculations.

(*) (**)


Maximum steady-state short-circuit current

For near-to-generator three-phase short-circuits fed directly from one synchronous generator or

one power station unit only, according to figure 11b or 11c, the steady-state short-circuit current Ikdepends on the excitation system, the voltage regulator action, and saturation influences.

Synchronous machines (generators, motors, or compensators) with terminal-fed static exciters do

not contribute to Ik in the case of a short-circuit at the terminals of the machine, but they

contribute to Ik if there is an impedance between the terminals and the short-circuit location.

A contribution is also given if, in case of a power station unit, the short-circuit occurs on the high-


For the calculation of the maximum steady-state short-circuit current, the synchronous generator

may be set at the maximum excitation.

For static excitation systems fed from the generator terminals and a short-circuit at the terminals,

the field voltage collapses as the terminal voltage collapses, therefore take λmax = λmin = 0 in this

case.

rGmaxmaxK II λ=

k

A contribution is also given if, in case of a power station unit, the short-circuit occurs on the high-

voltage side of the unit transformer



λmax may be obtained from figures 9

or 10 for cylindrical rotor generators

or salient-pole generators. The

saturated reactance xdsat is the

reciprocal of the saturated no-load

short-circuit ratio.

1,21,41,61,82,02,2

1,21,41,61,82,02,2

maxλ maxλd satX

d satX

0,81,01,21,41,61,82,02,22,42,62,8

0,81,01,21,41,61,82,02,22,42,62,8

λ λ

a) seria pierwsza b) seria druga


minλ minλ

0 1 2 3 4 5 7 80

0,20,40,60,8

6 0 1 2 3 4 5 7 80

0,20,40,60,8

6Zwarcie trójfazowe I /IKG rG Zwarcie trójfazowe I /IKG rG

Fig. 9. λmin and λmax factors of series 1 (left)

λmin and λmax factors of series 2 (right)

λmax curves of series 1 are based on

the highest possible excitation

voltage according to either 1,3 times

the rated excitation at rated apparent

power and power factor for cylindrical

rotor generators (figure 9a) or 1,6

times the rated excitation voltage for

salient-pole generators (figure 10a).



λ λ

a) seria pierwsza b) seria druga

2,02,53,03,54,04,55,05,5

2,02,53,03,54,04,55,05,5

maxλmaxλd satX

d satX

0,6

0,6

0,8

0,8

1,0

1,0

1,2

1,2

2,01,7

1,72,0

λmax -curves of series 2 are based on the

highest possible excitation-voltage

according to either 1,6 times the rated

excitation at rated apparent power and

power factor for cylindrical rotor

generators (figure 9b), or 2,0 times the

rated excitation voltage for salient-pole


Fig. 10. λmin and λmax factors of series 1 (left)

λmin and λmax factors of series 2 (right)

rG Zwarcie trójfazowe I /IKG rG

2,0

6Zwarcie trójfazowe I /IKG

6 0 1 2 3 4 5 7 80

0,51,01,5

4 5 7 80

0,51,01,52,0

minλ minλ

0 1 2 3

2,0rated excitation voltage for salient-pole

generators (figure 10b).

λmax -curves of series 1 or 2 may also be

applied in the case of terminal-fed static

exciters, if the short-circuit is at the high-

voltage side of the unit transformer of a

power station unit or in the system, and if

the maximum excitation voltage is chosen

with respect to the partial breakdown of the

terminal voltage of the generator during the

short-circuit.


Minimum steady-state short-circuit current

For the minimum steady-state short-circuit current in the case of a single-fed short-

circuit from one generator or one power station unit, constant no-load excitation

(voltage regulator not being effective) of the synchronous machine is assumed:

rGminminK IλI =


λmin may be obtained from figures 9 and 10. In the case of minimum steady-state

short-circuit introduce c = cmin, according to table 1 (slide 5).


Minimum steady-state short-circuit current

The calculation of the minimum steady-state short-circuit current in the case of a near-

togenerator short-circuit, fed by one or several similar and parallel working generators

with compound excitation, is made as follows:


For the effective reactance of the generators, introduce:

IkP is the steady-state short-circuit current of a generator at a three-phase terminal

short-circuit. The value should be obtained from the manufacturer.


DC component of the short-circuit current

The maximum d.c. component id.c. of the short-circuit current as shown in figures 1 and

2 may be calculated with sufficient accuracy by the following equation :

where

XRfteIi /2"Kdc

K 2 π−=

is the initial symmetrical short-circuit current;"KI


f is the nominal frequency;

t is the time;

R/X s the ratio according to Fig. 5 or the ratios according to the methods a) and c)

slides 19 - 22.

K


Joule integral and thermal equivalent short-circuit current

The joule integral is a measure of the energy generated in the resistive

element of the system by the short-circuit current. In this standard it is calculated

using a factor m for the time-dependent heat effect of the d.c. component of the

short-circuit current and a factor n for the time-dependent heat effect of the a.c.

component of the short-circuit current (see figures 11 and 12)


nmII += "Kth

The thermal equivalent short-circuit current is:



For a series of i ( i = 1, 2,....,r) three-phase successive individual short-circuit currents, the following

equation shall be used for the calculation of the Joule integral or the thermal equivalent short-circuit

current.

where is the initial symmetrical three-phase short-circuit

current for each short-circuit

"KiI

is the thermal equivalent short-circuit currentthI

(*)

(**)


is the factor for the heat effect of the d.c. component

for each short-circuit currentim

is the factor for the heat effect of the a.c. component

for each short-circuit currentin

is the duration of the short-circuit current for each

short-circuitiTK

is the sum of the durations for each short-circuit currentKT

The Joule integral and the thermal equivalent short-

circuit current should always be given with the

short-circuit duration with which they are

associated.

(**)

(***)



1,6

2,0a)

χ=1,9

1,6

2,0b)

I I / =10K K

1,251,5

The factors mi are obtained from Figure 11 using f · Tki and the factor k derived in [2]. The

factors ni are obtained from Figure 12 using Tki and the quotient , where Iki is the

steadystate short-circuit current for each short-circuit.K

"K II


Fig. 11. Factor m for the heat effect of the

d.c. component of the short-circuit current

Fig. 12. Factor n for the heat effect of the

a.c. component of the short-circuit current

10-2 -1102 4 6 2 4 6 s1tK

0

0,4

0,8

1,2

m

=1,91,81,71,61,5

1,41,31,2 1,1

10-2 -1102 4 6 2 4 6 1 2 46 s10tK

0

0,4

0,8

1,2

n

251,52,03,0

4,05,06,0



When a number of short-circuits occur with a short time interval in between them, the

resulting Joule integral is the sum of the Joule integrals of the individual short-circuit

currents, as given in equation (* slide 38)

For distribution networks (far-from-generator short-circuits) usually n=1 can be used.


For far-from-generator short-circuit with the rated short-circuit duration of 0,5 s or

more, it is permissible to take m + n = 1.

If the Joule integral or the thermal equivalent short-circuit current shall be calculated

for unbalanced short-circuits, replace with the appropriate unbalanced short-

circuit currents.

"KiI

1. Machowski J, Kacejko P. Zwarcia w systemach

elektroenergetycznych (Power System Short-Circuits – in

Polish), Wydawnictwo Naukowo-Techniczne, Warszawa 2002

2. INTERNATIONAL STANDARD IEC 60909-0 „Short-circuit

Bibliography

currents in three-phase a.c. systems” Calculation of currents


Documents

Short Circuit Presentation Lecture 14 SC Calculations According to Standard IEC 60909