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2 /36

Subject program

Lecture

General information on short-circuits, short-

circuit current time course

Principles of calculating asymmetrical short-

circuits

Equipment

impedance

symmetrical

components system

Line-to-earth short-circuits in networks with

an ineffective grounded neutral point

Project

Per unit method

Normalized

method

short-circuit

calculations

6 /36

Importance of short-circuit currents



Electrical power systems have to be planned, projected

and constructed in such a way to enable a safe, reliable

and economic supply of loads.



The knowledge about the loading of the equipment is

necessary for the design and determination of the

equipment rating.



Short-circuits during the system operation cannot be

avoided despite careful planning and good maintenance

of the system. Therefore, short-circuit currents have an

important influence on the design and operation of

equipment and the power system a whole.



Equipment and installations must withstand the

expected thermal and electromagnetic effects of short-

circuits. Switchgear and fuses have to switch-off short-

circuit currents in a safe way.

7 /36

Short-circuit classification



Based on the number of connected points –

symmetrical and asymmetrical



Based on fault impedance –

metallic

(direct) i

resistant

(occurring through

impedance, e.g. electrical arc)



Based on the short-circuit location –

far-from-generator

short-circuit and

near-to-

generator

short-circuit



Based on the number of short-circuit places –

single

and multiplace



Based on the location of short circuit places –

internal and

exterior



Based on the moment of short-circuit origin –

simultaneous

and non-simultaneous



Based on the short-circuit duration –

lasting (durable)

and going by

8 /36

Short-circuit statistics

Frequency of short-circuit occurrence:



Line-to-earth short-circuit –65% av.(from 30% to 97%)



Double line-to-earth short-circuit and line-to-line short-
circuit with earth –20% av. (from 0% to 55%)



Line-to-line short-circuit 10% av. (from 0% to 55%)



Three-phase short-circuit - 5% av. (from 0% to 35%)

Frequency of short-circuit occurrence depends on

nominal  voltage  of  the  network  and  the  type  of  line.
The  bigger  voltage  in  the  network  and  the  bigger
share  of  overhead  lines  the  bigger  share  of  line-to-
earth short-circuits.

10 /36

Causes of short circuits

Non-electrical causes:



Humidity and contamination of the insulation of

lines, devices



Ageing of insulation material



Mechanical damages of cables, poles, isolators



Device factory defect



Interference of animals e.g. birds, rodents



Falling over or too high trees



Bringing conductors closer during wind

11 /36

Short-circuit currents effects



Thermal effects

A short-circuit causes large current overloading, which are

accompanied by thermal energy proportional to short-

circuit duration. The short-circuit duration depends on the

duration of protection operation.



Dynamic effects

Short-circuit currents cause mechanical forces that affect

current conductors; this may lead to mechanical

destruction

equipment.

Short-circuits

stimulate

mechanical oscillations of generators which can cause

problems with power transfer stability.



Electric shock threat

Short-circuit currents flowing through earth can induce

impermissible touch and step voltages.



Voltage dips and overvoltages

The high value of short-circuit current causes the high

voltage of voltage drop in the network, which results in

voltage decreasing in the network nodes. Overvoltages

accompany line-to-earth short-circuits.



Displacement of the voltage neutral-to-eart

12 /36

Short-circuit currents effects

Accidental contact of overhead line conductors with a
crane.



Network and system effects

Resulting from switching off the parts of the network being embraced

with fault; economic effects



Threats caused by an electric arc

•

Cable melting-down

•

Insulating materials ignition (oil, paper-oil insulation), emission of

smoke and toxic gasses

•

Thermal and ultraviolet radiation of the arc

•

Air heating and blowing-out from the arc space

•

Reducing oxygen in the place where the arc is burning

13 /36

Minimal and maximal short-

circuits

Depending on the purpose of engineering studies
the maximal and minimal short-circuit currents
are calculated.

The maximal current is the main design criteria
for the rating of equipment to withstand the
effects of short-circuit currents, thermal and
electromagnetic.

The minimal short-circuit current is needed for the
design of protection and selection of settings of
protection relays.

The short-circuit current depends on various
parameters: voltage level, impedance of the
network between any generator unit and
the short-circuit location, number of generation
units, fault impedance, etc. Determination of
short-circuit currents requires detailed knowledge
about the elements of electrical power system.

14 /36

(

)

w +g = +

2Esin t

Ri L

( )

(

)

(

)

w +g - j

�

� g - j

i t

sin t

sin

( )

+ w

j =

arctg

Short-circuit current time course

Case 1: W1 open –

short-circuit from

unloaded state

Initial condition:

i(t 0 ) 0

E – voltage
R – resistance
L – inductance
Z – impedance
γ

– initial voltage phase

angle


– short-circuit

impedance angle

15 /36

( )

nok

i t

t i

( )

(

)

(

)

w +g - j

sin t

2I sin t

( )

(

)

�

� g - j

�

nok

nokm

sin

For the moment
t=0:

(0)= - i

nok

(0)

Short-circuit current time course

= = =

i(0) 0 i(t 0 )

-1,5

-1

-0,5

0,5

1,5

onk

– periodic component of short-

circuit current

nok

– aperiodic component of short-

circuit current

The principle of current continuity

in RL circuit

17 /36

( )

(

)

sin t

� w +g - j

(

) (

)

+ +

R R

X X

arctg

R R

( )

nok

i 0 i(0 ) i

0 i

( )

=- �

�

nok

nokm

0 i

-1,5

-1

-0,5

0,5

1,5

Short-circuit current time course

Case 2: W1 closed –

short-circuit from

loaded state

Initial condition:

i(t 0 ) i

18 /36

Voltage time course during short-circuit

(

)

(

)

�

w +g - j +j

g - j

�

2U sin t

K sin

– time constant

Voltage at the P point:

(

) (

)

j =

arctan

j =

arctan

19 /36

Voltage time course during short-circuit

�

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

When R

, K=0, and the voltage time course does

not include an aperiodic component. In practice, the K

coefficient has a small value, and the aperiodic component

is omitted.

