Fundamentals id 181497 Nieznany

SHORT

CIRCUITS IN ELECTRICAL

POWER SYSTEMS

dr hab. Irena Wasiak, prof. nadzw.

Institute of Electrical Power Engineering

2 /36

Subject program

Lecture

General information on short-circuits, short-circuit

current time course

Principles of calculating asymmetrical short-circuits

Equipment impedance in symmetrical components

system

Line-to-earth short-circuits in networks with an

ineffective grounded neutral point

Project

Per unit method

Normalized method of short-circuit calculations

3 /36

Principles of credit

The lecture is passed based on a written test (in English).

The project is passed based on individual work concerning
calculating short-circuit quantities in a selected electrical power
system.

The final mark is an average from these two forms.

4 /36

Literature

Basic
1. Notes from the lecture
2. Kanicki A.: Wyznaczanie wielkości zwarciowych w systemie

elektroenergetycznym. Available in e-format.

Additional

1. Kacejko P., Machowski J.: Zwarcia w sieciach

elektroenergetycznych. WNT, Warszawa 1993, 2002

2. Schlabbach J.: Short-circuit currents, IEE, London, 2005

Basic information

Short-circuit currents in power systems

Lecture 1

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 level and the
bigger share of overhead lines in the network the bigger frequency of
line-to-earth short-circuits.

9 /36

Causes of short

circuits

Electrical causes:

Lighting strokes

Switching overvoltages

Switching mistakes

Long-lasting current overloading

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 of 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-earth

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

(

)

ω + γ = +

2 Esin

Ri L

( )

(

)

(

)

−

ω + γ − ϕ −

⋅

γ − ϕ

2 E

i t

sin

( )

+ ω

ϕ =

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

( )

(

)

(

)

ω + γ − ϕ =

ω + γ − ϕ

2 E

sin t

2I sin t

( )

(

)

−

= −

⋅

γ − ϕ =

⋅

nok

nokm

2 E

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

16 /36

Short

circuit current time course

Short-circuit current time course in three
phases of the three-phase system,
when

=0, φ

=90°

Phase R

Phase T

Phase S

17 /36

( )

(

)

2 E

sin t

⋅

ω + γ − ϕ

(

) (

)

R R

X X

ϕ =

X X

arctg

R R

( )

−

nok

i 0

i(0 ) i

( )

= −⎡

−

⎤

⎣

⎦

nok

nokm

-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

(

)

(

)

−

⎤

⎡

ω + γ − ϕ + ϕ −

γ − ϕ

⎥

⎣

⎥⎦

2 U

sin

K sin

t=0

(

)

sin

– time constant

Voltage at the P point:

(

) (

)

ϕ =

arc tan

ϕ =

arc tan

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

(

)

(

)

( )

−

⎡

⎤

⎢

⎥

ω + γ − ϕ −

γ − ϕ

−

⎢

⎥

⎣

⎦

sin

t e

ω = π =

2 f

L C

≅

a b

L L

2 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

(

)

(

) (

)

−

⎤

⎡

ω + γ − ϕ + ϕ +

γ − ϕ

⎥

⎣

⎥⎦

2 U

sin

t e

2 L

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

generator short circuit

j X 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 (D, 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

generator short circuit

25 /36

The existence of additional fluxes in the generator circuits changes its
magnetic state and an equivalent reactance which represents 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

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 ]

[

Ω ]

27 /36

′ =

X X

E′

'
d

Near

generator short circuit

Transient state

– leakage reactance of the

field winding
X

– leakage reactance of the

armature winding

′

j X I

Transient electromotive force
(EMF)

28 /36

′

−

⎛

⎞

Δ =

−

⎜

⎟

⎜

⎟

⎝

⎠

Near

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

generator short circuit

Subtransient state

′′ =

– leakage reactance

of the rotor dumper
winding

E ′′

X ′′

d q

j X I

″

′′

Subtransient electromotive
force (EMF)

30 /36

Near

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

−

′′

⎛

⎞

′′

′

′′

Δ =

−

⎜

⎟

′′

′

⎝

⎠

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

generator short circuit

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

transient components:

′′

′

= Δ + Δ +

okd

−

′′

′

⎛

⎞

⎛

⎞

′′

′

−

⎜

⎟

⎜

⎟

′′

′

⎝

⎠

⎝

⎠

okd

−

′′

⎛

⎞

′′

−

⎜

⎟

⎜

⎟

′′

⎝

⎠

okq

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

32 /36

Near

generator short circuit

The time course of rms values of short-circuit ac current components.

Short-circuit at the terminals of unloaded generator.

Subtransient

component

Transient

component

AC current

Steady state

component

33 /36

Near

generator short circuit

The time course of rms values of short-circuit ac current components.

Short-circuit at the terminals of generator rating loaded.

Subtransient

component

Transient

component

AC current

Steady state

component

34 /36

Near

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.

35 /36

a) Armature dc current component
b) Armature ac current component and

transient dc currents in rotor windings

Near

generator short circuit

Transient
current in the
field winding

Transient
current in
damper
winding

AC component

envelope

36 /36

The time course of the total stator current

Near

generator short circuit

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