90°

= 0°

Coefficient K:

20 /36

Taking into account the network

capacitance

(

)

(

)

( )

�

w +g - j

g - j

�

sin t

sin

t e

w = p =

2 f

a b

L L

– the frequency of the circuit self-oscillations is from

couple of hundred Hz to couple kHz, the efficient value of

that component does not go over 20% I

t=0

)

Esin(





















21 /36

Taking into account the network

capacitance

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

The short-circuit current time course for the short-

circuit with voltage phase angle of 90°.

22 /36

Voltage time course during short-circuit

(

)

(

) (

)

�

w +g - j +j

g - j

�

2U sin t

sin

t e

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.5

The voltage time course during a short-circuit with the initial

short-circuit angle of 90°.

23 /36

Near-to-generator short circuit

= +

X X

= +

jX I

Generator is the source of short circuit current.

The equivalent
circuit diagram
of the generator
in steady-state

– leakage

reactance of stator
windings

– mutual

reactance of stator
and rotor

– steady-state component of short-

circuit current

d-axis synchronous reactance

24 /36

Consider the sequence of events associated with a
three-phase short-circuit on the unloaded generator.
Before the fault occurs, the field produces an air gap
flux entering the armature and produces time-varying
flux linkages for all mutually coupled circuits
consisting of three phase windings (a, b, c), a field
winding (F) and two damper windings (Q, Q).
A the instant t=0 the fault is applied. This forces flux
linkages to change. By the principle of constant flux
linkages the step change is not possible and all flux
linkages must remained fixed at least for an instant.

(According to magnetic inertia principle the step
change of flux linkages would mean a step change of
energy accumulated in the magnetic field of the
winding.

To counteract sudden flux changes transient dc fluxes
are induced in each winding which maintain flux
linkages constant. These transient fluxes decay to
zero with time constants depending on the resistance
and inductance of each circuit.

Near-to-generator short circuit

25 /36

The existence of additional fluxes in the generator
circuits  changes  its  magnetic  state  and  a
equivalent  reactance  which  represent  the
generator at this state.
At  the  first  moment  of  the  fault  transient  fluxes
appear  in  all  generator  windings;  this  state  is
called  subtransient  and  the  generator  is
represented  by  so  called  subtransient  reactance
X”

. After the decaying of transient dc flux in rotor

damper windings (time period of (

0,01-0,05

s) the

generator passes on to the transient state and is
represented by transient reactance. Then, when
the flux at the field winding decays (

0,6-1)

s the

generator reaches steady state and the
representing reactance is X

Near-to-generator short circuit

26 /36

In short-circuit calculations

we will analyze the

currents at the initial moment of the short-
circuit. This is a subtransient state for
generator, so it can be represented by the
reactance X

”

Generator equivalent circuit

diagram

100 S

�

– rated generator voltage [kV]

rated generator power [MVA ]

[  ]

27 /36

�= +

rf ad

X X



'
d

Near-to-generator short circuit

Transient state

– leakage

reactance of the field
winding
X

– leakage

reactance of the
armature winding

�

= +

jX I

Transient
electromagnetic force
(EMF)

28 /36

� �

�

D =

�

Near-to-generator short circuit

An additional transient flux in the magnetizing

winding decays with the time-constant T’

T’

– time-constant with

the armature circuits
open
(5-12) s

Typically, T’

is about ¼ that of T’

d0.

If the short-circuit occurs behind an outer

reactance:

An additional direct flux in the field
winding causes a positive sequence
additional current component in the
armature

29 /36

Near-to-generator short circuit



Subtransient state

�

�= +

rDf

– leakage

reactance of the
rotor dumper
winding



d q

jX I

�

= +

Subtransient
electromagnetic
force (EMF)

30 /36

Near-to-generator short circuit

An additional direct flux in the damper winding decays

with time-constant T’

�

� �

�

�+

�

� �

�

�+

If the short-circuit occurs behind an outer reactance:

T”

– time-constant with the armature

circuits open (0,02-0,2) s

�

� �

�

D =

�

� �

�

An additional direct flux in the damper

winding causes a positive sequence
additional current component in the
armature

Typical value of T”

is 2

cycles

31 /36

Near-to-generator short circuit

Alternating short-circuit current in d-axis is the sum of steady and transient

components:

�

� �

=D +D +

okd

d ud

�

� �

�

� �

�

okd

�

okq

Alternating short-circuit current in g-axis does not include
the field component (no field winding in the q-axis)

34 /36

Near-to-generator short circuit

Alternating-current component of short-circuit current for t=0 is

called the initial current:

(

)

(

)

(

)

� �

�

� �

�

= �

�+

+� �

� �

�

� �

�

� �

�

� � � �

okd

okq

t 0s

The forward wave moves at twice synchronous

speed with respect to the armature and
induces a second harmonic current in the
armature circuit; amplitude (5-10)% I



+

-

In the armature windings an aperiodic components appear as the result of

direct transient flux occurrence (by the principle of constant stator flux
linkage). It decays with the time-constant T

= (0,3-5) s. It induces

additional ac currents in the field winding, decaying to zero with time-
constant T

. Such an ac current produces a pulsating flux which is

stationary with respect to waves, one is going forward and one backward.
The backward is such as to oppose the stationary armature field.

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